Contribution of Steel Casing to Single Shaft Foundation Structural Resistance (2018)

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100 3.1. Introduction This chapter includes the findings from the experiments and the revisions proposed to AASHTO BDS and AASHTO SGS based on these findings. It also briefly describes a study on the economic impacts of applying the proposed revisions of the project in the designs of actual bridge structures and two design examples based on the proposed revisions. Sections 3.2 and 3.3 present the findings from the test results and comparisons with the ana- lytical program results. The experimentally obtained results for flexural and shear specimens were replicated by finite element models that were constructed based on the work done in the analytical program of Chapter 2. Finite element modeling, analyses, and comparison of results from the analyses of the test specimens with their experimental results are presented in this chapter. Based on the experimental moment–curvature (M-φ) curves and supporting finite element analyses results, new ultimate and damage-controlling limit states are proposed for displacement-based design purposes. The existing effective stiffness equations in the codes and design guidelines were evaluated by comparing with the experimental and finite element results. Sections 3.4 and 3.5 refer to the study on the economic impacts of applying the proposed revi- sions of the project in the designs of actual bridge structures and two design examples based on the proposed revisions, respectively. 3.2. Flexural Test Results and Findings 3.2.1. Force-Displacement Relationships of the Flexural Specimens Based on the loading protocol discussed in Section 2.3.3, Specimen S1 was tested under the cyclic displacement protocol shown in Figure 3.1. Details of the calculations for designing the loading protocol are presented in Appendix I. To facilitate comparison of results, all other 20 in. diameter specimens (Specimens S2R, S3, S4, and S6R) were subjected to the same cyclic displacement protocol that was used for Specimen S1. In compliance with the cyclic displace- ment protocol, the displacement at the load application point was applied in cycles of progres- sively increasing amplitude up to the maximum stroke of the actuator (that is ± 20 in.), and after reaching that maximum cyclic amplitude (maximum cyclic amplitude reached at cycle: 15 and 11 for 20 in. and 30 in. diameter specimens, respectively), testing continued with cycles at the same maximum displacement amplitude until failure of the specimen. The complete displacement history and instances of key observations that were made during the test are presented in the following section. The experimentally obtained force-displacement curve for the flexural specimens and their backbone curves are shown in Figures 3.2 and 3.3, respectively. The points when some of the C H A P T E R 3 Findings and Applications

Findings and Applications 101 key observations were made during the test (corresponding to the onset of visible local buckling, maximum strength, and rupture of steel tube) are marked on these curves. Detailed discussion about the observations made during the flexural tests is provided in Appendix I. 3.2.2. Comparison of the Flexural Specimens’ Strengths Comparison of the experimentally obtained strength of flexural specimens with each other and with their corresponding analytically calculated composite and non-composite section strengths are presented below. In order to compare the flexural specimen results with each other, the experimentally obtained strength for each flexural specimen was normalized to its analytical strength value, and normalized values were compared to each other. The analytical strengths were calculated using the PSDM considering each specimen’s test condition (such as applied axial load and composite or non-composite behavior) and the variation of each specimen’s measured material properties. Detailed calculations of the analytical strengths for each flexural specimen are provided in Section 1.1.3.1 of Appendix I. Figure 3.4 shows the dispersion of the calculated strength values for each flexural specimen using PSDM and various ways to account for the variation in material properties obtained from sample to sample (as there was some noticeable scatter in material properties, as shown in Section H.1.3 of Appendix H). In this figure, the analytically composite strength (F) has been calculated for all combinations of the uniaxial yield strength of the tube ( fy) and RCFST shaft longitudinal rebars ( fyr) obtained from test coupons and the uniaxial compressive strength of the RCFST shaft concrete ( f c′) obtained from cylinders for each specimen. These values are shown as gray circles in the figure. The average values of the strength computed using all of these combinations (F – [ fy, fyr, f c′]), and the strength that is calculated using average material properties (F[ f – y, f – yr, f – c′]), are shown as well. Note that the values of F – ( fy, fyr, f c′), and F( f – y, f – yr, f – c′) are close to each other. The same calculations (a) Cycles 1 to 6 (b) Cycles 7 to 16 –3.5 –2.5 –1.5 –0.5 0.5 1.5 2.5 3.5 0 1 2 3 4 5 6 La te ra l d isp la ce m en t, in End of cycle No. –20 –15 –10 –5 0 5 10 15 20 6 7 8 9 10 11 12 13 14 15 16 La te ra l d isp la ce m en t, in End of cycle No. Figure 3.1. Loading history for Specimen S1. (a) Cycles at displacements up to D‘y. (b) Cycles at displacements above that value.

(a) (b) (c) Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S1-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) East side rupture Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S2R-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) West side rupture Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S3-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) West side rupture Figure 3.2. Force-displacement curve measured from test of Specimen. (a) S1 (b) S2R (c) S3 (d) S4 (e) S5 (f) S6R.

(d) (e) (f) Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S4-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) West side rupture Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –90 –60 –30 0 30 60 90 S5-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) East side rupture Lateral Displacement, in. Fo rc e, k ip s –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S6R-Experiment Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) East side rupture Figure 3.2. (Continued).

104 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance (a) (b) (c) (d) (e) (f) Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S1-Backbone Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S2R-Backbone Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S3-Backbone Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S4-Backbone Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –90 –60 –30 0 30 60 90 S5-Backbone Lateral Displacement, in. Fo rc e, k ip –20 –16 –12 –8 –4 0 4 8 12 16 20 –50 –40 –30 –20 –10 0 10 20 30 40 50 S6R-Backbone Figure 3.3. Force-displacement backbone curve for Specimen. (a) S1 (b) S2R (c) S3 (d) S4 (e) S5 (f) S6R.

Findings and Applications 105 were done considering non-composite behavior of the cross-section for all flexural specimens and results are shown in Figure 3.5. The normalized strength values were calculated per Equations 3.1 and 3.2 : ˆ (3.1) , F F F C exp C PSDM = ˆ (3.2) , F F F NC exp NC PSDM = where Fexp = the experimentally obtained strength of the flexural specimen, FC,PSDM = the PSDM strength using average material properties F( f – y, f – yr, f – c′) for composite cross-section, and FNC,PSDM = the PSDM strength using average material properties F( f – y, f – yr, f – c′) for non-composite cross-section. Figure 3.4. Dispersion of PSDM analytical strength values (composite cross-section). Note: Non-composite cross-section is considered for all cases. Figure 3.5. Dispersion of PSDM analytical strength values (non-composite cross-section).

106 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance The calculated normalized strength values for each flexural specimen are shown in Figure 3.6. As shown in this figure, all normalized mean strength values are greater than one, which means that the experimentally obtained values are greater than the analytically predicted strengths using PSDM. Table 3.1 presents a summary of the experimentally obtained and the analytically calculated strength values for each flexural specimen. For Specimen S2R, which was axially post-tensioned to an axial value of 92.6 kips before testing, the analytical strengths are presented for cases with and without the axial load in the second row of Table 3.1. As shown in this table, the experi- mentally obtained strengths of the specimens are more than the theoretical composite section strength values. This suggests that the composite action was achieved for these specimens. For Specimen S1, the strength of the specimen is 32% and 48% higher than the analytically calcu- lated composite and non-composite strengths, respectively (FˆC and FˆNC respectively in Table 3.1). For the axially loaded flexural specimen (Specimen S2R), PSDM results show that the pres- ence of axial load increases the analytical strength values by 6.7% and 8.8% for the composite and non-composite cases, respectively. In order to do a similar comparison, the normalized Figure 3.6. Normalized flexural specimens strength values. S1 45.5 34.5 30.8 1.32 1.48 S2R 46.5 40.2 (no axial load) 42.9 (with axial load) 35.4 (no axial load) 38.5 (with axial load) 1.16 1.10 1.31 1.21 S3 38.3 35.4 31.2 1.10 1.23 S4 43.7 36.9 32.4 1.19 1.35 S6R 42.8 42.2 37.2 1.02 1.15 S5 83.1 68.0 58.2 1.22 1.43 Specimen Specimen Strength ( ), kips (Experimental) Composite Strength ( ), kips (Using PSDM) Non-Composite Strength ( ), kips (Using PSDM) Normalized Composite Strength, Normalized Non-Composite Strength, Table 3.1. Experimentally obtained and analytically calculated strengths comparison.

