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Generating As-Built 3D Models from Photos taken by Handheld Digital Camera

APPROVED BY SUPERVISING COMMITTEE:

Supervisor: Fernanda Leite Carlos H. Caldas

Generating As-Built 3D Models from Photos taken by Handheld Digital Camera

by Ankit Bhatla, B.Tech

Thesis Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of

Master of Science in Engineering

The University of Texas at Austin December 2011

Dedication

This thesis is dedicated to my family, friends and professors for their love, guidance, constant support and encouragement.

Acknowledgements

I would like to take this opportunity to thank my supervisor Dr. Fernanda Leite for showing confidence in my abilities and giving me the opportunity to work on this exciting thesis topic, I would also like to thank her for her wisdom, guidance and willingness to assist me throughout the course of this thesis. Also, I would like to thank the following individuals / organizations who helped me in carrying the research for this thesis: 1. Kristopher Pruner: for taking photos in the sweltering heat of Dallas and helping me generate the 3D models for the research. 2. Oscar Fierro and Soo Young Choe: for helping me in the 3D modeling of the Margaret Hunt Hill Bridge. 3. Jin Ouk Choi: without whom I would not have got the opportunity to work on this thesis. 4. Dr. Hemant Kaushik, Dr. Bulu Pradhan, Dr. Anjan Dutta and Dr. S.K. Deb: for their constant encouragement to engage in active research. 5. Nabeel Khwaja: for valuable inputs during the data collection phase. 6. Texas Department of Transportation (TxDOT), Interagency Cooperation Contract (IAC) program, Dallas District: for funding this project. 7. Dr. Carlos H. Caldas: for being the co-reader for this thesis. 8. My friends at CEPM: for an amazing 1 ½ years in Austin. 9. My family – for supporting me in my endeavors and decision to come to US for further studies.

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ABSTRACT Generating As-Built 3D Models from Photos taken by Handheld Digital Cameras Ankit Bhatla, MSE The University of Texas at Austin, 2011

Supervisor: Fernanda Leite

As-built documentation is an essential set of records, consisting of construction drawings, specifications and equipment location, which are kept for facility management purposes. These documents are constantly being created and modified throughout the life of a project. This process is usually manual and fraught with errors, which inhibits reliable decision making. Technological advancements have made it possible to generate 3D models to assess as-built conditions for construction monitoring purposes, such as verifying conformance to baseline project schedules and contract specifications. For this purpose, 3D point clouds are widely generated using laser scanners. However, this approach has limitations in the construction industry due to the expensive and fragile equipment, lack of portability and need of trained operators. This study aims at investigating an alternate technology to generate as-built 3D point clouds using photos taken using handheld digital cameras, compare them against the original as-built 3D models, and check for accuracy of the modeling process. This analysis can aid in more reliable and effective decision making due to its cost effectiveness and ease of use, particularly in heavy infrastructure projects which are continually undergoing rehabilitation work. To achieve these objectives, a set of guidelines are developed for vi

taking photographs that enable effective generation of 3D point clouds using off-the-shelf software packages. The accuracy of the modeling process is investigated using the results of the as-built 3D point cloud modeling of a 2000 feet under construction bridge in southern United States.. Finally, the range of tolerance and deviation of element dimensions is determined by comparing the photo based model to the actual as-built model (developed using 2D drawings). Furthermore, to compare point clouds of laser scanning and photogrammetry, a laser scan and an image based survey of an exterior wall of a university building was also done. Results show that this technology in its present state is not suitable for modeling infrastructure projects, however technological developments can enable this to be an efficient way to extract measurements of inaccessible objects for progress monitoring purposes and the models can also be stored for future dimension takeoffs for decision making and asset management purposes.

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Table of Contents ABSTRACT

VI

List of Tables ...........................................................................................................x List of Figures ...................................................................................................... xiv CHAPTER 1- Introduction ......................................................................................1 Problem Statement ..........................................................................................1 Motivation .......................................................................................................2 Research Scope ...............................................................................................3 Research Objectives ........................................................................................4 Organization Of Thesis ..................................................................................4 CHAPTER 2: As-Built Modeling ...........................................................................5 Overview .........................................................................................................5 Remote Sensing Techniques ...........................................................................7 Laser Scanning ................................................................................................7 Photogrammetry..............................................................................................9 Videogrammetry ...........................................................................................12 3D Range Camera .........................................................................................12 Applications Of Optical-Based Spatial Data Acquisition Techniques .........14 Comparison of optical-based spatial data acquisition techniques.................16 CHAPTER 3 - Research Methodology ..................................................................22 Evaluating Accuracy Of Optical Spatial Data Collection Techniques: Review ..........................................................................................................22 Accuracy Evaluation Of Photogrammetry ....................................................30 Software Packages Used ...............................................................................31 Image Acquisition From Field Survey..........................................................34 Image Processing To Generate 3d Model Using Collected Images .............36 As-Built Modeling Using The 3d Model In Autodesk Photofly..........37 Test Project Description................................................................................42 viii

Image Based Field Survey ............................................................................44 Image Processing ..........................................................................................46 Accuracy Assessment ...................................................................................49 CHAPTER 4 - Results ...........................................................................................51 Dimension Analysis ......................................................................................51 CHAPTER 5 - Validation ......................................................................................66 Methodology .................................................................................................66 Results ...........................................................................................................68 CHAPTER 6 - Conclusions ...................................................................................70 Appendices.............................................................................................................72 Appendix A ...................................................................................................73 Appendix B ...................................................................................................81 Appendix C .................................................................................................102 Appendix D .................................................................................................123 Appendix E .................................................................................................132 References ............................................................................................................144 Vita ..................................................................................................................... 149

ix

List of Tables Table 1:

Classification on the basis of type of sensor used...............................7

Table 2:

Comparison of the optical spatial data acquisition techniques .........20

Table 3:

Suggested Techniques for Basic Application Requirements ............21

Table 4:

Sample set of measurements ............................................................24

Table 5:

Summary of the image based survey ...............................................46

Table 6:

Summary of elements modeled in each section ................................49

Table 7(a): Section 1 Beams, referenced by scale set on the north side..............54 Table 7(b): Section 1 Beams, referenced by scale set on the north side..............55 Table 8:

Section 1 Box Girders, referenced by scale set on the north side .....56

Table 9:

Section 1 Distance between Holes, referenced by scale set on the north side...........................................................................................57

Table 10:

Summary of all Sections ...................................................................60

Table 11:

ANOVA summary for all sections....................................................64

Table 12:

Comparison between laser scan and photogrammetry point cloud based models ...........................................................................69

Table 13(a): Section 1 Beams, referenced by scale set on the south side .............73 Table 13(b): Section 1 Beams, referenced by scale set on the south side .............74 Table 14:

Section 1 Box Girders, referenced by scale set on the south side.....75

Table 15:

Section 1 Distance between Holes, referenced by scale set on the south side.....................................................................................76

Table 16(a): Section 1 Beams, referenced by scale set on both sides ...................77 Table 16(b): Section 1 Beams, referenced by scale set on both sides ...................78 Table 17:

Section 1 Box Girders, referenced by scale set on both sides ..........79 x

Table 18:

Section 1 Distance between Holes, referenced by scale set on both sides ..........................................................................................80

Table 19(a): Section 2 Beams, referenced by scale set on the north side..............81 Table 20:

Section 2 Box Girders, referenced by scale set on the north side .....85

Table 21:

Section 2 Distance between Holes, referenced by scale set on the north side .....................................................................................86

Table 22(a): Section 2 Beams, referenced by scale set on the south side .............89 Table 22(b): Section 2 Beams, referenced by scale set on the south side .............91 Table 23:

Section 2 Box Girders, referenced by scale set on the south side.....93

Table 24:

Section 2 Distance between Holes, referenced by scale set on the south side ..........................................................................................94

Table 25(a): Section 2 Beams, referenced by scale set on both sides ...................95 Table 25(b): Section 2 Beams, referenced by scale set on both sides ...................98 Table 26:

Section 2 Box Girders, referenced by scale set on both sides ..........99

Table 27:

Section 2 Distance between Holes, referenced by scale set on both sides ........................................................................................101

Table 28(a): Section 3 Beams, referenced by scale set on the north side............102 Table 28(b): Section 3 Beams, referenced by scale set on the north side............104 Table 29:

Section 3 Box Girders, referenced by scale set on the north side ...106

Table 30:

Section 3 Distance between Holes, referenced by scale set on the north side ...................................................................................107

Table 31(a): Section 3 Beams, referenced by scale set on the south sides ..........109 Table 31(b): Section 3 Beams, referenced by scale set on the south sides ..........112 Table 32:

Section 3 Box Girders, referenced by scale set on the south sides .113

Table 33:

Section 3 Distance between Holes, referenced by scale set on the xi

south sides .......................................................................................115 Table 34(a): Section 3 Beams, referenced by scale set on both sides .................117 Table 34(b): Section 3 Beams, referenced by scale set on both sides .................119 Table 35:

Section 3 Box Girders, referenced by scale set on both sides ........120

Table 36:

Section 3 Distance between Holes, referenced by scale set on both

sides .....................................................................................122

Table 37(a): Section 4 Beams, referenced by scale set on the north side............123 Table 37(b): Section 4 Beams, referenced by scale set on the north side............124 Table 38:

Section 4 Box Girders, referenced by scale set on the north side ...125

Table 39:

Section 4 Distance between Holes, referenced by scale set on the north side ...................................................................................125

Table 40(a): Section 4 Beams, referenced by scale set on the south side ...........126 Table 40(b): Section 4 Beams, referenced by scale set on the south side ...........127 Table 41:

Section 4 Box Girders, referenced by scale set on the south side...128

Table 42:

Section 4 Distance between Holes, referenced by scale set on the south side...................................................................................128

Table 43(a): Section 4 Beams, referenced by scale set on both sides .................129 Table 43(b): Section 4 Beams, referenced by scale set on both sides .................130 Table 44:

Section 4 Box Girders, referenced by scale set on both sides ........131

Table 45:

Section 4 Distance between Holes, referenced by scale set on both sides ........................................................................................131

Table 46(a): Section 5 Beams, referenced by scale set on the north side............132 Table 46(b): Section 5 Beams, referenced by scale set on the north side............133 Table 47:

Section 5 Box Girders, referenced by scale set on the north side ...134

Table 48:

Section 5 Distance between Holes, referenced by scale set on xii

the north side ...................................................................................135 Table 49(a): Section 5 Beams, referenced by scale set on the south side ...........136 Table 49(b): Section 5 Beams, referenced by scale set on the south side ...........137 Table 50:

Section 5 Box Girders, referenced by scale set on the south side...138

Table 51:

Section 5 Distance between Holes, referenced by scale set on the south side...................................................................................139

Table 52(a): Section 5 Beams, referenced by scale set on both sides .................140 Table 52(b): Section 5 Beams, referenced by scale set on both sides .................141 Table 53:

Section 5 Box Girders, referenced by scale set on both sides ........142

Table 54:

Section 5 Distance between Holes, referenced by scale set on both sides ........................................................................................143

xiii

List of Figures Figure 1:

Laser Scanner ......................................................................................9

Figure 2:

Obtaining 3D coordinate from Photogrammetry ..............................10

Figure 3:

3D range camera ...............................................................................13

Figure 4:

Scatter plot between the two sets of measurements ..........................25

Figure 5:

Difference between the two sets of measurements plotted against zero .......................................................................................25

Figure 6:

Correlation between the two sets of measurements ..........................26

Figure 7:

Summary of Methodology for Accuracy Assessment of Photogrammetry................................................................................31

Figure 8:

Workflow in Microsoft Photosynth ..................................................32

Figure 9:

Workflow in Autodesk Photofly ......................................................33

Figure 10:

Selecting camera locations................................................................35

Figure 11:

Multiple images from the same camera locations.............................35

Figure 13:

Draft quality mesh.............................................................................38

Figure 14:

Maximum quality mesh ....................................................................39

Figure 15:

Reference Points ...............................................................................39

Figure 16:

Setting the Coordinate Axis ..............................................................40

Figure 17:

Setting scale of the model .................................................................40

Figure 18:

Creating Polylines .............................................................................41

Figure 19:

Exported model in AutoCAD ...........................................................41

Figure 20(a):Margaret Hunt Hill bridge - Dallas, Texas, U.S.A, Rendered photo of the bridge ...........................................................43 Figure 20(b):Margaret Hunt Hill bridge - Dallas, Texas, U.S.A, xiv

Photo taken on June 27, 2011 ..........................................................43 Figure 21:

Margaret Hunt Hill Bridge divided into 5 sections - Dallas, Texas, U.S.A .....................................................................................45

Figure 22:

Refined 3D model along with the camera positions returned by the software ..................................................................................48

Figure 23:

Model exported to a CAD modeling software ..................................48

Figure 24:

Flowchart for accuracy assessment ...................................................50

Figure 25:

3D model generated using 2D drawings ...........................................50

Figure 26:

Height of box girder ..........................................................................51

Figure 27:

Dimensions of beam .........................................................................52

Figure 28:

Distance between holes .....................................................................52

Figure 30:

Section 2 deviations using all the 3 reference scales used ................58

Figure 31:

Section 3 deviations using all the 3 reference scales used ................58

Figure 32:

Section 4 deviations using all the 3 reference scales used ................59

Figure 33:

Section 5 deviations using all the 3 reference scales used ................59

Figure 34:

Scatter plot of differences against average values of dimensions for section 1 with scale set on the south side ....................................61

Figure 35:

Histogram of differences for section 1 with scale set on the south side ..........................................................................................61

Figure 36:

Q-Q plot of standardized percentage deviations, with scale set on the north side vs. standardized z-values for section 4..................62

Figure 37:

Q-Q plot of standardized percentage deviations, with scale set on the south side vs. standardized z-values for section 4 .................63

Figure 38:

Q-Q plot of standardized percentage deviations, with scale set on both sides vs. standardized z-values for section 4 .......................63 xv

Figure 39(a):

Photo based point cloud ..............................................................66

Figure 39(b):

Laser scan point cloud ................................................................67

Figure 40(a):

Exterior wall modeled using photo based point cloud ................67

Figure 40(b):

Exterior wall modeled using laser scan point cloud ...................67

Figure 41:

Methodology for accuracy assessment of model generated using photogrammetry point cloud .............................................68

xvi

CHAPTER 1- Introduction

PROBLEM STATEMENT 3D modeling can be used throughout the lifecycle of any construction project, for e.g. efficient communication and visualization in the preconstruction planning phase, tracking of progress during the construction phase and for facility management purposes by tracking the present condition of the facility against the as-built condition when the project was originally built. The use of remote sensing techniques like laser scanners for developing 3D point cloud models based as-built models of a construction project is becoming common these days. However, laser scanners are expensive and fragile equipment, which require trained operators for use. The modeling process using laser scanners is also time consuming and requires expensive software packages. Development of as-built models using photographs based 3D point cloud is relatively new in comparison to laser scanning. This image based reconstruction and 3D modeling of construction projects is easier and less time consuming than laser scanning. However, this modeling process needs to be checked for accuracy.

The aim of this thesis is to verify the photographs generated 3D point cloud based models for accuracy by comparing them to the dimensions of the 2D drawings based 3D model and finding the range of tolerance for use in the entire lifecycle of construction projects.

1

MOTIVATION The United States (US) economy is heavily dependent on its network of roads (4,059,302 miles of public road) and bridges (3,697 million square feet of bridges in 2008). However, the repair and maintenance of this infrastructure is capital intensive and hence a major portion of this network is in a depleted state. Poor roadway conditions are also a significant contributor to traffic fatalities as they account for approximately onethird of total traffic fatalities (TRIP 2010b). There are various plausible alternatives to reduce roadway congestion such as: building new facilities, such as roadways, interchanges and bridges, or expanding the capacity of current facilities. Building new facilities on new alignments and widening current roadways and bridges increases the transportation network mileage. Also, adding or widening ramps to existing interchanges can increase a roadway’s capacity. Taking the case of bridges in the US, 27 percent of bridges were found to be either structurally deficient (12.1%) or functionally obsolete (14.8%) (ASCE 2009), while 18% of bridges were structurally deficient or functionally obsolete in Texas (TRIP 2010b). Structural deficiency reflects the bridge’s integrity of structure with regards to the condition of the bridge deck, superstructure and substructure, while functionally obsolete reflects its geometry, under-clearance, and alignment to the roadway approaching the bridge (2030 Committee 2009). AASHTO in 2008 estimated that to repair these bridges, $48 billion would be required for the structurally deficient bridges and $91 billion for the functionally obsolete bridges. The National Surface Transportation Policy and Revenue Commission study showed that for the 15 year period from 2005 to 2020, $130 billion to $240 billion should be invested on highway capital investment, yet the current spending level is well short at $70.3 billion (ASCE 2009).

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It can be observed from the statistics above that there is a huge difference between the demand and supply of funds for the maintenance and upkeep of the road transportation network. The need of the hour is to develop an efficient infrastructure asset management process which can help the authorities monitor construction work, as well as enable them to make better decisions regarding maintenance planning. Optical spatial data collection techniques like photogrammetry can play an important role in aiding in the decision making progress by enabling fast, inexpensive and accurate generation of 3D models for analyzing the deformations and present conditions of infrastructure projects. This paper examines the accuracy of photogrammetry for developing as-built or as-is 3D models of infrastructure projects for the purposes mentioned above. An off-theshelf, point cloud generating software package is used to develop an as-built model of a bridge under construction in Dallas, Texas, U.S.A. The study procedures and results are included in this paper.

RESEARCH SCOPE The scope of the research included a literature review on the developments of remote sensing / optical spatial data collection techniques for 3D modeling, focusing on the use of photogrammetry for development of as-built 3D models of construction projects. The evaluation of off-the-shelf software packages for this purpose was done and this process was applied to an under construction project (located in Dallas, Texas). The accuracy of the process was then compared by comparing the dimensions of elements from the 3D model generated using photographs based point cloud, to those of the actual 3D as-built model of the bridge, developed from 2D drawings.

3

RESEARCH OBJECTIVES The objectives of the research are as follows: 1.

Formulation of a set of guidelines for taking photographs to generate as-built 3D models of construction projects.

2.

Development of the actual 3D model of the Margaret Hunt Hill Bridge using 2D drawings.

3.

Development of the 3D point cloud based model on photographs of the under construction bridge located in Dallas, Texas.

4.

Comparing the dimensions of selected elements from the photo generated point cloud based 3D model to the 2D drawings based 3D model and finding deviations.

5.

Finding deviations between 3D model generated using photo based point cloud with the model generated using laser scan point cloud.

6.

Discussion on limitations and potential applications of photogrammetry.

ORGANIZATION OF THESIS The thesis is organized in 6 chapters. It starts from explaining the recent developments in the development of as-built 3D models using optical spatial data collection techniques in Chapter 2. Chapter 3 is dedicated to elucidating the research methodology of the research. Chapter 4 explains the results of the process including the set of guidelines for taking photographs for generating 3D models using photographs. Chapter 5 deals with comparison of 3D model generated using photo based point cloud with the model generated using laser scan point cloud. Conclusions are presented in Chapter 6 followed by the appendix and the references used in this thesis. 4

CHAPTER 2: As-Built Modeling

OVERVIEW As built models depict the actual as-built condition of any completed project or facility. Capturing the as-built or as-is reality of any project / facility is important for several reasons including: 1.

Checking the present or as-is condition of a facility and tracking it against the asbuilt condition for maintenance and rehabilitation purposes (i.e., facility management) (Klein et al. 2011).

2.

A facility may not be constructed according to the design specified, changes may be made to the design specified, or the design model of a facility may not exist; hence, it is important to capture a facility’s or projects as-built information (Tang et al. 2010).

3.

