Guidelines for the Load and Resistance Factor Design and Rating of Riveted and Bolted Gusset-Plate Connections for Steel Bridges (2013)

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66 CHAPTER 3. FINDINGS AND APPLICATIONS This chapter will focus on the results of both the experimental load testing performed at Turner- Fairbank Highway Research Center and the analytical work performed at Georgia Tech. Although elastic load scenarios were investigated both analytically and experimentally for many, but not all specimens, the data gathered during these elastic loading scenarios will not be presented herein, but rather will be provided in the report appendices. This chapter is intended to convey only the results from the final failure load tests that were performed on each specimen in the testing matrix and the analytical work performed at Georgia Tech. A discussion of the specimen-specific loading protocols, the predicted and actual loads at failure, the failure mode, and accompanying pertinent data will be presented herein. EXPERIMENTAL SPECIMENS In total there were 13 connections tested; however, one of the tests, 490LS3, was an accidental failure where operator error uncontrollably crushed the specimen. The specimen geometry was retested and called 490LS3-1. All 12 specimens either failed via buckling of the gusset plate whereby the end of the compression diagonal moved out-of-plane, or by shear along the horizontal plane along the chord. All the raw data from the various instrumentation systems is graphically shown in Appendices E, F, G, and H, only data relevant to the discussion will be presented in this part of the report. Buckling failures were easy to distinguish because failure was visually apparent and in all specimens, buckling resulted in out-of-plane movement of the compression diagonal. A typical buckle is shown in Figure 44 where it can be seen that when the gusset plate buckles, the compression diagonal moves out-of-plane essentially as a rigid body. Unfortunately, post-test visual observations of all the specimens seem to indicate failure due to buckling. Even though shear may have been the failure mode, after so much shear deformation, the compression diagonal still moved out-of-plane. To isolate out the shear failures, both the FARO and DIC data had to be queried to determine whether or not shear had occurred. For instance, shown in Figure 45 are two plots created from FARO data. The vectors show the displacement of select bolt targets on the gusset plate, with the tail representing the pretest locations, and the head as the post-test locations amplified 25 times. In both plots, the six vectors in the upper left are for targets over the compression diagonal. In buckling failures, the large vector motions are isolated around the compression diagonal, whereas for shear failures, large vector motions are similar for both diagonals and vertical members and generally pointing to the right indicating the upper half of the plate sheared relative to the lower half. The DIC data was looked at to verify that there was a large amount of straining along this plane (generally in excess of 1.5% Tresca strain). Table 6 contains a summary of the member loads entering each experimental connection at failure (which was either buckling or shear). Also shown in Table 6 are shaded cells highlighting the failure mode and either the load in the compression diagonal or internal shear depending if it

67 was a buckling or shear failure. Only the static yield strength of the plate material is also shown. For further information on the testing of the plate material, see Appendix D. Figure 44. View looking down chord at out-of-plane sway buckle of gusset plate, specimen GP307SS3.

68 Figure 45. Vector motions of gusset plate targets amplified 25 times. Specimen 307SS3 (left). Specimen 307LS3 (right). -10 0 10 20 30 40 -10 0 10 20 30 40 50 60 70 Y- A xi s C oo rd in at e (in ch ) X-Axis Coordinate (inch) -10 0 10 20 30 40 -10 0 10 20 30 40 50 60 70 Y- A xi s C oo rd in at e (in ch ) X-Axis Coordinate (inch) g ( )

69 Table 6 Summary of Failure Loads and Modes of Experimental Specimens Specimen Phase 1 Phase 2 307SS3 490SS3 490LS3 a 490LS3-1 307LS3 307SL3 307SL4 490LS3-2 490SS3-1 307SS3-1 307SS3-2 307SS3-3 307SS3-4 Static Yield Strength (ksi) 36.4 46.4 45.6 48.5 48.2 46.6 33.0 45.5 45.7 47.2 47.8 37.9 38.0 Comp. Diag. Load b (kips) -716 -728 -498 -527 -796 -946 -1070 -865 -633 -446 -482 -519 -712 Tens. Diag. Load b (kips) 507 728 830 881 405 929 1066 483 915 285 696 735 1003 Vertical Load b (kips) 141 0 -234 -248 280 0 0 245 -195 90 -148 -154 -215 East Chord Load b (kips) -520 -528 -498 -529 290 -706 -770 -526 -659 -321 -512 -533 -680 West Chord Load b (kips) 345 501 441 446 994 620 740 427 435 196 321 354 533 Horizontal Shear Force (kips) 865 1029 939 995 849 1326 1510 953 1094 517 833 887 1213 Failure Mode Buckling Shear & Buckling Note a Buckling Buckling Shear Shear Buckling Shear Buckling Shear Shear Shear NOTES a – Specimen accidently crushed after failure of vertical actuator bracing b – Negative loads represent internal axial loads that are compressive

70 ANALYTICAL The parametric analytical study was performed by Georgia Tech and is reported in full detail in Appendix I. This included the detailed analysis of 201 finite element models that considered a wide variety of gusset plate geometries, under different loading configurations, different plate thicknesses, with and without multi-layered gussets, and also included the effects of corrosion. This section will only present the results of that study in terms of the various limit-states that were observed and how they relate to simple prediction equations. The goal of these analyses is to verify the predictive equations and to understand the statistical variation in the analytical models of each failure mode that can be used in the LRFD calibration task. As such, the analytical data is also complemented with the experimental results where appropriate. This report was written after the submission of Appendix I and there are some differences of interpretation of model results between the PI and the authors of Appendix I. These differences are mainly attributed to mixed-mode failure models where shear yielding and buckling appear to be occurring simultaneously, making it somewhat subjective. This is not to detract from the accuracy of what is reported in Appendix I, although keen readers may note differences between data reported in the main report and Appendix I. SYNTHESIS OF RESULTS It is important to make a distinction between design and rating in the results from this research, since the greater challenge pertains to rating of the existing inventory. It is more expensive to retrofit an existing gusset plate with inadequate rating than to increase the plate thickness in design. The sections to follow outline the results attained in both the experimental and analytical work in term of the individual failure modes that were observed. The statistical variation of this data is integral to the -factor calibrations that will be discussed in Chapter 4. Two of the limit- states will present different statistics, one using all the data, and the other using data from gusset plates 0.375 inches thick or greater. The reasoning behind this is that different calibrations were performed for the BDS and the MBE. The scatter associated with plates thinner than 0.375 inches was greater, leading to less favorable -factors. Therefore, for design it was assumed that a thickness limit could be imposed for the gusset plates and the data for “thin” gussets could be ignored. However, in rating, the plate thickness is a given and since the existing inventory of gusset plates has “thin” plates in it, the statistics used in determining MBE -factors must include all the data. Shear Failures Tables 7 and 8 summarize the associated relevant data for analytical and experimental connections that failed in shear. Within each table, the shear load at which the connection failed (Vfailure) and the nominal calculated resistance for shear yielding (Vny) and shear fracture (Vnu) are tabulated. While the parametric study did not use models with the fidelity required to capture shear fracture, nor was it observed in the seven experimental shear failures, the shear fracture calculations are shown for completeness. The nominal shear yield resistance does not consider

71 the  reduction factor used in the FHWA Guide (i.e., Vn=0.58FyAg) and this will be derived from the LRFD calibration in the next chapter. The ratios between the failure load and the associated resistance calculations are also tabulated in the tables which represent the professional factor to use in calibration. However, the shear fracture state will not be calibrated. The cells in the table shaded grey represent the controlling nominal resistance equation. In many cases it can be seen that the nominal shear fracture limit- state would control the design/rating, despite it not being an observed failure in the experimental connections, nor could that mode even be captured in the finite element models. This shows that there is probably some excess conservatism in the shear fracture equation, though this project does not have the required data to support or refute that claim. In total there were 44 observed shear yielding failures. The professional factor data is graphically shown in Figure 46. While they were not included in the statistical calculations of the professional factor, the data from the three experimental shear failures with simulated section loss and the I-35W U10 joint are shown in the plot. The data from the 41 failures (excluding those with section loss) are plotted on normal probability paper in Figure 47. The best-fit line on the probability paper was used to determine the professional factor statistics for the shear yielding limit-state; the average and coefficient of variation (COV) of the data is 1.017 and 0.069 respectively. Only one failure had a plate thinner than 0.375 inches. Its professional factor was near the mean; therefore, the statistics would not change when ignoring plates thinner than 0.375 inches.

72 Table 7 Shear Data of Analytical Connections that Failed in Shear Specimen Plate Thickness (inch) Length of Shear Plane (inches) Vfailure (kips) Full Plane Yield [0.58FyAg] (kips) Vfailure/Vny Full Plane Fracture [0.58FuAn] (kips) Vfailure/Vnu U N C H A M FE R E D E1WV-307SS 0.6250 59 1653 1557 1.06 1634 1.01 E3WV-307SL 0.4375 66.5 1604 1573 1.02 1336 1.20 0.5000 66.5 1856 1797 1.03 1527 1.22 0.6250 66.5 2333 2247 1.04 1909 1.22 E4WV-490SS 0.4375 54.8 1318 1290 1.02 1118 1.18 0.5000 54.8 1513 1475 1.03 1278 1.18 0.6250 54.8 1894 1843 1.03 1598 1.19 E1W-307SS 0.4375 a 59 1023 1090 0.94 1144 0.89 0.5000 a 59 1246 1246 1.00 1307 0.95 0.6250 59 1742 1557 1.12 1634 1.07 E3W-307SL 0.3750 a 66.5 1326 1348 0.98 1145 1.16 0.4375 a 66.5 1604 1573 1.02 1336 1.20 0.5000 66.5 1830 1797 1.02 1527 1.20 0.6250 66.5 2294 2247 1.02 1909 1.20 E4W-490SS 0.4375 a 54.8 1235 1290 0.96 1118 1.10 0.5000 54.8 1483 1475 1.01 1278 1.16 0.6250 54.8 1884 1843 1.02 1598 1.18 P8U-WV-INF-02 0.5000 a 105.6 2923 3246 0.90 3276 0.89 P14U-W-INF-01 0.6250 a 57.1 2052 2194 0.94 2210 0.93 C H A M FE R E D P5C-WV-NP-01 0.5000 a 69.5 1914 2136 0.90 2158 0.89 0.6250 69.5 2507 2671 0.94 2697 0.93 P6C-WV-NP-02 0.5000 128.1 3731 3938 0.95 3995 0.93 0.6250 128.1 4911 4922 1.00 4994 0.98 P7C-WV-INF-01 0.4375 142.2 3944 3825 1.03 3865 1.02 0.5000 142.2 4754 4371 1.09 4417 1.08 0.6250 142.2 6051 5464 1.11 5522 1.10 0.7000 142.2 6915 6120 1.13 6184 1.12 P8C-WV-INF-02 0.3125 94.1 1884 1808 1.04 1830 1.03 0.3750 94.1 2339 2169 1.08 2196 1.07 0.4375 94.1 2729 2531 1.08 2562 1.07 0.5000 94.1 3151 2893 1.09 2928 1.08 0.6250 94.1 3898 3616 1.08 3660 1.07 P14C-W-INF-01 0.5000 a 57.1 1626 1755 0.93 1768 0.92 0.6250 57.1 2132 2194 0.97 2210 0.96 P15C-CJ-01 0.5000 69.7 2304 2143 1.08 2167 1.06 P7C-HS1 0.7000 142.2 12317 12470 0.99 9276 1.33 P8C-HS1 0.5000 94.1 5815 5894 0.99 4392 1.32 I-35W U10 b 0.5000 104.0 2753.869 3076 0.90 3468 0.79 a – These specimens had mixed shear and buckling failure response and were included in both limit-states. b – This connection likely failed by buckling, though a significant portion of its horizontal plane was yielded at failure and it is shown for reference. The connection is not included in any statistical calculations.