Findings and Applications 107 composite strength of Specimen S2R with axial load (having FˆC,S2R = 1.10) is compared to the normalized composite strength of Specimen S1 (having FˆC,S1 = 1.32). This comparison does not show an increase in composite strength in the presence of axial load (i.e., FˆC,S2R < FˆC,S1). Specimens S3 and S4, which had bentonite slurry and grease at their steel-to-concrete inter- face, respectively, have lower normalized strength values than Specimen S1. However, both showed greater strengths than the analytically calculated strength for non-composite case. For Specimen S4, slippage at the interface of the steel tube and concrete core was observed, which is discussed in Appendix I. For Specimen S5, which had larger diameter and D/t ratio, the normalized strength values are less compared to Specimen S1. The normalized strengths are 7.6% and 3.4% less for com- posite and non-composite cross-sections, respectively, comparing to corresponding values for Specimen S1. The normalized strength values for Specimen S6R were also less than the corresponding values for Specimen S1. Specimen S6R had grease coating at the interior surface of the steel tube, and shear rings were welded at the top of the RCFST shaft part in order to achieve com- posite behavior at the RCFST shaft cross-section. The normalized strength values are 22.7% and 22.3% less than Specimen S1 composite and non-composite cases, respectively. However, as it is shown in Table 3.1, these values are more than one, which shows that the experimentally obtained strength is more than the analytically calculated cross-section strength values. Overall, the above variations from specimen to specimen are relatively small and fall within the realm of variations expected in experimental work. 3.2.3. Finite Element Modeling of the Flexural Tests To understand the behavior of the tested specimens thoroughly, the finite element models of the flexural test specimens were constructed and analyzed in LS-Dyna using the modeling procedures described in Section 2.2.3. The finite element analyses results and their discussion are available in Appendix J. 3.2.4. Finite Element Analyses of RCFST Shafts Embedded in the Soil To investigate the effect of soil embedment on the previous findings on the composite behav- ior of RCFST shafts, a finite element model of the 20 in. flexural test specimen, but embedded in an elastic soil continuum, was analyzed in LS-Dyna. Different configurations of the RCFST shaft embedded in the soil were analyzed, considering the reinforced concrete column attached at top and different combinations of the attached shear transfer mechanism along the shaft, as schematically shown in Figure 3.7. The characteristics of the six configurations considered here are summarized as follows: • Case 1: Similar to Specimen S1 but with RCFST shaft part embedded in soil. • Case 2: Similar to Case 1 but with shear rings modeled at the top of the RCFST shaft. • Case 3: Similar to Case 1 but with shear rings modeled at top of the RCFST shaft and below the location of maximum moment along the shaft (i.e., at a depth of 3.5Ds). • Case 4: A continuous RCFST shaft similar to Specimen S1 but with a height of 3Ds extending out of the soil. • Case 5: Similar to Case 4 with shear rings modeled at the top. • Case 6: Similar to Case 4 with two rings modeled at the top and below the location of maxi- mum moment under the soil (i.e., at a depth of 2Ds). Details of the finite element models and results of the analyses are provided in Appendix J.

108 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance From the finite element analyses performed in this section, the following findings are obtained: • Relying on the natural friction bond at the interface of the steel tube and the concrete core (µinterface = 0.5), the composite MPSDM capacity of the RCFST shaft was achieved at a depth of 2.5Ds below the soil level. • Using a shear transfer mechanism at the top end of the RCFST shaft makes it possible to achieve the composite MPSDM capacity immediately below the location of the attached shear transfer mechanisms in the presence of an interface friction bond corresponding to clean steel surface (i.e., corresponding to µinterface = 0.5). • When there is not sufficient interface friction bond, a shear transfer mechanism (such as shear rings) has to be provided above and below the point of the maximum moment below the soil level. 3.2.5. Moment–Curvature Relationships for the Flexural Test Specimens The moment–curvature (M-φ) hysteresis curves of the RCFST shaft’s cross-section for each tested flexural specimen are presented in Figure 3.8. The backbones of the M-φ hysteresis curves are shown in Figures 3.9 and 3.10. Backbone curves of moment–curvatures at different heights along the shaft for each specimen are drawn on the same plot. The cross-section curvatures were calculated from Equation 3.3 either using the measured strains from the strain gages attached on the steel tube at east and west elevations (See Figure 2.100 for elevations), or average strains obtained from string pot data. The M-φ calculated using string pot data is shown in Figure 3.10. To calculate M-φ using the longitudinal string pots that were mounted along the height of the shaft, the average strain along the span of the string pot was calculated by dividing the measured displacement by the initial span of the string pot. The location of strain gages and string pots for each flexural test specimen was shown in the instrumentation plan drawings provided in Appendix M. Soil top Bed rock Shear rings Case (1) (2) (3) (4) (5) (6) Figure 3.7. Schematics of different cases considered for the finite element analyses of the RCFST shafts embedded in the soil.

S1, z=2.5 in. S1, z=11.25 in. S1, z=20 in. S2R, z=2.5 in. S2R, z=11.25 in. S2R, z=20 in. S3, z=2.5 in. S3, z=11.25 in. S3, z=20 in. Figure 3.8. Moment–curvature hysteresis curves of the flexural test specimens recorded by the strain gages.

S4, z=2.5 in. S4, z=11.25 in. S4, z=20 in. S5, z=3.75 in. S5, z=16.75 in. S5, z=29.75 in. S6R, z=2.5 in. S6R, z=11.25 in. S6R, z=20 in. Figure 3.8. (Continued).

Findings and Applications 111   , (3.3) , ,( ) ( ) ( )φ = −z t t t D east z west z s where φ(z, t) = calculated curvature at elevation z of the RCFST shaft at time t of the test, east,z(t) = measured strain on the east side at elevation z of the steel tube at time t of the test, and west,z(t) = measured strain on the west side at elevation z of the steel tube at time t of the test. Figure 3.9. Backbones of the experimental moment–curvature curves calculated using strain gage data.

112 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance For all the specimens, the strain gages were recording properly until the point of visible local buckling. After this point, the strain gages attached close to where local buckling developed typically detached themselves from some specimens. The M-φ curves in Figure 3.8 were plotted using data from the beginning of the test up to the point when one of the corresponding strain gages detached. The curvatures measured for Specimen S1 were significantly lower than for other 20 in. specimens, which resulted in a higher flexural stiffness (i.e., the initial slope of the M-φ curve) for this specimen. However, as it is shown in Appendix I, the initial stiffness of all the 20 in. flexural specimens including Specimen S1 were close to each other, meaning that their M-φ curves should also be close to each other. It is believed that the data recorded by the strain gages for Specimen S1 (being unexplainably different) contained an unknown calibration error. Figure 3.10. Backbones of the experimental moment–curvature curves calculated using string pot data.

