Engineering lessons learned from fracture failure of

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plates at the bottom pin of the Southeast link11. Shortly after fracturing of .... ing the truck load of varying-amplitude nature as a constant- amplitude live load with ...

No. 35-10

Journal of Structural Engineering Vol. 35, No. 1, April-May 2008 pp. 73–81

Engineering lessons learned from fracture failure of the Paseo suspension bridge G. D. Chen∗ , C. Courtright∗ , L. R. Dharani *, ∗∗ , B. Xu∗ and B. Hartnagel∗∗∗ ∗

Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, 229 Toomey Hall, 400 West 13th Street Rolla, MO 65409-0050 USA. ∗∗ Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, 229 Toomey Hall, 400 West 13th Street Rolla, MO 65409-0050, USA. ∗∗∗ Bridge Division Missouri Department of Transportation, P.O. Box 270, Jefferson City, MO 65102. Received 27 February 2008;

Accepted 4 April 2008

One of the four vertical struts in the 1232-foot long Paseo Suspension Bridge fractured on January 22, 2003. Fatigue in normal conditions, overstressing and thermal contraction as a result of frozen pin conditions, as well as reduction in fracture toughness at low temperatures were identified as four relevant factors. To ascertain the most likely reason(s), material, fatigue, and fracture tests were performed on samples of the strut material while the bridge and strut were analyzed under service loading conditions. Numerical results and test data indicated that fatigue was not the primary reason for the fractured strut as supported by the visual inspection done two months prior to the incidence and the presence of a rough fracture surface. It was the mechanically frozen pin condition at the lower end of the strut that resulted in an unexpected bending stress and thus sudden fracture of the strut. The frozen pin condition was attributable to salt and sand accumulation in the strut housing. Low temperature was a contributing factor. An engineering lesson learned from this incidence was that the original design did not allow for routine maintenance without disassembling the link housing system. KEYWORDS: Fracture; crack propagation life; fracture toughness; frozen pin condition; suspension bridge.

The Paseo Bridge in Kansas City, MO, was built in 1952, spanning over the Missouri River as shown in Fig. 1. The bridge is a self-anchored suspension structure, currently supports Interstates I-29 and I-35, and US Highway 71, and carries an average of 89,000 vehicles daily. On January 22, 2003, the Paseo Bridge was closed to traffic when a pronounced gap between sections of the bridge’s deck sparked fears about the span’s safety. At the time, temperatures were reported to have hit a record low of 9◦ F below zero and wind chills approached 25◦ F below zero. Numerous long-span bridges in the nation’s inventory are constructed of steel. An understanding of the conditions causing fracture in the Paseo Bridge could better inform bridge inspectors as to signs to look for. Prevention of a similar occurrence elsewhere through better understanding of material and structural behaviours is crucial to maintaining normal traffic volume and flow throughout the nation’s transportation infrastructure. Therefore, identifying and pinpointing plausible reason(s) why the Southeastern vertical strut of the Paseo Suspension Bridge fractured after nearly 50 years of service is of paramount importance. Some of the previous tests related to the failure investigation of steel structures are summarized here. Frank1 performed a series of mechanical tests on bridge materials,

A7 and A373, which are very similar to the A36 (Holt et al2 ). When combined with thermal and live load fluctuations, initial flaws in manufactured and fabricated bridge members

Fig. 1 Overview of the Paseo Suspension Bridge

and details can lead to fatigue crack growth and eventual fracture of steel bridge components3,4 . Mean stresses due to dead load have significant effects on fatigue life, which are seen predominantly at long lives5 .

* E-mail:[email protected] (Discussion on this article must reach the editor before June 30, 2008) JOURNAL OF STRUCTURAL ENGINEERING VOL. 35, NO. 1, APRIL-MAY 2008