Timely access to information for construction and facility personnel is still a challenge in today’s technology intensive world (Kiziltas et al. 2008). A site engineer takes geometric measurements of just placed or partially placed construction objects for quality control purposes. These measurements are usually taken manually using measurement tapes (Dai and Lu 2010; Golparvar-Fard et al. 2011). The analysis of massive quantities of data to enable real time feedback to people performing construction operations is not possible using metrology techniques (Cheok et al. 2000).

Infrastructure modeling and Building Information Modeling can be used for this purpose. Infrastructure modeling is more recent, in comparison to building information 5

modeling, and consists of collecting infrastructure’s spatial data as a series of 3D point coordinates (Ikeuchi and Sato 2001) and then transforming these points into structured or object oriented representations such as CAD models (Remondino and El-Hakim 2006). Building Information Modeling (BIM) is a digital representation of the physical and functional characteristics of a facility. Its purpose is to serve as a shared knowledge resource for information about a facility, as well as forming a reliable basis for decisions during the facility’s life-cycle, from inception onward (Smith 2007). BIM has various advantages such as: increasing communication leading to greater stakeholder collaboration during the lifecycle of a project (Tang, Huber et al. 2010), visualization of the building form, rapid generation of multiple design alternatives, predictive analysis of building performance and automated generation of drawings and documents (Sacks et al. 2010). While a CAD model in the simplest terms represents an object as a set of planar surfaces, a BIM model attaches a database to an object and represents it in a semantically rich manner. The attached database holds object information like material characteristics and cost data.

BIM can be created from a CAD model of a facility (as-designed), but this model cannot capture the details about the as-built or as-is condition of the facility (Tang et al. 2010). To capture the as-built or the as-is conditions of any facility several optical spatial data collection and remote sensing techniques are available. However, the modeling process is heavily dependent on the quality (accuracy and resolution) of the retrieved spatial data. The greater the accuracy of the 3D points collected, the higher the precision of the final model (Zhu and Brilakis 2009).

6

REMOTE SENSING TECHNIQUES Non-contact spatial data collection (remote sensing) techniques, like optical spatial data collection techniques, have been successfully used for acquiring 3D point cloud information (Bosche 2010;

El-Omari and Moselhi 2008) and developing 3D

infrastructure models. Zhu and Brilakis (2009) and Fathi and Brilakis (2011) classified these techniques based on the type of sensors used as shown in Table 1.

No. Classification Description These techniques provide depth information using energy Active

reflection. Energy is transmitted to a scene and the reflected energy

Sensor

is retrieved. Laser scanning and 3D range cameras are examples of

1

active sensor techqniques. These techniques do not transmit any energy but utilize natural Passive

light available in the surroundings to capture 3D information.

Sensor

Photogrammetry and Videogrammetry are examples of passive

2

scanners.

Table 1:

Classification on the basis of type of sensor used

LASER SCANNING Laser scanning, as shown in Figure 1, is an active sensor technique that is usually based on the time of flight (TOF) principle (Frohlich and Mettenleiter 2004), also known as Light Detection and Ranging (LiDAR). Laser scanners create a point cloud of the geometric surfaces of an object. Shapes of the objects can then be reconstructed using 7

point clouds and used in the Architecture, Engineering and Construction industry (Frohlich and Mettenleiter 2004). Like 3D range cameras, laser scanning can generate point clouds of any object that is not obscured and lies in its line of view. This technology has high accuracy (in the order of a few milimetres) and its measurement range extends upto a few hundred metres (Golparvar-Fard et al. 2011; Jaselskis et al. 2003). The major limitations of laser scanning lies in the upfront investment (high equipment cost) and training of operators. Also, the equipment is not portable, cannot be tranported easily, and the process is time consuming; depending on the size of the object, a laser scan can take anywhere from a few hours or even days to complete. The analysis of the point cloud also takes more time when compared to other remote sensing techniques such as photogrammetry (Golparvar-Fard et al. 2011). The accuracy of laser scans is highly dependent on environmental and object parameters like surface reflectivity, surface texture and weather (Kavulya et al. 2011). For example, a building with large windows cannot be accurately captured using laser scanning because the laser beams pass through the structure’s window glass (Zhu and Brilakis 2009), sharp edges and corners (Tang et al. 2003).

8

Figure 1:

Laser Scanner 1

PHOTOGRAMMETRY “Photogrammetry involves deriving geometric information about an object using information derived from photographs” (Klein et al. 2011). It uses 2D images taken from digital cameras to create a 3D model of an object. Being a remote sensing technique, photogrammetry does not involve physically touching the object. Various outputs like 3D coordinates, 3D topographical structure and wire frame of a structure can be generated using this technique (Zhu and Brilakis 2009). This technique relies on passive triangulations to measure real world objects. A 3D (x,y,z) coordinate is obtained by locating the same point from two or more different camera positions, as shown in Figure 2.

1 (Source: http://www.nottingham.ac.uk/Archaeology/Images-Multimedia/research-

projects/digital-survey/digi-survey-01.JPG) 9

Camera position

Point (x,y,z)

Figure 2:

Obtaining 3D coordinate from Photogrammetry (adapted from: Dai and Lu (2010))

Some common steps in deriving geometric information using photogrammetry are as follows (Klein et al. 2011; Golparvar-Fard et al. 2011):1. Selecting common features in two or more than two images; 2. Calculating camera positions and orientations; 3. 3D information reconstruction using intersecting feature point locations.

This technology is available in several commercial software packages like Autodesk Photofly (Autodesk 2011a) and Microsoft Photosynth (Microsoft 2011). These software packages enable automatic stitching of photos by detecting common features in a sequence of images. However, the images need to be taken close to each other with a large overlap and repetition of feature points (El-Hakim 2001). Automated stitching of images generates a dense point cloud, but this process is prone to errors and noise caused due to the extraction of additional and unwanted features in the surroundings such as 10

trees, adjacent structures and clouds (Remondino and El-Hakim 2006). The automatic stitching process begins by locating common features in two or more images. Camera positions and orientations are then obtained using the feature points obtained after stitching of photos. Finally a process known as bundle adjustment is applied, this process refines the 3D coordinates describing the geometry as well as the parameters of relative motion and optical characteristics of the cameras employed to acquire the images. This is done according to an optimality criterion involving the corresponding image projections of all points (Triggs et al. 1999). Bundle adjsutment returns calibrated camera positions for all the images, this enables calculation of 3D coordinates of any point with a high degree of accuracy using triangulation which involves defining the same point in two images taken from different perspectives (Klein et al. 2011).

Readily available and affordable handheld digital cameras can be used to take photos of the infrastructure to be modeled. The photos are then joined in the mentioned software packages to generate a 3D point cloud of the structure. This technique relies on the natural lighting available to take photos and thus cannot be used in conditions with insufficient lighting. Another limitation of this feature is the inability to generate a point cloud when the surface of the object has little difference in texture or appearance of similar feature points in images (Remondino and El-Hakim 2006). (Klein et al. 2011) have highlighted several environmental limitations of the image based modeling technique. For example, limited feature points are extracted when wide angle shots cannot be taken due to nearby structures. Also nearby trees, vehicles and people sometime occlude critical building geometry. These problems can be mitigated by careful 11

planning before taking photos (Klein et al. 2011). One technique to mitigate some of these problems is to add artificial visual markers to increase the number of feature points (El-Hakim 2001).

VIDEOGRAMMETRY This technique is similar to photogrammetry except that video frames, instead of images, are used for measuring 3D coordinated of an object. Videogrammetry utilizes camcorders to capture numerous video frames in a video sequence and improves the accuracy of the 3D measurement results. Video frames are built upon the previous frames in a video sequence, enabling automatic and real time data collection. However, due to the low resolution of the captured video frames, the applications of videogrammetry are limited (Zhu and Brilakis 2009). This technique is also susceptible to changes in the light conditions and abrupt camcorder motion which hinders the extraction of features from the video frames and automatic matching of the extracted features (Remondino and ElHakim 2006). Zhu and Brilakis (2009) also highlighted the fact that a high degree of human involvement is required in order to minimize errors and achieve a high accuracy and photorealism.

3D RANGE CAMERA A 3D range camera, as shown in Figure 3, is especially useful in applications for detecting, tracking and modeling moving objects (Tezier 2008). It is an active sensor technique that can automatically compute the depth information and produce 3D images in real-time. Also, the 3D range camera is not dependent on the daylight and can be operated any time. The device works by projecting a line or a codified image onto the 12

object’s surface to reconstruct the object’s surface shape (Zhu and Brilakis 2009). The limitation of this technique is that it cannot be used to inspect materials with dark inclusions as it mistakes these inclusions for voids (Zhu and Brilakis 2009). These cameras are also more expensive than digital cameras and camcorders.

Figure 3:

3D range camera2

Tezier (2008) highlighted several benefits of using 3D Range Imaging Cameras: 1.

They deliver range, amplitude, and intensity maps in one frame and at the same time.

2.

They provide for safe and very short data acquisition time with high frame update rate for immediate range feedback.

3.

They provide for a wide field-of-view.

4.

They can capture both static and dynamic scenes.

2

(Source: http://activesensors.usu.edu/images/uploads/3dcamera.jpg) 13

5.

They are insensitive to background light and can be used anytime.

6.

These are small sized and compact devices.

7.

They are inexpensive when compared to laser scanners.

APPLICATIONS OF OPTICAL-BASED SPATIAL DATA ACQUISITION TECHNIQUES Zhu and Brilakis (2009) compared the various optical spatial data collection techniques to help construction engineers make a well-reasoned decision on which technology to use based the particular project. Furthermore, their research highlighted that the model data collected can be used for a number of purposes like: defect and deviation detection, construction job site planning, on-site safety enhancement and asbuilt documentation. 1.

Defect detection: (Gordon et al. 2003) utilized optical spatial data collection by a 3D laser scanner to generate a digital model containing as-built information. This model was then compared with a digital design model, so that unacceptable deviations could be detected. (Akinci et al. 2006) used spatial data acquired from construction sites and integrated these into the project models of their developed formalism for proactive construction quality control.

2.

Planning: They can be applied to generate a physical prototype model for feasibility studies, building planning and safety analysis (Goedert et al. 2005). Benefits like “organized site layouts, optimized site activities and improved construction productivity” can be achieved using the spatial data of temporary facilities (Zhu and Brilakis 2009).

3.

Job site safety: Teizer et al. (2010) developed a blind spot detection tool that determines the equipment blind spots rapidly and in 3D through analysis of point 14

cloud data from a laser scan inside the equipment cab. Caldas et al. (2004) proposed an obstacle avoidance systems using which the likelihood of the accidents like collisions of heavy equipment with people or power lines can be reduced using site spatial data. 4.

Building reconstruction / Archaelogical rehabilitation and restoration: Styliadis (2006) investigated the method of documenting historical buildings with the functionality of e-learning and meta-documentation based on their collected spatial data. Yilmaz et al. (2008) used digital close range imaging for documentation of historical caravansaries. Arias et al. (2007) used close range photogrammetric techniques for graphic and metric documentation of agroindustrial buildings located in Galicia, Spain. Lee and Choi (2004) used a combination of laser scanning and imaggery for building reconstruction. Similar work was also found in Cain (2000) where accurate interior and exterior ground plans of a monument were generated from the collected spatial data. These resulting plans could be used by architects and engineers for physical work at sites in the future. Riveiro et al. (2011) applied close range photogrammetry to generate 3D geometric models for the subsequent evaluation of the condition state of historical masonry bridge arches. The geometric model was used as the base and mechanical modeling and finite element analysis were applied to establish the failure load of the arches

5.

Construction progress: Golparvar-Fard et al. (2011) compared point clouds obtained from laser scanning and photogrammetry for detection and visualization of as-built status for construction projects. El-Omari and Moselhi (2008) used both laser scanning and photogrammetry to increase the speed and accuracy of the collected spatial data for construction progress purposes. Cheok et al. (2000) 15

assessed the progress of an excavation activity by analyzing terrain models generated from the spatial data of construction sites. El-Omari and Moselhi (2011) developed a control model that integrates laser scanned images with digital photos to produce 3D images of the scanned object to estimate quantities of work performed. 6.

Deformation measurement: Xiao et al. (2011) used photogrammetry for tracking 3D deformation of a transmission tower during load testing using artificial markers pasted on the deformation areas. Jiang and Jauregui (2007) proposed a refined distance constraint (RDC) approach for close range photogrammetry for use in bridge measurement. Maas and Hampel (2006) proposed a method of using collected spatial information to measure the geometric deformation of civil infrastructure such as pavements, bridges, and water reservoirs.

Other applications: Du and Teng (2007) investigated the use of spatial data to compute the necessary earthwork volume after a landslide. Armestoa et al. (2009) developed a methodology for measuring geometry of structural elements of a timber roof using photogrammetry and used the geometry for structural analysis using the Finite Element Method.

COMPARISON OF OPTICAL-BASED SPATIAL DATA ACQUISITION TECHNIQUES Based on the literature presented above, benefits and limitations of optical based spatial data acquisition techniques (photogrammetry, videogrammetry, 3D range cameras and laser scanning) are summarized in Table 2. The metrics proposed by NIST (2006) were used to evaluate these remote sensing techniques. These metrics consist of: 16

1.

Automation of spatial data retrieval: Classified as 2D or 3D based on whether the collected data has depth information or not.

2.

Spatial data accuracy: Measured using RMS (root mean square) of the difference between the actual values and the values obtained using the 3D point coordinates of the object.

3.

Spatial data resolution: Measured using the number of retrieved 3D points.

4.

Equipment cost;

5.

Equipment portability;

6.

Spatial Data speed: Measured using the capability to retrieve the data real time.

7.

Range distance.

8.

Operation time: whether the equipment is dependent on day light for operation.

The spatial data collected using photogrammetry and videogrammetry lacks information regarding the depth and hence 3D data cannot be retrieved automatically. However, with the advent of commercial software packages like Autodesk Photofly (Autodesk 2011a) and Microsoft Photosynth users can use the automatic stitching feature built in the software to stitch multiple images together and obtain the depth information. In videogrammetry, automatic stitching is limited to non-uniform texture regions (Remondino and El-Hakim 2006). Spatial data collected using 3D range camera and laser scanner contains depth information. The accuracy of the spatial data collected using laser scanner is greater than that collected using photogrammetry (Jaselskis et al. 2003). However, the spatial data collected using photogrammetry and videogrammetry is more accurate than that collected using 3D range cameras (Zhu and Brilakis 2009). With respect to spatial data resolution, laser scanning and videogrammetry have a greater 17

resolution than both 3D camera ranging and photogrammetry. Laser scanning and videogrammetry can retrieve millions of points (Guarnieri et al. 2004) while photogrammetry and 3D range camera can retrieve thousands of points (Remondino et al. 2005). Although thousands of points can be obtained in photogrammetry using automatic stitching software packages, this process is prone to stitching errors which can reduce the accuracy of the results (Remondino and El-Hakim 2006). With respect to the equipment cost, the digital cameras used for photogrammetry can cost anywhere around a few hundred dollars (Golparvar-Fard et al. 2011) and can be classified as “low”, the price of a 3D range camera is around several thousand dollars and can be classified as “Affordable” (Zhu and Brilakis 2009) whereas the price of laser scanner is of the magnitude of hundred thousand dollars (Golparvar-Fard et al. 2011; El-Omari and Moselhi 2011) and can be classified as “high”. With respect to equipment portability, digital cameras, video cameras like camcorders and 3D range cameras are portable as they are light weight; conversely, laser scanners are heavy and bulky (Zhu and Brilakis 2009; Golparvar-Fard et al. 2011). With respect to spatial data retrieval speed, video cameras and 3D range cameras enable real time data collection due to their high frame rates (25 – 30 fps) while laser scanners and photogrammetry cannot enable retrieval of real time data (Tezier 2008). With respect to range distance, photogrammetry and videogrammetry (several 10s of metres) (Mathews and Noble 2001) have a greater range than a 3D range camera (several metres) (PMDTEC 2011). The range of laser scanner is the maximum and can reach as high as a few hundred metres (Leica Geosystems 2011). With respect to operation time, 3D range cameras and laser scanners can operate independent of the daylight, whereas photogrammetry and videogrammetry can only work during the day (Zhu and Brilakis 2009). 18

Zhu and Brilakis (2009) based on extensive literature review suggested different remote sensing techniques based on different application requirements. These recommendations are presented in Table 3. Based on Table 3, photogrammetry is an extremely promising remote sensing technique given its low cost, portability and automatic generation of point clouds using off the shelf software packages. To further realize the potential benefits of this technique, its accuracy needs to be assessed for different types of projects. (Klein, Li and BecerikGerber 2011) assessed its accuracy using a university building in California, U.S.A. They compared the image based dimensions to the actual dimensions and observed the maximum error to be less than 4% with the average being between 1-3 % for sample space consisting of the building exterior and the interior rooms. This paper assesses the accuracy of photogrammetry using Autodesk Photofly (Autodesk 2011a) for a bridge under construction and presents the findings for this relatively more complex structure.

19

Photogrammetry Videogrammetry 3D

Automation Manual / Semi- Automated of

spatial automated

ranging

scanning

Automated

Automated

(limited to non

data

uniform

retrieval

regions)

Spatial

camera Laser

Accurate

texture

Accurate

Not as accurate Most accurate

data

as

accuracy

photogrammetry and videogrammetry

Spatial

Low

High

Low

High

Low (Hundreds)

Low

Affordable

High

data resolution Equipment

(thousands)

cost Equipment

Lightweight

Lightweight

Portable

Non-portable

portability Spatial

Non

real

time Real

Time Ream

time Non real time

data speed

retrieval

retrieval

retrieval

retrieval

Range

Medium

Medium

Short range

Long range

Sensitive to light

Sensitive to light

Operates

day Operates day

and night

and night

distance Operation time Table 2:

Comparison of the optical spatial data acquisition techniques (adapted from Zhu and Brilakis (2009)

20

Application Requirements

Techniques

3D data accuracy

Laser scanning / Photogrammetry

3D data details

Laser scanning

Fully automated 3D data retrieval

Laser scanning / 3D camera ranging / Photogrammetry

Nighttime operation

Laser scanning / 3D camera ranging

Low equipment cost

Photogrammetry / Videogrammetry / 3D camera ranging

Portability

Photogrammetry / Videogrammetry / 3D camera ranging

Long measurement range Table 3:

Laser scanning

Suggested Techniques for Basic Application Requirements (adapted from Zhu and Brilakis (2009))

21

CHAPTER 3 - Research Methodology

EVALUATING ACCURACY OF OPTICAL SPATIAL DATA COLLECTION TECHNIQUES: REVIEW Measuring accuracy of optical spatial data collection techniques for as-built modeling purposes is a challenge as the standards / metrics are not available (Dai and Lu 2010; Tang et al. 2010). Furthermore, most of the models that have been checked for accuracy measurement are limited to planar surfaces and there is a need for more research to model complex structures like columns, structural steel, archways etc (Tang et al. 2010).

Tang et al. (2010) proposed evaluation measures clustered into 3 categories: 1.

Measures related to algorithm design: Concerns with the capabilities of the algorithm and the input – output needs of the algorithm.

2.

Measures related to environmental / sensing conditions: Concerns with defining the environmental conditions of the reference / test conditions like types of objects present, level of sensor noise, level of occlusion, level of clutter, presence of moving objects, presence of specular surfaces, presence of dark surfaces and sparseness of data.

3.

Measures related to modeling performance: Evaluating the algorithm’s performance for a given set of environmental conditions. Can be evaluated based on geometric modeling accuracy, recognition accuracy, relationship modeling accuracy and level of detail.

Gordon et al. (2005) have classified errors into 3 types: 22

1.

Errors with the type of sensors used.

2.