Findings and Applications 113 For this reason, the experimental curvature data obtained from strain gages for Specimen S1 were not used in the comparisons below. Instead, the strains from the finite element analysis results of Specimen S1 test were used. The data from most of the string pots were valid for all the test durations. Note that the string pots located at the bottom of the shaft (z = 2.5 in. and 7.5 in. for 20 and 30 in. specimens, respectively) were attached to the foundation’s top surface at one end and to the steel tube at the other end. Therefore, the longitudinal displacement values that were read at this location include some of the strains developed in part of the steel tube part that was embedded in the foundation. This difference was corrected by assuming a modified initial string pot span cal- culated by matching the initial slope of the corresponding M-φ curve with the initial slope of the M-φ curves measured by the string pots mounted on the steel tube. The experimentally obtained moment–curvatures, together with those obtained from the LS-Dyna analysis results and the OpenSees cross-section analyses, were used to investigate the flexural stiffness of RCFST shafts and to assess the effectiveness of existing equations for calcu- lating the effective stiffness in different codes and design guideline documents. 3.2.6. Proposed Limit States for Displacement-Based Design A few limit states are needed for the purpose of conducting a displacement-based design, namely the ultimate curvature and the damage-controlling curvature. This section describes how these were defined for the RCFST studied. The flexural specimens test results showed that the RCFST shaft sustained a significant amount of ductility beyond the deflection corresponding to the onset of local buckling and up to the fracture of the steel tube. Also, it was observed that the maximum moment resisted by the RCFST shafts was reached after the start of local buckling. According to the finite element analyses, the onset of local buckling actually developed earlier than when it had been visually observed during the tests simply because it can be more easily observed from the magnified deflected shapes than can be plotted from the finite element results, as well as, more signifi- cantly, by comparing the strains on the outside and inside surface of the shell elements along the steel tube. Analyses results showed that local buckling started at a slightly larger compressive strain than the steel tube’s yield strain on the compression side. At that point, the tension side of the cross-section is already yielded because the location of the neutral axis is not in the middle of the cross-section due to the composite action. The ultimate limit state for the RCFST cross-section can be defined as the curvature cor- responding to the fracture of the steel tube. At the fracture state, it can be assumed that the RCFST cross-section is composite and fully plastic. Therefore, the curvature at fracture will be equal to the fracture strain of the steel tube on the tension side divided by its distance to the plastic neutral axis. Based on observations made by Brown et al. (2015), the fracture strain of the steel tube can be taken as 0.025 for circular RCFST cross-sections. In the tested flexural specimens, the fracture strain was recorded by the string pots prior to the fracture of the steel tube. The measured fracture strains were 0.029, 0.032, 0.022, 0.035, 0.022, and 0.031 for Speci- mens S1, S2R, S3, S4, S5, and S6R, respectively. The average of the recorded fracture strains of all the flexural specimens was 0.028, which is consistent with the value of 0.025 used hereafter. However, crushing of the concrete inside the RCFST can also limit the ultimate curvature. The curvature corresponding to the crushing of the concrete can be calculated by dividing the ultimate compressive strain of the confined concrete on the compression side to its distance to the plastic neutral axis. The ultimate compressive strain of the confined concrete for circular RCFST can be taken equal to 0.025, as proposed by Susantha et al. (2001). Therefore, taking these two limiting conditions into account, the ultimate curvature is the minimum given by the

114 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance ultimate state of fracture on the steel tube, or crushing of the infill concrete. Correspondingly, the proposed ultimate curvature (φu) can be calculated as:   , 2 (3.4) min r t y r t y u frac cu u frac o N cu o N ( )φ = φ φ φ = − + ≤ − − where φfrac and φcu are defined as shown in Figure 3.11 and frac = fracture strain of the steel tube equal to 2.5% (Brown et al. 2015), cu = ultimate compressive strain of the confined concrete equal to 2.5% for a circular RCFST cross-section (Susantha et al. 2001), ro = outside radius of the steel tube, in., t = thickness of the steel tube, in., and yN = distance from center of cross-section to the plastic neutral axis calculated using PSDM, in. A damage-controlling limit state can be defined by the curvature corresponding to the maxi- mum moment resisted by the RCFST cross-section. For all the tested flexural specimens, the maximum moment was reached at some point after the onset of the local buckling; past that point, the steel tube started to progressively lose its ability to resist moments as local buckling that developed at the bottom of the steel tube increased in severity. The damage-controlling limit curvature (φd) is proposed here to be taken as the average of the curvatures corresponding to the onset of the local buckling and to the fracture of the steel tube (φu). At the onset of the local buckling, the cross-section is not fully plastic. Therefore, the local buckling curvature is calculated by dividing the buckling strain by its distance to the posi- tion of the corresponding neutral axis at that particular moment. The location of this neutral axis will be at a point between the center of the cross-section and the plastic neutral axis. To calculate the local buckling curvature, the buckling strain of the steel tube and the location of the neutral axis at the onset of the local buckling have to be known. As a conservative approach for practical purposes and expediency to simplify the calculation of the local buckling curva- ture, the buckling strain can be divided by its distance to the center of the steel tube instead of the distance to the exact neutral axis location. Also, as a lower-bound approach, the buckling strain can be substituted by the yield strain of the steel tube. As mentioned before, onset of local buckling on the compression side occurs at a strain that is slightly more than yield strain of the steel tube. Te n. Co m p. Plastic N.A. Center of cross-section. Concrete strain profile Steel tube strain profile Figure 3.11. Calculation of limit state curvatures for RCFST cross-section.

Findings and Applications 115 The process of calculation of φd can be summarized as:    2 , 1 2 2 2 (3.5) 1 2 3min r t r t y r t y d d y o frac o N cu o N φ = φ + φ φ   φ = − + − +       ≤ − − where φ1, φ2, and φ3 are defined as shown in Figure 3.11 and y is the yield strain of the steel tube. The calculated limit state curvatures for the test specimens are presented in Table 3.2. Fig- ure 3.12 shows the history of the measured curvatures versus the actuator displacement. The reported values for maximum experimental curvatures (φexp.max.) are related to the maximum curvature measured during the test. The maximum curvatures occurred after rupturing of the steel tubes. The measured curvatures at the point where the first fracture of the steel tube was recorded are named as the experimental fracture curvature (φexp.fract.) in Table 3.2. The ratio of the experimental fracture curvature over the proposed ultimate curvature is shown in the far right column of the table. The average difference between the experimental fracture curva- ture and the proposed ultimate curvature is about 78%. This can be attributed to differences in the position of the calculated and experimental plastic neutral axes and differences between the actual fracture strain and the 0.025 value that is proposed to be used in the ultimate curvature formula. In calculation of confined concrete properties as well as position of plastic neutral axis (using PSDM), the average of the measured material properties were used. This can result in variations between calculated and experimental fracture curvature values. Some error can also be due to the correction factor used to subtract the deformation of the steel tube part embedded in the foundation as discussed before. The calculated limit state curvatures are compared to the experimentally obtained curva- tures for the tested specimens in Figure 3.13. As shown in this figure, all the test specimens developed plastic curvatures larger than the proposed ultimate curvature (Equation 3.4) prior to their failure. It is also shown that the damage limiting curvature proposed by Equa- tion 3.5 falls in the vicinity of the curvature corresponding to the maximum moment resisted by specimens. S1 1.61E-04 1.70E-03 5.08E-03 9.31E-04 1.70E-03 2.87E-03 4.06E-03 1.69 S2R 1.81E-04 1.74E-03 4.73E-03 9.63E-04 1.74E-03 3.24E-03 3.82E-03 1.85 S3 1.61E-04 1.67E-03 5.35E-03 9.17E-04 1.67E-03 3.04E-03 3.21E-03 1.82 S4 1.66E-04 1.67E-03 5.37E-03 9.18E-04 1.67E-03 2.94E-03 3.57E-03 1.76 S5 9.64E-05 1.04E-03 4.53E-03 5.69E-04 1.04E-03 1.86E-03 2.28E-03 1.78 S6R 1.92E-04 1.70E-03 5.08E-03 9.47E-04 1.70E-03 3.08E-03 3.42E-03 1.81 Specimen 1/in. 1/in. 1/in. 1/in. 1/in. 1/in. 1/in. Table 3.2. Calculated proposed limit state curvatures for the flexural test specimens.