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Although correlations between fracture toughness and Charpy impact energy exist, they should be applied with caution due to their empirical nature and applicability in specific temperature ranges and material heats6 . Barsom7 developed equations specific to bridge steels in the lower shelf and transition regions of temperature-absorbed energy plots, the temperatures experienced during normal service conditions. His correlations were used in AASHTO8 fracture toughness requirements for bridge steels. Charpy V-notch impact test results for A36 steel can be found in Structural Alloys Handbook2 . The specimens were from service failure, brittle fracture of a stringer bridge, and reported by Frank1 . The most accepted model to describe crack growth behaviour, proposed in the early 1960’s, is the Paris Equation5 . The primary factor affecting fatigue crack growth rates in structural steels is the applied stress intensity factor range9 . Their conservative estimates for ferrite-pearlite steels (A36) were confirmed by Fisher10 . The objectives of this study are to identify several plausible reasons for this failure from operational and environmental points of view, pinpoint one most likely reason or combined effect, and simulate the fracture process of the strut. To achieve these objectives, service loads applied on the bridge (range and number of cycles of live load) were estimated based on the traffic (truck) counts, and a series of tests were performed to determine basic material properties, establish a stress and cycles-to-failure (S-N) relation for crack initiation life estimation, establish the relation between fracture toughness and temperature, establish the crack growth rate data for crack propagation life estimation, establish a detailed finite element model, and simulate strut failure process. FRACTURE FAILURE AND PLAUSIBLE REASONS Description of Fracture in Southeast Strut The Paseo Bridge is supported by two intermediate steel towers (Piers 3 and 4) and two end piers (2 and 5) as shown in Fig. 2. The total length of the main bridge is 1232 feet, including one main span of 616 feet and two side spans of 308 feet each. The bridge deck is supported on two stiffening girders that are suspended on two main cables through vertical suspenders. Each stiffening girder is tied down to the end piers with one vertical hanger at each end of the bridge. As illustrated in Fig. 3, each hanger consists of an upper and a lower link connected with rivets by a strut (S 24 × 120). The upper and lower links are connected with the stiffening girder and the end pier by two 11-inch diameter pins, respectively. Failure occurred near the lower link where the web of the failed strut is connected to the lower pin. In this area, both flanges of the strut are tapered off, creating a discontinuous

Fig. 2 Elevation and part of plan view of Paseo suspension bridge 74

region of stress flow or local stress concentration as shown in Fig. 4(c).

Fig. 3 Link anchorage details

The Southeast vertical hanger lost its function due to fracture of the strut. As shown in Fig. 4(a), the bridge deck of the Southern side span rose approximately 8 inches above the approach deck. The following day, it was found that the strut (web) in the Southeast lower link anchorage assembly was fractured as illustrated in Fig. 4(b) or 4(c) for a closedup view. During the inspection for all four struts, it was also found that the Southwest strut was cracked mainly due to the significantly increased load as a result of fracturing of the Southeast strut. By the time this study began, the replaced failed steel components were stored for several months in a field shop of the Kansas City Division of the Missouri Department of Transportation (MODOT). The fracture surface became rusty as shown in Fig. 5. Close examination on the failed strut indicated that the fracture surface was pretty rough, implying that the fracture was unlikely due to long-term fatigue. Possible Reasons A detailed inspection of the Paseo Bridge was performed by the Parsons Engineering Group in November, 2002, approximately two months prior to fracture of the Southeast strut. Referred to as links in the Parsons evaluation, it was reported that longitudinal motion of the links was observed11 . This indicated that at the time of inspection the pins were in working condition, allowing free rotation of the superstructure. Upon inspection, no section loss or corrosion to the links was visible. Additionally, it was observed that debris and rust were accumulated around the lower link housings. Fretting rust was also noticed at top pins of links on the south end. No mention of similar observable fretting rust on the lower pins

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Fig. 6 Conditions of two pins in the lower link (a) Southeastern pin (b) Southwestern pin

Therefore, the damage of the strut must have been caused by overstressing due to live loads and/or thermal contraction. Associated with the low temperature during the strut failure, fracture may also result from the reduction in fracture toughness. Finally, the accumulated fatigue effect on the strut for nearly 50 years of service is another possibility even though the Parsons’ visual inspection did not indicate so. Fig. 4 Bridge failure and strut fracture detail (a) Rise in bridge deck (b) Region of strut failure (c) Fracture detail

Fig. 5 Fracture surface

was found, however pack rust was observed between the plates at the bottom pin of the Southeast link11 . Shortly after fracturing of the vertical strut, the lower links on the South end of the bridge were inspected. The surface condition of the pin on the Southeast side was severely corroded as indicated in Fig. 6(a). For comparison, the pin on the Southwest side is shown in Fig. 6(b). Since the Parsons’ inspection, temperature continued to drop till 9◦ F below zero, which coincided with the strut fracture. As a result, the Southeast pin must have been frozen and the strut was subjected to both tension and flexure, a changed loading condition from the originally axial force member.