73 Table 8 Shear Data of Experimental Connections that Failed in Shear Specimen Plate Thickness (inch) Length of Shear Plane (inches) Vfailure (kips) Full Plane Yield [0.58FyAg] (kips) Vfailure/Vny Full Plane Fracture [0.58FuAn] (kips) Vfailure/Vnu U N C H A M FE R E D GP307SL3 0.3750 66.5 1326 1348 0.98 1145 1.16 GP307SL4 0.5000 66.5 1510 1273 1.19 1452 1.04 GP490SS 0.3750 54.8 1030 1106 0.93 959 1.07 GP490SS-1 0.3750 54.8 1095 1089 1.00 1150 0.95 GP307SS3-2 a 0.3750 59 833 779 1.07 1041 0.80b GP307SS3-3 a 0.3750 59 887 787 1.13 987 0.90b GP307SS3-4 a 0.3750 59 1213 1242 0.98 1274 0.95b a – These connections had simulated corrosion and were not considered in the statistical analysis of shear failures. b – The net section calculation only subtracted the area of the holes in the shear plane; it neglected the effects of the simulated section loss as they were not coincident with each other. Figure 46. Shear yielding professional factor data. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0 100 200 300 400 Shear Plane Slenderness (L/t) Analytical Failures Experimental Failures Experimental Failures w/Section Loss I-35W U10 V fa ilu re /V n

74 Figure 47. Shear yielding professional factor plotted on normal probability paper. Buckling Failures The reporting of buckling failures ignored connections that had edge stiffening, multi-layered gusset plates, or simulated section loss. The effects of these parameters were investigated independently and were purposely excluded to avoid influencing the statistics on buckling. The data were analyzed according to a buckling calculation method similar to that in the FHWA Guide. The FHWA Guide recommends an equivalent column approach using a Whitmore section. For this work, the Whitmore section is determined using the 30 dispersion angle. Other angles were explored, though they did not change the results and it was deemed better to retain the 30 degree dispersion angle since it is so widely used in the literature. However, this work will explore the influence of the column length in terms of both the physical length calculation and the K-factor. The physical column length is schematically shown in Figure 48. The current FHWA Guide recommends averaging the three lengths from the Whitmore section to the nearest adjacent fastener line, taken at the two ends and middle of the Whitmore section (i.e., average of L1, Lmid, L3 as shown in Figure 48). If the Whitmore section intersects a fastener line, that length is considered zero. This is considered the average length, or Lavg. The other length explored was just the length taken at the middle of the Whitmore section, or Lmid. Tables 9 through 13 outline the data for all the specimens that failed by buckling. In total, there were 124 data points including four experimental connections from this study, five experimental y = 14.308x - 14.554 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.75 0.85 0.95 1.05 1.15 1.25 S ta nd ar d N or m al V ar ia bl e Vfailure/Vn

75 connections from the Oregon State University testing (23), and one data point representing the I- 35W U10 connection. The data summarize the length of the equivalent column in terms of Lavg and Lmid. The buckling parameter, , is calculated at each of these lengths using equivalent column length factors of 1.2 and 0.5, using the equations below. ߣ௔௩௚ ൌ ቀ௄௅ೌೡ೒௥గ ቁ ଶ ி೤ ா ൌ 12 ቀ ௄௅ೌೡ೒ ௧గ ቁ ଶ ி೤ ா (Eq. 6) ߣ௠௜ௗ ൌ ቀ௄௅೘೔೏௥గ ቁ ଶ ி೤ ா ൌ 12 ቀ ௄௅೘೔೏ ௧గ ቁ ଶ ி೤ ா (Eq. 7) where K is the equivalent column length factor, t is the plate thickness, Fy is the plate’s yield strength, and E is the plate’s modulus of elasticity. The five columns to the extreme right of the tables represent the ratio between the actual buckling load of the plate to the unfactored, calculated resistance using the associated -value. The calculated resistance just uses the noncomposite column buckling equations in Section 6.9.4 in the LRFD Bridge Design Specification. This ratio will be referred to as the professional factor. Ideally the professional factor should be 1.0 and values less than 1.0 represent unconservative predictions while those greater than 1.0 represent conservative values. The plots shown in Figure 49 show the variation of professional factor against the associated - values. For both equivalent column length formulations (Lavg and Lmid), the higher K-factors produce very conservative professional factors as the plates become more slender. K-factors less than 1.0 produce much better professional factors, yet in all cases there are still many unconservative professional factors for connections with very compact plates. These plots seem to indicate that having a K-factor of 0.5 and using the Lmid column length produces the most favorable professional factors (i.e., closest values to 1.0 with the least scatter). However, even using K=0.5 and Lmid, there are still a large number of connections with professional factors much less than 1.0. To understand where this comes from, the same plot in Figure 49(d) is reproduced in Figure 50 with a different y-axis scale and with the analytical connections being segregated into those with and without chamfered members. This clearly shows that the connections with the poor professional factors are mostly those with chamfered members. The poor buckling prediction for chamfered members is better illustrated in Figure 51. In this figure, essentially the same connection geometry is being compared except for the notion that one uses chamfered members and the other uses unchamfered members. For each case a Von Mises stress contour is shown at failure of each connection where the grey-pink color represents areas that have exceeded yield. The connection with the unchamfered member buckles in a sidesway mode with relatively little yielding and in this case, the Whitmore buckling prediction is accurate. When the members are chamfered, the gusset still buckles, though after a significant amount of yielding around the horizontal and vertical planes of the compression diagonal of which the Whitmore buckling model tends to over predict the available strength. Therefore a two-folded check is recommended that determines the buckling resistance from the minimum of

76 the Whitmore buckling check using K=0.5 and Lmid, or the load in the compression member that would cause a partial plane around that member to yield. The length of the partial plane is schematically shown in Figure 52. In most cases of subdivided Warren joints, there will be two partial shear planes around a compression member. It is the length along the nearest adjoining fastener pattern between the gusset edge and the intersection with the other fastener pattern. Three simple rules are used to determine which partial plane is critical: 1. The one that parallels the chamfer in the member, 2. The one nearest the smaller framing angle between the compression member and other adjoining members, 3. The one with the minimum shear area if the first two criteria are equal. In general, the partial plane shear yielding is not intended to be checked for chord or vertical members because there is not an admissible shear plane that would cause out-of-plane instability of the gusset plate. Using this two-folded approach to predict buckling does provide an overall better approximation of buckling resistance. The data for the 124 models and specimens evaluated with the combined Whitmore buckling and partial plane shear yield model is presented in Tables 14 through 18, using both Lavg and Lmid and K=0.5. The two columns to the extreme right show the professional factors of the controlling resistance from either Whitmore buckling (using Lavg and Lmid) or partial plane shear yield. Predictions controlled by Whitmore buckling are shaded yellow whereas those controlled by partial plane shear yielding are shaded green. Graphically, this data is represented in Figures 53 and 54 in terms of the professional factor and -value. In both cases, the partial shear plane yield check reduces the propensity of professional factors less than 1.0, and using Lmid produces the least number of professional factors less than 1.0. All the data from Tables 14 through 18 are plotted on normal probability paper in Figure 55. The plots are broken down by those data calculated with Lmid and Lavg, and further separated considering all the data, and neglecting the data from plates thinner than 3/8 of an inch thick. The data from plates thinner than 3/8 of an inch produced the most scattered professional factors. Therefore calibrations for rating would have to consider all the data since the current inventory has plates thinner than 3/8 of an inch. However, for design calibration, the data can be parsed assuming new gusset plate designs mandate a minimum of 3/8 inch gusset thickness. Most of the data sets plot linearly on the normal probability paper indicating that the normal probability distribution fits them well. The one exception is Whitmore buckling calculated with Lmid for all the data, because the upper tail data deviates quite a bit from the best-fit line. However, in resistance factor calibration, the lower tail data controls and a best-fit line can neglect the upper tail data points.(22) The best-fit lines from the data represented on normal probability paper can be

77 used to calculate the calibration statistics. The means and coefficients of variation are shown in Table 19. While not presented in this report, the scatter in the Whitmore predictions minimized when K was approximately 0.3. However, this K-value does not have a physical meaning and K is recommended to be 0.5 for all gusset plates. The data presented also show that the best predictions of buckling strength come from using Lmid versus the current use of Lavg by the FHWA Guide. Overlap of the Whitmore section into other adjoining members was included in the analysis and there appears to be no reason to truncate it, thus making evaluations simpler. Finally, it was shown that for very compact plates, the Whitmore buckling model overpredicts the buckling resistance and a partial shear plane yielding concept has to be used in conjunction with it to accurately predict buckling resistance. Free Edge Slenderness There is a common perception that the buckling strength of a gusset-plated connection may be correlated to the slenderness of the free edge. Figure 56 shows the failure load normalized to the yield load on the Whitmore section versus the non-dimensional buckling parameter, . Two data series are shown for  calculated with Lmid and Lfree_edge. The data based on Lmid was not plotted if the partial plane shear yield criteria was controlled, hence why there appear to be more data points for the free edge. There appears to be no correlation to the buckling resistance using the free edge slenderness since the data is spread through a variety of  values, and nowhere near the column buckling curves. The data based on Lmid is highly correlated and tracks the AASHTO column buckling curve quite well. 30° 30° Whitmore Width Lm id L1 L3 Figure 48. Calculation of equivalent column length.

78 Table 9 Summary of Models with Buckling Failures Specimen Thick. (inch) Fy (ksi) Wwhitmore (inch) Lmid (inch) Lavg (inch) Pfailure (kips) avg mid Pfailure/Pn K=1.2 K=0.5 K=1.2 K=0.5 Lavg K=1.2 Lavg K=0.50 Lmid K=1.2 Lmid K=0.5 E1WV-307SS 0.2500 36.4 24.43 13.16 6.20 380 1.35 0.23 6.09 1.06 1.50 0.94 5.91 1.32 0.3125 530 0.87 0.15 3.90 0.68 1.37 1.01 4.22 1.26 0.4375 817 0.44 0.08 1.99 0.35 1.26 1.08 2.40 1.21 0.5000 974 0.34 0.06 1.52 0.26 1.26 1.12 2.06 1.22 E2WV-307LS 0.2500 48.2 27.32 18.11 10.20 398 4.84 0.84 15.27 2.65 3.33 0.86 10.49 1.82 0.3125 653 3.10 0.54 9.77 1.70 2.79 0.99 8.81 1.61 0.4375 1091 1.58 0.27 4.99 0.87 1.83 1.06 5.36 1.36 0.5000 1305 1.21 0.21 3.82 0.66 1.64 1.08 4.30 1.31 0.6250 1703 0.78 0.13 2.44 0.42 1.43 1.09 2.87 1.23 E3WV-307SL 0.2500 46.6 33.09 13.16 4.40 568 0.87 0.15 7.80 1.35 1.06 0.78 6.52 1.29 0.3125 738 0.56 0.10 4.99 0.87 0.97 0.80 4.34 1.10 0.3750 946 0.39 0.07 3.46 0.60 0.96 0.84 3.22 1.05 0.4375 1145 0.28 0.05 2.55 0.44 0.95 0.87 2.45 1.02 E4WV-490SS 0.2500 46.4 21.55 13.16 7.20 444 2.32 0.40 7.76 1.35 2.35 1.05 7.84 1.56 0.3125 597 1.49 0.26 4.97 0.86 1.77 1.06 5.39 1.37 0.4375 874 0.76 0.13 2.53 0.44 1.37 1.05 2.88 1.20 E5WV-490LS 0.2500 45.6 21.55 18.11 12.10 296 6.45 1.12 14.45 2.51 4.42 0.96 9.90 1.72 0.3125 459 4.13 0.72 9.25 1.61 3.50 1.01 7.85 1.46 0.4375 803 2.11 0.37 4.72 0.82 2.24 1.09 5.01 1.31 0.5000 975 1.61 0.28 3.61 0.63 1.94 1.11 4.07 1.29 0.6250 1276 1.03 0.18 2.31 0.40 1.60 1.12 2.73 1.23 E1W-307SS 0.2500 36.4 24.43 13.16 13.20 322 6.13 1.06 6.09 1.06 5.05 1.13 5.02 1.12 0.3125 466 3.92 0.68 3.90 0.68 3.73 1.11 3.71 1.11 0.3750 595 2.72 0.47 2.71 0.47 2.76 1.08 2.74 1.08 0.4375 723 2.00 0.35 1.99 0.35 2.13 1.07 2.12 1.07 0.5000 881 1.53 0.27 1.52 0.26 1.87 1.11 1.86 1.11