Errors with the data processing algorithm employed

3.

Errors with the analysis

Errors with the analysis are common when measurements are made from point clouds. Features need to be identified from the point cloud first while some software packages enable automatic feature detection. In other cases, features need to be identified manually. Dimensions of any object can be calculated by fitting planes to a set of points in the point cloud and then measuring the perpendicular distance between them.

Dai and Lu (2010) stated that the accuracy of photogrammetry is dependent on the precision of the camera, quality of the photos and also on the functionality of the photo processing software. They also proposed several methods for the analysis of photogrammetry accuracy: 1.

Visual assessment of agreement: Plotting the photograph based measurements with the tape readings. Assessment can be made from observing the deviation of the sample points from the line with a slope of 45 degrees (y = x). Another approach suggested is plotting the difference between the two sets of measurements against zero.

Consider the following set of measurements of the dimensions object as shown in Table 4, one made manually using tapes and the other made using photogrammetry. Deviation of the sample points from the line with a slope of 45 degrees (y = x) is shown

23

in Figure 4 and the differences between the two sets of measurements against zero is shown in Figure 5.

Measurement no. Tape (cm) Photogrammetry (cm)

Table 4:

1

36

38

2

40

41

3

56

55

4

18

20

5

22

21

Sample set of measurements

24

(y = x)

Figure 4:

Scatter plot between the two sets of measurements

Figure 5:

Difference between the two sets of measurements plotted against zero

25

2.

Analytical assessment of agreement: Applies the correlation coefficient technique to evaluate agreement between the two sets of measurements.

Taking the sample data set as shown in Table 4 above, this technique assesses the accuracy of photogrammetry by plotting a linear trend line along with the correlation coefficient as shown in Figure 6.

Figure 6:

3.

Correlation between the two sets of measurements

Ninety-Five percent limits of agreement: Proposed by Bland and Altman (1986), this technique identifies the sample mean and the sample standard deviation to set the upper and lower limits of agreement as followsUpper / Lower limit = 𝑥̅ ± 1.96 𝑠 26

Where 𝑥̅ is the sample mean and 𝑠 is the sample standard deviation of the

difference between the difference of two sets of measurements

This technique can only be applied when the following holds true:

1)

The scatter plot of the difference against the average values of the two sets of measurements should not indicate any divergence or convergence. In other words the distribution of the data points should not follow any pattern about the mean of the difference.

2)

The histogram of the differences should be normally distributed about the sample mean.

Assuming that the sample given in 4 satisfies the given conditions, this technique can be applied as follows to give Upper and Lower limits of agreement: 𝑥̅ =0.6 cm

𝑠 =1.52 cm

Upper limit = 𝑥̅ ± 1.96 𝑠 = 3.57 cm

Lower limit = 𝑥̅ ± 1.96 𝑠 = -2.37 cm Thus, it can be stated with 95% likelihood that, any geometric measurement of that object taken by photogrammetry would not differ from the corresponding tape measurement by more than 3.57 cm and no less than -2.37 cm. 27

4.

Confidence intervals on limits of agreement: establishes a 95% confidence interval around the limits of agreement so as to infer the true values with respect to the whole population. This technique employs the statistic of the t-distribution with n-1 degrees of freedom (Dai and Lu 2010). Thus, it overcomes the limitation of the previous technique, which is dependent on the sample data and changes with varying samples, by allowing the estimation of the confidence interval of the true population mean using the sample data. This is a two-step process, the first step involves calculation of the 95% limits of agreement for the mean difference between the two sets of measurements as follows-

Where:

[𝑥̅ −

𝑡𝑛−1,0.025 𝑠 √𝑛

,

𝑥̅ +

𝑡𝑛−1,0.025 𝑠 √𝑛

]

𝑡𝑛−1,0.025 is the statistic of the t-distribution with n-1 degrees of freedom and 95% confidence interval n is the sample size s is the sample standard deviation

For the sample data set shown in Table 4, this technique establishes the following confidence intervals for the mean difference between the two sets of measurements: where 𝑡𝑛−1,0.025 = 3.495 [-1.77, 2.97] cm

28

For the second step, the confidence interval around the limits of agreement can be estimated as follows (Dai and Lu 2010): [𝐿𝐿 − 𝑡𝑛−1,0.025 1.71𝑠/√𝑛, 𝐿𝐿 + 𝑡𝑛−1,0.025 1.71𝑠/√𝑛] [𝑈𝐿 − 𝑡𝑛−1,0.025 1.71𝑠/√𝑛, 𝑈𝐿 + 𝑡𝑛−1,0.025 1.71𝑠/√𝑛] The above equation gives the following result: 95% confidence interval around the lower limit and upper limits of agreement is: [-5.83 cm, 2.29 cm] and [-1.09 cm, 7.03 cm] respectively.

Thus, it can be stated with 95% likelihood that, any geometric measurement taken from the entire population of that object taken by photogrammetry would not differ from the corresponding tape measurement by more than 7.03 cm and no less than -5.83 cm.

Golparvar-Fard et al. (2011) compared the accuracy of laser scanning and photogrammetry by modeling a masonry block and a column. For laser scanning, actual images of the block were superimposed on the point cloud to enable automatic reconstruction of the block geometry. The same was not possible for photogrammetry because of a lower density point clouds and hence the surface of the block had to be manually created using geometric constraints. Accuracy of both techniques were finally measured by comparing the ratios of for each dimension (x, y and z) and the deviations were reported. Bosche (2010) suggested to measure the accuracy by comparing the deviations between the as-designed and the as-built poses of all recognized objects from a laser scan. Guarnieri et al. (2004) used Photomodeler 3 to model a church in Italy. The

3

(http://www.photomodeler.com/)

29

software enabled the user to manually define lines, edges, curves and surfaces. This model was exported for analysis. The object coordinates recovered from the model were compared against those obtained from a total station based survey and the RMS error was reported. Klein et al. (2011) used manual methods to extract dimensions and 3D coordinates from the 3D reconstruction obtained using Autodesk Photofly (Autodesk 2011a). Major building geometry like facades, wall openings and building elevations were created using polylines in Autodesk Photoscene editor (Autodesk 2011a). The generated lines and polylines were exported to Autodesk AutoCAD (Autodesk 2011b) for measurement and compared to the manual field measurements. Aim of the research was to verify if the accuracy of the extracted dimensions was within 2% of those obtained from the manual field measurements.

ACCURACY EVALUATION OF PHOTOGRAMMETRY This research focuses on evaluating the modeling performance based on the geometric modeling accuracy (Tang et al. 2010) and reporting the errors with analysis (Gordon et al. 2005) using the Ninety-Five percent limits of agreement (Bland and Altman 1986).

The flow chart shown in Figure 7 summarizes the methodology used in this research for accuracy evaluation of photogrammetry.

30

Image Processing 1. Import photos and upload to the server 2. Server returns a draft mesh 3. Check for unstitched photos and wrong camera positions 4. Manually stitch unstitched / wrongly stiched photos to refine the model 5. Re-upload photos to server 6. Delete noise and refine mesh Figure 7:

Element Modeling 1. Define reference points 2. Set coordinate axis 3. Join reference points using lines 4. Set the model scale (reference distance) 5. Export model to CAD application

Summary of Methodology for Accuracy Assessment of Photogrammetry

SOFTWARE PACKAGES USED The initial approach was to employ two software packages for this project: Autodesk Photofly (Autodesk 2011a) and Microsoft Photosynth (Microsoft 2011). However, due to various benefits of Autodesk Photofly (Autodesk 2011a), as explained in the following section, it was decided to continue the research only with it. The process of generating point cloud using both the packages differs a little, Autodesk Photofly (Autodesk 2011a) provides the user with more flexibility to edit and refine the point cloud whereas this feature is not available in Microsoft Photosynth (Microsoft 2011). It 31

was observed that the density of point cloud obtained using Autodesk Photofly (Autodesk 2011a) was greater than Microsoft Photosynth (Microsoft 2011) and it also afforded the user with more flexibility to generate 3D models. It was then decided that Autodesk Photofly (Autodesk 2011a) would be the preferred software package for generating future models for this thesis. The workflow for generating point clouds in Microsoft Photosynth (Microsoft 2011) is shown in Figure 8 and that for Autodesk Photofly (Autodesk 2011a) is shown in Figure 9.

Select

Upload

•Select source photos using the Photosynth desktop application.

•Upload photos to Photosynth servers.

View

•View the generated 3D photo scene and the point cloud thus generated.

Export

•Export the point cloud using Autodesk plugins to Autodesk AutoCAD.

Figure 8:

Workflow in Microsoft Photosynth (Microsoft 2011)

32

Select

•Select source photos and upload to Photofly servers using Autodesk Photosynth editor.

Edit

•View and edit the draft mesh returned from the server; check for wrong camera positions, perform manual stitching, add photos. •Resubmit model to Photofly servers.

Refine

•Select mesh quality and refine the model. •Resubmit model to Photofly servers.

View

•View / edit the refined mesh. •Resubmit to Photofly servers.

Export

•Export the scene as a point cloud to AutoCAD and / or as a Youtube video.

Figure 9:

Workflow in Autodesk Photofly (Autodesk 2011a)

33

IMAGE ACQUISITION FROM FIELD SURVEY It was first decided that a 3D model of a completed building in Austin, Texas, U.S.A be generated so as to better understand the software packages and also to formulate some guidelines for taking photos for the under-construction bridge. Before taking photographs, the user guides of both Microsoft Photosynth (Microsoft 2011) and Autodesk Photofly (Autodesk 2011a) were obtained to better understand the software requirements for taking photographs. Furthermore, several iterations were done using different camera settings to arrive at the guidelines for taking photographs. They are as follows: 1.

Selection of camera location before taking photos as shown in Figure 10.

2.

Location should be selected such that the entire section can be covered in a single shot or at maximum 3 photos as shown in Figure 11.

3.

The empty sky portion in the photos should be minimized as it interferes in the model generation algorithm.

4.

Short length of the sections should be used for generating models (around 150 ft.).

5.

Camera settings should capture maximum contrast / texture to enable automatic generation of models and to minimize manual stitching of photos.

6.

Maximum of 100 photos per section should be taken (70 – 80 is optimal). The software is not designed to handle more photos.

34

Camera location

Figure 10:

Selecting camera locations

Camera location Camera view

Figure 11:

Multiple images from the same camera locations

35

IMAGE PROCESSING TO GENERATE 3D MODEL USING COLLECTED IMAGES The workflow in Autodesk Photofly (Autodesk 2011a) and Microsoft Photosynth (Microsoft 2011) has been shown above in Figure 8 and 9 respectively.

The process starts with uploading the photos to both Microsoft Photosynth (Microsoft 2011) and Autodesk Photofly (Autodesk 2011a)servers on the web using their desktop applications. Microsoft Photosynth (Microsoft 2011) generated 3D model and point cloud is immediately available for viewing as shown in Figure 12 (a).

Figure 12(a): Point Cloud from Microsoft Photosynth (Microsoft 2011) ;

Figure 12(b): Point Cloud from Autodesk Photofly (Autodesk 2011a) 36

The process with Autodesk Photofly (Autodesk 2011a) is more complex but it affords the user with a number of additional features to manually join photos and increase the quality and accuracy of the model. Photos are uploaded to the Autodesk Photofly (Autodesk 2011a) servers for computation of the photo scene using Autodesk Photoscene editor (Autodesk 2011a). Autodesk Photofly (Autodesk 2011a) uses triangulation to generate 3D triangular meshes from the photos. The first model returned by the Autodesk Photofly (Autodesk 2011a) servers is in the “draft” state, which means that it could be refined based on the needs of the user. If some photos could not be automatically stitched then those had to be stitched manually by locating common points in 3 different photos. After locating the points, the model is again uploaded on the Autodesk Photofly (Autodesk 2011a) servers for computation of the new mesh. The draft quality mesh thus obtained is shown in Figure 13. This mesh is then checked for proper stitching of photos by manually browsing through some photos and superimposing them on the obtained mesh. The mesh is then cleaned and the noise (unwanted mesh generated of the trees and nearby objects) is removed. The point cloud is then generated from the refined mesh and is shown in Figure 12 (b).

As-Built Modeling Using The 3d Model In Autodesk Photofly As explained in the previous section, when the draft mesh is found to be satisfactory, the mesh is uploaded again on the Autodesk Photofly (Autodesk 2011a) servers to generate a maximum quality mesh as shown in Figure 14. The next step involves selecting reference points in Photoscene Editor (Autodesk 2011a) as shown in 37

Figure 15. This is a manual process and the reference points thus selected are used to model the geometry of the desired structure or any object in the model. After selecting the reference points, the coordinate axis is set as shown in Figure 16. The scale of the model is then set using an already known dimension as shown in Figure 17. Setting the coordinate axis helps in creating polylines to model the structure / an object in the model using the reference points created above as shown in Figure 18. Photoscene editor (Autodesk 2011a) affords the user options to constrain the polylines along the coordinate axis / planes for accurate geometric modeling.

Figure 13:

Draft quality mesh

38

Figure 14:

Maximum quality mesh

Figure 15:

Reference Points

39

Figure 16:

Setting the Coordinate Axis

Figure 17:

Setting scale of the model

40

Figure 18:

Creating Polylines

After modeling the geometry of the structure / the object, the model can be exported to AutoCAD as shown in Figure 19.

Figure 19:

Exported model in AutoCAD

41

It was observed that the density of point cloud obtained using Autodesk Photofly (Autodesk 2011a) was greater than Microsoft Photosynth (Microsoft 2011) and it also afforded the user with more flexibility to generate 3D models. Hence, it was decided that Autodesk Photofly (Autodesk 2011a) would be the preferred software package for generating future models. After a successful trial of Autodesk Photofly (Autodesk 2011a)on the completed building, it was tested to generate a model of an underconstruction bridge in Dallas, Texas, U.S.A. As the author was not physically present at the site to take photos, another student who was present at the project site was asked to take photos of the bridge.

TEST PROJECT DESCRIPTION The Margaret Hunt Hill Bridge, located in downtown Dallas, Texas, U.S.A, was used as the test project to assess the accuracy of photogrammetry for use in modeling highway infrastructure projects. The structure is a 6 lane, 1870 ft. long cable stayed steel bridge designed by Santiago Calatrava. The bridge is currently under construction, as shown in Figure 20, and it is scheduled for completion in March 2012. This project was chosen because it has characteristics that are typical of a highway infrastructure project, such as: 1.

Structure comprises repeating units and the structure has little variation in contrast and texture along the length.

2.

The bridge spans over a river.

3.

Some elements of the structure are occluded due to the presence of natural vegetation at the site.

42

The bridge deck consists mostly of planar members like beams and box girders. While the central and the exterior box girders are vertical with respect to the ground, the other members of the bridge deck, including the beams, are inclined due to a cross slope along the width of the bridge.

Figure 20(a): Margaret Hunt Hill bridge - Dallas, Texas, U.S.A, Rendered photo of the bridge

Figure 20(b): Margaret Hunt Hill bridge - Dallas, Texas, U.S.A, Photo taken on June 27, 2011

43

IMAGE BASED FIELD SURVEY For data collection purposes, the bridge was divided into 5 sections along the length, as shown in Figure 21, to enable accurate computation of the 3D point cloud, which is designed to work best with 70-80 photos. The lack of texture and contrast due to repeating units in the bridge structure presented another challenge, as the software relies on the inherent difference in the texture of the structure to stitch the photos together and generate a 3D model. To overcome this challenge, several test photos were taken to determine the best camera setting for the study. Since the bridge was an active construction zone, prior permission was obtained from the authorities before performing a survey. The permission was difficult to obtain and hence the survey team had very limited time, which depended on the construction schedule, to take the photographs. Also, no markers could be posted on the different elements of the bridge due to contractual clauses. An off the shelf DSLR camera was used to take photos at a resolution of 16 MP and the following strategy was employed to take photos of each of the sections: 1.

Camera locations were selected in a circular path around each bridge section.

2.

Locations were selected such that the entire section was covered in a single shot or at maximum 3 photos.

3.

The empty sky portion in the photos was minimized as it interfered with the model generation algorithm.

4.

Camera setting which captured the maximum contrast / texture was selected.

5.

No. of photos per section were limited to 100 photos.

44

Figure 21:

Margaret Hunt Hill Bridge divided into 5 sections - Dallas, Texas, U.S.A

Summary of the image based survey showing the actual number of photos, the number of photos used in the photo based model and the image processing time, including the manual stitching time, required to generate the model for each of the sections is presented in Table 5.

45

Image Processing

Date

Section

No. of photos

Time taken to

stitched

generate model

No. of photos

(hours) 7/1/11

1

54

54

8

7/16/11

2

74

74

5

7/16/11

3

75

75

5

7/22/11

4

107

24

12

7/1/11

5

41

41

7

Table 5:

Summary of the image based survey

IMAGE PROCESSING The flowchart for image processing has been shown in Figure 7. The photos were uploaded to the servers of the software in order to generate point clouds for each section. The software generates automatic camera calibration and structure calculations in order to produce these point clouds (Klein et al. 2011). Any photos that were not automatically stitched by the software were stitched manually. The manual stitching was accomplished by selecting common reference points in the photos that were stitched and the photos that were not stitched. Sections 1 and 5 needed approximately 50% of the photos to be 46

stitched manually, sections 2 and 3 required approximately 20% of the photos to be stitched manually and in section 4, only 24 photos out 107 could be stitched. The inability to stitch all of the photos of section 4 was due to the river that runs under this section of the bridge. This obstacle made it difficult to take photos with a significant overlap, in a circular path around the section. Overall, the lack of difference in texture and contrast of the surface of the bridge made it difficult to automatically stitch all of the photos. Once the editing was complete, the model was resubmitted to the software server. The amount of time and effort spent on manual stitching was dependent on the camera locations, picture quality of each section and the model generating algorithm of the software. More time was taken for the sections that involved more manual stitching as shown in Table 5. Section 4 took the maximum time because several unsuccessful attempts were made to manually stitch the photos.

The 3D model returned by the software after the editing process along with the camera positions, as shown in Figure 22, was used to model the bridge beams, exterior box girder, and the holes for electrical fixtures on the central box girder. These elements were manually modeled by defining reference points in the structure and connecting these points with reference lines. The coordinate system was also manually defined at this stage. The generated elements were then exported to a CAD modeling software, as shown in Figure 23, in order to evaluate dimension accuracy. As can be seen in Figure 23, not all the floors beams, holes for electrical fixtures and the entire box girders along the section length could be modeled. This can be attributed to the precision of the camera, quality of the photos and functionality of the image processing software as suggested by Dai and Lu (2010). The summary of the elements modeled in each of the section and the time taken 47

to model the elements is shown in Table 6. More time to model was taken for those sections which had more elements like section 2 and 3.

Figure 22:

Refined 3D model along with the camera positions returned by the software

Figure 23:

Model exported to a CAD modeling software

48

Section

Floor Beams

Holes

Exterior Box Girder Heights

Manual 3D points

Lines

Time Taken to Model Elements (hours)

1

18

16

18

126

139

1.5

2

29

27

21

185

200

4

3

27

29

16

169

179

3.5

4

13

8

7

74

75

1.5

5

16

16

16

112

119

3

Table 6:

Summary of elements modeled in each section

ACCURACY ASSESSMENT The flowchart for accuracy assessment is shown in Figure 24 below. The models generated using photos were compared against the 3D model developed using the 2D drawings, which was used as the "ground truth". The model included the following elements and their corresponding dimensions: bridge beams, the exterior box girder, central box girder and the holes for electrical fixtures located in the central box girder. The 3D model used for comparison is shown in Figure 25. Dimensions of the following elements were extracted from the model for comparison: 1.

Height of exterior box girder.

2.

Distance between the holes for electrical fixtures, on the central box girder.