TEMPERATURE AND LIVE LOAD CYCLE Daily temperature data, reported for the downtown airport in Kansas City, MO, was obtained to analyze what temperatures the bridge was exposed to during the period following the Parsons’ inspection. The day fracture occurred was the coldest day since the Parsons’ report that longitudinal motion was observed for the links. Figure 7 shows the temperature history giving the daily high and low for the months of November, 2002 until January, 2003. For a comprehensive fatigue evaluation, it would be desirable to determine traffic load spectrums (peak stress versus number of cycles) that can be developed with field measurements12 . For this study, however, such data were not available from MODOT. More importantly, the fracture of the Paseo Bridge is later on found to be closely related to the frozen pin condition that significantly changed the boundary conditions of the bridge structure. Due to the “sudden” nature of fracturing of the strut, it is impractical, if not impossible, to obtain traffic load spectrums that reflect the actuallive load at the time of fracturing. Therefore, in this study, only the traffic data for the Paseo Bridge supplied by MODOT was

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the number of trucks per cycle, yields a minimum number of 319 cycles per day on each vertical strut. Note that treating the truck load of varying-amplitude nature as a constantamplitude live load with equivalent number of cycles is generally on the conservative side for the fatigue evaluation. MATERIAL, FATIGUE AND FRACTURE TESTS

Fig. 7 Temperature change in Downtown Kansas City Airport

utilized. The average daily traffic volume was given in Table 1 for both the north and south bound lanes. MODOT suggested that approximately 11.5% of these vehicles be trucks. TABLE 1 AVERAGE DAILY TRAFFIC COUNT FOR PASEO BRIDGE Year 1995 1998 1999 2003

North bound All vehicles Trucks 34968 4021 40075 4609 41828 4810 45024 5178

South bound All vehicles Trucks 39506 4543 43181 4966 47161 5424 43949 5054

To allow for fatigue and fracture evaluations, the HS2044 Lane Load was applied to the long-span bridge structure to determine the peak live load applied on the strut is presented in Section 5. Corresponding to the lane load concept, the equivalent number of live load cycles associated with the peak live load was considered for truck traffic. A cycle was defined by applying the maximum number of trucks of length, 28 feet, to each lane with a spacing of 84.5 feet in between trucks. The length of 28 feet corresponds to the minimum length of a standard AASHTO HS 20 truck and the 84.5 foot spacing was calculated, considering the minimum safety distance, and a loading equivalent to AASHTO lane loading of 640 lbs/ft plus a concentrated load. The total length of the span corresponding to one cycle of the bending moment at the location of the fractured strut due to the frozen pin condition was determined from the influence line analysis of a bridge model established in SAP2000, as shown in Fig. 813 . It is equal to the combined length of one side span and the main span or a total of 924 ft, thus approximately 8 trucks could be in each lane at once. Using 4 lanes, 32 trucks traveling across the deck constituted a cycle.

Fig. 8 Moment influence line at the bottom end of the strut after the frozen lower link pin

According to the traffic counts in 1999 and 2003, the average number of trucks passing though the bridge is approximately 10,200 trucks per day. Dividing this total by 32, 76

Although there is no indication of fatigue cracking around the fractured strut based on the inspection report11 , it would still be desirable to confirm whether the fracture of the Southeast strut initiated from a fatigue crack at the cope flange of the strut over the 50-year service of the bridge. In combination of lack of material specifications, a series of material, fatigue, and fracture tests were performed in this study as detailed in Chen et al13 . Following are a summary of the test data and results. Tensile Tests Five tensile specimens were obtained from the fractured Southeast strut and prepared according to ASTM E8. Each measured 10 inches in length and had a cross section of approximately 0.71 inch by 0.22 inch. It was tested under displacement controlled loading at a rate of 0.2 inches per minute. The average of the test results indicated that the material tested had a Young’s Modulus of 28,500 ksi, yield stress of 36.2 ksi, ultimate stress of 61 ksi, and reduction in area of 46.9%. These values compare well to those from the steel of the same decade such as A7 and A3731 . Fatigue Tests A total of 25 specimens were machined according to ASTM E 606 with rectangular cross sections. The specimens were oriented to reflect the tensile loads on the strut during service loading conditions. Each specimen was tested under a nonzero mean sine stress wave of 5 Hz. The maximum stress for each case was predetermined to range from 37.5 ksi to 55 ksi in increments of 2.5 ksi, depending on the particular specimen. The minimum value was selected to be slightly above zero for measurement accuracy. In the well-known strain-life method5 , the stress amplitude (Δσ) and the plastic strain (Δεp ) can be related to the reversals to failure (2Nf ) or twice the number of cycles to failure for sinusoidal loading. For determining the four fatigue constants needed in the strain-life method5 , best fitting equations were developed through stress amplitude versus 2Nf and plastic strain amplitude versus 2Nf . The four fatigue constants are the fatigue strength coefficient (σf = 70.7 ksi), the fatigue strength exponent (b = −0.066), the fatigue ductility coefficient (σf = 0.0077), and fatigue ductility exponent (c = −0.28). Considering the coped flange on the Southeastern strut to act as a notch, Neuber’s rule5 was applied to determine the local stress and strain at the notch root, which would be different from the nominally applied far field stress and strain. The stress concentration factor needed for the application of the Neuber’s rule was found to be approximately 3.76 from a finite element model assuming the pin in the lower link is free to rotate13 . The local strain amplitude needed in the strain-life approach was obtained by solving the hysteresis equation and the Neuber’s rule written in terms of stress and strain amplitude5 . The number of reversals to failure (2Nf )