79 Table 10 Summary of Models with Buckling Failures –Continued Specimen Thick. (inch) Fy (ksi) Wwhitmore (inch) Lmid (inch) Lavg (inch) Pfailure (kips) avg mid Pfailure/Pn K=1.2 K=0.5 K=1.2 K=0.5 Lavg K=1.2 Lavg K=0.50 Lmid K=1.2 Lmid K=0.5 E2W-307LS 0.2500 48.2 27.32 18.11 18.10 326 15.25 2.65 15.27 2.65 8.59 1.49 8.60 1.49 0.3125 541 9.76 1.69 9.77 1.70 7.30 1.33 7.30 1.33 0.3750 756 6.78 1.18 6.79 1.18 5.90 1.25 5.91 1.25 0.4375 963 4.98 0.86 4.99 0.87 4.73 1.20 4.74 1.20 0.5000 1146 3.81 0.66 3.82 0.66 3.77 1.15 3.78 1.15 0.625 1504 2.44 0.42 2.44 0.42 2.53 1.09 2.54 1.09 E3W-307SL 0.2500 46.6 33.09 13.16 14.30 501 9.21 1.60 7.80 1.35 6.80 1.26 5.76 1.14 0.3125 728 5.89 1.02 4.99 0.87 5.06 1.16 4.28 1.08 0.3750 946 4.09 0.71 3.46 0.60 3.80 1.10 3.22 1.05 0.4375 1145 3.01 0.52 2.55 0.44 2.90 1.05 2.45 1.02 E4W-490SS 0.2500 46.4 21.55 13.16 13.20 400 7.81 1.36 7.76 1.35 7.11 1.41 7.07 1.40 0.3125 568 5.00 0.87 4.97 0.86 5.16 1.30 5.13 1.30 0.3750 713 3.47 0.60 3.45 0.60 3.75 1.22 3.73 1.22 0.4375 874 2.55 0.44 2.53 0.44 2.89 1.20 2.88 1.20 E5W-490LS 0.2500 45.6 21.55 18.11 16.50 253 11.99 2.08 14.45 2.51 7.03 1.22 8.47 1.47 0.3125 406 7.68 1.33 9.25 1.61 5.77 1.15 6.95 1.29 0.3750 588 5.33 0.93 6.42 1.11 4.83 1.17 5.82 1.27 0.4375 760 3.92 0.68 4.72 0.82 3.93 1.17 4.74 1.24 0.5000 937 3.00 0.52 3.61 0.63 3.25 1.18 3.91 1.24 0.6250 1248 1.92 0.33 2.31 0.40 2.25 1.17 2.67 1.20 P5U-WV-NP-01 0.2500 53 43.18 23.83 12.83 525 8.43 1.46 29.07 5.05 4.39 0.84 15.16 2.63 0.3125 780 5.39 0.94 18.61 3.23 3.34 0.80 11.53 2.00 0.3750 1050 3.75 0.65 12.92 2.24 2.60 0.80 8.98 1.55 0.4000 1170 3.29 0.57 11.36 1.97 2.39 0.81 8.25 1.45 0.4375 1350 2.75 0.48 9.49 1.65 2.11 0.82 7.27 1.34 0.5000 1635 2.11 0.37 7.27 1.26 1.71 0.83 5.90 1.21 0.6250 2145 1.35 0.23 4.65 0.81 1.31 0.83 3.96 1.05

80 Table 11 Summary of Models with Buckling Failures –Continued Specimen Thick. (inch) Fy (ksi) Wwhitmore (inch) Lmid (inch) Lavg (inch) Pfailure (kips) avg mid Pfailure/Pn K=1.2 K=0.5 K=1.2 K=0.5 Lavg K=1.2 Lavg K=0.50 Lmid K=1.2 Lmid K=0.5 P6U-WV-NP-02 0.2500 53 46.18 18.54 7.50 520 2.88 0.50 17.60 3.06 1.39 0.52 8.49 1.47 0.3125 791 1.84 0.32 11.26 1.96 1.11 0.59 6.62 1.17 0.3750 1107 1.28 0.22 7.82 1.36 1.03 0.66 5.36 1.06 0.4375 1446 0.94 0.16 5.75 1.00 1.00 0.72 4.41 1.02 0.5000 1808 0.72 0.12 4.40 0.76 1.00 0.78 3.69 1.01 0.6000 2396 0.50 0.09 3.06 0.53 1.00 0.85 2.83 1.02 0.6250 2531 0.46 0.08 2.82 0.49 1.00 0.86 2.65 1.01 P8U-WV-INF-02 0.5000 53 49.64 25.27 11.80 1974 1.78 0.31 8.17 1.42 1.57 0.85 6.97 1.35 P13U-W-NP-01 0.2500 53 46.64 19.56 8.60 644 3.79 0.66 19.59 3.40 2.24 0.68 11.59 2.01 0.3125 957 2.42 0.42 12.54 2.18 1.71 0.74 8.82 1.53 0.3750 1271 1.68 0.29 8.71 1.51 1.38 0.77 6.78 1.28 0.4000 1403 1.48 0.26 7.65 1.33 1.31 0.79 6.17 1.23 0.4375 1584 1.24 0.21 6.40 1.11 1.22 0.80 5.32 1.16 0.5000 1914 0.95 0.16 4.90 0.85 1.15 0.83 4.31 1.10 0.6250 2525 0.61 0.11 3.13 0.54 1.05 0.85 2.91 1.02 P14U-W-INF-01 0.2500 53 43.64 11.82 4.10 546 0.86 0.15 7.15 1.24 0.68 0.50 3.84 0.79 0.3125 812 0.55 0.10 4.58 0.79 0.71 0.58 2.92 0.78 0.3750 1106 0.38 0.07 3.18 0.55 0.75 0.66 2.30 0.80 0.4375 1386 0.28 0.05 2.34 0.41 0.77 0.70 1.82 0.81 0.5000 1652 0.22 0.04 1.79 0.31 0.78 0.73 1.50 0.81 0.6250 2156 0.14 0.02 1.14 0.20 0.79 0.75 1.20 0.81 P5C-WV-NP-01 0.2500 53 49.70 8.57 2.86 780 0.42 0.07 3.76 0.65 0.70 0.61 2.53 0.78 0.3125 1050 0.27 0.05 2.41 0.42 0.71 0.65 1.74 0.76 0.3750 1305 0.19 0.03 1.67 0.29 0.71 0.67 1.32 0.75 0.4000 1410 0.16 0.03 1.47 0.26 0.72 0.68 1.23 0.74 0.4375 1590 0.14 0.02 1.23 0.21 0.73 0.70 1.15 0.75 0.5000 1890 0.10 0.02 0.94 0.16 0.75 0.72 1.06 0.77

81 Table 12 Summary of Models with Buckling Failures –Continued Specimen Thick. (inch) Fy (ksi) Wwhitmore (inch) Lmid (inch) Lavg (inch) Pfailure (kips) avg mid Pfailure/Pn K=1.2 K=0.5 K=1.2 K=0.5 Lavg K=1.2 Lavg K=0.50 Lmid K=1.2 Lmid K=0.5 P6C-WV-NP-02 0.2500 53 60.03 7.82 2.60 814 0.35 0.06 3.13 0.54 0.59 0.52 1.82 0.64 0.3125 1153 0.22 0.04 2.00 0.35 0.64 0.59 1.33 0.67 0.3750 1514 0.15 0.03 1.39 0.24 0.68 0.64 1.13 0.70 0.4375 1853 0.11 0.02 1.02 0.18 0.70 0.67 1.02 0.72 P7C-WV-INF-01 0.2500 53 57.00 13.7 4.60 1217 1.08 0.19 9.61 1.67 1.26 0.87 8.80 1.61 0.3125 1647 0.69 0.12 6.15 1.07 1.16 0.92 6.10 1.36 0.3750 2112 0.48 0.08 4.27 0.74 1.14 0.97 4.52 1.27 P8C-WV-INF-02 0.2500 53 50.60 8.5 2.80 882 0.40 0.07 3.70 0.64 0.78 0.68 2.76 0.86 P9C-P-NP-01 0.2000 53 26.32 8.86 3.00 353 0.72 0.12 6.28 1.09 0.85 0.67 4.52 1.00 P13C-W-NP-01 0.2500 53 46.64 11.13 3.70 858 0.70 0.12 6.34 1.10 0.93 0.73 5.00 1.10 0.3125 1172 0.45 0.08 4.06 0.70 0.91 0.78 3.50 1.02 0.3750 1502 0.31 0.05 2.82 0.49 0.92 0.83 2.59 0.99 0.4000 1634 0.27 0.05 2.48 0.43 0.93 0.84 2.33 0.99 0.4375 1832 0.23 0.04 2.07 0.36 0.93 0.86 2.00 0.98 0.5000 2112 0.18 0.03 1.59 0.28 0.92 0.87 1.65 0.96 0.6250 2640 0.11 0.02 1.01 0.18 0.90 0.86 1.30 0.92 P14C-W-INF-01 0.2500 53 47.11 8.14 2.70 644 0.37 0.06 3.39 0.59 0.60 0.53 1.99 0.66 0.3125 910 0.24 0.04 2.17 0.38 0.64 0.59 1.44 0.68 0.3750 1190 0.17 0.03 1.51 0.26 0.68 0.64 1.19 0.71 0.4375 1442 0.12 0.02 1.11 0.19 0.69 0.67 1.05 0.72 0.5000 1708 0.09 0.02 0.85 0.15 0.71 0.69 0.97 0.73 P19C-MTB 0.6000 53 64.50 3.91 1.30 3737 0.02 0.00 0.14 0.02 0.92 0.91 0.96 0.92 P20C-MTB 0.6000 53 60.03 7.58 2.50 2843 0.06 0.01 0.51 0.09 0.76 0.75 0.92 0.77 P1C-MTB 0.3500 53 26.32 9.01 3.00 831 0.24 0.04 2.12 0.37 0.94 0.87 2.05 0.99 P5C-HS1 0.4000 108 49.70 8.57 2.86 2535 0.33 0.06 2.99 0.52 0.68 0.60 2.01 0.73 P5C-HS2 0.2000 108 49.70 8.57 2.86 960 1.33 0.23 11.97 2.08 0.78 0.49 6.08 1.06 P7C-HS2 0.3500 108 59.20 0.87 4.60 3544 1.13 0.20 0.04 0.01 1.26 0.86 0.81 0.79 P8C-HS2 0.2500 108 49.28 8.5 2.80 1617 0.82 0.14 7.54 1.31 0.85 0.64 5.20 1.05