116 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance For displacement-based design, the M-φ curve of the RCFST cross-section can be developed up to the proposed ultimate curvature by fiber-section analysis assuming composite behavior and using expected material properties for the steel tube, confined concrete, and rebars. The M-φ curve then can be idealized with an elastic perfectly plastic response, following the pro- cedure outlined in Section 8.5 of the AASHTO SGS (2014), to estimate the plastic moment capacity of the composite RCFST cross-section. The linear portion of the idealized curve should pass through the M-φ curve at the point corresponding to the first yield on the tension side of the steel tube. The stress–strain relationship for the confined concrete in compression can be modeled using proper models for the RCFST sections. The stress–strain relationship pro- posed by Susantha et al. (2001) was used for the confined concrete material behavior in this research project. The tensile behavior of the concrete can be modeled as shown in Figure 3.14 S2R at z = 2.5" West side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) S4 at z = 2.5" West side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) S1 at z = 2.5" East side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) S6R at z = 2.5" East side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) S5 at z = 3.75" East side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (west side) S3 at z = 2.5" West side rupture Onset of visible local buckling Max. strength at pos. disp. Max. strength at neg. disp. First rupture (east side) Figure 3.12. Measured experimental curvatures of the flexural specimens.

Findings and Applications 117 Figure 3.13. Calculated proposed limit state curvatures for the flexural test specimens. Crack strain Schematic Stress- Strain relationship for confined concrete Compression Tension Figure 3.14. Stress–strain model for concrete.

118 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance by assuming a tensile strength equal to 10% of the unconfined compressive strength of the concrete. The rebars can be modeled according to Section 8.4 of the AASHTO SGS (2014). In summary, the applied and proposed limit state curvatures are as follows: • First yield curvature is defined as the curvature corresponding to the first yield on the tension side of the steel tube. • Damage-controlling curvature is proposed as the average of the curvatures corresponding to the onset of the local buckling and the fracture of the steel tube as calculated in Equation 3.5. • Ultimate curvature is proposed as the smaller curvature corresponding to the fracture of the steel tube and the crushing of the confined concrete inside the steel tube of the RCFST. The ultimate curvature is calculated in Equation 3.4. • Idealized equivalent yield curvature is defined as the curvature corresponding to the idealized plastic moment capacity of the RCFST, which is calculated from the idealized M-φ curve. The idealization of the M-φ curve can be done according to the procedure outlined in Section 8.5 of the AASHTO SGS (2014) by considering the expected material properties and the proposed ultimate curvature limit for composite RCFST. • Maximum experimental fracture curvature is defined as the experimentally measured curva- ture corresponding to the point where the first fracture in the steel tube happened. Table 3.3 shows the experimentally obtained yield curvatures, idealized equivalent yield cur- vatures, and the first yield curvature obtained from fiber-section analysis in OpenSees using the average stress-strain curves from the steel tube coupon test results, confined concrete properties, and rebar tensile tests. The experimentally obtained maximum base moment and composite PSDM moment using the average material properties are also presented in this table. 3.2.7. Effective Flexural Stiffness Equations for Force-Based Design The slope of the M-φ curve (∂M/∂φ) corresponds to the flexural stiffness of the cross-section (EI). Figure 3.15 shows a typical EI-φ curve for an RCFST cross-section, illustrating how cross- section stiffness varies under increasing curvature. In general, the flexural stiffness behavior of an RCFST cross-section can be divided into three regions. At the beginning, at low curvatures, before concrete cracks, the cross-section is totally elastic and the stiffness of the cross-section is equal to sum of EI of the steel tube and EI of reinforced concrete. At this stage, the position of the neutral axis is at the center of the cross-section (Region 1 in Figure 3.15). By reaching the cracking curvature, φcr (Region 2), the flexural behavior of the cross-section becomes nonlinear due to progressive tensile failure of the concrete and the development of cracks. The steel tube Yield curvature, 1/in. Flexural strength, kip.ft Experimental Positive Drift Experimental Negative Drift Average OpenSees Experimental PSDM S1 1.32E-04 -1.45E-04 1.39E-04 1.17E-04 759 576 S2R 1.51E-04 -1.49E-04 1.50E-04 1.60E-04 775 708 S3 1.67E-04 -1.86E-04 1.77E-04 1.20E-04 639 592 S4 1.27E-04 -1.32E-04 1.29E-04 1.20E-04 729 617 S5 1.24E-04 -1.63E-04 1.44E-04 8.00E-05 2078 1755 S6R 2.02E-04 -1.40E-04 1.71E-04 1.50E-04 714 705 Specimen Table 3.3. Yield curvature and flexural strength of the test specimens.

Findings and Applications 119 is elastic in this region. At this stage, the neutral axis starts to move toward the compression side and the flexural stiffness of the cross-section gradually decreases. The rate of decrease of the flex- ural stiffness significantly grows after reaching the curvature corresponding to the first yield of the steel tube (Region 3). In this region, cracking of the concrete core generally grows slower, but loss of stiffness is significant due to plastification. The onset of local buckling occurs in Region 3. In structural analyses where the beam-column elements are modeled as elastic components with a concentrated plastic hinge, a reduced elastic flexural stiffness called effective flexural stiffness, (EI)eff , is assigned to the elastic portion of the member. When defining the effective flexural stiffness, it is assumed that a certain portion of the concrete is cracked and does not contribute to the stiffness of the cross-section. The effective flexural stiffness is also used when calculating the elastic critical buckling load to determine the axial compressive strength. The equivalent flexural stiffness (EI)eq that is used in Section 8.5 of the AASHTO SGS (2014) can also be calculated by simply dividing the moment at the first yield point over the correspond- ing curvature value in the moment–curvature curve (i.e., first yield curvature). The first yield point of RCFST is defined in Section 3.2.6 as the point corresponding to first yield on the tension side of the steel tube. A few equations for calculating the effective flexural stiffness of RCFST have been proposed and recommended by researchers, codes, and design guidelines. The equations defining the flexural stiffness of RCFST given by AASHTO Seismic Guide Specifications (AASHTO SGS, 2014), WSDOT Bridge Design Manual (2016), and AISC 360 (2005, 2010, and 2016) are pre- sented in the following subsections. 3.2.7.1. AASHTO Seismic Guide Specifications (AASHTO SGS [2014]) Two equations for calculating the effective flexural stiffness of CFST are given in the com- mentary of Section 7.6 of the AASHTO SGS (2014). These are presented here in Equations 3.6 and 3.7. According to AASHTO SGS (2014), both equations can be used to estimate the effec- tive flexural stiffness of CFSTs. AASHTO SGS (2014) limits the use of these equations to fully composite CFSTs with no internal reinforcement. The effect of externally applied axial load on stiffness is not considered in these equations. EI E I E I eff s s c c 2.5 C7.6-1 (3.6)( ) = + φ/φu N or m al iz ed ∂ M /∂ φ 0.2 0.4 0.60.8 1 0 0.2 0.4 0.6 0.8 1 First crack by reaching to on the concrete (Logarithmic scale) First yield at the steel tube (1) Elastic response (2) Cracked concrete, elastic steel (3) Nonlinear response Increase of the cracked area Figure 3.15. Typical flexural stiffness-curvature (EI-e) curve for RCFST cross-section.