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was obtained using strain-life equation for each of the stress levels used to predict the residual life curve shown in Fig. 9. It can be seen from Fig. 9 that, when the pin is not mechanically frozen (free to rotate), the predicted residual life of the vertical strut is practically infinite. This is calculated by taking the number of cycles for 100% live load and a constant dead load of 120 kips.

In Eq. (1) above, the Young’s Modulus, E, and the Charpy breaking energy, Cv , must be in √ psi and ft-lb, respectively. The units of KIC will be in psi in Barsom used this relationship in developing the AASHTO fracture toughness requirements for bridge steels6 . Table 2 lists the fracture toughness, KIC , calculated using Eq. (1) from the average breaking energy of the five specimens at each temperature.

Charpy Impact Tests According to ASTM E399, the minimum specimen thickness required for a valid plane strain fracture toughness (KIC ) test is prohibitively large because this material has very low yield strength (36.2 ksi). Therefore, instead of determining the KIC using the standard plane strain fracture toughness test (ASTM E399), Charpy V-notch test was performed following ASTM E23. The results obtained from Charpy V-notch testing at different temperatures when correlated with service conditions have been found to predict the likelihood of brittle fracture accurately14 .

Fig. 10 Absorbed energy at various temperatures TABLE 2 FRACTURE TOUGHNESS CALCULATED FROM EQ. (1) Temperature ◦ F 136.0 109.5 104.0 86.8 70.0 50.4 30.3 10.0 −9.9

Breaking energy (Cv ) ft-lbf 84.57 59.03 49.96 28.48 17.03 11.56 7.89 5.11 4.11

KIC ksi∗ in1/2 110 92 84 64 49 41 34 27 24

Fig. 9 Residual life estimation curve for Paseo bridge struts

Charpy V-notch specimens were oriented so that the long axis of the specimens correlated to the tensile/compressive axis of loading in the service conditions of the struts. The V-notch was oriented so that fracture would occur transversely to the rolled direction of the material, the same plane of cracking and fracture that occurred in the Southeastern strut. Each Charpy V-notch specimen measured 2.165 inches in length and had a cross section of 0.394 inch by 0.394 inch. The V-notch is located at the middle of the specimen and has a depth of 0.079 inches with a notch angle of 45◦ . Charpy V-notch impact tests were performed in the temperature range of −10◦ F to 140◦ F. Temperatures below room temperature were obtained using an alcohol bath and dry ice. Temperatures above room temperature were obtained using a laboratory oven. The breaking energy, Cv , was recorded and the test repeated until five valid tests had been performed at each temperature. Breaking energy versus temperature was plotted as shown in Fig. 10. The curve is characterized by the lowershelf and transition region of breaking temperature, which is consistent with those of Frank1 . It should be noted that approximately 20 times the energy was required for fracture between the extremes of the chosen temperature range. The fracture toughness can then be determined from the fracture energy by15 , 2 KIC = 5Cv E

(1)