82 Table 13 Summary of Models and Specimens with Buckling Failures Specimen Thick. (inch) Fy (ksi) Wwhitmore (inch) Lmid (inch) Lavg (inch) Pfailure (kips) avg mid Pfailure/Pn K=1.2 K=0.5 K=1.2 K=0.5 Lavg K=1.2 Lavg K=0.65 Lmid K=1.2 Lmid K=0.5 P3C-WV-P01 0.2500 53 87.08 7.57 7.57 2250 2.93 0.51 2.93 0.51 3.25 1.20 3.25 1.20 0.3125 53 87.08 7.57 7.57 2900 1.88 0.33 1.88 0.33 2.19 1.15 2.19 1.15 0.3750 53 87.08 7.57 7.57 3550 1.30 0.23 1.30 0.23 1.76 1.13 1.76 1.13 0.4375 53 87.08 7.57 7.57 4250 0.96 0.17 0.96 0.17 1.57 1.13 1.57 1.13 0.5000 53 87.08 7.57 7.57 4900 0.73 0.13 0.73 0.13 1.44 1.12 1.44 1.12 0.6250 53 87.08 7.57 7.57 6350 0.47 0.08 0.47 0.08 1.34 1.14 1.34 1.14 GP307SS3 0.3750 36.4 24.43 13.16 6.20 716 0.60 0.10 2.71 0.47 1.38 1.12 3.30 1.31 GP490SS3 0.3750 46.4 21.55 13.16 7.20 728 1.03 0.18 3.45 0.60 1.49 1.05 3.81 1.25 GP490LS3 0.3750 45.6 21.55 18.11 12.10 527 2.87 0.50 6.42 1.11 2.33 0.88 5.22 1.14 GP307LS3 0.3750 48.2 27.32 18.11 10.20 796 2.15 0.37 6.79 1.18 1.97 0.94 6.22 1.32 OSU 1 0.2500 47.0 34.78 26.7 15.53 290 10.95 1.90 32.38 5.62 4.41 0.78 13.05 2.27 OSU 2 0.2500 45.1 34.78 26.7 15.53 325 10.51 1.82 31.07 5.39 4.95 0.88 14.62 2.54 OSU 3 0.3750 45.9 34.78 26.7 15.53 545 4.76 0.83 14.06 2.44 2.46 0.64 7.27 1.26 OSU 4 0.2500 45.1 34.78 26.7 15.53 261 10.51 1.82 31.06 5.39 3.97 0.71 11.74 2.04 OSU 5 0.3750 46.1 34.78 26.7 15.53 579 4.78 0.83 14.12 2.45 2.61 0.68 7.72 1.34 I35W U10 0.5000 51.0 60.87 15.7 5.23 2388 0.34 0.06 3.04 0.53 0.88 0.79 2.65 0.96

83 (a) (b) (c) (d) Figure 49. Professional factor data of buckling failures evaluated with: (a) K=1.2 and Lavg. (b) K=0.50 and Lavg. (c) K=1.2 and Lmid. (d) K=0.50 and Lmid. 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 P f a i l u r e / P n avg Analytical Experimental I-35W U10 0 1 2 3 4 5 6 7 8 9 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P f a i l u r e / P n avg Analytical Experimental I-35W U10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 5 10 15 20 25 30 35 P f a i l u r e / P n mid Analytical Experimental I-35W U10 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0 1 2 3 4 5 6 P f a i l u r e / P n mid Analytical Experimental I-35W U10

84 Figure 50. Professional factor breakdown between chamfered and unchamfered models using K=0.5 and Lmid. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0 1 2 3 4 5 6 P fa ilu re /P n mid Analytical Unchamfered Analytical Chamfered Experimental I-35W U10

85 Figure 51. Difference in buckling with chamfered and unchamfered member. (Top) Schematics of each connection. (Bottom) Von Mises stresses at failure (stresses exceeding yield are shown in grey/pink).

86  C on tro lli ng P ar tia l P la ne  Other Partial Plane Other Partial Plane 45° 45° C on tro llin g P ar tia l P la ne O th er P ar tia l P la ne 45° 45° Controlling Partial Plane Figure 52. Schematic of various partial shear plane. (Top-Left) Controlling plane dictated by framing  being less than . (Top-Right) Controlling plane is dictated by one with shorter length because first two criteria are equal. (Bottom) Controlling plane is that paralleling the member chamfer.

87 Table 14 Summary of Two-Folded Buckling Evaluation Criteria Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) Lavg (inch) mid (K=0.5) avg (K=0.5) PFailure (kips) Pwhitmore using Lavg (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lavg a ,b Controlling Ratio using Lmid a, b E1WV-307SS 0.250 36.4 24.43 23.97 13.16 6.20 1.06 0.23 380 403 287 358 1.06 1.32 0.313 0.68 0.15 530 522 420 447 1.19 1.26 0.438 0.35 0.08 817 754 674 626 1.30 1.30 0.500 0.26 0.06 974 868 797 716 1.36 1.36 E2WV-307LS 0.250 48.2 27.32 27.68 18.11 10.20 2.65 0.84 398 464 219 547 0.86 1.82 0.313 1.70 0.54 653 658 407 684 0.99 1.61 0.438 0.87 0.27 1091 1028 804 958 1.14 1.36 0.500 0.66 0.21 1305 1207 1000 1094 1.19 1.31 0.625 0.42 0.13 1703 1557 1380 1368 1.25 1.25 E3WV-307SL 0.250 46.6 33.09 27.68 13.16 4.40 1.35 0.15 568 724 439 529 1.07 1.29 0.313 0.87 0.10 738 926 673 661 1.12 1.12 0.375 0.60 0.07 946 1125 901 794 1.19 1.19 0.438 0.44 0.05 1145 1322 1123 926 1.24 1.24 E4WV-490SS 0.250 46.4 21.55 22.18 13.16 7.20 1.35 0.40 444 423 286 422 1.05 1.56 0.313 0.86 0.26 597 561 437 528 1.13 1.37 0.438 0.44 0.13 874 828 729 739 1.18 1.20 E5WV-490LS 0.250 45.6 21.55 24.18 18.11 12.10 2.51 1.12 296 309 172 452 0.96 1.72 0.313 1.61 0.72 459 456 315 565 1.01 1.46 0.438 0.82 0.37 803 739 612 791 1.09 1.31 0.500 0.63 0.28 975 875 757 904 1.11 1.29 0.625 0.40 0.18 1276 1140 1040 1131 1.13 1.23 E1W-307SS 0.250 36.4 24.43 26.15 13.16 13.20 1.06 1.06 322 286 287 390 1.13 1.12 0.313 0.68 0.68 466 419 420 488 1.11 1.11 0.375 0.47 0.47 595 548 549 586 1.08 1.08 0.438 0.35 0.35 723 674 674 683 1.07 1.07 0.500 0.26 0.27 881 796 797 781 1.13 1.13 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling.

88 Table 15 Summary of Two-Folded Buckling Evaluation Criteria (Continued) Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) Lavg (inch) mid avg PFailure (kips) Pwhitmore using Lavg (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lavg a ,b Controlling Ratio using Lmid a, b E2W-307LS 0.250 48.2 27.32 31.5 18.11 18.10 2.65 2.65 326 219 219 623 1.49 1.49 0.313 1.70 1.69 541 407 407 778 1.33 1.33 0.375 1.18 1.18 756 606 605 934 1.25 1.25 0.438 0.87 0.86 963 804 804 1090 1.20 1.20 0.500 0.66 0.66 1146 1000 1000 1245 1.15 1.15 0.625 0.42 0.42 1504 1380 1380 1557 1.09 1.09 E3W-307SL 0.250 46.6 33.09 31.5 13.16 14.30 1.35 1.60 501 397 439 602 1.26 1.14 0.313 0.87 1.02 728 630 673 753 1.16 1.08 0.375 0.60 0.71 946 861 901 903 1.10 1.05 0.438 0.44 0.52 1145 1086 1123 1054 1.09 1.09 E4W-490SS 0.250 46.4 21.55 23.98 13.16 13.20 1.35 1.36 400 285 286 456 1.41 1.40 0.313 0.86 0.87 568 436 437 570 1.30 1.30 0.375 0.60 0.60 713 584 585 684 1.22 1.22 0.438 0.44 0.44 874 728 729 799 1.20 1.20 E5W-490LS 0.250 45.6 21.55 27.8 18.11 16.50 2.51 2.08 253 207 172 520 1.22 1.47 0.313 1.61 1.33 406 353 315 650 1.15 1.29 0.375 1.11 0.93 588 502 464 780 1.17 1.27 0.438 0.82 0.68 760 648 612 910 1.17 1.24 0.500 0.63 0.52 937 791 757 1040 1.18 1.24 0.625 0.40 0.33 1248 1069 1040 1300 1.17 1.20 P5U-WV-NP-01 0.250 53 43.18 46.17 23.83 12.83 5.05 1.46 525 623 199 793 0.84 2.63 0.313 3.23 0.94 780 969 390 992 0.80 2.00 0.375 2.24 0.65 1050 1310 676 1190 0.88 1.55 0.400 1.97 0.57 1170 1444 807 1269 0.92 1.45 0.438 1.65 0.48 1350 1642 1010 1388 0.97 1.34 0.500 1.26 0.37 1635 1966 1355 1587 1.03 1.21 0.625 0.81 0.23 2145 2595 2045 1984 1.08 1.08 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling.

89 Table 16 Summary of Two-Folded Buckling Evaluation Criteria (Continued) Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) Lavg (inch) mid avg PFailure (kips) Pwhitmore using Lavg (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lavg a ,b Controlling Ratio using Lmid a, b P6U-WV-NP-02 0.250 53 46.18 41.07 18.54 7.50 3.06 0.50 520 994 352 893 0.58 1.47 0.313 1.96 0.32 791 1339 679 1116 0.71 1.17 0.375 1.36 0.22 1107 1674 1044 1339 0.83 1.06 0.438 1.00 0.16 1446 2001 1415 1562 0.93 1.02 0.500 0.76 0.12 1808 2324 1782 1785 1.01 1.01 0.600 0.53 0.09 2396 2833 2356 2143 1.12 1.12 0.625 0.49 0.08 2531 2959 2497 2232 1.13 1.13 P8U-WV-INF-02 0.500 53 49.64 57.26 25.27 11.80 1.42 0.31 1974 2314 1459 2059 0.96 1.35 P13U-W-NP-01 0.250 53 46.64 44.67 19.56 8.60 3.40 0.66 644 941 320 809 0.80 2.01 0.313 2.18 0.42 957 1297 625 1011 0.95 1.53 0.375 1.51 0.29 1271 1642 989 1213 1.05 1.28 0.400 1.33 0.26 1403 1777 1139 1294 1.08 1.23 0.438 1.11 0.21 1584 1978 1364 1415 1.12 1.16 0.500 0.85 0.16 1914 2309 1736 1617 1.18 1.18 0.625 0.54 0.11 2525 2958 2465 2022 1.25 1.25 P14U-W-INF-01 0.250 53 43.64 33.10 11.82 4.10 1.24 0.15 546 1087 690 799 0.68 0.79 0.313 0.79 0.10 812 1389 1039 999 0.81 0.81 0.375 0.55 0.07 1106 1688 1379 1199 0.92 0.92 0.438 0.41 0.05 1386 1983 1710 1399 0.99 0.99 0.500 0.31 0.04 1652 2277 2033 1599 1.03 1.03 0.625 0.20 0.02 2156 2863 2662 1998 1.08 1.08 P5C-WV-NP-01 0.250 53 49.70 40.24 8.57 2.86 0.65 0.07 780 1278 1004 692 1.13 1.13 0.313 0.42 0.05 1050 1615 1384 864 1.21 1.21 0.375 0.29 0.03 1305 1949 1751 1037 1.26 1.26 0.400 0.26 0.03 1410 2083 1895 1106 1.27 1.27 0.438 0.21 0.02 1590 2282 2109 1210 1.31 1.31 0.500 0.16 0.02 1890 2614 2461 1383 1.37 1.37 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling.