3.

Length and width of the floor beams.

49

Accuracy assessment

Image based as-built model

2D drawings based as-built model

Compare dimensions

Height of exterior box girders

Distances between the holes for electrical fixtures, on the central box girder

Figure 24:

Flowchart for accuracy assessment

Figure 25:

3D model generated using 2D drawings

50

Length and width of the floor beams

CHAPTER 4 - Results

DIMENSION ANALYSIS The as-built models generated using photos were scaled in Autodesk Photofly (Autodesk 2011a) by manually defining a reference distance. The lengths of the line joining the first and the last hole on the sides of the box girders were used to set the reference scale of each section. The model was then exported to a CAD modeling software and dimensions of the elements under investigation were extracted for comparison purposes. The dimension analysis was performed as follows: 1.

As shown in Figure 26, the height of the exterior box was estimated by taking the average of all the intermediate heights, Heights 1-19 in Figure 26, modeled using the software on either sides of the central box girder.

Figure 26:

Height of box girder

51

2.

As shown in Figure 27, the length of the beam was estimated by taking the average of the two lengths modeled, while the width of the beam was estimated by taking the average of the two beams modeled.

Figure 27: 3.

Dimensions of beam

As shown in Figure 28, the distance between the holes was taken as the length of the line joining the holes on either side of the central box girder.

Figure 28:

Distance between holes

52

The deviations were calculated by subtracting the 2D drawings based 3D model dimensions from the dimensions extracted from the photo based model. These deviations were divided by the ground truth (dimensions from the drawing based 3D model) to represent them as a percentage deviation. The results of section 1 are presented in Tables 7-9 (all dimensions are in feet). The results of section 1,2,3,4 and 5 are presented in Appendices A - E respectively (all dimensions are in feet).

As can be seen from Table 7(b), the deviations in the widths were found to be excessive and hence they were removed from the analysis to prevent any skewness in the analysis. The high percentage error in width can be explained by the fact that the actual width of the beam was comparable to the deviation observed and the ratio of deviation to the actual width of the beam was very high. Furthermore, the max. deviations in all the sections were mostly observed mostly at the extreme ends of the section, which were hard to model. The deviations for section 1-5, using all the different scales used, were plotted against 0 and are shown in Figure 29-33. The summary of deviations observed for all sections is presented in Table 10. Except for section 3 and section 4, the dimensions of all the other sections were found to be less than the dimensions obtained from the 2D drawings based 3D model. Section 4 showed the maximum deviation from the mean, this can be attributed to the fact that the river Trinity was flowing below the section, which made it extremely difficult to take photos in a closed path around the section. This affected the quality of the model generated and hence the results.

53

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.9366 50.9549 51.4458

0.7235

1.39%

2

52.1693 51.6948 51.2617 51.4783

0.6910

1.32%

3

52.1693 51.4498 50.8081 51.1290

1.0404

1.99%

4

52.1693 51.4522 51.3093 51.3808

0.7886

1.51%

5

52.1693 51.3521 50.6162 50.9842

1.1852

2.27%

6

52.1693 50.8215 50.0809 50.4512

1.7181

3.29%

7

52.1693 51.0252 49.7716 50.3984

1.7709

3.39%

8

52.1693 49.8907 52.2440 51.0674

1.1020

2.11%

9

52.1693 49.7007 48.2710 48.9859

3.1835

6.10%

10

52.1693 51.4431 51.8041 51.6236

0.5457

1.05%

11

52.1693 51.6932 51.9346 51.8139

0.3554

0.68%

12

52.1693 52.3941 52.1714 52.2828

-0.1135

-0.22%

13

52.1693 52.3540 52.1127 52.2334

-0.0641

-0.12%

14

52.1693 51.9408 52.0856 52.0132

0.1561

0.30%

15

52.1693 52.1127 51.8449 51.9788

0.1905

0.37%

16

52.1693 51.6398 51.4174 51.5286

0.6407

1.23%

17

52.1693 52.3521 51.2390 51.7956

0.3738

0.72%

18

52.1693 52.4969 52.3654 52.4312

-0.2619

-0.50%

Table 7(a): Section 1 Beams, referenced by scale set on the north side 54

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 2.5506 1.2484 1.8995

-0.5688

-42.74%

2

1.3307 1.6644 1.7359 1.7002

-0.3695

-27.76%

3

1.3307 1.7108 1.3637 1.5373

-0.2066

-15.52%

4

1.3307 1.7756 1.6374 1.7065

-0.3758

-28.24%

5

1.3307 2.0729 1.8431 1.9580

-0.6273

-47.14%

6

1.3307 1.7721 1.6961 1.7341

-0.4034

-30.31%

7

1.3307 1.7194 1.7575 1.7385

-0.4078

-30.64%

8

1.3307 2.7465 1.7866 2.2666

-0.9359

-70.33%

9

1.3307 3.4365 1.3711 2.4038

-1.0731

-80.64%

10

1.3307 1.3024 1.7214 1.5119

-0.1812

-13.62%

11

1.3307 1.6332 1.7816 1.7074

-0.3767

-28.31%

12

1.3307 2.0658 1.7643 1.9151

-0.5844

-43.91%

13

1.3307 1.5117 1.6896 1.6007

-0.2700

-20.29%

14

1.3307 1.6468 1.9066 1.7767

-0.4460

-33.52%

15

1.3307 1.2468 1.7404 1.4936

-0.1629

-12.24%

16

1.3307 1.1323 1.9888 1.5606

-0.2299

-17.27%

17

1.3307 1.4874 1.8559 1.6717

-0.3410

-25.62%

18

1.3307 1.3703 1.6011 1.4857

-0.1550

-11.65%

Table 7(b): Section 1 Beams, referenced by scale set on the north side 55

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.8361

0.0139

0.49%

2

2.8500 2.8244

0.0256

0.90%

3

2.8500 2.7928

0.0572

2.01%

4

2.8500 2.8769

-0.0269

-0.94%

5

2.8500 2.9276

-0.0776

-2.72%

6

2.8500 2.7336

0.1164

4.08%

7

2.8500 2.7710

0.0790

2.77%

8

2.8500 2.9633

-0.1133

-3.98%

9

2.8500 3.1911

-0.3411

-11.97%

10

2.8500 2.9562

-0.1062

-3.73%

11

2.8500 2.7917

0.0583

2.05%

12

2.8500 2.8318

0.0182

0.64%

13

2.8500 2.7483

0.1017

3.57%

14

2.8500 2.7114

0.1386

4.86%

15

2.8500 2.7351

0.1149

4.03%

16

2.8500 2.7577

0.0923

3.24%

17

2.8500 2.7235

0.1265

4.44%

18

2.8500 2.8355

0.0145

0.51%

19

2.8500 2.7057

0.1443

5.06%

Table 8:

Section 1 Box Girders, referenced by scale set on the north side 56

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.0113

-0.0113

-0.06%

(2,3)

20.000 20.0303

-0.0303

-0.15%

(3,4)

20.000 19.9674

0.0326

0.16%

(4,5)

20.000 19.7162

0.2838

1.44%

(5,6)

20.000 20.5410

-0.5410

-2.63%

(6,7)

20.000 19.6086

0.3914

2.00%

(7,8)

20.000 20.1825

-0.1825

-0.90%

(9,10)

20.000 19.9466

0.0534

0.27%

(10,11) 20.000 20.1944

-0.1944

-0.96%

(11,12) 20.000 20.0474

-0.0474

-0.24%

(12,13) 20.000 20.2630

-0.2630

-1.30%

(13,14) 20.000 19.9926

0.0074

0.04%

(14,15) 20.000 20.1875

-0.1875

-0.93%

(15,16) 20.000 19.9699

0.0301

0.15%

Table 9:

Section 1 Distance between Holes, referenced by scale set on the north side

57

Figure 29:

Section 1 deviations using all the 3 reference scales used

Figure 30:

Section 2 deviations using all the 3 reference scales used

Figure 31:

Section 3 deviations using all the 3 reference scales used

58

Figure 32:

Section 4 deviations using all the 3 reference scales used

Figure 33:

Section 5 deviations using all the 3 reference scales used

59

Section

Scale Set on North

Scale Set on South

Two Scale Points

#

Side

Side

Used

Avg.

Std. Dev.

Avg.

Std. Dev.

Avg.

Std. Dev.

1

0.61%

2.82%

1.03%

2.81%

0.81%

2.86%

2

1.36%

2.06%

1.89%

2.03%

1.55%

2.04%

3

-1.11%

5.22%

-2.33%

5.26%

-1.96%

5.46%

4

-7.64%

10.73%

-1.05%

10.11%

-4.39%

10.96%

5

1.05%

2.40%

0.71%

2.41%

0.88%

2.40%

Table 10:

Summary of all Sections

One of the objectives of the research was to report the errors with analysis (Gordon et al. 2005) using the Ninety-Five percent limits of agreement (Bland and Altman 1986) as explained in Chapter 3. However, it was found that the assumptions for Ninety-Five percent limits of agreement were not satisfied for any of the sections: scatter plot of the difference against the average values of the two sets of measurements followed a pattern about the mean of the difference. Also, the histogram of the differences was not normally distributed about the sample mean. Results of dimensions scaled by scale set on the south side for section 1 are shown in Figure 34 and 35.

60

Figure 34:

Scatter plot of differences against average values of dimensions for section 1 with scale set on the south side

Figure 35:

Histogram of differences for section 1 with scale set on the south side

As can be seen in Table 10, each section was scaled separately using 2 scale points. Then, each section was divided into 2 parts (north and south) and scaled using a reference dimension on either side. The aim was to verify whether selecting a different scale point affected the deviations and also to verify the results of (Klein et al. 2011), who observed the mean of deviations to decrease with the increase in scale points. ANOVA was done to verify statistically if the there was a difference in means of 61

deviations when different scale points and multiple scale points were used. ANOVA was performed using Palisades StatTools (Palisades 2011) using the Tukey correction factor at 95% confidence level. The results for all sections are presented in Table 10 respectively. Section 4 was not included in the analysis as the assumption that the data set should be normally distributed could not be satisfied, as shown in Figure 36-38. The quantile quantile (Q-Q) plot of standardized percentage deviation for dimensions, scaled using all the 3 reference scales, against standardized z-values didn't fall on the line (y=x).

Figure 36:

Q-Q plot of standardized percentage deviations, with scale set on the north side vs. standardized z-values for section 4

62

Figure 37:

Q-Q plot of standardized percentage deviations, with scale set on the south side vs. standardized z-values for section 4

Figure 38:

Q-Q plot of standardized percentage deviations, with scale set on both sides vs. standardized z-values for section 4

63

The null and the alternate hypothesis to verify statistically if the there was a difference in means of deviations when different scale points and multiple scale points were defined as follows: Ho = The means of deviations when different scale points and multiple scale points are used are the same. Ha = The means of deviations when different scale points and multiple scale points are used are different.

Section #

1

2

3

5

p-value

0.7572

0.3668

0.3822

0.7922

Table 11:

ANOVA summary for all sections

As can be seen from Table 11 above, due to the high p-value (>0.05), the null hypothesis stating that the means of deviations using different scale points are equal at 95% confidence level cannot be rejected and holds true. Thus the results of Klein et al. (2011) could not be validated statistically using this experiment. They used this technique to model the exterior of a university building which had well defined rectangular geometry consisting of edges, corners and difference in texture on the exterior walls. This enabled Autodesk Photofly (Autodesk 2011a) to recognize feature points and generate the point cloud. The difference in the results between the results of Klein et al. (2011) and this study can be attributed to: 1.

Environmental factors like presence of natural vegetation and ponds at the site which prevented photos to be taken in a circular path around each section.

64

2.

Lack of texture on the surface of the structure, which is essential for the recognition of feature points.

3.

Lack of difference in the structure due to repetition of members, lack of well defined corners / edges which enables recognition of feature points and selection of reference points.

The challenges highlighted using this test project are characteristics of any typical infrastructural project and need to be overcome by the technology to make it more effective and attractive for as-built modeling to aid in reliable decision making.

65

CHAPTER 5 - Validation METHODOLOGY To further assess the accuracy of photogrammetry, comparison between point clouds generated by laser scanners and photogrammetry was done. A laser scan using Leica GeoSystems ScanStation C10 (Leica Geosystems 2011b), which is a time-of-flight laser scanner, of an exterior wall of a university building was done followed by an image based survey. It took a trained field technician approximately an hour to laser scan the wall, while it took the authors 5 minutes to take photos of the same. Post processing of the laser scan data to generate a point cloud took another 1-2 hours. The point cloud from the laser scan is shown in Figure 39 (b), Image processing was done using Autodesk Photofly (Autodesk 2011a) to generate the point cloud as shown in Figure 39 (a). A total of 14 photos were taken using an off the shelf digital camera at 10 MP resolution and it took approximately 1.5 hours to generate the point cloud. Autodesk Revit (Autodesk 2011c) was used to generate models of the exterior wall along with the opening using both the point clouds, as shown in Figure 40. The accuracy assessment for this case was performed as shown in Figure 41.

Figure 39(a): Photo based point cloud 66

Figure 39(b): Laser scan point cloud

Figure 40(a): Exterior wall modeled using photo based point cloud

Figure 40(b): Exterior wall modeled using laser scan point cloud 67

Accuracy assessment

Image based as-built model

Laser scan based as-built model

Compare dimensions

Height and width of wall

Figure 41:

Height and width of wall opening

Methodology for accuracy assessment of model generated using photogrammetry point cloud

RESULTS The results of the comparison between laser scan and photogrammetry point cloud based models is shown in Table 12. Deviations were divided by the laser scan dimensions to get the percentage deviation. All dimensions from photogrammetry were less than the laser scan dimensions by more than 7% except for the width of the wall. Deviation in the width of the wall was less because the scale of the model was set according to this dimension.

68

Wall

Opening

Table 12:

Laser

Photo

Scan

Based



%∆

H (ft)

20.000

H (ft)

18.000

-2.000

-10.0

W (ft)

150.651

W (ft)

150.827

0.176

0.1

H (ft)

8.833

H (ft)

7.667

-1.166

-13.2

W (ft)

7.000

W (ft)

6.458

-0.542

-7.7

Comparison between laser scan and photogrammetry point cloud based models

The results concur with those of Golparvar-Fard et al. (2011) who concluded, after comparing 8 point cloud models from laser scanning and photogrammetry, that laser scanning is more accurate. However, photogrammetry can be extremely useful to extract as-built semantic information (i.e., progress, productivity, quality and safety) through the content of the images without putting additional burden on the project management teams. One specific application where accuracy is not important is during the site clearing and mobilization phase of the project, where photogrammetry can be used for surveying the site to locate the laydown yard, as well as for locating the positions of cranes and heavy equipment to ensure adequate clearance for job site safety purposes. This technology is also suitable for visualization and communication purposes, wherein the 3D model generated using photographs can be used by the project management team to remotely monitor the construction progress. However, for higher accuracy applications like defect detection, this technology in its present state is not the most appropriate.

69

CHAPTER 6 - Conclusions This research investigated the use of an off the shelf photogrammetry software package to model an under-construction bridge in southern United States to study the accuracy of the process for progress monitoring and infrastructure asset management purposes. How the major objectives of the research were met are described below: 1.

Development of the 3D point cloud based model on photographs of the Margaret Hunt Hill Bridge. The bridge was divided into 5 sections for modeling purposes.

2.

Comparing the dimensions of selected elements from the photo based 3D model to the 2D drawings based 3D model and finding deviations. Although this technology is promising, the results indicate that in its present form it is not suitable for modeling purposes. Significant differences to the order of about 2% +/- 5% were observed for length of beams, height of exterior box girder and distance between the holes for electrical fixtures when compared to the 3D model developed

using

the

2D

drawings.

The

dimensions

obtained

from

photogrammetry were observed to be less than the 3D model for sections 1, 2 and 5 and more for sections 3 and 4. Environmental factors like occlusion due to natural vegetation, presence of water bodies prevented taking photos for optimal functioning of the software. These, along with lack of texture and repetition of members, were the greatest challenges observed in the modeling process. The greatest deviations were observed at extreme ends of the sections which was difficult to model due to few feature point recognition by the software package. 3.

Finding deviations between 3D model generated from photo based point cloud with the model generated using laser scan point cloud. Validation of 70

photogrammetry was done by comparing the photo based point cloud with laser scan point cloud for an exterior wall and a deviation of more than 7% was observed further demonstration that a point cloud generated from a laser scanner is much more suitable for generating as-built models of facilities. 4.

Discussion on limitations and potential applications of this technology. Based on technological developments, as suggested by Klein et al. (2011) and validated in the paper, this technology has the potential to be used for: 1. Measuring elements that are inaccessible from the line of sight; 2. Efficient dimension takeoffs for progress measurement purposes; 3. Serving as a digital storage for visualization and future dimension takeoffs, for decision making and asset management purposes; 4. For visualization purposes and communication of construction progress. It is hoped that in the near future, with technological advancements, construction will be able to reap full benefits of this emerging technology.