Fatigue Crack Growth Crack propagation in metallic materials is commonly described using the empirical crack growth law presented by Paris, Eq. (2). da m (2) = C (ΔK) dN The constants C and m are material parameters determined experimentally, da/dN is the crack growth in one cycle and ΔK is the stress intensity factor range5 . If the material constants C and m are known, then Eq. (2) can be integrated between the initial and critical crack length to determine the crack propagation life. However, the material of the strut was unknown, and the constants C and m need to be determined. Eight compact tension specimens were machined from the strut material according to ASTM E 647. Finished specimen thickness was 0.735 inches. According to ASTM E 647, the specimen’s uncracked ligament would be of sufficient magnitude that valid specimens could not be arranged between the existing rivet holes in the strut material. It was decided to use an existing rivet hole to load the specimen, thus other dimensions of the compact tension specimen were determined based on this 1 inch diameter of the existing hole. One 5 inch by 4.8 inch finished sample is shown in Fig. 11, in which ‘a’ represents the length of a crack and ‘W ’ is the length of the specimen.

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and bending. Taking the actual conditions into effect, rolled shape with a coped flange, the propagation life would be even shorter.

Fig. 12 Crack propagation life estimation curves (pin free to rotate)

FINITE ELEMENT MODELING Global and Local Models Fig. 11 Compact tension specimen: orientation and finishing sample

Specimens were tested under a harmonic loading of 5 Hz, varying between 400 and 11,000 lbs. The crack length was determined by the compliance method (ASTM E 647). For compact tension specimens, the stress-intensity factor range, ΔK, was plotted against the crack growth rate, da/dN , on a log-log scale and the constants C and m in Eq. (2) were de−10 termined by a power-law curve fit. √ They are C = 7× 10 and m = 2.8, when ΔK is in ksi in and da/dN is in inch per cycle. Fracture occurs when the maximum stress intensity factor reaches a critical value or the material fracture toughness, KIC 5 . To determine the crack propagation life for the vertical struts of the Paseo Bridge, it was assumed that they behave like an edge cracked plate subject to tension. An initial crack length of 0.005 inch (invisible by naked eyes) was considered and Eq. (2) was integrated numerically between the initial and the critical crack lengths. When the pin at the lower link of the failed strut is free to rotate, crack propagation life estimation curves were generated in Fig. 12 for three live load conditions √ on the struts at a temperature of 60◦ F, where KIC = 45 ksi in. It is clearly seen from Fig. 12 that the crack propagation life under 50% design live load and 100% dead load exceeds 2 million cycles, which is practically infinite when the pin is free to rotate. This load condition represents a realistic estimation of the live load since the web of the failed strut was connected with four additional plates as illustrated in Fig. 4(b), and together they transferred the loads applied on the strut. With the frozen pin condition and temperature of −10◦ F (KIC = 24 from Table 2), the same initial crack length of strut. 0.005 inch was used to estimate crack propagation life. The stresses produced from thermal loading were estimated from a finite element model of the suspension bridge (Table 7.3 in Chen et al13 ). It was found that sudden fracture would occur in less than 200 cycles of live loading or within one day, combined with the deadload and thermal loading effects. It should be noted that this is a conservative estimate for the strut geometry, edge cracked plate subject to tension 78

A finite element model of the strut was developed to understand the stress intensity factor at the location of flange coping, the area of crack initiation in the failed strut, and the process of failure. The model was established using the commercially available software ABAQUS. The strut assemblies consisted of a central rolled shape with two additional plates riveted to each side at the ends to provide bearing surface on the pins as shown in Fig. 4(b) and (c). Due to symmetry of the rolled shape S24× 120, half of the shape was modelled and shown in Fig. 13(a). It consisted of the lower 43 inches of the strut, measured from the center of the lower pin. This length was chosen to include four rows of rivet holes, two above, and two below the location of crack initiation. This model, referred to as the global model, consisted of 8835 nodes and 5408 hexahedral elements. The surface of the hole for the 11-inch diameter pin is fully fixed in the global model and the back surface of the plate is constrained for transverse displacements as the model is only half of the strut. A local model of the area of crack initiation was produced from individual elements of the global model. This allowed for a finer mesh, thus more accurate calculations in the area of crack initiation. The location of the local model in relation to the global model is shown in Fig. 14. Two global elements were chosen from the global clusters of elements and used as the boundaries for the elements in the local model. The local model also consisted of 3-dimensional solid hexahedral elements. The number of elements is 8086 and the number of nodes is 6912. The mesh of the local model is given in Fig. 14. The mesh at the crack tip for the model with a 0.005 inches long crack is given in Fig. 13(b). It should be noted that the physical width of the crack was 0.001 inches and the radius of the crack tip was modelled as 0.0005 inches. Dead, Live and Thermal Loads Load on the fractured strut was estimated from three sources: the dead payload (DL)used on the bridge deck during repairing to reposition the raised deck, the calculation of live load (LL) using HS 20-44 loading8 on a SAP2000 model of the