90 Table 17 Summary of Two-Folded Buckling Evaluation Criteria (Continued) Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) Lavg (inch) mid avg PFailure (kips) Pwhitmore using Lavg (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lavg a ,b Controlling Ratio using Lmid a, b P6C-WV-NP-02 0.250 53 60.03 46.53 7.82 2.60 0.54 0.06 814 1552 1269 1011 0.80 0.80 0.313 0.35 0.04 1153 1957 1721 1264 0.91 0.91 0.375 0.24 0.03 1514 2360 2158 1517 1.00 1.00 0.438 0.18 0.02 1853 2761 2586 1770 1.05 1.05 P7C-WV-INF-01 0.250 53 57.00 70.98 13.70 4.60 1.67 0.19 1217 1397 755 1220 1.00 1.61 0.313 1.07 0.12 1647 1796 1212 1525 1.08 1.36 0.375 0.74 0.08 2112 2188 1665 1830 1.15 1.27 P8C-WV-INF-02 0.250 53 50.60 48.53 8.50 2.80 0.64 0.07 882 1303 1027 873 1.01 1.01 P9C-P-NP-01 0.200 53 26.32 25.00 8.86 3.00 1.09 0.12 353 530 355 435 0.81 1.00 P13C-W-NP-01 0.250 53 46.64 43.33 11.13 3.70 1.10 0.12 858 1175 782 784 1.09 1.10 0.313 0.70 0.08 1172 1496 1153 980 1.19 1.19 0.375 0.49 0.05 1502 1813 1513 1177 1.28 1.28 0.400 0.43 0.05 1634 1939 1654 1255 1.30 1.30 0.438 0.36 0.04 1832 2128 1863 1373 1.33 1.33 0.500 0.28 0.03 2112 2441 2205 1569 1.35 1.35 0.625 0.18 0.02 2640 3065 2872 1961 1.35 1.35 P14C-W-INF-01 0.250 53 47.11 33.06 8.14 2.70 0.59 0.06 644 1215 977 798 0.81 0.81 0.313 0.38 0.04 910 1534 1334 998 0.91 0.91 0.375 0.26 0.03 1190 1850 1679 1197 0.99 0.99 0.438 0.19 0.02 1442 2165 2017 1397 1.03 1.03 0.500 0.15 0.02 1708 2480 2348 1597 1.07 1.07 P19C-MTB 0.600 53 64.50 77.8 3.91 1.30 0.02 0.00 3737 4098 4062 3209 1.16 1.16 P20C-MTB 0.600 53 60.03 47.13 7.58 2.50 0.09 0.01 2843 3803 3680 2459 1.16 1.16 P1C-MTB 0.350 53 26.32 25.5 9.01 3.00 0.37 0.04 831 960 838 776 1.07 1.07 P5C-HS1 0.400 108 49.70 40.24 8.57 2.86 0.52 0.06 2535 4192 3460 2255 1.12 1.12 P5C-HS2 0.200 2.08 0.23 960 1950 905 1127 0.85 1.06 P7C-HS2 0.350 108 59.20 70.98 0.87 4.60 0.01 0.20 3544 4126 4463 3480 1.02 1.02 P8C-HS2 0.250 108 49.28 48.53 8.50 2.80 1.31 0.14 1617 2509 1545 1778 0.91 1.05 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling.

91 Table 18 Summary of Two-Folded Buckling Evaluation Criteria (Continued) Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) Lavg (inch) mid avg PFailure (kips) Pwhitmore using Lavg (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lavg a ,b Controlling Ratio using Lmid a, b P3C-WV-P01 0.2500 53 87.08 69.08 7.57 7.57 0.51 0.51 2250 1867 1867 2124 1.20 1.20 0.3125 0.33 0.33 2900 2519 2519 2654 1.15 1.15 0.3750 0.23 0.23 3550 3151 3151 3185 1.13 1.13 0.4375 0.17 0.17 4250 3769 3769 3716 1.14 1.14 0.5000 0.13 0.13 4900 4377 4377 4247 1.15 1.15 0.6250 0.08 0.08 6350 5577 5577 5309 1.20 1.20 E1WV-307SS c 0.375 36.4 24.43 23.97 13.16 6.20 0.47 0.10 716 639 549 537 1.33 1.33 E4WV-490SS c 0.375 46.4 21.55 22.18 13.16 7.20 0.60 0.18 728 696 585 633 1.15 1.25 E5WV-490LS c 0.375 45.6 21.55 24.18 18.11 12.10 1.11 0.50 527 599 464 678 0.88 1.14 E2WV-307LS c 0.375 48.2 27.32 27.68 18.11 10.20 1.18 0.37 796 846 605 821 0.97 1.32 OSU 1 d 0.250 47.0 34.78 41.62 26.70 15.53 5.62 1.90 290 371 128 706 0.78 2.27 OSU 2 d 0.250 45.1 5.39 1.82 325 368 128 677 0.88 2.54 OSU 3 d 0.375 45.9 2.44 0.83 545 850 432 1034 0.64 1.26 OSU 4 d 0.250 45.1 5.39 1.82 261 368 128 677 0.71 2.04 OSU 5 d 0.375 46.1 2.45 0.83 579 853 432 1039 0.68 1.34 I35W U10 0.500 51.0 60.87 46.75 15.70 5.23 0.53 0.06 2388 3030 2494 1720 1.39 1.39 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling. c – Denotes an experimental specimen. d – Oregon State University specimen reported in Reference 23.

92 Figure 53. Plot of professional factors using two-folded Whitmore and partial plane shear approach to predict buckling with Lmid. Figure 54. Plot of professional factors using two-folded Whitmore and partial plane shear approach to predict buckling with Lavg. 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0 1 2 3 4 5 6 P fa ilu re /P n mid Whitmore Analytical Partial Shear Analytical Whitmore Experimental Partial Shear Experimental 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P fa ilu re /P n avg Whitmore Analytical Partial Shear Analytical Whitmore Experimental Partial Shear Experimental

93 (a) (b) (c) (d) Figure 55. Failures using two-folded approach plotted on normal probability paper. (a) Using Lavg and all data points. (b) Using Lavg and neglecting plates thinner than 3/8 inches. (c) Using Lmid and all data points. (d) Using Lmid and neglecting plates thinner than 3/8 inches. y = 4.6761x - 5.0673 y = 5.6331x - 6.0777 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 S t a n d a r d N o r m a l V a r i a b l e Pfailure/Pn Whitmore Partial Shear y = 4.4672x - 4.8398 y = 6.879x - 7.8263 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 S t a n d a r d N o r m a l V a r i a b l e Pfailure/Pn Whitmore Partial Shear y = 5.857x - 7.4268 y = 6.1162x - 6.9683 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 S t a n d a r d N o r m a l V a r i a b l e Pfailure/Pn Whitmore Partial Shear Whitmore (neglected points) y = 7.9176x - 9.7051 y = 7.3163x - 8.6574 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 S t a n d a r d N o r m a l V a r i a b l e Pfailure/Pn Whitmore Partial Shear

94 Table 19 Calibration Statistics for Gusset Plate Buckling Using All Data Neglecting Plates <3/8” Thick Whitmore Partial Shear Whitmore Partial Shear Lavg Average 1.084 1.079 1.083 1.138 COV 0.197 0.165 0.207 0.128 Lmid Average 1.268 1.139 1.226 1.183 COV 0.135 0.144 0.103 0.116 Figure 56. Buckling resistance comparison between Lmid and Lfree. Chord Splice In Chapter 1 it was noted that there were anomalies that arose due to checking compression or tension chord splices with the Whitmore approach as demonstrated in the FHWA Guide. In particular, an assumption of the load sharing between the gusset plate and alternate chord splice plates had to be made, and dividing the load based on cross-sectional area was deemed appropriate. However, the area of the gusset plate was based on the Whitmore section, which is questionable. In this project, only analytical models were observed to fail in the chord splice. The resistance of the chord splice was treated as if it were a composite beam in bending. That is, the gusset plate and associated splice plates were assumed composite with each other to resist the axial chord 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 5 10 15 20 25 30 35 40 P fa ilu re /P y (12Fy/E)(0.5/t)2(Lfree or Lmid)2 Lfree Lmid AASHTO Column Curve Lfree Lmid

95 splice load, along with the bending due to the eccentricity of the loads from the centroid of the section. Failure was assumed as the first yield in the composite section for gross sections and first reaching the tensile strength for net sections. For tension chord splices both gross and net sections should be considered with stresses of Fy and Fu applied to the appropriate gross and net sections. For compression chord splices, a critical buckling stress should be used; however, if KL/r of the gusset plate is less than 25 (which is usually the case), the full yield stress can be assumed. In this case K=0.5 and L would be the center-to-center distance between fastener lines at the ends of the adjoining chords. Therefore, three resistance equations exist, one for compression chord splices, and two for tension chord splices.      gpg gg cr AeS AS FP (Eq. 8)      gpg gg y AeS AS FP (Eq. 9)      npn nn u AeS AS FP (Eq. 10) where Ag is the gross area of all the plates, An is the net area of all the plates, Sg is the gross area section modulus of all the plates, Sn is the net area section modulus of all the plates, and ep is the eccentricity from the resultant load in the splice and the centroid of An or Ag. In total there were 33 analytical models that were identified to fail in the chord splice. The resistance of each was calculated according to either Eq. 8 or 9 depending on the loading within the chord splice. The net section resistance was not checked for tension chord splices because the analytical models did not have the fidelity to capture net section failure. The failure load from the model is divided by the calculated resistance and reported in Table 20 as the professional factor for each of the failures. The same data is plotted on normal probability paper and shown in Figure 57. Both data sets plot linearly indicating that the normal probability distribution is appropriate. The best-fit line through each data set can be used to calculate the statistics for use in the resistance factor calibration. Considering all plate thicknesses, the mean would be 1.224 and the COV is 0.164. Neglecting the failures of plates thinner than 3/8 of an inch, the mean is 1.284 and the COV is 0.163. The approach of calculating resistance via a composite section analysis differs from the way shown in Appendix I. In Appendix I, a different approach published by Kulicki and Reiner was

96 assessed.(24) The professional factors do not vary too much between the methods; however the composite section method presented herein was primarily chosen because it was easier to describe and codify. Table 20 Chord Splice Professional Factor Data Model Plate Thickness (inch) RFEA/Rn P1-C-CCS-WV-M 0.2500 1.01 0.3125 1.08 0.3750 1.34 0.4000 1.32 0.4375 1.39 0.5000 1.43 0.6250 1.44 P2-C-TCS-WV-M 0.2500 1.18 0.3125 1.24 0.3750 1.30 0.4000 1.28 0.4375 1.26 0.5000 1.31 0.6250 1.39 P4-C-WV-P 0.8000 1.58 P10-C-P-NP 0.2000 0.95 0.2500 1.07 0.3125 1.18 0.3750 1.26 0.4375 1.30 0.5000 1.35 P11-C-W-M 0.2500 0.90 0.3125 1.26 0.3750 1.35 0.4500 1.40 0.5000 1.45 P13-C-W-NP 0.4000 a 0.84 0.4375 a 0.91 0.5000 a 1.01 0.6250 a 1.16 P19-C-CCS-NEG 0.6000 1.18 P20-C-CCS-NEG 0.6000 1.06

97 Figure 57. Chord splice professional factors plotted on normal probability paper. Tension Members One of the shortfalls of both the experimental and parametric studies was the lack of tension failures. Perhaps this shows that gusset plates are primarily susceptible to shear and buckling but this cannot be definitively proven through the results attained in this project. The overarching reason this occurred is that the finite element modeling methodology made the models computationally efficient by not explicitly modeling fastener holes. This means net section failure modes could not be captured in the modeling. The current FHWA Guide recommends three checks for tension members: Whitmore yield and fracture checks, plus a block shear check. Block Shear This research specifically did not address the block shear limit-state because there is an abundant amount of experimental data available in the available literature. The best summary of the available block shear data can be found in Huns, Grondin, and Driver.(25) This paper summarizes 133 experiments reported from eight different sources. The paper also provides the professional factor and COV for the test data using the existing AASHTO block shear equation (Eqn. 6.13.4- 1) to be 1.18 and 0.060 respectively. This data can directly be used to calibrate a block shear - factor in Chapter 4. y = 4.9618x - 6.0751 y = 4.7773x - 6.1345 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 0 0.5 1 1.5 2 St an da rd N or m al V ar ia bl e RFEA/Rn All Data Thicknesses >3/8"

98 Whitmore Yield and Fracture Only three parametric models (P16C, P17C. and P18C) had just tension diagonal and/or vertical members that demonstrated pure tensile failure modes. All other models or specimens had tension members in conjunction with compression members that failed in buckling or shear. Therefore, no data are available to provide a statistically significant sample to derive professional factors for tensile failure modes. Coupling of Tension Modes with Other Limit-States To assess the relevance of these failure models, they were checked against all the tension members in connections that were identified to have failed in other modes (shear yielding, buckling, chord splice, etc.). This did not include the checks for parametric models P16C, P17C, and P18C. Out of 155 connections that were identified to fail in shear, buckling, or in the chord splice (not including models with corrosion or edge stiffening), only 15 would have been controlled by Whitmore yield or block shear. This is demonstrated in Table 21, which outlines the specific models and specimens that had professional factors in excess of 1.00 for Whitmore yield, Whitmore fracture, and block shear indicating that the limit-state had been exceeded. The right-handed column of this table shows the professional factors for the observed failure mode without considering tensile failure modes. Cells that are highlighted grey represent the most conservative professional factor that would control the design of the joints. In only three connection geometries would the Whitmore yield or block shear criterion control. While this does not provide statistical data to calibrate the limit-states, it does show that an extra level of conservatism is added into the calibrated limit-states of buckling and shear yielding considering that tensile modes must be checked also. Other Tensile Failure Modes The three tension checks on parametric models P16C, P17C, and P18C are shown in Table 22, which are the only connections that have pure tension failure. Unfortunately, the professional factor data shown in Table 22 do not support the three tension failure models well. Only the block shear check on the tension diagonal of P18C has a conservative professional factor. The other two connections failed from excessive yielding but all three tension limit-state models produce unconservative professional factors. The yielding patterns of each of these connections can be found in Appendix I and each show that failure planes may go beyond the three traditional tension limit-state checks. Specifically, it appears that there is a coupling of closely spaced tension diagonals wherein a block shear type failure mechanism can develop on a plane bounded by multiple members. These alternate failure patterns are shown in Figure 58, some of which have been suggested by Astaneh-Asl.(26) Since this research did not include the effects of net sections, it is beyond the scope of this research to draw any conclusions regarding these coupled mechanism failures. This is a needed area of research.