71

Appendices

72

APPENDIX A Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.7177 50.7402 51.2290

0.9404

1.80%

2

52.1693 51.4770 51.0457 51.2614

0.9080

1.74%

3

52.1693 51.2330 50.5940 50.9135

1.2558

2.41%

4

52.1693 51.2354 51.0931 51.1643

1.0051

1.93%

5

52.1693 51.1357 50.4030 50.7694

1.4000

2.68%

6

52.1693 50.6074 49.8699 50.2387

1.9307

3.70%

7

52.1693 50.8102 49.5618 50.1860

1.9833

3.80%

8

52.1693 49.6804 52.0238 50.8521

1.3172

2.52%

9

52.1693 49.4913 48.0676 48.7795

3.3899

6.50%

10

52.1693 51.2264 51.5858 51.4061

0.7632

1.46%

11

52.1693 51.4754 51.7158 51.5956

0.5737

1.10%

12

52.1693 52.1733 51.9515 52.0624

0.1069

0.20%

13

52.1693 52.1334 51.8932 52.0133

0.1560

0.30%

14

52.1693 51.7219 51.8662 51.7941

0.3753

0.72%

15

52.1693 51.8931 51.6264 51.7598

0.4096

0.79%

16

52.1693 51.4222 51.2007 51.3115

0.8579

1.64%

17

52.1693 52.1315 51.0231 51.5773

0.5920

1.13%

18

52.1693 52.2757 52.1447 52.2102

-0.0409

-0.08%

Table 13(a): Section 1 Beams, referenced by scale set on the south side 73

Beam #

Wac

W1

W2

Wavg ∆W = Wavg - Wac

%∆W

1

1.3307 2.5398 1.2431 1.8915

-0.5608

-42.14%

2

1.3307 1.6574 1.7286 1.6930

-0.3623

-27.23%

3

1.3307 1.7036 1.3579 1.5308

-0.2001

-15.03%

4

1.3307 1.7681 1.6305 1.6993

-0.3686

-27.70%

5

1.3307 2.0642 1.8353 1.9498

-0.6191

-46.52%

6

1.3307 1.7646 1.6889 1.7268

-0.3961

-29.76%

7

1.3307 1.7121 1.7501 1.7311

-0.4004

-30.09%

8

1.3307 2.7349 1.7791 2.2570

-0.9263

-69.61%

9

1.3307

1.3653 2.3937

-1.0630

-79.88%

10

1.3307 1.2969 1.7142 1.5056

-0.1749

-13.14%

11

1.3307 1.6263 1.7741 1.7002

-0.3695

-27.77%

12

1.3307 1.7569 2.0571 1.9070

-0.5763

-43.31%

13

1.3307 1.5053 1.6824 1.5939

-0.2632

-19.78%

14

1.3307 1.6399 1.8986 1.7693

-0.4386

-32.96%

15

1.3307 1.2416 1.7331 1.4874

-0.1567

-11.77%

16

1.3307 1.1275 1.9804 1.5540

-0.2233

-16.78%

17

1.3307 1.4812 1.8481 1.6647

-0.3340

-25.10%

18

1.3307 1.3645 1.5944 1.4795

-0.1488

-11.18%

3.422

Table 13(b): Section 1 Beams, referenced by scale set on the south side 74

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.8361

0.0139

0.49%

2

2.8500 2.8244

0.0256

0.90%

3

2.8500 2.7928

0.0572

2.01%

4

2.8500 2.8769

-0.0269

-0.94%

5

2.8500 2.9276

-0.0776

-2.72%

6

2.8500 2.7336

0.1164

4.08%

7

2.8500 2.7710

0.0790

2.77%

8

2.8500 2.9633

-0.1133

-3.98%

9

2.8500 3.1911

-0.3411

-11.97%

10

2.8500 2.9562

-0.1062

-3.73%

11

2.8500 2.7917

0.0583

2.05%

12

2.8500 2.8318

0.0182

0.64%

13

2.8500 2.7483

0.1017

3.57%

14

2.8500 2.7114

0.1386

4.86%

15

2.8500 2.7351

0.1149

4.03%

16

2.8500 2.7577

0.0923

3.24%

17

2.8500 2.7235

0.1265

4.44%

18

2.8500 2.8355

0.0145

0.51%

19

2.8500 2.7057

0.1443

5.06%

Table 14:

Section 1 Box Girders, referenced by scale set on the south side 75

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 19.9269

0.0731

0.37%

(2,3)

20.000 19.9459

0.0541

0.27%

(3,4)

20.000 19.8833

0.1167

0.59%

(4,5)

20.000 19.6331

0.3669

1.87%

(5,6)

20.000 20.4544

-0.4544

-2.22%

(6,7)

20.000 19.5260

0.4740

2.43%

(7,8)

20.000 20.0975

-0.0975

-0.49%

(9,10)

20.000 19.8625

0.1375

0.69%

(10,11) 20.000 20.1093

-0.1093

-0.54%

(11,12) 20.000 19.9629

0.0371

0.19%

(12,13) 20.000 20.1776

-0.1776

-0.88%

(13,14) 20.000 19.9083

0.0917

0.46%

(14,15) 20.000 20.1025

-0.1025

-0.51%

(15,16) 20.000 19.8858

0.1142

0.57%

Table 15:

Section 1 Distance between Holes, referenced by scale set on the south side

76

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.9366 50.9549 51.4458

0.7235

1.39%

2

52.1693 51.6948 51.2617 51.4783

0.6910

1.32%

3

52.1693 51.4498 50.8081 51.1290

1.0404

1.99%

4

52.1693 51.4522 51.3093 51.3808

0.7886

1.51%

5

52.1693 51.3521 50.6162 50.9842

1.1852

2.27%

6

52.1693 50.8215 50.0809 50.4512

1.7181

3.29%

7

52.1693 51.0252 49.7716 50.3984

1.7709

3.39%

8

52.1693 49.8907 52.2440 51.0674

1.1020

2.11%

9

52.1693 49.7007 48.2710 48.9859

3.1835

6.10%

10

52.1693 51.2264 51.5858 51.4061

0.7632

1.46%

11

52.1693 51.4754 51.7158 51.5956

0.5737

1.10%

12

52.1693 52.1733 51.9515 52.0624

0.1069

0.20%

13

52.1693 52.1334 51.8932 52.0133

0.1560

0.30%

14

52.1693 51.7219 51.8662 51.7941

0.3753

0.72%

15

52.1693 51.8931 51.6264 51.7598

0.4096

0.79%

16

52.1693 51.4222 51.2007 51.3115

0.8579

1.64%

17

52.1693 52.1315 51.0231 51.5773

0.5920

1.13%

18

52.1693 52.2757 52.1447 52.2102

-0.0409

-0.08%

Table 16(a): Section 1 Beams, referenced by scale set on both sides 77

Beam #

Wac

W1

W2

Wavg ∆W = Wavg - Wac

%∆W

1

1.3307 2.5506 1.2484 1.8995

-0.5688

-42.74%

2

1.3307 1.6644 1.7359 1.7002

-0.3695

-27.76%

3

1.3307 1.7108 1.3637 1.5373

-0.2066

-15.52%

4

1.3307 1.7756 1.6374 1.7065

-0.3758

-28.24%

5

1.3307 2.0729 1.8431 1.9580

-0.6273

-47.14%

6

1.3307 1.7721 1.6961 1.7341

-0.4034

-30.31%

7

1.3307 1.7194 1.7575 1.7385

-0.4078

-30.64%

8

1.3307 2.7465 1.7866 2.2666

-0.9359

-70.33%

9

1.3307 3.4365 1.3711 2.4038

-1.0731

-80.64%

10

1.3307 1.2969 1.7142 1.5056

-0.1749

-13.14%

11

1.3307 1.6263 1.7741 1.7002

-0.3695

-27.77%

12

1.3307 1.7569 2.0571 1.9070

-0.5763

-43.31%

13

1.3307 1.5053 1.6824 1.5939

-0.2632

-19.78%

14

1.3307 1.6399 1.8986 1.7693

-0.4386

-32.96%

15

1.3307 1.2416 1.7331 1.4874

-0.1567

-11.77%

16

1.3307 1.1275 1.9804 1.5540

-0.2233

-16.78%

17

1.3307 1.4812 1.8481 1.6647

-0.3340

-25.10%

18

1.3307 1.3645 1.5944 1.4795

-0.1488

-11.18%

Table 16(b): Section 1 Beams, referenced by scale set on both sides 78

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.8481

0.0019

0.07%

2

2.8500 2.8363

0.0137

0.48%

3

2.8500 2.8046

0.0454

1.59%

4

2.8500 2.8890

-0.0390

-1.37%

5

2.8500 2.9400

-0.0900

-3.16%

6

2.8500 2.7452

0.1048

3.68%

7

2.8500 2.7827

0.0673

2.36%

8

2.8500 2.9758

-0.1258

-4.41%

9

2.8500 3.2047

-0.3547

-12.45%

10

2.8500 2.9687

-0.1187

-4.16%

11

2.8500 2.7917

0.0583

2.05%

12

2.8500 2.8318

0.0182

0.64%

13

2.8500 2.7483

0.1017

3.57%

14

2.8500 2.7114

0.1386

4.86%

15

2.8500 2.7351

0.1149

4.03%

16

2.8500 2.7577

0.0923

3.24%

17

2.8500 2.7235

0.1265

4.44%

18

2.8500 2.8355

0.0145

0.51%

19

2.8500 2.7057

0.1443

5.06%

Table 17:

Section 1 Box Girders, referenced by scale set on both sides 79

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.0113

-0.0113

-0.06%

(2,3)

20.000 20.0303

-0.0303

-0.15%

(3,4)

20.000 19.9674

0.0326

0.16%

(4,5)

20.000 19.7162

0.2838

1.44%

(5,6)

20.000 20.5410

-0.5410

-2.63%

(6,7)

20.000 19.6086

0.3914

2.00%

(7,8)

20.000 20.1825

-0.1825

-0.90%

(9,10)

20.000 19.8625

0.1375

0.69%

(10,11) 20.000 20.1093

-0.1093

-0.54%

(11,12) 20.000 19.9629

0.0371

0.19%

(12,13) 20.000 20.1776

-0.1776

-0.88%

(13,14) 20.000 19.9083

0.0917

0.46%

(14,15) 20.000 20.1025

-0.1025

-0.51%

(15,16) 20.000 19.8858

0.1142

0.57%

Table 18:

Section 1 Distance between Holes, referenced by scale set on both sides

80

APPENDIX B

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.2745 51.5875 51.4310

0.7383

1.42%

2

52.1693 51.8670 51.8131 51.8401

0.3293

0.63%

3

52.1693 51.6428 51.1653 51.4041

0.7653

1.47%

4

52.1693 51.4358 51.4101 51.4230

0.7464

1.43%

5

52.1693 51.3828 51.8845 51.6337

0.5356

1.03%

6

52.1693 51.6774 51.7382 51.7078

0.4615

0.88%

7

52.1693 51.3787 51.5983 51.4885

0.6808

1.30%

8

52.1693 51.5179 51.4544 51.4862

0.6832

1.31%

9

52.1693 51.3424 51.5392 51.4408

0.7285

1.40%

10

52.1693 51.6153 51.0643 51.3398

0.8295

1.59%

11

52.1693 51.8292 52.1939 52.0116

0.1578

0.30%

12

52.1693 50.9055 52.1402 51.5229

0.6464

1.24%

13

52.1693 51.5978 51.6689 51.6334

0.5360

1.03%

14

52.1693 51.3711 51.4492 51.4102

0.7591

1.46%

15

52.1693 51.6325 51.3613 51.4969

0.6724

1.29%

16

52.1693 52.1369 51.6769 51.9069

0.2624

0.50%

Table 19(a): Section 2 Beams, referenced by scale set on the north side 81

17

52.1693

51.4427 52.1163 51.7795

18

52.1693

52.0746 52.3984 52.2365 -0.0672 -0.13%

19

52.1693

51.5042 52.1033 51.8038

0.3656

0.70%

20

52.1693

52.2060 52.0743 52.1402

0.0291

0.06%

21

52.1693

51.9275 51.5486 51.7381

0.4312

0.83%

22

52.1693

51.0965 51.5731 51.3348

0.8345

1.60%

23

52.1693

51.8114 51.5083 51.6599

0.5095

0.98%

24

52.1693

52.1871 52.2740 52.2306 -0.0613 -0.12%

25

52.1693

52.2854 51.9893 52.1374

0.0320

0.06%

26

52.1693

50.9724 51.7977 51.3851

0.7843

1.50%

27

52.1693

51.7924 51.6709 51.7317

0.4376

0.84%

28

52.1693

52.0597 52.0738 52.0668

0.1026

0.20%

29

52.1693

51.3370 51.9222 51.6296

0.5397

1.03%

Table 19(a) Continued:

0.3898

0.75%

Section 2 Beams, referenced by scale set on the north side

82

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.1803 1.2307 1.2055

0.1252

9.41%

2

1.3307 1.7120 1.7352 1.7236

-0.3929

-29.53%

3

1.3307 1.4396 1.1320 1.2858

0.0449

3.37%

4

1.3307 1.3149 1.3725 1.3437

-0.0130

-0.98%

5

1.3307 1.3516 1.1883 1.2700

0.0608

4.57%

6

1.3307 1.2803 1.2089 1.2446

0.0861

6.47%

7

1.3307 1.3065 1.3342 1.3204

0.0104

0.78%

8

1.3307 1.2672 1.1831 1.2252

0.1056

7.93%

9

1.3307 1.2835 1.3448 1.3142

0.0165

1.24%

10

1.3307 1.2159 1.4736 1.3448

-0.0140

-1.06%

11

1.3307 1.3762 1.2489 1.3126

0.0182

1.36%

12

1.3307 1.2142 1.8459 1.5301

-0.1994

-14.98%

13

1.3307 1.2832 1.2691 1.2762

0.0546

4.10%

14

1.3307 1.2817 1.3504 1.3161

0.0146

1.10%

15

1.3307 1.3183 1.3433 1.3308

-0.0001

-0.01%

16

1.3307 1.3127 1.2912 1.3020

0.0288

2.16%

17

1.3307 1.4067 1.3091 1.3579

-0.0272

-2.04%

Table 19(b): Section 2 Beams, referenced by scale set on the north side

83

18

1.3307 1.2916 1.4134 1.3525 -0.0218 -1.64%

19

1.3307 1.3059 1.5842 1.4451 -0.1144 -8.59%

20

1.3307 1.3491 1.1529 1.2510

0.0797

5.99%

21

1.3307 1.3134 1.2079 1.2607

0.0700

5.26%

22

1.3307 1.3440 1.3524 1.3482 -0.0175 -1.32%

23

1.3307 1.3335 1.2869 1.3102

0.0205

1.54%

24

1.3307 1.3096 1.2746 1.2921

0.0386

2.90%

25

1.3307 1.3238 1.2873 1.3056

0.0251

1.89%

26

1.3307 1.3214 1.4073 1.3644 -0.0337 -2.53%

27

1.3307 1.3156 1.1941 1.2549

0.0759

5.70%

28

1.3307 1.3210 1.1586 1.2398

0.0909

6.83%

29

1.3307 1.3379 1.2600 1.2990

0.0317

2.39%

Table 19(b) Continued:

Section 2 Beams, referenced by scale set on the north side

84

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.7542

0.0958

3.36%

2

2.8500 2.7101

0.1399

4.91%

3

2.8500 2.8739

-0.0239

-0.84%

4

2.8500 2.7281

0.1219

4.28%

5

2.8500 2.6775

0.1725

6.05%

6

2.8500 2.7918

0.0582

2.04%

7

2.8500 2.7368

0.1132

3.97%

8

2.8500 2.7217

0.1283

4.50%

9

2.8500 2.7128

0.1372

4.81%

10

2.8500 2.7047

0.1453

5.10%

11

2.8500 2.7442

0.1058

3.71%

12

2.8500 2.7576

0.0924

3.24%

13

2.8500 2.7193

0.1307

4.59%

14

2.8500 2.6885

0.1615

5.67%

15

2.8500 2.6407

0.2093

7.34%

16

2.8500 2.6189

0.2311

8.11%

17

2.8500 2.7933

0.0567

1.99%

Table 20:

Section 2 Box Girders, referenced by scale set on the north side

85

18

2.8500 2.7686 0.0814 2.86%

19

2.8500 2.8115 0.0385 1.35%

20

2.8500 2.7988 0.0512 1.80%

21

2.8500 2.7962 0.0538 1.89%

Table 20 Continued: Section 2 Box Girders, referenced by scale set on the north side

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.1804

-0.1804

-0.89%

(2,3)

20.000 20.0786

-0.0786

-0.39%

(3,4)

20.000 20.1472

-0.1472

-0.73%

(4,5)

20.000 20.0314

-0.0314

-0.16%

(5,6)

20.000 20.1132

-0.1132

-0.56%

(6,7)

20.000 20.0151

-0.0151

-0.08%

(7,8)

20.000 20.0183

-0.0183

-0.09%

(8,9)

20.000 19.9658

0.0342

0.17%

(9,10)

20.000 19.9590

0.0410

0.21%

(10,11) 20.000 19.9422

0.0578

0.29%

(11,12) 20.000 19.9413

0.0587

0.29%

Table 21:

Section 2 Distance between Holes, referenced by scale set on the north side

86

(12,13) 20.000 19.8549

0.1451

0.73%

(13,14) 20.000 19.9090

0.0910

0.46%

(14,15) 20.000 19.8572

0.1428

0.72%

(16,17) 20.000 19.6456

0.3544

1.80%

(17,18) 20.000 19.9601

0.0399

0.20%

(18,19) 20.000 19.8939

0.1061

0.53%

(19,20) 20.000 19.9562

0.0438

0.22%

(20,21) 20.000 20.1966

-0.1966

-0.97%

(21,22) 20.000 19.9298

0.0702

0.35%

(22,23) 20.000 20.1492

-0.1492

-0.74%

(23,24) 20.000 20.2422

-0.2422

-1.20%

(24,25) 20.000 20.2415

-0.2415

-1.19%

(25,26) 20.000 20.2883

-0.2883

-1.42%

(26,27) 20.000 20.6141

-0.6141

-2.98%

Table 21 Continued: Section 2 Distance between Holes, referenced by scale set on the north side

87

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.02838 51.33988 51.1841

0.9852

1.89%

2

52.1693 51.61804

51.5912

0.5781

1.11%

3

52.1693 51.39491 50.91971 51.1573

1.0120

1.94%

4

52.1693 51.18891 51.16333 51.1761

0.9932

1.90%

5

52.1693 51.13616 51.63545 51.3858

0.7835

1.50%

6

52.1693 51.42935 51.48986 51.4596

0.7097

1.36%

7

52.1693 51.13208 51.35063 51.2414

0.9279

1.78%

8

52.1693 51.27061 51.20742 51.2390

0.9303

1.78%

9

52.1693 51.09596 51.29181 51.1939

0.9754

1.87%

10

52.1693 51.36755 50.81919 51.0934

1.0759

2.06%

11

52.1693 51.58042 51.94337 51.7619

0.4074

0.78%

12

52.1693 50.66115 51.88993 51.2755

0.8938

1.71%

13

52.1693 51.35013 51.42089 51.3855

0.7838

1.50%

14

52.1693 51.12452 51.20224 51.1634

1.0059

1.93%

15

52.1693 51.38466 51.11477 51.2497

0.9196

1.76%

16

52.1693 51.88664 51.42885 51.6577

0.5116

0.98%

17

52.1693 51.19578 51.86614 51.5310

0.6383

1.22%

51.5644

Table 22(a): Section 2 Beams, referenced by scale set on the south side

88

18

52.1693 51.82464 52.14689 51.9858

0.1835

0.35%

19

52.1693 51.25698

51.5551

0.6142

1.18%

20

52.1693 51.95541 51.82434 51.8899

0.2794

0.54%

21

52.1693 51.67825 51.30117 51.4897

0.6796

1.30%

22

52.1693 50.85124 51.32555 51.0884

1.0809

2.07%

23

52.1693 51.56271 51.26106 51.4119

0.7574

1.45%

24

52.1693

52.02308 51.9798

0.1895

0.36%

25

52.1693 52.03443 51.73975 51.8871

0.2822

0.54%

26

52.1693 50.72773 51.54907 51.1384

1.0309

1.98%

27

52.1693

51.42288 51.4833

0.6860

1.31%

28

52.1693 51.80981 51.82385 51.8168

0.3525

0.68%

29

52.1693 51.09058 51.67297 51.3818

0.7875

1.51%

51.9366

51.5438

Table 22(a) Continued:

51.8532

Section 2 Beams, referenced by scale set on the south side

89

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.174635 1.224793 1.1997

0.1310

9.84%

2

1.3307 1.703782 1.726871 1.7153

-0.3846

-28.90%

3

1.3307

1.126566 1.2796

0.0511

3.84%

4

1.3307 1.308588 1.365912 1.3373

-0.0066

-0.49%

5

1.3307 1.345112 1.182596 1.2639

0.0668

5.02%

6

1.3307 1.274155 1.203097 1.2386

0.0921

6.92%

7

1.3307 1.300229 1.327796 1.3140

0.0167

1.25%

8

1.3307 1.261117 1.177421 1.2193

0.1114

8.37%

9

1.3307 1.277339 1.338345 1.3078

0.0229

1.72%

10

1.3307 1.210064 1.466527 1.3383

-0.0076

-0.57%

11

1.3307 1.369594 1.242905 1.3062

0.0245

1.84%

12

1.3307 1.208372

1.5227

-0.1920

-14.43%

13

1.3307 1.277041 1.263008 1.2700

0.0607

4.56%

14

1.3307 1.275548 1.343918 1.3097

0.0210

1.58%

15

1.3307 1.311972 1.336852 1.3244

0.0063

0.47%

16

1.3307 1.306399 1.285002 1.2957

0.0350

2.63%

17

1.3307 1.399948 1.302816 1.3514

-0.0207

-1.55%

1.43269

Table 22(b) Continued:

1.83704

Section 2 Beams, referenced by scale set on the south side

90

18

1.3307

1.2854

1.406616 1.3460

-0.0153

-1.15%

19

1.3307 1.299632 1.576596 1.4381

-0.1074

-8.07%

20

1.3307 1.342624 1.147366 1.2450

0.0857

6.44%

21

1.3307 1.307096 1.202102 1.2546

0.0761

5.72%

22

1.3307 1.337549 1.345908 1.3417

-0.0110

-0.83%

23

1.3307 1.327099 1.280723 1.3039

0.0268

2.01%

24

1.3307 1.303314 1.268482 1.2859

0.0448

3.37%

25

1.3307 1.317446 1.281121 1.2993

0.0314

2.36%

26

1.3307 1.315057 1.400545 1.3578

-0.0271

-2.04%

27

1.3307 1.309285 1.188368 1.2488

0.0819

6.15%

28

1.3307 1.314659 1.153039 1.2338

0.0969

7.28%

29

1.3307 1.331478 1.253952 1.2927

0.0380

2.85%

Table 22(b): Section 2 Beams, referenced by scale set on the south side

91

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.7410

0.1090

3.83%

2

2.8500 2.6971

0.1529

5.37%

3

2.8500 2.8601

-0.0101

-0.35%

4

2.8500 2.7150

0.1350

4.74%

5

2.8500 2.6646

0.1854

6.50%

6

2.8500 2.7784

0.0716

2.51%

7

2.8500 2.7237

0.1263

4.43%

8

2.8500 2.7086

0.1414

4.96%

9

2.8500 2.6998

0.1502

5.27%

10

2.8500 2.6917

0.1583

5.55%

11

2.8500 2.7310

0.1190

4.17%

12

2.8500 2.7444

0.1056

3.71%

13

2.8500 2.7062

0.1438

5.04%

14

2.8500 2.6756

0.1744

6.12%

15

2.8500 2.6280

0.2220

7.79%

16

2.8500 2.6063

0.2437

8.55%

17

2.8500 2.7799

0.0701

2.46%

Table 23:

Section 2 Box Girders, referenced by scale set on the south side

92

18

2.8500 2.7553

0.0947

3.32%

19

2.8500 2.7980

0.0520

1.82%

20

2.8500 2.7854

0.0646

2.27%

21

2.8500 2.7828

0.0672

2.36%

Table 23 Continued: Section 2 Box Girders, referenced by scale set on the south side

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.0835

-0.0835

-0.42%

(2,3)

20.000 19.9822

0.0178

0.09%

(3,4)

20.000 20.0505

-0.0505

-0.25%

(4,5)

20.000 19.9352

0.0648

0.32%

(5,6)

20.000 20.0167

-0.0167

-0.08%

(6,7)

20.000 19.9190

0.0810

0.41%

(7,8)

20.000 19.9222

0.0778

0.39%

(8,9)

20.000 19.8700

0.1300

0.65%

(9,10)

20.000 19.8632

0.1368

0.69%

(10,11) 20.000 19.8465

0.1535

0.77%

(11,12) 20.000 19.8456

0.1544

0.78%

Table 24:

Section 2 Distance between Holes, referenced by scale set on the south side 93

(12,13) 20.000 19.7596

0.2404

1.22%

(13,14) 20.000 19.8134

0.1866

0.94%

(14,15) 20.000 19.7619

0.2381

1.20%

(16,17) 20.000 19.5513

0.4487

2.29%

(17,18) 20.000 19.8643

0.1357

0.68%

(18,19) 20.000 19.7984

0.2016

1.02%

(19,20) 20.000 19.8604

0.1396

0.70%

(20,21) 20.000 20.0997

-0.0997

-0.50%

(21,22) 20.000 19.8341

0.1659

0.84%

(22,23) 20.000 20.0525

-0.0525

-0.26%

(23,24) 20.000 20.1450

-0.1450

-0.72%

(24,25) 20.000 20.1443

-0.1443

-0.72%

(25,26) 20.000 20.1909

-0.1909

-0.95%

(26,27) 20.000 20.5152

-0.5152

-2.51%

Table 24 Continued: Section 2 Distance between Holes, referenced by scale set on the south side

94

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 51.2745 51.5875 51.4310

0.7383

1.42%

2

52.1693 51.8670 51.8131 51.8401

0.3293

0.63%

3

52.1693 51.6428 51.1653 51.4041

0.7653

1.47%

4

52.1693 51.4358 51.4101 51.4230

0.7464

1.43%

5

52.1693 51.3828 51.8845 51.6337

0.5356

1.03%

6

52.1693 51.6774 51.7382 51.7078

0.4615

0.88%

7

52.1693 51.3787 51.5983 51.4885

0.6808

1.30%

8

52.1693 51.5179 51.4544 51.4862

0.6832

1.31%

9

52.1693 51.3424 51.5392 51.4408

0.7285

1.40%

10

52.1693 51.6153 51.0643 51.3398

0.8295

1.59%

11

52.1693 51.8292 52.1939 52.0116

0.1578

0.30%

12

52.1693 50.9055 52.1402 51.5229

0.6464

1.24%

13

52.1693 51.5978 51.6689 51.6334

0.5360

1.03%

14

52.1693 51.3711 51.4492 51.4102

0.7591

1.46%

15

52.1693 51.6325 51.3613 51.4969

0.6724

1.29%

16

52.1693 52.1369 51.6769 51.9069

0.2624

0.50%

17

52.1693 51.4427 52.1163 51.7795

0.3898

0.75%

Table 25(a): Section 2 Beams, referenced by scale set on both sides

95

18

52.1693 51.82464 52.14689 51.9858

0.1835

0.35%

19

52.1693 51.25698

51.5551

0.6142

1.18%

20

52.1693 51.95541 51.82434 51.8899

0.2794

0.54%

21

52.1693 51.67825 51.30117 51.4897

0.6796

1.30%

22

52.1693 50.85124 51.32555 51.0884

1.0809

2.07%

23

52.1693 51.56271 51.26106 51.4119

0.7574

1.45%

24

52.1693

52.02308 51.9798

0.1895

0.36%

25

52.1693 52.03443 51.73975 51.8871

0.2822

0.54%

26

52.1693 50.72773 51.54907 51.1384

1.0309

1.98%

27

52.1693

51.42288 51.4833

0.6860

1.31%

28

52.1693 51.80981 51.82385 51.8168

0.3525

0.68%

29

52.1693 51.09058 51.67297 51.3818

0.7875

1.51%

51.9366

51.5438

Table 25(a) Continued:

51.8532

Section 2 Beams, referenced by scale set on both sides

96

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.1803 1.2307 1.2055

0.1252

9.41%

2

1.3307 1.7120 1.7352 1.7236

-0.3929

-29.53%

3

1.3307 1.4396 1.1320 1.2858

0.0449

3.37%

4

1.3307 1.3149 1.3725 1.3437

-0.0130

-0.98%

5

1.3307 1.3516 1.1883 1.2700

0.0608

4.57%

6

1.3307 1.2803 1.2089 1.2446

0.0861

6.47%

7

1.3307 1.3065 1.3342 1.3204

0.0104

0.78%

8

1.3307 1.2672 1.1831 1.2252

0.1056

7.93%

9

1.3307 1.2835 1.3448 1.3142

0.0165

1.24%

10

1.3307 1.2159 1.4736 1.3448

-0.0140

-1.06%

11

1.3307 1.3762 1.2489 1.3126

0.0182

1.36%

12

1.3307 1.2142 1.8459 1.5301

-0.1994

-14.98%

13

1.3307 1.2832 1.2691 1.2762

0.0546

4.10%

14

1.3307 1.2817 1.3504 1.3161

0.0146

1.10%

15

1.3307 1.3183 1.3433 1.3308

-0.0001

-0.01%

16

1.3307 1.3127 1.2912 1.3020

0.0288

2.16%

17

1.3307 1.4067 1.3091 1.3579

-0.0272

-2.04%

Table 25(b): Section 2 Beams, referenced by scale set on both sides

97

18

1.3307

1.2854

1.406616 1.3460

-0.0153

-1.15%

19

1.3307 1.299632 1.576596 1.4381

-0.1074

-8.07%

20

1.3307 1.342624 1.147366 1.2450

0.0857

6.44%

21

1.3307 1.307096 1.202102 1.2546

0.0761

5.72%

22

1.3307 1.337549 1.345908 1.3417

-0.0110

-0.83%

23

1.3307 1.327099 1.280723 1.3039

0.0268

2.01%

24

1.3307 1.303314 1.268482 1.2859

0.0448

3.37%

25

1.3307 1.317446 1.281121 1.2993

0.0314

2.36%

26

1.3307 1.315057 1.400545 1.3578

-0.0271

-2.04%

27

1.3307 1.309285 1.188368 1.2488

0.0819

6.15%

28

1.3307 1.314659 1.153039 1.2338

0.0969

7.28%

29

1.3307 1.331478 1.253952 1.2927

0.0380

2.85%

Table 25(b) Continued:

Section 2 Beams, referenced by scale set on both sides

98

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.7410

0.1090

3.83%

2

2.8500 2.6971

0.1529

5.37%

3

2.8500 2.8601

-0.0101

-0.35%

4

2.8500 2.7150

0.1350

4.74%

5

2.8500 2.6646

0.1854

6.50%

6

2.8500 2.7784

0.0716

2.51%

7

2.8500 2.7237

0.1263

4.43%

8

2.8500 2.7086

0.1414

4.96%

9

2.8500 2.6998

0.1502

5.27%

10

2.8500 2.6917

0.1583

5.55%

11

2.8500 2.7310

0.1190

4.17%

12

2.8500 2.7444

0.1056

3.71%

13

2.8500 2.7062

0.1438

5.04%

14

2.8500 2.6756

0.1744

6.12%

15

2.8500 2.6280

0.2220

7.79%

16

2.8500 2.6063

0.2437

8.55%

17

2.8500 2.7799

0.0701

2.46%

Table 26:

Section 2 Box Girders, referenced by scale set on both sides

99

18

2.8500

2.7553

0.0947

3.32%

19

2.8500

2.7980

0.0520

1.82%

20

2.8500

2.7854

0.0646

2.27%

21

2.8500

2.7828

0.0672

2.36%

Table 26 Continued: Section 2 Box Girders, referenced by scale set on both sides

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.0835

-0.0835

-0.42%

(2,3)

20.000 19.9822

0.0178

0.09%

(3,4)

20.000 20.0505

-0.0505

-0.25%

(4,5)

20.000 19.9352

0.0648

0.32%

(5,6)

20.000 20.0167

-0.0167

-0.08%

(6,7)

20.000 19.9190

0.0810

0.41%

(7,8)

20.000 19.9222

0.0778

0.39%

(8,9)

20.000 19.8700

0.1300

0.65%

(9,10)

20.000 19.8632

0.1368

0.69%

(10,11) 20.000 19.8465

0.1535

0.77%

(11,12) 20.000 19.8456

0.1544

0.78%

Table 27:

Section 2 Distance between Holes, referenced by scale set on both sides 100

(12,13)

20.000 19.7596

0.2404

1.22%

(13,14)

20.000 19.8134

0.1866

0.94%

(14,15)

20.000 19.7619

0.2381

1.20%

(16,17)

20.000 19.5513

0.4487

2.29%

(17,18)

20.000 19.8643

0.1357

0.68%

(18,19)

20.000 19.7984

0.2016

1.02%

(19,20)

20.000 19.8604

0.1396

0.70%

(20,21)

20.000 20.0997

-0.0997

-0.50%

(21,22)

20.000 19.8341

0.1659

0.84%

(22,23)

20.000 20.0525

-0.0525

-0.26%

(23,24)

20.000 20.1450

-0.1450

-0.72%

(24,25)

20.000 20.1443

-0.1443

-0.72%

(25,26)

20.000 20.1909

-0.1909

-0.95%

(26,27)

20.000 20.5152

-0.5152

-2.51%

Table 27 Continued: Section 2 Distance between Holes, referenced by scale set on both sides

101

APPENDIX C Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 52.3985 52.6964 52.5475

-0.3781

-0.72%

2

52.1693 53.2911 54.1317 53.7114

-1.5421

-2.96%

3

52.1693 53.6456 54.4103 54.0280

-1.8587

-3.56%

4

52.1693 52.5602 52.7993 52.6798

-0.5104

-0.98%

5

52.1693 51.2167 51.3848 51.3008

0.8685

1.66%

6

52.1693 52.4225 52.5136 52.4681

-0.2987

-0.57%

7

52.1693 52.9441 52.6202 52.7822

-0.6129

-1.17%

8

52.1693 53.2832 52.8050 53.0441

-0.8748

-1.68%

9

52.1693 51.6700 52.7712 52.2206

-0.0513

-0.10%

10

52.1693 51.6080 53.0139 52.3110

-0.1416

-0.27%

11

52.1693 51.6387 50.9609 51.2998

0.8695

1.67%

12

52.1693 51.1545 51.2020 51.1783

0.9911

1.90%

13

52.1693 51.4759 52.6844 52.0802

0.0891

0.17%

14

52.1693 51.6966 50.4749 51.0858

1.0836

2.08%

15

52.1693 55.4131 54.9395 55.1763

-3.0070

-5.76%

16

52.1693 55.9741 56.9512 56.4627

-4.2934

-8.23%

Table 28(a): Section 3 Beams, referenced by scale set on the north side

102

17

52.1693 55.9181 56.6749 56.2965

-4.1272

-7.91%

18

52.1693 56.2070 55.6833 55.9452

-3.7759

-7.24%

19

52.1693 55.7960 55.2475 55.5218

-3.3525

-6.43%

20

52.1693 55.2634 55.9692 55.6163

-3.4470

-6.61%

21

52.1693 54.2795 55.1775 54.7285

-2.5592

-4.91%

22

52.1693 54.4884 56.7187 55.6036

-3.4343

-6.58%

23

52.1693 53.9442 54.7114 54.3278

-2.1585

-4.14%

24

52.1693 55.2314 55.3487 55.2901

-3.1208

-5.98%

25

52.1693 54.0087 54.1405 54.0746

-1.9053

-3.65%

26

52.1693 55.0068 55.8940 55.4504

-3.2811

-6.29%

27

52.1693 54.7746 55.3101 55.0424

-2.8731

-5.51%

Table 28(a) Continued:

Section 3 Beams, referenced by scale set on the north side

103

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.3956 1.4448 1.4202

-0.0895

-6.73%

2

1.3307 1.4124 1.9526 1.6825

-0.3518

-26.44%

3

1.3307 1.3266 1.6714 1.4990

-0.1683

-12.65%

4

1.3307 1.2956 1.3846 1.3401

-0.0094

-0.71%

5

1.3307 1.3160 1.3578 1.3369

-0.0062

-0.47%

6

1.3307 1.3502 1.3497 1.3500

-0.0193

-1.45%

7

1.3307 1.2108 1.3611 1.2860

0.0447

3.36%

8

1.3307 1.3379 1.3876 1.3628

-0.0321

-2.41%

9

1.3307 1.3374 1.9334 1.6354

-0.3047

-22.90%

10

1.3307 1.3077 2.3217 1.8147

-0.4840

-36.37%

11

1.3307 1.3204 1.3188 1.3196

0.0111

0.83%

12

1.3307 1.3080 1.4542 1.3811

-0.0504

-3.79%

13

1.3307 1.3571 2.0002 1.6787

-0.3480

-26.15%

14

1.3307 1.3161 1.7672 1.5417

-0.2110

-15.85%

15

1.3307 1.6220 1.8330 1.7275

-0.3968

-29.82%

16

1.3307 1.3459 1.7140 1.5300

-0.1993

-14.97%

17

1.3307 1.4270 1.4307 1.4289

-0.0982

-7.38%

Table 28(b): Section 3 Beams, referenced by scale set on the north side

104

18

1.3307 1.4768 1.3388 1.4078

-0.0771

-5.79%

19

1.3307 1.3602 1.5971 1.4787

-0.1480

-11.12%

20

1.3307 1.4680 1.4982 1.4831

-0.1524

-11.45%

21

1.3307 1.5678 1.3375 1.4527

-0.1220

-9.16%

22

1.3307 1.4801 1.9866 1.7334

-0.4027

-30.26%

23

1.3307 1.3528 1.4316 1.3922

-0.0615

-4.62%

24

1.3307 1.8034 1.8746 1.8390

-0.5083

-38.20%

25

1.3307 1.3737 1.4070 1.3904

-0.0597

-4.48%

26

1.3307 1.3082 1.3271 1.3177

0.0131

0.98%

27

1.3307 1.3297 1.4834 1.4066

-0.0759

-5.70%

Table 28(b) Continued:

Section 3 Beams, referenced by scale set on the north side

105

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.5679

0.2821

9.90%

2

2.8500 2.6660

0.1840

6.46%

3

2.8500 2.6533

0.1967

6.90%

4

2.8500 2.6617

0.1883

6.61%

5

2.8500 2.6356

0.2144

7.52%

6

2.8500 2.6717

0.1783

6.26%

7

2.8500 2.6603

0.1897

6.66%

8

2.8500 2.6704

0.1796

6.30%

9

2.8500 2.6956

0.1544

5.42%

10

2.8500 2.8756

-0.0256

-0.90%

11

2.8500 3.2267

-0.3767

-13.22%

12

2.8500 2.9362

-0.0862

-3.02%

13

2.8500 2.6996

0.1504

5.28%

14

2.8500 2.7311

0.1189

4.17%

15

2.8500 2.7742

0.0758

2.66%

16

2.8500 2.5828

0.2672

9.37%

Table 29:

Section 3 Box Girders, referenced by scale set on the north side

106

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.2275

-0.2275

-1.12%

(2,3)

20.000 20.1142

-0.1142

-0.57%

(3,4)

20.000 20.3126

-0.3126

-1.54%

(4,5)

20.000 20.2843

-0.2843

-1.40%

(5,6)

20.000 20.1680

-0.1680

-0.83%

(6,7)

20.000 20.1972

-0.1972

-0.98%

(7,8)

20.000 20.1625

-0.1625

-0.81%

(8,9)

20.000 20.1898

-0.1898

-0.94%

(9,10)

20.000 20.3171

-0.3171

-1.56%

(10,11) 20.000 20.3045

-0.3045

-1.50%

(11,12) 20.000 20.4223

-0.4223

-2.07%

(12,13) 20.000 20.2959

-0.2959

-1.46%

(13,14) 20.000 20.2678

-0.2678

-1.32%

(14,15) 20.000 20.3439

-0.3439

-1.69%

(16,17) 20.000 22.1366

-2.1366

-9.65%

(17,18) 20.000 21.6927

-1.6927

-7.80%

(18,19) 20.000 21.7446

-1.7446

-8.02%

Table 30:

Section 3 Distance between Holes, referenced by scale set on the north side

107

(19,20) 20.000

21.7591

-1.7591

-8.08%

(20,21) 20.000

21.7067

-1.7067

-7.86%

(21,22) 20.000

21.6382

-1.6382

-7.57%

(22,23) 20.000

21.5288

-1.5288

-7.10%

(23,24) 20.000

21.4831

-1.4831

-6.90%

(24,25) 20.000

21.3200

-1.3200

-6.19%

(25,26) 20.000

21.3014

-1.3014

-6.11%

(26,27) 20.000

21.3471

-1.3471

-6.31%

(27,28) 20.000

21.1763

-1.1763

-5.55%

(28,29) 20.000

21.3866

-1.3866

-6.48%

Table 30 Continued: Section 3 Distance between Holes, referenced by scale set on the north side