120 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance where Ic = moment of inertia of the concrete core about the elastic neutral axis of the composite section, in4, Is = moment of inertia of the steel tube about the elastic neutral axis of the composite sec- tion, in4, Ec = modulus of elasticity of concrete, ksi, and Es = modulus of elasticity of steel, ksi. 0.88 0.352 C7.6-2 (3.7)EI E I n A A E Ieff s s c s s s( ) = +  ≥ where Ac = area of the concrete, in2, As = area of the steel section (the steel tube), in2, and n = modular ratio. 3.2.7.2. WSDOT Bridge Design Manual (2016) The WSDOT Bridge Design Manual (WSDOT 2016) defines the effective stiffness of circu- lar CFT as defined in Equation 3.8 to be used to “evaluate deflections, deformation, buckling resistance, and moment magnification” (WSDOT 2016). The effect of internal reinforcement and externally applied axial load are considered to increase the effective stiffness of the con- crete, as shown by Equation 3.9, taken from Lehman and Roeder (2012) as a modified form of the equation proposed by Roeder et al. (2010). According to Lehman and Roeder (2012), P0 is equal to 0.95 f c′Ac + fy As. WSDOT (2016) does not specify how to calculate P0. EI E I C E Ieff s s c c 7.10.2-3 (3.8)( ) = + ′ where 0.15 0.9 7.10.2-4 (3.9) 0 C P P A A A A A s r s r c ′= + + + + + ≤ and P = factored axial load, kips, P0 = nominal compressive resistance without moment, kips, and Ar = area of the internal reinforcing, in2. 3.2.7.3. AISC 360 (2005, 2010) Section I of the 2005 and 2010 AISC Specification for Structural Steel Buildings (AISC 360 [2005, 2010]), provides an equation for the effective flexural stiffness of filled composite mem- bers to be used to calculate the elastic critical buckling load of such composite members (Equa- tion 3.10). The effect of the external axial load is not accounted for in this equation. I2-12 (3.10)3EI E I E I C E Ieff s s s r c c( ) = + + where C3 is the coefficient for calculation of effective rigidity: 0.6 2 0.9 I2-13 (3.11)3C A A A s c s = + +     ≤

Findings and Applications 121 and Ir = moment of inertia of reinforcing bars about the elastic neutral axis of the composite sec- tion, in4. 3.2.7.4. AISC 360 (2016) The effective flexural stiffness of filled composite members in the 2016 edition of the AISC Specification for Structural Steel Buildings has been revised as following: I2-12 (3.12)3EI E I E I C E Ieff s s s r c c( ) = + + where 0.45 3 0.9 I2-13 (3.13)3C A A A A A s r c s r = + + + +     ≤ 3.2.7.5. Comparison and Summary of Results These effective flexural stiffness equations are summarized in Table 3.4. Table 3.5 shows the (EI)eff values calculated for each flexural specimen tested as part of this research project, using the various above specified equations. The idealized Mp values are also shown in this table. These values were determined by calculating bi-linearized curves using the effective stiffness (EIeff) from different existing formulas as the elastic part and the procedure outlined in Section 8.5 of the AASHTO SGS (2014). The idealized yield curvature can simply be calculated by dividing the idealized Mp over the effective stiffness (EIeff). This idealized yield curvature is shown in this table noted as Equivalent φyi. The average values of material properties were used in the calculations. The effective stiffness values are compared to the experimental Considers Internal Reinforcement Considers External Axial Load AASHTO SGS (2016) C7.6-1 No No AASHTO SGS (2016) C7.6-2 No No WSDOT (2016) 7.10.2-3 Yes Yes AISC 360 (2005, 2010) I2-12 Yes No AISC 360-16 (2016) I2-13 Yes No Table 3.4. Summary of the effective flexural stiffness equations.

Specimen , kip.ft , 1/in. Method , kip.in2 Idealized , kip.ft Equivalent , 1/in. S1 576 1.70E 03 Elastic 5.09E+07 545 1.28E 04 AASHTO SGS (2016) C7.6-1 3.25E+07 559 2.07E 04 AASHTO SGS (2016) C7.6-2 3.79E+07 553 1.75E 04 WSDOT (2016) 2.77E+07 565 2.45E 04 AISC 360 (2005, 2010) 4.34E+07 549 1.52E 04 AISC 360 (2016) 4.18E+07 550 1.58E 04 S2R 708 1.74E 03 Elastic 5.39E+07 680 1.51E 04 AASHTO SGS (2016) C7.6-1 3.37E+07 700 2.50E 04 AASHTO SGS (2016) C7.6-2 4.00E+07 691 2.07E 04 WSDOT (2016) 3.12E+07 705 2.71E 04 AISC 360 (2005, 2010) 4.55E+07 686 1.81E 04 AISC 360 (2016) 4.37E+07 687 1.89E 04 S3 592 1.67E 03 Elastic 5.44E+07 576 1.27E 04 AASHTO SGS (2016) C7.6-1 3.38E+07 591 2.10E 04 AASHTO SGS (2016) C7.6-2 4.04E+07 584 1.74E 04 WSDOT (2016) 2.85E+07 599 2.53E 04 AISC 360 (2005, 2010) 4.58E+07 580 1.52E 04 AISC 360 (2016) 4.40E+07 581 1.58E 04 S4 617 1.67E 03 Elastic 5.48E+07 597 1.31E 04 AASHTO SGS (2016) C7.6-1 3.40E+07 614 2.16E 04 AASHTO SGS (2016) C7.6-2 4.07E+07 606 1.79E 04 WSDOT (2016) 2.85E+07 623 2.62E 04 AISC 360 (2005, 2010) 4.61E+07 602 1.57E 04 AISC 360 (2016) 4.43E+07 603 1.63E 04 S5 1755 1.04E 03 Elastic 2.82E+08 1623 6.91E 05 AASHTO SGS (2016) C7.6-1 1.61E+08 1669 1.24E 04 AASHTO SGS (2016) C7.6-2 2.05E+08 1646 9.64E 05 WSDOT (2016) 1.27E+08 1701 1.60E 04 AISC 360 (2005, 2010) 2.28E+08 1637 8.64E 05 AISC 360 (2016) 2.14E+08 1642 9.19E 05 S6R 705 1.70E 03 Elastic 5.37E+07 640 1.43E 04 AASHTO SGS (2016) C7.6-1 3.36E+07 658 2.35E 04 AASHTO SGS (2016) C7.6-2 3.99E+07 650 1.96E 04 WSDOT (2016) 2.83E+07 668 2.83E 04 AISC 360 (2005, 2010) 4.54E+07 645 1.71E 04 AISC 360 (2016) 4.36E+07 647 1.78E 04 Table 3.5. Comparison of the calculated effective stiffness values of the flexural test specimens.

Findings and Applications 123 M-φ and EI-φ curves in Figure 3.16. Fiber-section analyses curves are also presented in this figure. Fiber-section analysis was performed in OpenSees using the average stress–strain curve from coupon tests for the steel tube and reinforcing bars and from average of cylinder tests for the concrete; the curve shown in Figure 3.14 was used considering confined concrete properties. Comparing the (EI)eff values shows that, generally, all the equations predict values that fall in Region 2 of the curve shown in Figure 3.15, ranging between 0.5 to 0.8 of the elastic stiffness, (a) (b) (c) WSDOT Figure 3.16. Experimental M-e and EI-e curves for flexural test specimens. (a) S1 (b) S2R (c) S3 (d) S4 (e) S5 (f) S6R.

124 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance (d) (e) (f) Figure 3.16. (Continued).