99 Table 21 Tension Failure Predictions of Connections Identified to Fail in Alternative Mode Model or Specimen Plate Thickness (inch) Member Type Professional Factors (Tfailure/Tn) Whitmore Yield Whitmore Fracture Block Shear Other Failure Modes E2W-307LS3 0.5000 Chord a a 1.01 1.306 (WB) 0.6250 Chord 1.06 1.245 (PPSY) E5WV-490LS 0.3750 Diagonal 0.97 0.87 1.03 1.136 (WB) P2C 0.2500 Chord a a 1.52 1.229 (CS) 0.3125 Chord 1.43 1.295 (CS) 0.3750 Chord 1.60 1.356 (CS) 0.4000 Chord 1.52 1.339 (CS) 0.4375 Chord 1.52 1.324 (CS) 0.5000 Chord 1.45 1.371 (CS) 0.6250 Chord 1.29 1.458 (CS) P5C-WV-NP-01 0.5000 Chord a a 1.00 1.367 (PPSY) 0.6250 Chord 1.15 0.94 (FPSY) P8C-WV-INF-02 0.3125 Diagonal 0.69 0.48 1.05 1.04 (FPSY) 0.3750 Diagonal 0.72 0.49 1.09 1.08 (FPSY) 0.4375 Diagonal 0.72 0.49 1.09 1.08 (FPSY) 0.5000 Diagonal 0.72 0.50 1.10 1.09 (FPSY) 0.6250 Diagonal 0.72 0.49 1.09 1.08 (FPSY) P8C-HS1 0.5000 Diagonal 0.70 0.71 1.30 0.85 (FPSY) 0.2500 Diagonal 0.60 0.61 1.12 1.047 (WB) 307SL4 b 0.5000 Diagonal 1.05 0.64 0.89 1.19 (FPSY) 490SS3-1 b 0.3750 Diagonal 1.07 0.86 1.02 1.00 (FPSY) a – Calculation is for a chord member which Whitmore analysis will no longer apply to based on chord splice check. b – Denotes an experimental specimen. FPSY=Full Plane Shear Yield WB=Whitmore Buckling PPSY=Partial Plane Shear Yield CS=Chord Splice

100 Table 22 Tension Checks for P16C, P17C, and P18C Model or Specimen Plate Thickness (inch) Member Type Professional Factors (Tfailure/Tn) Whitmore Yield Whitmore Fracture Block Shear P16C-CJ-02 0.85 Diagonal 0.57 0.39 0.78 P17C-POS 0.60 Diagonal 0.84 0.61 0.98 Vertical 0.44 0.31 0.54 P18C-POS 0.60 Diagonal 0.77 0.53 1.31 Vertical 0.39 0.28 0.55 Figure 58. Alternate fracture patterns for connections P16C, P17C, and P18C. Multi-Layered Plates Only two analytical geometries and one experimental geometry were tested with multi-layered, or shingle plates. This does not provide enough data to make any firm conclusions regarding how multi-layered plates fail; however, their treatment in the previously described resistance equations will be assessed. The only experimental connection tested with a shingle plate was GP307SS3-4. This connection tested a shingle plate combined with simulated section loss and was described in Chapter 2. The connection failed in shear at an internal shear load of 1213 kips. The relevant connection properties for shear calculations are presented in Table 23. The individual shear resistances for each plate are calculated individually (using =1.00) and added together to determine the total nominal resistance. This assumption neglects any composite behavior between the plate layers and should be a conservative assumption. In fact, the professional factor for shear in the connection is 0.98 indicating that the calculation procedure fits within the scatter band of all the other full plane shear yield data, and it is appropriate to consider the total shear resistance to be the total of the individual shear resistances.

101 The analytical base geometries of P3C and P5C were each analyzed with three different combinations of gusset and shingle plate thicknesses. A summary of these six connections is presented in Table 24, all of which failed in buckling. The compression resistance is calculated using the two-folded approach described in the prior section. The extreme right-hand column presents the professional factor of these six shingle plated connections using the two-folded compression resistance approach. In the calculations, the gusset and shingle plates are considered to be uncoupled and the strength of each is added together for the total resistance. In all six cases the professional factors conservatively vary between 1.09 and 1.26 indicating that the methodology is conservative. Table 23 Shear Calculations of Specimen GP307SS3-4 Specimen Plate Thickness (inch) Yield Strength (ksi) Width of Plate (inch) Ag (inch2) VFailure (kips) Vnominal d (kips) Vfailure/Vnominal GP307SS3-4 South Gusset 0.375 38.0 59.0 22.13 1213 488 0.98 North Gusset 0.367 a 38.0 59.0 12.97 c 286 North Shingle 0.375 46.3 46.0 b 17.25 463 a – The real thickness of the plate was reported because an ultrasonic thickness meter had to be used to determine the remaining section thickness. This was not done for plates with no simulated section loss. b – Width of shingle plate was taken at middle of simulate corrosion section. c – The gross area was reduced by the simulated section loss of (48 inch)*(0.185 inch)=8.880 inch2. d – =1.00 was used in the shear resistance calculation.

102 Table 24 Buckling Calculations of Models with Multi-Layered Gusset Plates Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Lmid (inch) mid PFailure (kips) Pwhitmore using Lmid (kips) Ppartial_sh ear (kips) Controlling Ratio using Lmid a, b P5C-SP1-1.5:1 Gusset 0.300 53 49.70 40.24 8.57 0.45 1425 1309 830 1.16 Shingle 0.200 29.32 28.78 8.57 1.02 407 396 P5C-SP2-1:1 Gusset 0.300 53 49.70 40.24 8.57 0.45 1710 1309 830 1.20 Shingle 0.300 29.32 28.78 8.57 0.45 772 593 P5C-SPR-1.6:1 Gusset 0.400 53 49.70 40.24 8.57 0.26 2010 1895 1106 1.26 Shingle 0.250 29.32 28.78 8.57 0.65 592 495 P3-C-SP(2:1)-WV-P Gusset 0.500 53 87.08 69.08 7.57 0.13 5850 4377 4247 1.10 Shingle 0.250 48.71 34.21 7.57 0.51 1045 1052 P3-C-SP(2:1)-WV-P Gusset 0.400 53 87.08 69.08 7.57 0.20 4500 3399 3398 1.09 Shingle 0.200 48.71 34.21 7.57 0.80 742 841 P3-C-SP(1:1)-WV-P Gusset 0.300 53 87.08 69.08 7.57 0.35 3950 2391 2548 1.26 Shingle 0.200 48.71 34.21 7.57 0.80 742 841 a - Green shading represents cases controlled by Partial Shear Plane Yielding. b - Yellow shading represents cases controlled by Whitmore Buckling.

103 Edge Stiffening In the previous section it was shown that the free edge slenderness could not be correlated to the buckling strength of the connection. However, if properly implemented, supplemental stiffening could be used to enhance the buckling resistance of some gusset plates. Experimentally this was investigated with the GP490LS3-2 geometry that had exterior 3x3x1/2 inch angles applied to the free edges. Though not a direct comparison, the results of this test could be compared to the GP490LS3-1 geometry, which was the unstiffened version of the geometry. However, the yield strength and load proportioning between the connections was slightly different. Schematics of the two connections are shown in Figure 35 and Figure 27. The data from the two connections is summarized in Table 25. Because these two specimens were tested under different load proportioning, two columns are provided in Table 25 that report the load in both the compression and tension diagonals at failure of the connection. For the experimental 490LS3 geometry, the externally applied stiffeners result in a 64% increase in buckling resistance over the unstiffened geometry. Since the two experimental connections were tested under different load proportioning, a more direct comparison was made analytically with the E5-490LS geometry, which did use the same loading scenario for each geometry. Data are also shown in Table 25 for the unstiffened, stiffened with internal angles, and stiffened with external angles (refer to Figure 34 for description of interior and exterior angles). The data show the internal angle stiffening option only results in a 3% increase in buckling capacity, though the external angle option results in a 45% increase in buckling resistance. The reason for the large increase in compressive strength is due to this geometry. Using the new two-folded compression resistance check, this geometry has a Whitmore buckling resistance of 464 kips versus 678 for the partial plane shear yield. In this case, the angles are able to suppress the Whitmore buckling until the partial plane shear yield controls the failure. The E4-490SS geometry was also analytically investigated to show the relative increase in compressive strength between internally and externally applied 3x3x1/2 inch angles. The internal angles had no gain in compression resistance while the external angles produced a 17% gain. The unstiffened version of E4-490SS had a mixed failure mode between buckling and full plane horizontal shear yield. For this connection, the Whitmore buckling criteria predicts failure at 585 kips while the partial plane shear yielding occurs at 633 kips, which are only different by 8%. This shows that as the connection gets closer to being controlled by the partial plane shear yield criteria, the less effective the edge stiffening strategy will become. Table 25 also shows the results between the stiffened and unstiffened version of the analytical P5U and P14C geometries. Both these stiffened connections resulted in 24% and 8% increases in buckling strength, respectively. The P5U connection was predicted to fail at a compression diagonal load of 807 kips and 1269 kips using the respective Whitmore and partial plane shear yield resistance equations. With this large disparity, it is expected that the edge stiffening

104 approach would be fruitful, and the results prove this with a 45% gain in compressive strength. With the P14C connection, the calculated resistances are 2348 and 1597 kips for the respective Whitmore and partial plane shear yield resistance equations respectively. In this case, since the partial shear equation already controls the compressive strength, the edge stiffening approach would not be considered effective, and in the end it only results in an 8% gain in compressive resistance. Further analytical work was performed on P5U and P14C connections to understand how the stiffness of the stiffening element influences the buckling resistance. This was done by varying the size of the angle and, for just the P5U connection, the plate thickness too. Figure 59 demonstrates the relationship between a percent increase in the compression resistance and a relative ratio of the moment of inertia of the angles to the stiffness of the gusset plates, Istiffener/Igp. The calculation of the angle’s moment of inertia must be taken about the surface of the plate as depicted in Figure 60. As shown in the figure, there is a variation in the increase in compression strength versus the angle stiffness and gusset plate thickness. A couple of observations can be made from Figure 59. First, there appears to be a limiting stiffness by which no additional gain in compression resistance can be achieved, and this limit appears to be approximately at an Istiffener/Igp ratio of 500. The gain in compressive resistance is also proportional to the geometry of the connection according to the assertions above. From the data, it appears that adding stiffness to the free edge suppresses buckling until the next limit-state begins to control. That is, if the connection was relatively compact and would have failed either the partial or full plane shear checks, then the extra stiffness will not provide much benefit; this was the case with the E4-490SS and P14C geometries. However, in the case of the GP490LS3 and P5U geometries which are more slender connections, the added stiffness to the free edge can suppress the buckling until the partial shear or full plane shear yield limits govern. For simplicity, the added cross-section from the stiffening technique should not be considered in the resistance equation.