108

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 53.04824 53.34984 53.1990

-1.0297

-1.97%

2

52.1693 53.95191 54.80293 54.3774

-2.2081

-4.23%

3

52.1693 54.31081 55.08499 54.6979

-2.5286

-4.85%

4

52.1693 53.21195 53.45401 53.3330

-1.1637

-2.23%

5

52.1693 51.85179 52.02197 51.9369

0.2324

0.45%

6

52.1693 53.07254 53.16477 53.1187

-0.9494

-1.82%

7

52.1693 53.60061 53.27269 53.4366

-1.2673

-2.43%

8

52.1693 53.94391 53.45978 53.7018

-1.5325

-2.94%

9

52.1693 52.31071 53.42556 52.8681

-0.6988

-1.34%

10

52.1693 52.24794 53.67127 52.9596

-0.7903

-1.51%

11

52.1693 52.27902 51.59282 51.9359

0.2334

0.45%

12

52.1693 51.78882

51.8369

51.8129

0.3564

0.68%

13

52.1693

53.33769 52.7259

-0.5566

-1.07%

14

52.1693 52.33764 51.10079 51.7192

0.4501

0.86%

15

52.1693 56.10022 55.62075 55.8605

-3.6912

-7.08%

16

52.1693 56.66818 57.65739 57.1628

-4.9935

-9.57%

17

52.1693 56.61148 57.37767 56.9946

-4.8253

-9.25%

52.1142

Table 31(a): Section 3 Beams, referenced by scale set on the south sides

109

18

52.1693 56.90397 56.37377 56.6389

-4.4696

-8.57%

19

52.1693 56.48787 55.93257 56.2102

-4.0409

-7.75%

20

52.1693 55.94867 56.66322 56.3059

-4.1366

-7.93%

21

52.1693 54.95257

55.4071

-3.2378

-6.21%

22

52.1693 55.16406 57.42201 56.2930

-4.1237

-7.90%

23

52.1693 54.61311 55.38982 55.0015

-2.8322

-5.43%

24

52.1693 55.91627 56.03502 55.9756

-3.8063

-7.30%

25

52.1693 54.67841 54.81184 54.7451

-2.5758

-4.94%

26

52.1693 55.68888 56.58709 56.1380

-3.9687

-7.61%

27

52.1693 55.45381 55.99595 55.7249

-3.5556

-6.82%

Table 31(a) Continued:

55.8617

Section 3 Beams, referenced by scale set on the south sides

110

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.412905 1.462716 1.4378

-0.1071

-8.05%

2

1.3307 1.429914 1.976812 1.7034

-0.3727

-28.01%

3

1.3307

1.692125 1.5176

-0.1869

-14.04%

4

1.3307 1.311665 1.401769 1.3567

-0.0260

-1.96%

5

1.3307 1.332318 1.374637 1.3535

-0.0228

-1.71%

6

1.3307 1.366942 1.366436 1.3667

-0.0360

-2.70%

7

1.3307 1.225814 1.377978 1.3019

0.0288

2.16%

8

1.3307

1.404806 1.3796

-0.0489

-3.68%

9

1.3307 1.353984 1.957374 1.6557

-0.3250

-24.42%

10

1.3307 1.323915 2.350489 1.8372

-0.5065

-38.06%

11

1.3307 1.336773 1.335153 1.3360

-0.0053

-0.40%

12

1.3307 1.324219 1.472232 1.3982

-0.0675

-5.07%

13

1.3307 1.373928 2.025002 1.6995

-0.3688

-27.71%

14

1.3307

1.789113 1.5608

-0.2301

-17.29%

15

1.3307 1.642113 1.855729 1.7489

-0.4182

-31.43%

16

1.3307 1.362589 1.735254 1.5489

-0.2182

-16.40%

17

1.3307 1.444695 1.448441 1.4466

-0.1159

-8.71%

1.34305

1.35449

1.33242

Table 31(b): Section 3 Beams, referenced by scale set on the south sides

111

18

1.3307 1.495112 1.355401 1.4253

-0.0946

-7.11%

19

1.3307 1.377066 1.616904 1.4970

-0.1663

-12.50%

20

1.3307 1.486203 1.516778 1.5015

-0.1708

-12.83%

21

1.3307 1.587241 1.354085 1.4707

-0.1400

-10.52%

22

1.3307 1.498453 2.011234 1.7548

-0.4241

-31.87%

23

1.3307 1.369575 1.449352 1.4095

-0.0788

-5.92%

24

1.3307 1.825762 1.897845 1.8618

-0.5311

-39.91%

25

1.3307 1.390734 1.424447 1.4076

-0.0769

-5.78%

26

1.3307 1.324422 1.343556 1.3340

-0.0033

-0.25%

27

1.3307 1.346188 1.501794 1.4240

-0.0933

-7.01%

Table 31(b) Continued:

Section 3 Beams, referenced by scale set on the south sides

112

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.5679

0.2821

9.90%

2

2.8500 2.6660

0.1840

6.46%

3

2.8500 2.6533

0.1967

6.90%

4

2.8500 2.6617

0.1883

6.61%

5

2.8500 2.6356

0.2144

7.52%

6

2.8500 2.6717

0.1783

6.26%

7

2.8500 2.6603

0.1897

6.66%

8

2.8500 2.6704

0.1796

6.30%

9

2.8500 2.6956

0.1544

5.42%

10

2.8500 2.8756

-0.0256

-0.90%

11

2.8500 3.2267

-0.3767

-13.22%

12

2.8500 2.9362

-0.0862

-3.02%

13

2.8500 2.6996

0.1504

5.28%

14

2.8500 2.7311

0.1189

4.17%

15

2.8500 2.7742

0.0758

2.66%

16

2.8500 2.5828

0.2672

9.37%

Table 32:

Section 3 Box Girders, referenced by scale set on the south sides

113

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.2275

-0.2275

-1.12%

(2,3)

20.000 20.1142

-0.1142

-0.57%

(3,4)

20.000 20.3126

-0.3126

-1.54%

(4,5)

20.000 20.2843

-0.2843

-1.40%

(5,6)

20.000 20.1680

-0.1680

-0.83%

(6,7)

20.000 20.1972

-0.1972

-0.98%

(7,8)

20.000 20.1625

-0.1625

-0.81%

(8,9)

20.000 20.1898

-0.1898

-0.94%

(9,10)

20.000 20.3171

-0.3171

-1.56%

(10,11) 20.000 20.3045

-0.3045

-1.50%

(11,12) 20.000 20.4223

-0.4223

-2.07%

(12,13) 20.000 20.2959

-0.2959

-1.46%

(13,14) 20.000 20.2678

-0.2678

-1.32%

(14,15) 20.000 20.3439

-0.3439

-1.69%

(16,17) 20.000 22.1366

-2.1366

-9.65%

(17,18) 20.000 21.6927

-1.6927

-7.80%

(18,19) 20.000 21.7446

-1.7446

-8.02%

Table 33:

Section 3 Distance between Holes, referenced by scale set on the south sides 114

(19,20)

20.000 21.7591

-1.7591

-8.08%

(20,21)

20.000 21.7067

-1.7067

-7.86%

(21,22)

20.000 21.6382

-1.6382

-7.57%

(22,23)

20.000 21.5288

-1.5288

-7.10%

(23,24)

20.000 21.4831

-1.4831

-6.90%

(24,25)

20.000 21.3200

-1.3200

-6.19%

(25,26)

20.000 21.3014

-1.3014

-6.11%

(26,27)

20.000 21.3471

-1.3471

-6.31%

(27,28)

20.000 21.1763

-1.1763

-5.55%

(28,29)

20.000 21.3866

-1.3866

-6.48%

Table 33 Continued: Section 3 Distance between Holes, referenced by scale set on the south sides

115

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 52.3985 52.6964 52.5475

-0.3781

-0.72%

2

52.1693 53.2911 54.1317 53.7114

-1.5421

-2.96%

3

52.1693 53.6456 54.4103 54.0280

-1.8587

-3.56%

4

52.1693 52.5602 52.7993 52.6798

-0.5104

-0.98%

5

52.1693 51.2167 51.3848 51.3008

0.8685

1.66%

6

52.1693 52.4225 52.5136 52.4681

-0.2987

-0.57%

7

52.1693 52.9441 52.6202 52.7822

-0.6129

-1.17%

8

52.1693 53.2832 52.8050 53.0441

-0.8748

-1.68%

9

52.1693 51.6700 52.7712 52.2206

-0.0513

-0.10%

10

52.1693 51.6080 53.0139 52.3110

-0.1416

-0.27%

11

52.1693 51.6387 50.9609 51.2998

0.8695

1.67%

12

52.1693 51.1545 51.2020 51.1783

0.9911

1.90%

13

52.1693 51.4759 52.6844 52.0802

0.0891

0.17%

14

52.1693 51.6966 50.4749 51.0858

1.0836

2.08%

15

52.1693 55.4131 54.9395 55.1763

-3.0070

-5.76%

16

52.1693 55.9741 56.9512 56.4627

-4.2934

-8.23%

17

52.1693 55.9181 56.6749 56.2965

-4.1272

-7.91%

Table 34(a): Section 3 Beams, referenced by scale set on both sides 116

18

52.1693 56.90397 56.37377 56.6389

-4.4696

-8.57%

19

52.1693 56.48787 55.93257 56.2102

-4.0409

-7.75%

20

52.1693 55.94867 56.66322 56.3059

-4.1366

-7.93%

21

52.1693 54.95257

55.4071

-3.2378

-6.21%

22

52.1693 55.16406 57.42201 56.2930

-4.1237

-7.90%

23

52.1693 54.61311 55.38982 55.0015

-2.8322

-5.43%

24

52.1693 55.91627 56.03502 55.9756

-3.8063

-7.30%

25

52.1693 54.67841 54.81184 54.7451

-2.5758

-4.94%

26

52.1693 55.68888 56.58709 56.1380

-3.9687

-7.61%

27

52.1693 55.45381 55.99595 55.7249

-3.5556

-6.82%

Table 34(a) Continued:

55.8617

Section 3 Beams, referenced by scale set on both sides

117

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.3956 1.4448 1.4202

-0.0895

-6.73%

2

1.3307 1.4124 1.9526 1.6825

-0.3518

-26.44%

3

1.3307 1.3266 1.6714 1.4990

-0.1683

-12.65%

4

1.3307 1.2956 1.3846 1.3401

-0.0094

-0.71%

5

1.3307 1.3160 1.3578 1.3369

-0.0062

-0.47%

6

1.3307 1.3502 1.3497 1.3500

-0.0193

-1.45%

7

1.3307 1.2108 1.3611 1.2860

0.0447

3.36%

8

1.3307 1.3379 1.3876 1.3628

-0.0321

-2.41%

9

1.3307 1.3374 1.9334 1.6354

-0.3047

-22.90%

10

1.3307 1.3077 2.3217 1.8147

-0.4840

-36.37%

11

1.3307 1.3204 1.3188 1.3196

0.0111

0.83%

12

1.3307 1.3080 1.4542 1.3811

-0.0504

-3.79%

13

1.3307 1.3571 2.0002 1.6787

-0.3480

-26.15%

14

1.3307 1.3161 1.7672 1.5417

-0.2110

-15.85%

15

1.3307 1.6220 1.8330 1.7275

-0.3968

-29.82%

16

1.3307 1.3459 1.7140 1.5300

-0.1993

-14.97%

17

1.3307 1.4270 1.4307 1.4289

-0.0982

-7.38%

Table 34(b): Section 3 Beams, referenced by scale set on both sides 118

18

1.3307 1.4768 1.3388 1.4078

-0.0771

-5.79%

19

1.3307 1.3602 1.5971 1.4787

-0.1480

-11.12%

20

1.3307 1.4680 1.4982 1.4831

-0.1524

-11.45%

21

1.3307 1.5678 1.3375 1.4527

-0.1220

-9.16%

22

1.3307 1.4801 1.9866 1.7334

-0.4027

-30.26%

23

1.3307 1.3528 1.4316 1.3922

-0.0615

-4.62%

24

1.3307 1.8034 1.8746 1.8390

-0.5083

-38.20%

25

1.3307 1.3737 1.4070 1.3904

-0.0597

-4.48%

26

1.3307 1.3082 1.3271 1.3177

0.0131

0.98%

27

1.3307 1.3297 1.4834 1.4066

-0.0759

-5.70%

Table 34(b) Continued:

Section 3 Beams, referenced by scale set on both sides

119

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.5364

0.3136

11.00%

2

2.8500 2.6333

0.2167

7.60%

3

2.8500 2.6208

0.2292

8.04%

4

2.8500 2.6291

0.2209

7.75%

5

2.8500 2.6033

0.2467

8.66%

6

2.8500 2.6390

0.2110

7.40%

7

2.8500 2.6277

0.2223

7.80%

8

2.8500 2.6377

0.2123

7.45%

9

2.8500 2.6956

0.1544

5.42%

10

2.8500 2.8756

-0.1230

-4.32%

11

2.8500 3.2267

-0.4741

-16.64%

12

2.8500 2.9362

-0.1836

-6.44%

13

2.8500 2.6996

0.0530

1.86%

14

2.8500 2.7311

0.0215

0.76%

15

2.8500 2.7742

-0.0216

-0.76%

16

2.8500 2.5828

0.1698

5.96%

Table 35:

Section 3 Box Girders, referenced by scale set on both sides

120

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 19.9798

0.0202

0.10%

(2,3)

20.000 19.8678

0.1322

0.67%

(3,4)

20.000 20.0638

-0.0638

-0.32%

(4,5)

20.000 20.0359

-0.0359

-0.18%

(5,6)

20.000 19.9210

0.0790

0.40%

(6,7)

20.000 19.9498

0.0502

0.25%

(7,8)

20.000 19.9155

0.0845

0.42%

(8,9)

20.000 19.9425

0.0575

0.29%

(9,10)

20.000 20.0683

-0.0683

-0.34%

(10,11) 20.000 20.0558

-0.0558

-0.28%

(11,12) 20.000 20.1722

-0.1722

-0.85%

(12,13) 20.000 20.0473

-0.0473

-0.24%

(13,14) 20.000 20.0196

-0.0196

-0.10%

(14,15) 20.000 20.0947

-0.0947

-0.47%

(16,17) 20.000 22.1366

-2.1366

-9.65%

(17,18) 20.000 21.6927

-1.6927

-7.80%

(18,19) 20.000 21.7446

-1.7446

-8.02%

Table 36:

Section 3 Distance between Holes, referenced by scale set on both sides 121

(19,20) 20.000 21.7591 -1.7591 -8.08% (20,21) 20.000 21.6382 -1.6382 -7.57% (21,22) 20.000 21.0852 -1.0852 -5.15% (22,23) 20.000 21.5288 -1.5288 -7.10% (23,24) 20.000 21.4831 -1.4831 -6.90% (24,25) 20.000 21.3200 -1.3200 -6.19% (25,26) 20.000 21.3014 -1.3014 -6.11% (26,27) 20.000 21.3471 -1.3471 -6.31% (27,28) 20.000 21.1763 -1.1763 -5.55% (28,29) 20.000 21.3866 -1.3866 -6.48%

Table 36 Continued: Section 3 Distance between Holes, referenced by scale set on both sides

122

APPENDIX D Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 55.9700 55.7597 55.8649

-3.6956

-7.08%

2

52.1693 55.7683 55.7984 55.7834

-3.6141

-6.93%

3

52.1693 55.4349 55.6365 55.5357

-3.3664

-6.45%

4

52.1693 55.5986 56.0224 55.8105

-3.6412

-6.98%

5

52.1693 55.6436 54.1668 54.9052

-2.7359

-5.24%

6

52.1693 54.7528 54.9075 54.8302

-2.6609

-5.10%

7

52.1693 54.7983 55.2690 55.0337

-2.8643

-5.49%

8

52.1693 55.5151 55.3016 55.4084

-3.2391

-6.21%

9

52.1693 55.0780 55.1461 55.1121

-2.9428

-5.64%

10

52.1693 55.2385 55.2779 55.2582

-3.0889

-5.92%

11

52.1693 55.1035 54.7528 54.9282

-2.7589

-5.29%

12

52.1693 55.4368 54.7983 55.1176

-2.9482

-5.65%

13

52.1693 55.7693 55.5151 55.6422

-3.4729

-6.66%

Table 37(a): Section 4 Beams, referenced by scale set on the north side

123

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.2467 2.6417 1.9442

-0.6135

-46.10%

2

1.3307 1.6430 1.8592 1.7511

-0.4204

-31.59%

3

1.3307 0.7598 2.1595 1.4597

-0.1290

-9.69%

4

1.3307 1.1832 1.4887 1.3360

-0.0052

-0.39%

5

1.3307 3.1126 1.5553 2.3340

-1.0033

-75.39%

6

1.3307 2.3830 1.6057 1.9944

-0.6637

-49.87%

7

1.3307 2.3699 1.3579 1.8639

-0.5332

-40.07%

8

1.3307 1.7051 2.2191 1.9621

-0.6314

-47.45%

9

1.3307 1.8221 1.5085 1.6653

-0.3346

-25.14%

10

1.3307 1.1752 1.6991 1.4372

-0.1065

-8.00%

11

1.3307 1.7801 2.0909 1.9355

-0.6048

-45.45%

12

1.3307 1.6515 2.3493 2.0004

-0.6697

-50.33%

13

1.3307 1.1360 1.5945 1.3653

-0.0346

-2.60%

Table 37(b): Section 4 Beams, referenced by scale set on the north side

124

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.8745

-0.0245

-0.86%

2

2.8500 2.7428

0.1072

3.76%

3

2.8500 2.8527

-0.0027

-0.09%

4

2.8500 4.3185

-1.4685

-51.53%

5

2.8500 3.6385

-0.7885

-27.67%

6

2.8500 3.3275

-0.4775

-16.75%

7

2.8500 2.9166

-0.0666

-2.34%

Table 38:

Hole #

Section 4 Box Girders, referenced by scale set on the north side

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 19.1857

0.8143

4.24%

(2,3)

20.000 20.8617

-0.8617

-4.13%

(3,4)

20.000 21.5183

-1.5183

-7.06%

(4,5)

20.000 20.7750

-0.7750

-3.73%

(6,7)

20.000 21.5008

-1.5008

-6.98%

(7,8)

20.000 21.4667

-1.4667

-6.83%

Table 39:

Section 4 Distance between Holes, referenced by scale set on the north side

125

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 52.52785 52.33048 52.4292

-0.2599

-0.50%

2

52.1693 52.33855

52.3527

-0.1834

-0.35%

3

52.1693 52.02565 52.21486 52.1203

0.0490

0.09%

4

52.1693 52.17929 52.57702 52.3782

-0.2089

-0.40%

5

52.1693 52.22152 50.83554 51.5285

0.6408

1.23%

6

52.1693

51.3855

51.53069 51.4581

0.7112

1.36%

7

52.1693

51.4282

51.86996 51.6491

0.5202

1.00%

8

52.1693 52.10092 51.90055 52.0007

0.1686

0.32%

9

52.1693

51.75461 51.7227

0.4466

0.86%

10

52.1693 51.84133 51.87831 51.8598

0.3095

0.59%

11

52.1693 51.71463

51.3855

51.5501

0.6192

1.19%

12

52.1693 52.02744

51.4282

51.7278

0.4415

0.85%

13

52.1693 52.33949 52.10092 52.2202

-0.0509

-0.10%

51.6907

52.3668

Table 40(a): Section 4 Beams, referenced by scale set on the south side

126

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.170028 2.479235 1.8246

-0.4939

-37.12%

2

1.3307 1.541956 1.744859 1.6434

-0.3127

-23.50%

3

1.3307 0.713072 2.026691 1.3699

-0.0392

-2.94%

4

1.3307 1.110433 1.397145 1.2538

0.0769

5.78%

5

1.3307 2.921175 1.459649 2.1904

-0.8597

-64.61%

6

1.3307 2.236446 1.506949 1.8717

-0.5410

-40.66%

7

1.3307 2.224151 1.274389 1.7493

-0.4186

-31.45%

8

1.3307 1.600236 2.082625 1.8414

-0.5107

-38.38%

9

1.3307 1.710041 1.415727 1.5629

-0.2322

-17.45%

10

1.3307 1.102925 1.594605 1.3488

-0.0181

-1.36%

11

1.3307 1.670624

1.8165

-0.4858

-36.50%

12

1.3307 1.549933 2.204818 1.8774

-0.5467

-41.08%

13

1.3307 1.066136 1.496438 1.2813

0.0494

3.71%

1.96231

Table 40(b): Section 4 Beams, referenced by scale set on the south side

127

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.6977

0.1523

5.34%

2

2.8500 2.5741

0.2759

9.68%

3

2.8500 2.6773

0.1727

6.06%

4

2.8500 4.0529

-1.2029

-42.21%

5

2.8500 3.4147

-0.5647

-19.82%

6

2.8500 3.1229

-0.2729

-9.57%

7

2.8500 2.7372

0.1128

3.96%

Table 41:

Hole #

Section 4 Box Girders, referenced by scale set on the south side

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 18.0058

1.9942

11.08%

(2,3)

20.000 19.5787

0.4213

2.15%

(3,4)

20.000 20.1949

-0.1949

-0.97%

(4,5)

20.000 19.4973

0.5027

2.58%

(6,7)

20.000 20.1785

-0.1785

-0.88%

(7,8)

20.000 20.1465

-0.1465

-0.73%

Table 42:

Section 4 Distance between Holes, referenced by scale set on the south side

128

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693

55.9700

55.7597

55.8649

-3.6956

-7.08%

2

52.1693

55.7683

55.7984

55.7834

-3.6141

-6.93%

3

52.1693

55.4349

55.6365

55.5357

-3.3664

-6.45%

4

52.1693

55.5986

56.0224

55.8105

-3.6412

-6.98%

5

52.1693

55.6436

54.1668

54.9052

-2.7359

-5.24%

6

52.1693

51.3855

51.53069 51.4581

0.7112

1.36%

7

52.1693

51.4282

51.86996 51.6491

0.5202

1.00%

8

52.1693 52.10092 51.90055 52.0007

0.1686

0.32%

9

52.1693

51.75461 51.7227

0.4466

0.86%

10

52.1693 51.84133 51.87831 51.8598

0.3095

0.59%

11

52.1693 51.71463

51.3855

51.5501

0.6192

1.19%

12

52.1693 52.02744

51.4282

51.7278

0.4415

0.85%

13

52.1693 52.33949 52.10092 52.2202

-0.0509

-0.10%

51.6907

Table 43(a): Section 4 Beams, referenced by scale set on both sides

129

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307

1.2467

2.6417

1.9442

-0.6135

-46.10%

2

1.3307

1.6430

1.8592

1.7511

-0.4204

-31.59%

3

1.3307

0.7598

2.1595

1.4597

-0.1290

-9.69%

4

1.3307

1.1832

1.4887

1.3360

-0.0052

-0.39%

5

1.3307

3.1126

1.5553

2.3340

-1.0033

-75.39%

6

1.3307 2.236446 1.506949 1.8717

-0.5410

-40.66%

7

1.3307 2.224151 1.274389 1.7493

-0.4186

-31.45%

8

1.3307 1.600236 2.082625 1.8414

-0.5107

-38.38%

9

1.3307 1.710041 1.415727 1.5629

-0.2322

-17.45%

10

1.3307 1.102925 1.594605 1.3488

-0.0181

-1.36%

11

1.3307 1.670624

1.8165

-0.4858

-36.50%

12

1.3307 1.549933 2.204818 1.8774

-0.5467

-41.08%

13

1.3307 1.066136 1.496438 1.2813

0.0494

3.71%

1.96231

Table 43(b): Section 4 Beams, referenced by scale set on both sides

130

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.8745

-0.0245

-0.86%

2

2.8500 2.7428

0.1072

3.76%

3

2.8500 2.8527

-0.0027

-0.09%

4

2.8500 4.3185

-1.4685

-51.53%

5

2.8500 3.4147

-0.5647

-19.82%

6

2.8500 3.1229

-0.2729

-9.57%

7

2.8500 2.7372

0.1128

3.96%

Table 44:

Hole #

Section 4 Box Girders, referenced by scale set on both sides

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 19.1857

0.8143

4.07%

(2,3)

20.000 20.8617

-0.8617

-4.31%

(3,4)

20.000 21.5183

-1.5183

-7.59%

(4,5)

20.000 20.7750

-0.7750

-3.87%

(6,7)

20.000 20.1785

-0.1785

-0.89%

(7,8)

20.000 20.1465

-0.1465

-0.73%

Table 45:

Section 4 Distance between Holes, referenced by scale set on both sides

131

APPENDIX E Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 52.3985 52.6964 52.5475

-0.3781

-0.72%

2

52.1693 53.2911 54.1317 53.7114

-1.5421

-2.96%

3

52.1693 53.6456 54.4103 54.0280

-1.8587

-3.56%

4

52.1693 52.5602 52.7993 52.6798

-0.5104

-0.98%

5

52.1693 51.2167 51.3848 51.3008

0.8685

1.66%

6

52.1693 52.4225 52.5136 52.4681

-0.2987

-0.57%

7

52.1693 52.9441 52.6202 52.7822

-0.6129

-1.17%

8

52.1693 53.2832 52.8050 53.0441

-0.8748

-1.68%

9

52.1693 51.6700 52.7712 52.2206

-0.0513

-0.10%

10

52.1693 51.6080 53.0139 52.3110

-0.1416

-0.27%

11

52.1693 51.6387 50.9609 51.2998

0.8695

1.67%

12

52.1693 51.1545 51.2020 51.1783

0.9911

1.90%

13

52.1693 51.4759 52.6844 52.0802

0.0891

0.17%

14

52.1693 51.6966 50.4749 51.0858

1.0836

2.08%

15

52.1693 55.4131 54.9395 55.1763

-3.0070

-5.76%

16

52.1693 55.9741 56.9512 56.4627

-4.2934

-8.23%

Table 46(a): Section 5 Beams, referenced by scale set on the north side

132

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.3956 1.4448 1.4202

-0.0895

-6.73%

2

1.3307 1.4124 1.9526 1.6825

-0.3518

-26.44%

3

1.3307 1.3266 1.6714 1.4990

-0.1683

-12.65%

4

1.3307 1.2956 1.3846 1.3401

-0.0094

-0.71%

5

1.3307 1.3160 1.3578 1.3369

-0.0062

-0.47%

6

1.3307 1.3502 1.3497 1.3500

-0.0193

-1.45%

7

1.3307 1.2108 1.3611 1.2860

0.0447

3.36%

8

1.3307 1.3379 1.3876 1.3628

-0.0321

-2.41%

9

1.3307 1.3374 1.9334 1.6354

-0.3047

-22.90%

10

1.3307 1.3077 2.3217 1.8147

-0.4840

-36.37%

11

1.3307 1.3204 1.3188 1.3196

0.0111

0.83%

12

1.3307 1.3080 1.4542 1.3811

-0.0504

-3.79%

13

1.3307 1.3571 2.0002 1.6787

-0.3480

-26.15%

14

1.3307 1.3161 1.7672 1.5417

-0.2110

-15.85%

15

1.3307 1.6220 1.8330 1.7275

-0.3968

-29.82%

16

1.3307 1.3459 1.7140 1.5300

-0.1993

-14.97%

Table 46(b): Section 5 Beams, referenced by scale set on the north side

133

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.5364

0.3136

11.00%

2

2.8500 2.6333

0.2167

7.60%

3

2.8500 2.6208

0.2292

8.04%

4

2.8500 2.6291

0.2209

7.75%

5

2.8500 2.6033

0.2467

8.66%

6

2.8500 2.6390

0.2110

7.40%

7

2.8500 2.6277

0.2223

7.80%

8

2.8500 2.6377

0.2123

7.45%

9

2.8500 2.6626

0.1874

6.58%

10

2.8500 2.8404

0.0096

0.34%

11

2.8500 3.1872

-0.3372

-11.83%

12

2.8500 2.9002

-0.0502

-1.76%

13

2.8500 2.6665

0.1835

6.44%

14

2.8500 2.6976

0.1524

5.35%

15

2.8500 2.7402

0.1098

3.85%

Table 47:

Section 5 Box Girders, referenced by scale set on the north side

134

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.1069

-0.1069

-0.53%

(2,3)

20.000 20.0877

-0.0877

-0.44%

(3,4)

20.000 19.9293

0.0707

0.35%

(4,5)

20.000 19.9281

0.0719

0.36%

(5,6)

20.000 20.4127

-0.4127

-2.02%

(6,7)

20.000 20.3389

-0.3389

-1.67%

(8,9)

20.000 19.8208

0.1792

0.90%

(9,10)

20.000 20.0249

-0.0249

-0.12%

(10,11) 20.000 20.1095

-0.1095

-0.54%

(11,12) 20.000 19.9379

0.0621

0.31%

(12,13) 20.000 19.6197

0.3803

1.94%

(13,14) 20.000 19.9070

0.0930

0.47%

(14,15) 20.000 19.9361

0.0639

0.32%

(15,16) 20.000 19.9971

0.0029

0.01%

Table 48:

Section 5 Distance between Holes, referenced by scale set on the north side

135

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693 53.04824 53.34984 53.1990

-1.0297

-1.97%

2

52.1693 53.95191 54.80293 54.3774

-2.2081

-4.23%

3

52.1693 54.31081 55.08499 54.6979

-2.5286

-4.85%

4

52.1693 53.21195 53.45401 53.3330

-1.1637

-2.23%

5

52.1693 51.85179 52.02197 51.9369

0.2324

0.45%

6

52.1693 53.07254 53.16477 53.1187

-0.9494

-1.82%

7

52.1693 53.60061 53.27269 53.4366

-1.2673

-2.43%

8

52.1693 53.94391 53.45978 53.7018

-1.5325

-2.94%

9

52.1693 52.31071 53.42556 52.8681

-0.6988

-1.34%

10

52.1693 52.24794 53.67127 52.9596

-0.7903

-1.51%

11

52.1693 52.27902 51.59282 51.9359

0.2334

0.45%

12

52.1693 51.78882

51.8369

51.8129

0.3564

0.68%

13

52.1693

53.33769 52.7259

-0.5566

-1.07%

14

52.1693 52.33764 51.10079 51.7192

0.4501

0.86%

15

52.1693 56.10022 55.62075 55.8605

-3.6912

-7.08%

16

52.1693 56.66818 57.65739 57.1628

-4.9935

-9.57%

52.1142

Table 49(a): Section 5 Beams, referenced by scale set on the south side

136

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307 1.412905 1.462716 1.4378

-0.1071

-8.05%

2

1.3307 1.429914 1.976812 1.7034

-0.3727

-28.01%

3

1.3307

1.692125 1.5176

-0.1869

-14.04%

4

1.3307 1.311665 1.401769 1.3567

-0.0260

-1.96%

5

1.3307 1.332318 1.374637 1.3535

-0.0228

-1.71%

6

1.3307 1.366942 1.366436 1.3667

-0.0360

-2.70%

7

1.3307 1.225814 1.377978 1.3019

0.0288

2.16%

8

1.3307

1.404806 1.3796

-0.0489

-3.68%

9

1.3307 1.353984 1.957374 1.6557

-0.3250

-24.42%

10

1.3307 1.323915 2.350489 1.8372

-0.5065

-38.06%

11

1.3307 1.336773 1.335153 1.3360

-0.0053

-0.40%

12

1.3307 1.324219 1.472232 1.3982

-0.0675

-5.07%

13

1.3307 1.373928 2.025002 1.6995

-0.3688

-27.71%

14

1.3307

1.789113 1.5608

-0.2301

-17.29%

15

1.3307 1.642113 1.855729 1.7489

-0.4182

-31.43%

16

1.3307 1.362589 1.735254 1.5489

-0.2182

-16.40%

1.34305

1.35449

1.33242

Table 49(b): Section 5 Beams, referenced by scale set on the south side

137

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.7560

0.0940

3.30%

2

2.8500 2.7264

0.1236

4.34%

3

2.8500 2.7100

0.1400

4.91%

4

2.8500 2.7523

0.0977

3.43%

5

2.8500 2.7667

0.0833

2.92%

6

2.8500 2.7476

0.1024

3.59%

7

2.8500 2.7360

0.1140

4.00%

8

2.8500 2.7959

0.0541

1.90%

9

2.8500 2.8349

0.0151

0.53%

10

2.8500 2.8125

0.0375

1.32%

11

2.8500 2.6192

0.2308

8.10%

12

2.8500 2.7740

0.0760

2.67%

13

2.8500 2.7386

0.1114

3.91%

14

2.8500 2.7814

0.0686

2.41%

15

2.8500 2.8232

0.0268

0.94%

Table 50:

Section 5 Box Girders, referenced by scale set on the south side

138

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.1773

-0.1773

-0.88%

(2,3)

20.000 20.1580

-0.1580

-0.78%

(3,4)

20.000 19.9991

0.0009

0.00%

(4,5)

20.000 19.9978

0.0022

0.01%

(5,6)

20.000 20.4841

-0.4841

-2.36%

(7,8)

20.000 20.4101

-0.4101

-2.01%

(8,9)

20.000 19.8902

0.1098

0.55%

(9,10)

20.000 20.0950

-0.0950

-0.47%

(10,11)

20.000 20.1799

-0.1799

-0.89%

(11,12)

20.000 20.0077

-0.0077

-0.04%

(12,13)

20.000 19.6884

0.3116

1.58%

(13,14)

20.000 19.9767

0.0233

0.12%

(14,15)

20.000 20.0059

-0.0059

-0.03%

(15, 16) 20.000 20.0671

-0.0671

-0.33%

Table 51:

Section 5 Distance between Holes, referenced by scale set on the south side

139

Beam #

Lac

L1

L2

Lavg

∆L = Lac - Lavg

%∆L

1

52.1693

51.3759

54.5878

52.9819

-0.8126

-1.56%

2

52.1693

55.3112

51.9918

53.6515

-1.4822

-2.84%

3

52.1693

55.2343

52.7420

53.9882

-1.8189

-3.49%

4

52.1693

53.3463

51.3543

52.3503

-0.1810

-0.35%

5

52.1693

53.6636

51.7981

52.7309

-0.5616

-1.08%

6

52.1693

52.5487

51.7900

52.1694

0.0000

0.00%

7

52.1693

53.5094

51.8749

52.6922

-0.5228

-1.00%

8

52.1693

53.0444

49.8861

51.4653

0.7041

1.35%

9

52.1693

52.5850

50.1979

51.3915

0.7779

1.49%

10

52.1693 52.84401 52.56805 52.7060

-0.5367

-1.03%

11

52.1693 52.44602 52.66167 52.5538

-0.3845

-0.74%

12

52.1693 50.10556 51.29792 50.7017

1.4676

2.81%

13

52.1693

52.07733 51.5704

0.5989

1.15%

14

52.1693 52.47733 51.39967 51.9385

0.2308

0.44%

15

52.1693 54.68483

54.0064

-1.8371

-3.52%

16

52.1693 52.21261 51.45627 51.8344

0.3349

0.64%

51.0635

53.328

Table 52(a): Section 5 Beams, referenced by scale set on both sides

140

Beam #

Wac

W1

W2

Wavg

∆W = Wavg - Wac

%∆W

1

1.3307

1.2007

3.4882

2.3445

-1.0138

-76.18%

2

1.3307

4.4023

1.6989

3.0506

-1.7199

-129.25%

3

1.3307

3.4048

0.8645

2.1347

-0.8040

-60.42%

4

1.3307

2.6094

1.4869

2.0482

-0.7175

-53.92%

5

1.3307

2.7771

1.4793

2.1282

-0.7975

-59.93%

6

1.3307

1.9681

1.5599

1.7640

-0.4333

-32.56%

7

1.3307

2.8167

2.1021

2.4594

-1.1287

-84.82%

8

1.3307

3.2239

1.3191

2.2715

-0.9408

-70.70%

9

1.3307

2.6920

1.4441

2.0681

-0.7374

-55.41%

10

1.3307 1.639518 1.453168 1.5463

-0.2156

-16.21%

11

1.3307

1.5053

-0.1746

-13.12%

12

1.3307 1.485782 2.781802 2.1338

-0.8031

-60.35%

13

1.3307

1.609012 1.6187

-0.2880

-21.65%

14

1.3307 1.497924 1.954517 1.7262

-0.3955

-29.72%

15

1.3307 2.504034 1.627476 2.0658

-0.7351

-55.24%

16

1.3307 1.947392 1.510769 1.7291

-0.3984

-29.94%

1.54258

1.62848

1.46792

Table 52(b): Section 5 Beams, referenced by scale set on both sides

141

Height #

Hac

H

∆H = Hac - H

%∆H

1

2.8500 2.7464

0.1036

3.64%

2

2.8500 2.7169

0.1331

4.67%

3

2.8500 2.7005

0.1495

5.25%

4

2.8500 2.7427

0.1073

3.76%

5

2.8500 2.7571

0.0929

3.26%

6

2.8500 2.7380

0.1120

3.93%

7

2.8500 2.7265

0.1235

4.33%

8

2.8500 2.7861

0.0639

2.24%

9

2.8500 2.8349

0.0151

0.53%

10

2.8500 2.8125

0.0375

1.32%

11

2.8500 2.6192

0.2308

8.10%

12

2.8500 2.7740

0.0760

2.67%

13

2.8500 2.7386

0.1114

3.91%

14

2.8500 2.7814

0.0686

2.41%

15

2.8500 2.8232

0.0268

0.94%

Table 53:

Section 5 Box Girders, referenced by scale set on both sides

142

Hole #

Lac

L

∆L = Lac - L

%∆L

(1,2)

20.000 20.1069

-0.1069

-0.53%

(2,3)

20.000 20.0877

-0.0877

-0.44%

(3,4)

20.000 19.9293

0.0707

0.35%

(4,5)

20.000 19.9281

0.0719

0.36%

(5,6)

20.000 20.4127

-0.4127

-2.02%

(6,7)

20.000 20.3389

-0.3389

-1.67%

(8,9)

20.000 19.8902

0.1098

0.55%

(9,10)

20.000 20.0950

-0.0950

-0.47%

(10,11) 20.000 20.1799

-0.1799

-0.89%

(11,12) 20.000 20.0077

-0.0077

-0.04%

(12,13) 20.000 19.6884

0.3116

1.58%

(13,14) 20.000 19.9767

0.0233

0.12%

(14,15) 20.000 20.0059

-0.0059

-0.03%

(15,16) 20.000 20.0671

-0.0671

-0.33%

Table 54:

Section 5 Distance between Holes, referenced by scale set on both sides

143

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148

Vita

Ankit Bhatla was born on 4th February 1989 in Chandigarh, India. At the age of 2, his family moved to New Delhi, India. He did his schooling from the Army Public School, New Delhi and graduated with honors. Being son of architect parents, he had natural inclination towards design and Civil Engineering. He joined the prestigious Indian Institute of Technology (IIT) Guwahati in 2006 and obtained his Bachelors of Technology degree in civil engineering in 2010. During the course of his undergraduate studies, he excelled both in academia, securing a high GPA and also co-authored several research papers in construction management and artificial intelligence applications in civil engineering. He did his Bachelors thesis on the topic "Implementing Lean Construction in IIT Guwahati". He also held several positions of responsibility during that time. Motivated to continue studying and developing skills to further his interest in construction management, he joined the Construction Engineering and Project Management Master's program at the University of Texas at Austin, Texas. During the course of his graduate studies he served as a grader, teaching assistant and a graduate research assistant, thus acquiring all the necessary skills to succeed in academia and research. He graduated with honors in 2011. His aim is to be a successful project manager developing world class infrastructure and industrial projects, and finally have a construction management consultancy firm of his own.

Permanent address: L - 4 / 6, DLF Phase 2, Gurgaon - 122002, 149

Haryana, India Email: [email protected]

This thesis was typed by Ankit Bhatla.

150