Findings and Applications 125 (EI)elastic. Values predicted by WSDOT (2016) are less than those obtained by the other equations. AISC 360-16 (2016) gives the highest effective flexural stiffness. The stiffness predicted by AISC 360-10 (2010) is close to the AISC 360-16 (2016) values. Values predicted by both AASHTO formulas are between WSDOT and AISC formulas. Also, comparing the fiber-section analysis and the experimental data shows that this method and the material models used are reliable for generating M-φ curves. The calculated (EI)eff values are compared to the equivalent stiffness values, (EI)eq, that were calculated using M and φ at the first yield point in Table 3.6. In fact, the (EI)eq is the slope of the elastic part of the idealized M-φ curve that is defined according to Section 8.5 of the AASHTO SGS (2016). According to Table 3.6, considering all of the test specimens, the average of the val- ues predicted by WSDOT (2016) and AASHTO SGS C7.6-1 (2016) were 16% and 1% less than (EI)eq, respectively, and the values predicted by AISC 360-10 (2010), AISC 360-16 (2016), and AASHTO SGS C7.6-2 (2016) were 35%, 29%, and 19% more than (EI)eq, respectively. Using the results of fiber-section analysis, the cracked area of concrete at a certain curvature of φ can be calculated as shown in Figure 3.17. The effect of the cracked concrete region of the RCFST cross-section on its flexural stiffness is shown in Figure 3.18, as calculated by fiber- section analysis of Specimen S1. The variation of EI with respect to the cracked concrete area is shown in this figure. The EI was calculated by differentiating the M-φ curve and was normalized to the initial flexural stiffness of the concrete part of the cross-section (EcIc). The ratio of the contribution of the concrete part to the total cross-section stiffness (αc) up to the first yield point was computed by Equation 3.14 and is also shown in this figure. E I M E I E Ic c c s s s r 1 (3.14)α = ∂ ∂φ − −     It is seen that, in general, flexural stiffness is less sensitive to the cracked concrete area prior to the first yield point compared to after that point. The calculated effective stiffness values are also projected on the normalized stiffness curve. The stiffness values obtained by AISC 360-10 (2010) and AISC 360-16 (2016) both show 15–20% cracked area. This value is about 30% for AASHTO SGS C7.6-2 (2016), 45% for AASHTO SGS C7.6-1 (2016), and 50% for WSDOT (2016). Knowing that the effective stiffness values are used to model RCFST members when conduct- ing elastic structural analyses of complete structures, it is important to compare the curvature distributions obtained using the finite element results of the RCFST members modeled by the fully nonlinear elements, with an equivalent elastic member modeled using the effective flex- ural stiffness. For this purpose, a nonlinear cantilever RCFST shaft with Specimen S1’s cross- section and height (158 in.) was modeled and subjected to pushover analysis using OpenSees. The schematic cross-section, M-φ curve, and global force-displacement pushover curves of the nonlinear column are shown in Figure 3.19. The deformation of the column is calculated by double integration of the curvature diagram along the column. A closed-form equation can be derived between the curvature and deformation diagrams up to first yield of the RCFST column. In fact, the lateral stiffness of the cantilever column prior to first yield point is directly related to the flexural stiffness of the RCFST cross-section, as shown in Figure 3.19. In this figure, Mp is the idealized plastic moment calculated using the idealized elasto-plastic behavior of M-φ curve. For a partially yielded member, the deformation at the top of the column becomes more affected by the plastic rotations developing over the plastified portion of the column. Therefore, the curvature ductility at the bottom of the column increases faster than the displacement ductility (Bruneau et al. 2011). In this case, the relationship between the cross-section ductility and the global displacement ductility is much more complex. Figure 3.20 shows the schematic curvature diagrams along the column at the equivalent and ultimate displacements.

Specimen , Method S1 3.28E+07 Elastic 1.55 AASHTO SGS (2016) C7.6-1 0.99 AASHTO SGS (2016) C7.6-2 1.16 WSDOT (2016) 0.85 AISC 360 (2005, 2010) 1.32 AISC 360 (2016) 1.27 S2R 3.52E+07 Elastic 1.53 AASHTO SGS (2016) C7.6-1 0.95 AASHTO SGS (2016) C7.6-2 1.14 WSDOT (2016) 0.88 AISC 360 (2005, 2010) 1.29 AISC 360 (2016) 1.24 S3 3.52E+07 Elastic 1.54 AASHTO SGS (2016) C7.6-1 0.96 AASHTO SGS (2016) C7.6-2 1.15 WSDOT (2016) 0.81 AISC 360 (2005, 2010) 1.30 AISC 360 (2016) 1.25 S4 3.53E+07 Elastic 1.55 AASHTO SGS (2016) C7.6-1 0.96 AASHTO SGS (2016) C7.6-2 1.15 WSDOT (2016) 0.81 AISC 360 (2005, 2010) 1.31 AISC 360 (2016) 1.25 S5 1.52E+08 Elastic 1.85 AASHTO SGS (2016) C7.6-1 1.06 AASHTO SGS (2016) C7.6-2 1.34 WSDOT (2016) 0.84 AISC 360 (2005, 2010) 1.49 AISC 360 (2016) 1.41 S6R 3.34E+07 Elastic 1.61 AASHTO SGS (2016) C7.6-1 1.00 AASHTO SGS (2016) C7.6-2 1.19 WSDOT (2016) 0.85 AISC 360 (2005, 2010) 1.36 AISC 360 (2016) 1.30 Table 3.6. Comparison of the calculated equivalent stiffness values of the flexural test specimens.

Findings and Applications 127 Cracked area N.A. Equivalent rebar ring Te ns io n Co mp re ss io n (3.15) (3.16) Figure 3.17. Calculation of the cracked area of the concrete part of the RCFST cross-section. Figure 3.18. Flexural stiffness versus the cracked concrete area of the RCFST cross-section. Cross section M–φ Global pushover F Nonlinear structure Figure 3.19. Schematic cross-section M-e and the global pushover curves for a nonlinear column.

128 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance A proper equivalent linear structure representation for the considered nonlinear column would be the one that, for a lateral top force corresponding to MP at the bottom, the drift at the top reaches the equivalent yield displacement. The response of this equivalent linear structure is schematically shown in Figure 3.21. The flexural stiffness of this linear model can be calculated by dividing MP by the curvature cor- responding to the equivalent yield displacement. Figure 3.22 shows the moment and curvature distributions along the RCFST shaft at the point corresponding to the first yield curvature (φy) at the base, equivalent yield curvature (φyi) at the base, equivalent yield displacement (Dyi) at the top, the point when the base moment reaches the Mp, and for the equivalent linear structure. The flexural stiffness of the equivalent linear structure (EI)lin is 3.64E+07; that is 10% less than the equivalent flexural stiffness (EI)eq. The calculated values of (EI)lin and (EI)eff for the analyzed RCFST shaft are compared in Table 3.7. The flexural stiffness values of Table 3.7 are plotted in Figure 3.23. As shown in this figure, the effective stiffness given by AASHTO SGS C7.6-2 (2016) was the closest one to the stiffness of the (EI)lin with a 4% difference. The values given by WSDOT (2016) and AISC 360-10 (2010) had the largest difference from (EI)lin with 24% and 19% differ- ences, respectively. This suggests that the AASHTO SGS C7.6-2 (2016) equation is more suitable to be used in member scale analyses. This suggestion was made based on the limited analyses done in this section. To summarize the above findings, for displacement-based design, the ultimate curvature cal- culated by Equation 3.4 is recommended as the ultimate limit state. It is to be used in conjunction with the damage-controlling limit state that was proposed by Equation 3.5. The proposed state El ev at io n Curvature at Curvature at Figure 3.20. Schematic curvature diagrams along the column at the equivalent and ultimate displacements. Equivalent Linear structure Bottom cross section M– Equivalent linear structure F M MP MP EIlin. Figure 3.21. Equivalent linear structure.

Findings and Applications 129 Figure 3.22. Curvature distribution along an RCFST cantilever column. For the equivalent linear structure: = 3.64E+07 kip.in2 Method , kip.in2 Elastic 5.09E+07 1.40 1.55 Equivalent 3.28E+07 0.90 1.00 AASHTO SGS (2016) C7.6-1 3.25E+07 0.89 0.99 AASHTO SGS (2016) C7.6-2 3.79E+07 1.04 1.16 WSDOT (2016) 2.77E+07 0.76 0.84 AISC 360 (2005, 2010) 4.34E+07 1.19 1.32 AISC 360 (2016) 4.18E+07 1.15 1.27 Table 3.7. Comparison of different flexural stiffness calculations for an RCFST cantilever column. Figure 3.23. Effect of tensile strength of the concrete on the crack distribution along a deformed RCFST cantilever column.