105 Table 25 Increase in Compression Resistance with Edge Stiffening Specimen or Model Stiffening type Plate Thickness (inch) Yield Strength (ksi) Cfailure a (kip) Tfailure b (kip) Increase over Unstiffened Geometry GP490LS3-1 Experimental None 0.375 48.5 527 881 c GP490LS3-2 Experimental External 3x3x1/2 angles 0.375 45.5 865 483 1.64 E5-490LS Analytical None 0.375 45.6 579 579 c E5-490LS- SES Analytical Internal 3x3x1/2 angles 0.375 45.6 598 598 1.03 E5-490LS- EES Analytical External 3x3x1/2 angles 0.375 45.6 839 839 1.45 E4-490SS Analytical None 0.375 46.4 712 712 c E4-490SS- SES Analytical Internal 3x3x1/2 angles 0.375 46.4 715 715 1.00 E4-490SS- EES Analytical External 3x3x1/2 angles 0.375 46.4 835 835 1.17 P5U-WV-NP Analytical None 0.400 53 1170 936 c P5U-EES- WV-NP Analytical External 3x3x1/2 angles 0.400 53 1455 1164 1.24 P14C-W-INF Analytical None 0.500 53 1708 1452 c P14C-EES- W-INF Analytical External 3.5x3.5x1/2 angles 0.500 53 1845 1568 1.08 a – Load in tension diagonal at failure. b – Load in the compression diagonal at failure. c – This is the unstiffened geometry that represents the baseline for comparison.

106 Figure 59. Increase in compression resistance for externally applied stiffening angles. ܫ௚௣ ൌ ൫௧೒൯ య ଵଶ ܫ௦௧௜௙௙௘௡௘௥ ൌ ௕೑భ௧೑భయ ଷ ൅ ௧೑మ൫௕೑మି௧೑భ൯య ଵଶ ൅ ݐ௙ଶ൫ ௙ܾଶ െ ݐ௙ଵ൯ ቀ ௕೑మି௧೑భ ଶ ൅ ݐ௙ଵቁ ଶ Figure 60. Calculation of external angle properties. Corrosion Four experimental connections and 10 analytical connections had simulated section loss (i.e., corrosion), all either failed in buckling or full plane shear yielding. A description of the experimental connections was provided in Chapter 2, and the analytical connections are described in Appendix I. This section will describe how the new resistance equations for shear 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 0 200 400 600 800 1000 1200 1400 1600 1800 2000 In cr ea se in C om pr es si on R es is ta nc e Istiffener/Igp P5U-EES, tg=0.3 inch P5U-EES, tg=0.4 inch P5U-EES, tg=0.5 inch P14C-EES, tg=0.5 inch GP490LS3-2

107 and buckling can be used to evaluate the reduction in resistance due to section loss. Since the consideration of section loss due to corrosion is a challenge when developing a rating on existing bridges, plates thinner than 0.375 inch were included in the analysis. The methodology used in the resistance equations is to average out any section loss over the entire area being evaluated into an equivalent thickness to use in the compression and shear resistance equations. As an example, Figure 61 shows one of the investigated corrosion patterns in the P8C connection (see Appendix I for more details). There are two thicknesses of remaining section and three distinct holes along the horizontal plane above the chords. It is not obvious via inspection what the minimum shear plan area will be so both possible shear planes should be investigated. To calculate the equivalent thickness (taverage), calculate the real area in the shear plane and divide by the total width of the plane. Using Figure 61 as an example, the minimum shear area on the full shear plane is 29.075 inch2, divided by the 94.1 inch wide plane yields taverage=0.309 inch. When calculating the nominal shear resistance of the full plane, taverage=0.309 inch would be used rather than the nominal thickness of 0.500 inch. The same notion would extend to partial shear planes. For compression checks, the equivalent thickness on a Whitmore section must be calculated. The philosophy used projects any corrosion onto the Whitmore plane in the direction of the member. This is better illustrated in Figure 62, which uses three different colors to represent the different remaining plate thicknesses. Lines paralleling the framing angle of the section loss project from the middle of the section loss onto the Whitmore plane. For easier visualization, the Whitmore plane is colored depicting the areas where the various remaining section is being projected onto the Whitmore plane. The total cross-sectional area considering the remaining section thicknesses is calculated over the entire width of the Whitmore plane, then divided by the total width of the Whitmore plane to determine the equivalent thickness. A summary of the experimental connection results and associated resistance equation predictions is provided in Table 26. Of the four connections, only one failed in buckling and the buckling professional factor is a conservative 1.30. The remaining three experimental connections failed in full plane shear yielding and their associated professional factors vary from 0.98 to 1.13, which fits within the scatter band of normal full plane shear failures shown in Figure 46. Of the four experimental connections, the resistance equations correctly identified the failure mode in three of them, lending further credence to the approach. Therefore, the equivalent thickness approach used for both buckling and shear is considered a valid approach because it is either conservative, or fits within the associated statistics that -factors will be calibrated with. Table 27 shows the same type of results associated with the 10 analytical connections with simulated section loss. Some of these connections had multi-layered plates and are described in this section. Out of the 10 simulations, the correct failure mode was only identified half the time, though in each situation (buckling and shear), the professional factors were within the scatter bands used in the -factor calibrations.

108 The data presented in this section show that for the evaluation of gusset plates with section loss, the resistance prediction equations for shear yielding and buckling can provide conservative resistance predictions. This approach relies on using an equivalent thickness approach where the section loss is “smeared” over the entire plane of failure. In these cases, the resistance equations produced conservative predictions, even if the section loss was unbalanced across the plate, if only one of two plates in the connection had section loss, or if multi-layered plates were used. Area m in=29.075 inch² taverage=0.309 inch Area=31.675 inch² taverage=0.337 inch 48.5 Partial Shear PlaneAreamin=12.789 inch²taverage=0.264 inch 94.1 0.35 inch 0.25 inch 0.00 inch Remaining Thickness Legend Figure 61. Evaluation of equivalent shear area through section loss for P8C.

109 49 .2 Whitmore Planetaverage=(0.50)(7.3)+(0.35)(7.8)+(0.00)(9.3)+(0.35)(0.8)+(0.50)(24.0) / 49.2 taverage= 0.379 inch 7.3 7.8 9.3 0.8 24 .0 0.35 inch 0.25 inch 0.00 inch Remaining Thickness Legend Figure 62. Evaluation of equivalent Whitmore plane thickness for section loss in P8C.

110 Table 26 Resistance Predictions of Experimental Connection with Section Loss Specimen Plate Thickness (inch) a Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Whitmore Buckling taverage (inch) b Full Plane Shear taverage (inch) c Partial Plane Shear taverage (inch) d Pfailure (kips) e Vfailure (kips) e Vny (kips) Pn_whit (kips) Pn_ps (kips) Pfailure/Pn f Vfailure/Vn f GP307SS3-1 0.3710 47.2 24.43 26 0.191 0.241 0.211 446 517 390 170 212 1.30 0.67 0.3660 47.2 24.43 26 0.194 0.238 0.213 384 172 214 GP307SS3-2 0.3650 47.8 24.43 26 0.248 0.239 0.261 482 833 391 221 266 0.94 1.07 0.3670 47.8 24.43 26 0.250 0.238 0.263 389 292 268 GP307SS3-3 0.3710 37.9 24.43 26 0.268 0.232 0.229 519 887 301 202 185 1.07 1.13 0.3750 37.9 24.43 26 0.375 0.375 0.375 486 283 303 GP307SS3-4 0.3670 38 24.43 26 0.258 0.220 0.217 712 1213 286 194 176 1.09 0.98 0.3750 38 24.43 26 0.375 0.375 0.375 488 284 304 0.3750 46.3 12.87 20.73 0.375 0.375 0.375 468 174 295 a – For some plates, the measured thickness using an ultrasonic thickness gauge was used for the plate thickness and remaining section. This was done because the thickness milled away was variable depending on how the plate was clamped to the mill, and this eliminated any variability in the remaining section calculation. b – The average thickness of the Whitmore section by projecting all section loss between the Whitmore section and the adjoining member fastener lines onto the Whitmore section. c – The average thickness of the full width shear plane considering the minimum shear section along that plane. d – The average thickness of the partial shear plane considering the minimum section along that plane. e – Cells shaded grey represent the failure mode of the connection. f – Cells shaded green mean the calculated resistance is controlled by full plane shear yielding; yellow shading represents cases controlled by calculated compression resistance.

111 Table 27 Resistance Predictions of Analytical Connection with Section Loss Specimen Plate Thickness (inch) Yield Strength (ksi) Whitmore Width (inch) Length of Partial Shear Plane (inch) Whitmore Buckling taverage (inch) a Full Plane Shear taverage (inch) b Partial Plane Shear taverage (inch) c Pfailure (kips) d Vfailure (kips) d Vny (kips) Pn_whit (kips) Pn_ps (kips) Pfailure/Pn e Vfailure/Vn e P8C-C1 0.5000 53 49.28 48.53 0.379 0.309 0.264 1281 1982 1788 1848 920 1.39 1.11 P8C-C2 0.5000 53 49.28 48.53 0.405 0.367 0.315 1596 2469 2124 1977 1098 1.45 1.16 P8C-COS 0.5000 53 49.28 48.53 0.378 0.309 0.264 1743 2696 894 1848 920 0.65 1.15 0.5000 53 49.28 48.53 0.500 0.500 0.500 1446 2443 1746 P14U-C1 0.5000 53 43.64 33.1 0.328 0.349 0.262 1316 1253 1225 1334 838 1.57 1.02 P14U-C2 0.5000 53 43.64 33.1 0.348 0.349 0.262 1330 1266 1225 1413 840 1.58 1.03 P14U-COS 0.5000 53 43.64 33.1 0.328 0.349 0.262 1498 1426 612 1334 838 0.61 0.96 0.5000 53 43.64 33.1 0.500 0.500 0.500 878 2033 1600 P8C-C1-SP 0.5000 53 49.28 48.53 0.378 0.309 0.264 1953 3021 1788 1848 920 1.33 1.09 0.2500 53 32.32 30.5 0.250 0.250 0.250 988 656 549 P8C-COS-SP 0.5000 53 49.28 48.53 0.378 0.309 0.264 1995 3086 894 1848 920 0.62 1.09 0.5000 53 49.28 48.53 0.500 0.500 0.500 1446 2443 1746 0.2500 53 32.32 30.5 0.250 0.250 0.250 494 656 549 P14U-C1-SP 0.5000 53 43.64 33.1 0.328 0.349 0.262 1708 1626 1225 1334 838 1.21 0.87 0.2500 53 26.32 23.95 0.250 0.250 0.250 646 416 579 P14U-COS-SP 0.5000 53 43.64 33.1 0.328 0.349 0.262 1680 1599 612 1334 838 0.56 0.88 0.5000 53 43.64 33.1 0.500 0.500 0.500 878 2033 1600 0.2500 53 26.32 23.95 0.250 0.250 0.250 323 416 579 C1=corrosion pattern 1 in both plates; C2=corrosion pattern 2 in both plates; COS=corrosion pattern 1 in only one plate; C1-SP=corrosion pattern 1 in both plates with a shingle plate on both sides; COS-SP=corrosion pattern 1 in only one plate with shingle plate only over the corroded plate a – The average thickness of the Whitmore section by projecting all section loss between the Whitmore section and the adjoining member fastener lines onto the Whitmore section. b – The average thickness of the full width shear plane considering the minimum shear section along that plane. c – The average thickness of the partial shear plane considering the minimum section along that plane. d – Cells shaded grey represent the failure mode of the connection. e – Cells shaded green mean the calculated resistance is controlled by full plane shear yielding; yellow shading represents cases controlled by calculated compression resistance.