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bridge and thermal effects (TH) on the failed strut as a result of the frozen pinned connection. Six specific loading cases were chosen in this investigation as summarized in Table 3. Note that these force and moment represent 25% of the total force and moment through each strut since only half of the strut was modelled as shown in Fig. 13(a) and half of the load was considered to pass through the two additional plates that were riveted into the web of the strut as illustrated in Fig. 4(b).

LEFM limits would have to be sufficiently long. For example, for load case 1 in Table 3, the crack length would have to be greater than 0.27 inches. The initial crack width considered in this study was significantly smaller than the limit, invalidating the KI evaluation approach. Therefore, elasticplastic analysis in ABAQUS was necessary to calculate the J-integral values16,17 .

Fig. 14 Relation between local and global models

Fig. 13 ABAQUS global and local models (a) Half middle plate of strut assembly (b) Meshes around the tip of a crack

The combination of an axial force and a moment was converted to a distributed surface stress applied on the top surface of the global model including the flanges. Stresses at the boundaries of the local model (Fig. 14), were found by first analyzing the global model, obtaining the resulting stresses corresponding to the boundaries of the elements in the local model and then applying those to the finer mesh of the local model. J-Integral Evaluation To understand whether elastic analysis with KI evaluation of the fracture process is sufficient, the limits of the validity of linear elastic fracture mechanics (LEFM) were checked13 . Based on the known yield stress and stress intensity factor for the given loading, the initial crack length from the

Elastic-plastic analysis was performed for each of the six load cases described in Table 3. Two crack lengths, 0.005 inches for JI1 in Table 3 and 0.001 inches for JI2 in Table 3, were considered. The crack length of 0.005 inches was selected because that is the smallest crack discernable with many test instruments. The critical JIC values in Table 3 were calculated from the predicted fracture toughness KIC in Eq. (1) by16   2 1 − v2 KIC JIC = (3) E in which v is the Poisson ratio. It is evident from Table 3 that if the pin were free to rotate, sudden fracture would never have happened even with an initial defect of 0.005 inches and low temperatures as the bending moment is always zero. For example, at a temperature of −10◦ F, the JI1 value (= 0.47 lb/in from Case 1) was still less than the critical value JIC = 19 lb/in. Thus, failure of the strut by fatigue is unlikely. If the pin froze, Case 2 indicated that fracture of the web of the strut did not occur without thermal effects. Even when the temperature dropped to 30◦ F, fracture was unlikely to occur in the web of the strut. As temperature continued to drop, however, J increased rapidly and exceeded JIC . The likelihood of strut fracture increased substantially. Therefore, low temperature was a contributing factor to the failure of the strut.

TABLE 3 LOAD MATRIX AND J-INTEGRALS Load case 1 2 3 4 5 6

Load description DL + LL DL + LL DL + LL + TH DL + LL + TH DL + LL + TH DL + LL + TH

Temperature ◦ F 60 60 30 10 0 −10

Pin condition Unfrozen Frozen Frozen Frozen Frozen Frozen

Force (kip) 73 73 85 93 97 100

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Moment (kip-in) 0 2125 9963 15188 17800 20400