130 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance limit for limiting the damage was close to the point where maximum resistance was achieved in the test specimens. Also, for fiber-section analysis of RCFST cross-sections it is recommended to use confined concrete properties and consider 10% of the uniaxial compressive strength as the tensile strength of the concrete. The ultimate compressive strain for the confined concrete is recommended to be taken equal to 0.025 as proposed by Susantha et al. (2001). For the steel tube, a fracture strain of 0.025, proposed by Brown et al. (2015), confirmed by the experimental results obtained here, is recommended regardless of steel grade and D/t ratio. The strain value at the onset of the local buckling is recommended to be taken equal to the yield strain of the steel tube as a conservative value. By comparing results from the tests and finite element analyses with the existing effective stiffness equations described above for RCFSTs, it can be concluded that, in general, all the equations predict reasonable values for the effective flexural stiffness. All the equations consider a flexural stiffness that is less than the initial elastic stiffness of the cross-section. This reduction could be attributed to the development of cracks in the concrete under bending. The maximum contribution of the concrete is 0.4 times the elastic stiffness of the concrete (EcIc) for AASHTO SGS (2016) C7.6-1, and it is 0.9 for WSDOT (2016), AISC 360-10 (2010), and AISC 360-16 (2016). Note that AASHTO SGS (2016) C7.6-2 does not explicitly consider the EcIc parameter. WSDOT (2016), AISC 360-10 (2010), and AISC 360-16 (2016) consider the effect of the internal reinforcement on the stiffness of the cross-section, while only WSDOT (2016) takes into account the effect of the compressive axial load. Based on the equivalent linear structure analyses, it is recommended that the AASHTO SGS C7.6-2 (2016) equation be used in calculating the effective flexural stiffness of RCFST members in linear analyses. However, if an expression that takes into account the effect of the compressive axial load is desired, the WSDOT (2016) equation can be used, recognizing that it provides a lower stiffness leading to longer estimated period (and thus lower seismic design forces and larger predicted displacements). 3.3. Shear Test Results and Findings 3.3.1. Force-Displacement Relationships of Shear Specimens The 12OD shear specimens were tested under the cyclic displacement protocol that is shown in Figure 3.24. This loading protocol was constructed using the same procedure described in Section 2.3.3, but here using results from pushover analysis of the finite element model of the shear specimen including the modular stiffeners and the pantograph device. The displacement loading was applied by the actuator to the loading beam of the pantograph device. Details of the finite element model used for loading protocol design are presented in Section J.3 of Appendix J. The experimentally obtained force-displacement curve for the flexural specimens and their backbone curves are shown in Figures 3.25 and 3.26, respectively. In these figures, the horizontal axis shows the shear span deformation that was recorded by string pots (and LEDs). Except for Specimen SH3, which was a hollow tube, some slippage was observed during the testing of shear specimens. This slippage happened mostly (and only for certain lateral displacement ranges) at the interface of the connection between the top of the shear specimen and loading beam of the pantograph. No slippage was observed at both ends of the shear span. Figure 3.27 shows a comparison between the force-displacement relation that is obtained using the applied displacement and shear span displacement for hollow (SH3) and concrete-filled shear specimen (e.g., SH4 as a representative specimen for comparison purpose). Figure 3.28 shows the difference between applied displacement and the measured shear span displacement for hollow (SH3) and concrete-filled shear specimen (e.g., again SH4).

Findings and Applications 131 For Specimen SH3 (a hollow tube), diagonal local buckling started to develop after reaching the maximum strength. The failure of Specimen SH3 happened by rupturing the steel tube in the middle of the shear span. Figure 3.29 shows the deformation of Specimen SH3 at different loading states. For all the other specimens, excessive diagonal deformations on the surface of the steel tube were observed after they reached their maximum strength. This deformation could be because of the fail- ure of the diagonal compressive concrete strut that likely developed in the core of the specimen, as lateral displacement increased in the shear span. After reaching maximum strength, strength of the specimens progressively decreased until cracking developed in the steel tube, when sudden loss of strength occurred. For all concrete-filled shear specimens, the failure of the specimen happened by fracture of the steel tube on the tensile sides of the cross-section at both ends of the shear span. (a) Cycles 1 to 6 (b) Cycles 7 to 14 Cycle D isp la ce m en t, in 0 1 2 3 4 5 6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2 0.3 0.4 0.5 Displacement at the actuator Cycle D isp la ce m en t, in 6 7 8 9 10 11 12 13 14 –2.5 –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 2.5 Displacement at the actuator Figure 3.24. Loading history for Specimen S1. (a) Cycles at displacements up to D‘y. (b) Cycles at displacements above that value.

(a) (b) (c) Shear Displacement, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH3-Experiment shear deformation Shear Displacement, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH4-Experiment shear deformation Shear Displacement, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH5-Experiment shear deformation Figure 3.25. Force-displacement curve measured from test of shear specimen. (a) SH3 (b) SH4 (c) SH5 (d) SH6 (e) SH7 (f) SH1R.

Shear Displacement, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH6-Experiment shear deformation Shear Displacement, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH7-Experiment shear deformation Shear Displacement using LED8, in. Fo rc e, k ip s –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH1R-Experiment shear deformation (d) (e) (f) Figure 3.25. (Continued).

134 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Shear Displacement, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH3-Backbone Shear Displacement, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH4-Backbone Shear Displacement, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH5-Backbone Shear Displacement, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH6-Backbone Shear Displacement, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH7-Backbone Shear Displacement using LED8, in. Fo rc e, k ip –2 –1.5 –1 –0.5 0 0.5 1 1.5 2 –400 –300 –200 –100 0 100 200 300 400 SH1R-Backbone (c) (d) (e) (f) (a) (b) Figure 3.26. Force-displacement backbone curve for shear specimen. (a) SH3 (b) SH4 (c) SH5 (d) SH6 (e) SH7 (f) SH1R.

Findings and Applications 135 Figure 3.27. Force-displacement relations comparison for applied displacement and measured shear span displacement. Figure 3.28. Comparison of applied displacement and measured shear span displacement. Diagonal buckling on the tube Tube ruptures (a) After Reaching Maximum Strength (b) Specimen Failure Figure 3.29. Deformation of SH3 shear specimen (hollow tube).

136 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance This was expected as both ends of the shear spans experience high strains caused by the interaction of bending and shear forces. Figure 3.30 shows the deformed RCFST shear specimen at different loading states (Specimen SH1R is shown as a representative one for the purpose of this figure). Some of the specimens were fully cut open to show the state of the infill concrete after the test. A typical result is shown in Figure 3.31. As shown in the figure, the infill concrete within the shear span was pulverized into fine particles. Sheared aggregates were observed in the crushed infill concrete. Cone shaped intact parts of the concrete core at both ends of the shear span were observed, as shown in Figure 3.31. Concrete outside of the shear span was in good condition. 3.3.2. Comparison of the Shear Specimens’ Shear Strengths The experimentally obtained shear strengths from the shear specimens are compared here with the existing shear strength equations from the AASHTO LRFD Bridge Design Specifications Excessive diagonal deformation of the steel tube due to strut failure in the concrete core (a) After Reaching Maximum Strength (b) Specimen Failure Tube ruptures Tube ruptures Figure 3.30. Deformation of RCFST shear specimen (SH1R shaft 6#4, #3@3”). Pulverized concrete of the RCFST after shear test Both ends of shear span Sheared aggregates Figure 3.31. Infill concrete state after shear test.

Findings and Applications 137 (AASHTO BDS 2014) and those from the WSDOT Bridge Design Manual LRFD (WSDOT BDM 2016). Although the AASHTO BDS (2014) does not directly provide an equation for composite shear strength of CFSTs, it is assumed here that a practicing engineer could calculate the respec- tive nominal shear strength of the circular steel tube and concrete section, as given by Sec- tions 6.12.1.2.3c and 5.8.3.3, respectively, and, using engineering judgment, sum them up to estimate the composite shear strength. This would be done as follows: • For circular steel tubes: V F As cr g0.5 6.12.1.2.3c-1 (3.17)( )= where VS: shear strength contribution from the steel shaft; in which Fcr = shear buckling resistance (ksi) taken as the larger of either: ( )=     ≤ 1.60 0.58 6.12.1.2.3c-2 (3.18)1 5 4 F E L D D t Fcr v y or: ( )=     ≤ 0.78 0.58 6.12.1.2.3c-3 (3.19)2 3 2 F E D t Fcr y where Ag = gross area of the section based on the design wall thickness, in2. E = modulus of elasticity of the steel, ksi, Fy = yield strength of the steel tube, ksi, D = outside diameter of the tube, in., Lv = distance between points of maximum and zero shear, in., and t = design wall thickness taken equal to 0.93 times the nominal wall thickness for ERW round HSS. • For concrete: V f Ac c c0.0316 5.8.3.3-3 (3.20)( )= β ′ Where Vc = the shear strength contribution from the concrete infill, β = taken equal to 2.0, f ′c = uniaxial compressive strength of the concrete, ksi, and Ac = area of the concrete section, in2. By summing these two values, the nominal shear strength of RCFST (Vn) would be: (3.21)V V Vn s c= +