112 Rivet Shear Strength Though this research did not address the strength of rivets extensively, the opportunity was taken to analyze the historical data available in the available literature to assess the current MBE technique (up to the 2011 2nd Edition) for evaluating rivet shear strength, which the FHWA Guide mostly copied. Historically, fastener shear resistance equations took the form shown in Equation 11 and will be discussed in terms of rivets. Rn=R1R2R3FuA (Eq. 11) where:  is the resistance factor R1 is a shear-to-tensile ratio of the driven rivet stock R2 is a connection length factor R3 is a fill plate factor Fu is the tensile strength of the driven rivet stock A is the cross-sectional area of all the shear planes In previous versions of the MBE and BDS, much of this equation was built-in to the resistance tables for individual fastener strength. The shear-to-tensile ratio, R1, is commonly believed to be 0.58 based on the Von Mises shear failure; however, for fasteners it has been reported to be as high as 0.85.(10) The connection length reduction, R2, accounts for the shear lag that develops through the length of connection in the direction of force and will be discussed further in another section. The fill plate factor accounts for a reduction in overall connection strength when filler plates are used in thickness transitions. The fill plate factor is not considered in this research. The ultimate tensile strength of the fastener is represented by Fu and the cross-section area, A, is the sum of all shear planes considering the undriven rivet cross-section. Strength Data The 2011 2nd Edition of the MBE published four factored strengths for rivets as shown in Table 28. The 18 ksi value for rivets constructed prior to 1936 or of unknown origin assumed that the tensile strength of the rivet stock was conservatively taken as 46 ksi with a 0.58 shear-to-tensile ratio and a -factor of 0.67.(27) Up until 1931, rivets fell under the ASTM A7 specification and it was published by Ferris that rivets from this era have tensile strengths that range from 46-56 ksi.(28) The ASTM A141 rivet specification was tentatively passed in 1932 and officially in 1933 and it cannot be determined why the code writers chose 1936 as the transition date over 1933. Likewise, once the A141 specification was passed, it listed rivet tensile strengths of 52-62 ksi which gives rise to the 21 ksi factored shear strength for rivets constructed after 1936. For A502 rivets, the MBE adopted the values published in the 2002 17th Edition of the Standard Specifications for Highway Bridges. However, the FHWA Guide increased the strengths of A502 rivets by 2 ksi over these values to “adjust for an error in calibration which took place in

113 the translation from older manuals.”(29) All these strengths had to be reduced by an extra 20% when the connection length exceeded 50 inches, which is further explained in the next section. A variety of ultimate rivet shear strength data was collected from available literature sources as well as tests performed as part of this research project reported in Appendix C.(30-52) Sources were published between the years of 1882 and 1970, and encompassed rivet grades of unknown origin, ASTM A141, ASTM A195, and ASTM A502 Grade 1. No test data for ASTM A502 Grade 2 could explicitly be found. Shown in Figure 63 is a histogram of all ultimate rivet shear strengths. It is most important to note that the ultimate shear stresses are presented in terms of the undriven rivet area. Therefore the shear stresses would be expected to be artificially high since they are based on the undriven rivet area, whereas in reality the rivet probably has an area equal to the standard oversize hole it has filled. However, built-in to the distribution would be cases of mis-installation where the rivet only partially filled the hole. The data plotted as iron rivets are from six different reports from the Watertown Arsenal conducted between the years 1882 and 1896 from a total of 95 rivet or rivet group tests. Chemistries were never reported for the rivets and they were only reported as “iron” as opposed to “steel” rivets that were also tested. The iron rivets from the late 1800’s are considered to be the worst possible rivet that could be found on a truss bridge with gusset-plated connections, and thought to be a good representative for rivets of an unknown origin. The data plotted as steel rivets encompass data reported as “steel” or “carbon” rivets produced between the years of 1882 and 1970 from 369 tests on rivets or rivet groups. Some of the steel rivets were reportedly alloyed with chrome and nickel. The data plotted as “Manganese” rivets appeared from one study conducted in 1940 that demonstrated much higher strength than those that were reported as “Carbon” rivets. In total there were 29 connection tests performed with Manganese rivets. Though they were reported as “Manganese” the chemical composition of these rivets met the ASTM A195 at the time. The rivet shear statistics needed in the calibration are shown in Table 29. For the purposes of this evaluation, rivets will be divided into three categories: unknown origin, A141/A502 Gr.1, and A195/A502 Gr.2, which will be assigned ultimate tensile strengths, Fu, or 50, 60, and 80 ksi, respectively. These Fu values were thought to be representative values. However, a new shear-to- tensile ratio of 0.85 is being proposed, as it best fits the data using the assumed tensile strengths. Therefore the nominal shear strength will be 0.85Fu of the rivet stock. It is important to note that the assumed shear-to-tensile ratio is somewhat fictitious and really represents a curve-fit to shear test data. That is, multiplying the ultimate tensile test result from a rivet removed from service by 0.85 will not produce an accurate ultimate shear stress for rating purposes. The 0.85 factor is accounting for differences in the shear area based on normalizing the data back to an undriven rivet diameter, so in reality the ratio is more like 0.74 (considering oversized holes add about 15% additional shear area over the undriven rivet diameter). The average shear strength, respective bias factors to the nominal strength, and coefficients of variation are also shown in the table for each grade of rivet.

114 Table 28 Reproduction of Table 6A.6.12.5.1-1 from 2nd Edition MBE Rivet Type and Year of Construction F (ksi) Constructed prior to 1936 or of unknown origin 18 Constructed after 1936 but of unknown origin 21 ASTM A502 Grade I 25 ASTM A502 Grade II 30 Figure 63. Ultimate rivet shear strength data (1882-1970) plotted on normal probability paper. y = 0.1451x - 6.4023 y = 0.2246x - 17.032 y = 0.1889x - 10.149 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 0.0 20.0 40.0 60.0 80.0 100.0 St an da rd N or m al V ar ia bl e Ultimate Shear Stress (ksi) (based on undriven rivet area) Iron Manganese Steel Steel (neglected points) Manganese (neglected points)

115 Table 29 Rivet Shear Strength Statistics Rivet Type Assumed Tensile Strength, Fu (ksi) Assumed Shear Strength, 0.85Fu (ksi) Experimental Average Shear Strength (ksi) Bias Factor () Coefficient of Variation Iron (unknown) 50 42.5 44.1 1.038 0.156 Steel (A141, A502 Gr. 1) 60 51.0 53.7 1.053 0.099 Manganese Steel (A195 and A502 Gr.2) 80 68.0 75.8 1.115 0.059 Connection Length Reduction Connection tests have shown that, for very long connections, the shear strength of a fastener group does not equal the strength of a single fastener multiplied by the total number of fasteners in the connection. In prior design specifications, the connection reduction factor was taken as 0.8 for connections up to 50 inches in length and 0.64 for connections in excess of 50 inches. This was somewhat hidden as the initial factor was always built-in to the resistance and the code reader would only see an additional 0.80 reduction for connections in excess of 50 inches. This step function led to an enigma, because at 50 inches in length there was a sudden 20% reduction in strength when in reality it is probably a continuous function. The data used to determine the connection length effect was that reported by Tide (53) (neglecting the two outlier points he outlined). In addition, the rivet connection data published by Davis and Woodruff (40) was added to this data set. The data is disseminated in terms of the connection length professional factor being the real strength divided by the predicted value. The predicted value of the connection strength is based on the strength of an individual fastener multiplied by the number of fasteners in the connection. The professional factor is plotted against the overall length of the connection and is shown in Figure 64, with the rivet and bolt data points segregated. As seen in the figure, the data is quite scattered especially for connections in excess of 40 inches in length (note that some of the data points are hidden by others). Tide further showed that the scatter in the data can be better explained after considering the geometric proportioning of the joint. He outlined a two-folded check where the designer must check ratios between gross plate area to fastener shear area and compare to the respective yield and tensile properties of the plate. Agross > (0.85 As_fastener Fv_fastener)/Fy plate (Eq. 12) Anet > (0.85 As_fastener Fv_fastener)/Fu_ plate (Eq. 13)

116 Once these two inequalities were checked, it was found that if the connection geometry was proportioned such that both or one of the inequalities passed, the data were banded about a reduction ratio of 0.90 for all connection lengths. Connections failing both inequalities demonstrated much lower connection reduction factors that are more tightly banded around a reduction of 0.70. To demonstrate this better, the data shown in Figure 64 is reproduced in Figure 65 where the data shown as circles pass both inequalities, squares represent connections that passed only one inequality, and data shown as triangles fail both inequalities. The data passing one or both inequalities shown in Figure 65 tend to band around a connection length reduction of 0.90, and those that fail both inequalities tend to band around a reduction of 0.7. Finally, the connection length professional factors are plotted on normal probability paper in Figure 66. The data was broken down into two sets, those that failed both Tide criteria, and those that met one or both Tide criteria. Both sets are fairly linear indicating the assumed normal probability distribution is accurate. Table 30 shows the statistical parameters of the data shown in Figure 66 attained from the best- fit line through the data. The statistics are presented assuming that the resistance limit-state check will assume the designer or load rater will have to check the two Tide inequalities. Therefore, a 0.90 connection length reduction will be applied to all connections despite length. In this case, the data show an average reduction of 0.932 for a bias of 1.035 and COV of 0.077. The data for connections failing both Tide inequalities are assumed to have a reduction of 0.70 and show an average of 0.702 (bias of 1.002) and COV of 0.103. Since the statistical parameters are worst for connections that fail both Tide inequalities, only they will be used in rivet strength calibrations. From the perspective of the designer or load rater, resistance values will have to be multiplied by 0.78 (ratio of 0.7/0.9) to account for situations where connections fail both the Tide inequalities.

117 Figure 64. Bolt and rivet connection data showing connection length effect. Figure 65. Bolt and rivet data segregated by Tide stiffness and strength criteria. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 0 20 40 60 80 100 R at io o f P re di ct ed to Ex pe rim en ta l R es ul ts Connection Length (inch) Rivets High-Strength Bolts 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0 20 40 60 80 100 R at io o f P re di ct ed to Ex pe rim en ta l R es ul ts Connection Length (inch) Passes both criteria Fails one criterion Fails both criteria

118 Figure 66. Connection length professional factors plotted on normal probability paper. Table 30 Statistics of Connection Length Reduction Nominal Length Reduction, R2 Average (R2) Bias Factor (R2) COV One or both inequalities satisfied 0.90 0.932 1.035 0.077 Neither inequality satisfied 0.70 0.702 1.002 0.103 SUMMARY OF PROFESSIONAL FACTOR STATISTICS Table 31outlines all the professional factor statistics for the various limit-states discussed in this chapter. Only the bias () and the COV are shown. Limit-states involving net section failures do not have any professional factor data because none were observed in the experiments nor could the analytical models identify them. Therefore, only the limit-states shown in Table 31 will be calibrated in the next chapter. y = 13.774x - 9.6701 y = 13.879x - 12.934 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 1.2 St an da rd N or m al V ar ia bl e Pfailure/Pn Fails both Tide criteria Passes one or both Tide criteria

119 Table 31 Summary of Professional Factor Statistics Limit State  COV Full Plane Shear Yielding () (all data considered) 1.017 0.069 Full Plane Shear Yielding () (neglecting plates thinner than 0.375 inch) 1.017 0.069 Bu ck lin g Whitmore Buckling (all data considered) 1.268 0.135 Whitmore Buckling (neglecting plates thinner than 0.375 inch) 1.226 0.103 Partial Plane Shear (all data considered) 1.139 0.144 Partial Plane Shear (neglecting plates thinner than 0.375 inch) 1.183 0.116 Block Shear 1.180 0.060 Chord Splice (all data considered) 1.224 0.164 Chord Splice (neglecting plates thinner than 0.375 inch) 1.284 0.163 R iv et S he ar Unknown Origin (assumed 42.5 ksi shear strength) 1.038 0.156 A141/A502 Gr. 1 (assumed 51.0 ksi shear strength) 1.053 0.099 A195/A502 Gr. 2 (assumed 68.0 ksi shear strength) 1.115 0.059 Connection Length Effect (failing both Tide criteria, 0.70) 1.002 0.103 Connection Length Effect (passes one or both Tide criteria, 0.70) 1.035 0.077 Analysis Factor 1.000 0.000