JIC (lb/in) 67 67 36 23 21 19

JI1 (lb/in) 0.47 36.3 53.3 81.7 95.3 231

JI21 (lb/in) 0.02 0.39 13.1 58.0 71.0 180

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On the other hand, Cases 4 and 5 indicated a possibility of strut fractures at a temperature higher than that when the strut actually failed. This is attributable to the fact that the live load and thermal effects included in Table 3 were estimated for a worst scenario situation. In what follows, the percentage reduction of the loads and the effect of initial defects (0.005 inches versus 0.001 inches) at the time of strut failure are analyzed based on the fact that the strut did not fail at 0◦ F and the crack propagation life of the strut is negligible under the frozen pin condition as discussed in Section 4.4. To make JI2 at 0◦ F (Case 5) equal to the J-Integral for Case 3 or slightly less than JIC , the axial load and the moment need to be reduced by 14% and 79%, respectively, which falls in the practical range of service live loads as well as thermal effects. For JI1 , however, the corresponding force and moment must be reduced by more than 33% and 840%, respectively, which is unrealistic. Therefore, it was likely that the initial defect was approximately 0.001 inches and the lower pin of the Southeastern hanger was likely frozen at a temperature below zero. Fracture Process of the Strut To identify the location of crack initiation and propagation, a series of local models with various initial crack lengths were established in ABAQUS. When there is no initial flaw or crack, Fig. 15(a), the stress contour is shown in Fig. 16(a). It is observed from Fig. 16(a) that crack is likely initiated near the flange coping area due to high stress concentration and propagated towards the closest hole. To further see the propagation of an initial crack, as shown in Fig. 15(b) and (c), two additional models with a crack length of 0.5 inch for Crack Pattern 1 and 1.1 inch for Crack Pattern 2, respectively, were analyzed. Their corresponding stress contours are presented in Fig. 16(b) and (c). As a result of the previous cracks, the maximum stress occurs in the opposite side of the hole near the flange coping area. To understand how sensitive the

location of the maximum stress, the third crack pattern was introduced in Fig. 15(d). Its corresponding stress contour is also presented in Fig. 16(d). By comparing Crack Pattern 2 and Pattern 3, one can see that the locations of the maximum stress identified from the two models are practically the same. To finish up the analysis for crack propagation, the fourth crack pattern in Fig. 15(e) was created and the stress contour is shown in Fig. 16(e). By comparing Fig. 16(e) with the actual fracture pattern, Fig. 16(f), one can conclude that the models accurately predict the crack initiation and propagation locations of the actual damage pattern. CONCLUSIONS Based on extensive tests and analyses, the following conclusions can be drawn: 1. The mechanical frozen condition of the lower link pin was the root cause of the failure of the Southeast strut of the Paseo Bridge. As a result, the strut was subjected to significant bending in addition to its design axial action as the temperature dropped to below zero. Therefore, the strut was overstressed and fractured when its fracture toughness was reduced at low temperatures. 2. Fatigue was not a contributing factor for the strut failure. If the lower link pins were free to rotate, the crack initiation life of the strut is practically infinite even under the worst scenario of live loads and at low temperatures. 3. Fracture initiated at the point where the flange of the rolled section S24 × 120 was coped from the web. The mechanical freezing of the lower link pin has been attributed to salt and sand accumulation in the lower link housing, discovered during the bridge inspection two months prior to failure. 4. Greasing the upper and lower pins during normal inspections would have prevented the freezing condition of the lower link pin. However, the original design of the lower link housing did not allow for the routine maintenance of the pin without dissembling the housing system. An engineering lesson learned from this incidence was lack of access to the lower link area for proper maintenance. ACKNOWLEDGEMENTS

Fig. 15 Crack patterns near the location of strut failure

Financial supports to complete this study were provided in part by MODOT and U.S. DOT through the University Transportation Center at the University of Missouri-Rolla. The opinions, findings, and conclusions expressed in this paper are those of the authors. They don’t necessarily represent those of the sponsors. REFERENCES 1. Frank, K. A., “Mechanical and chemical properties of selected steels used in bridge structures”, Report No. FHWA-RD-75-79, Federal Highway Administration, November 1974, pp 255–323. Fig. 16 (a-e) Stress distributions corresponding to different crack patterns (f) actual work 80

2. Holt, J. M., Gibson, C. and Ho, C. Y. (eds.), “Struct. Alloys Handbook”, 3, 1996 (CINDAS/Purdue University, West Lafayette).

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3. Fisher, J. W., Pense, A. W., Hausammann, H. and Irwin, G. R., “Quinnipiac River Bridge cracking”, ASCE Jl. of the Struct. Division, 106(4), 1980, pp 773–789.

11. Parsons Engineering Group, “2002 Paseo Bridge evaluation report”, Missouri Department of Transportation, April 2003.

4. Fisher, J. W., Yen, B. T. and Frank, K. H., “Minimizing fatigue and fracture in steel bridges”, Transactions of the ASME, Jl. of Engg. Materials and Tech., 102(1), 1980, pp 20–25.

12. Chen, G. D., M. Barker, L. R. Dharani and C. Ramsay, “Signal Mast Arm Fatigue Failure Investigation”, MODOT Report RDT03-010, May 2003.

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