138 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance The recent update of WSDOT BDM (2016), contrary to the AASHTO BDS (2014), provides an equation for the nominal shear strength of CFST and RCFST, which is based on the research done by Roeder et al. (2016) as: 2 (3.22)V V V Vn WSDOT st srl c= + + η( ) where 0.6 0.5 0.6 0.5 5 1 5 10 0.0316 ksi 0 V F A V F A P P V A f st yt st srl yrl srl c c c ( ) ( ) ( ) = = η = +  ≤ = ′ and Fyt = yield strength of the steel tube, ksi, Ast = cross-sectional area of the steel tube, in2, Fyrl = yield strength of longitudinal rebar, ksi, Asrl = total cross-sectional area of longitudinal rebars, in2, P = external axial load, kips, P0 = axial capacity of the RCFST, kips, Ac = cross-sectional area of the concrete infill, in2, and f c′ = uniaxial compressive strength of the concrete infill, ksi. Table 3.8 presents the maximum strength experimentally obtained from the shear specimens and the corresponding shear strengths calculated from Equations 3.21 and 3.22. As shown in this table, the experimentally obtained strengths for the CFST and RCFST specimens are practi- cally similar to each other. A maximum strength of 414 kips was obtained for Specimen SH6, which had larger diameter longitudinal bars (6#6) with respect to other shear specimens, but it was observed that the presence of longitudinal rebars had only a minor effect on the shear strength. For reference, the strength of the CFST (Specimen SH4, with no internal reinforce- ment) was 396 ksi. Use of 1% and 2.2% of longitudinal reinforcement in Specimens SH5 and SH6, respectively, increased the strength to 397 ksi and 414 ksi, respectively. Comparing the shear strengths of Specimens SH7 and SH1R with that of Specimen SH5 shows that the exis- tence of spiral reinforcement did not have a significant effect on the shear strength either, as it only increased the shear strength by 10 and 7 kips for Specimens SH7 and SH1R, respectively, compared to that of SH5. Figure 3.32 compares the experimental backbone curve of Specimen SH3 (hollow) and Speci- men SH4 (CFST). As shown in this figure, the initial stiffness of the shear specimens is similar to each other. However, the maximum shear strength of Specimen SH3 was 57.1% of that obtained for Specimen SH4, and ultimate behavior was most different (as described earlier). The experimental backbone curves of all concrete-filled 12OD shear specimens (CFST and RCFSTs) are compared with the existing shear strength equations in AASHTO BDS (2014) and WSDOT BDM (2016) in Figure 3.33. As shown in this figure, the AASHTO BDS (2014) equa- tions used as described above give conservative values for the shear strength of the tested CFST and RCFSTs. The shear strength calculated by the WSDOT BDM (2016) equation was closer to the experimentally obtained shear strength values.

Findings and Applications 139 Specimen Specimen Strength ( ), kips (Experimental) AASHTO BDS (2014) ( ), kips WSDOT BDM (2016) ( ), kips SH2 (16OD CFST) 437 189 401 2.31 1.09 SH3 (12OD Hollow) 226 154 318 1.47 0.71 SH4 (12OD CFST) 396 170 357 2.33 1.11 SH5 (12OD RCFST 6#4 1%) 397 170 379 2.34 1.05 SH6 (12OD RCFST 6#6 2.2%) 414 170 405 2.44 1.02 SH7 (12OD RCFST 6#4 #3@4) 407 170 379 2.39 1.07 SH1R (12OD RCFST 6#4 #3@3) 404 170 379 2.38 1.07 Table 3.8. Comparison of experimentally obtained strengths and existing shear strength equations. Shear displacement, in. Fo rc e, k ip -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -400 -300 -200 -100 0 100 200 300 400 SH3 SH4 Figure 3.32. Comparison of backbone curve of Specimens SH3 and SH4.

140 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Figure 3.34 shows the experimental backbone curve of Specimen SH3 (12OD Hollow) and the shear strength calculated by the AASHTO BDS (2014) using Equation 3.17. As shown in the figure, the experimentally obtained shear strength for the circular HSS tube was more than that estimated by AASHTO BDS (2014), which is conservative. However, by comparison, Table 3.8 notes that the strength predicted by the WSDOT BDM (2016) equation is unconservative in this case, which indicates that this equation should not be used for hollow tubes (or presumably tubes infilled with materials weaker/softer than the concretes used in past experiments). 3.3.3. Finite Element Modeling of the Shear Tests The finite element models of the shear tests and the analyses results and discussion are avail- able in Appendix J. Actuator displacement, in. Fo rc e, k ip -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -400 -300 -200 -100 0 100 200 300 400 SH4 SH5 SH6 SH7 SH1R AASHTO Spec. WSDOT BDM, 2016 Figure 3.33. Comparison of backbone curves of tested CFST and RCFSTs with existing shear strength equations. Actuator displacement, in. Fo rc e, ki p -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 -400 -300 -200 -100 0 100 200 300 400 SH3-Backbone AASHTO Spec. Figure 3.34. Comparison of backbone curve of Specimen SH3 (12OD Hollow) and the shear strength calculated by AASHTO BDS (2014).

Findings and Applications 141 3.3.4. Discussion of Finite Element Analyses Results of the Shear Tests The finite element analysis results of the shear tests are presented in this section. Figure 3.35 shows the finite element results for Specimen SH4 (12 in. diameter CFST). In this figure, the numerically obtained hysteresis curves are compared with the experimental results, with the “X” axis displaying actuator and shear span displacements in Figures 3.35a and 3.35b, respec- tively. As shown in Figure 3.35a, the initial global stiffness of the test setup was well captured by the finite element model. Also, as shown in Figure 3.35b, the initial stiffness of the specimen at the shear span was also well matched with the experimentally obtained results. As mentioned before, no failure criteria were defined for the concrete and steel materials, and, therefore, no failure is exhibited by the finite element analyses. In fact, in the finite element analyses, the con- crete’s strength kept increasing progressively at larger drifts. This increase was consistent with the development of a diagonal compression strut in the concrete. In such numerical models, the compressive strength in the developed diagonal strut keeps increasing at greater lateral displace- ment. This behavior is observed in Figure 3.36 which shows the shear force respectively carried by the steel tube and the concrete of Specimen SH4. (a) (b) Sh ea r Fo rc e, ki ps Actuator Displacement, in. -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-2.5 -400 -200 0 200 400 Exp. SH4 (CFST) FEA Sh ea r Fo rc e, ki ps Shear span Displacement, in. -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -400 -200 0 200 400 Exp. SH4 (CFST) FEA Figure 3.35. Finite element analysis and experimental results comparison for Specimen SH4. (a) Actuator displacement. (b) Shear span displacement on the X axis. Shear span displacement, in. Sh ea r f or ce , k ip s -1.5 -1 -0.5 0 0.5 1 1.5 -200 0 200 FEA Concrete part FEA tube part Figure 3.36. Shear force carried by the steel tube and the concrete part of Specimen SH4.

142 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Figures 3.37 and 3.38 show Von-Mises stress contours on the surface of the steel tube at the point where the steel tube yields (i.e., first yield point of the steel tube according to the finite ele- ment results), and at the point where the maximum experimental strength was obtained during the test. As shown in these figures, the yielding of the steel tube started from the center of the cross-section near the midspan of the specimen, and propagated toward the shear span ends at larger displacement. Figure 3.39 shows principal stress vectors on the concrete at the middle of the cross-section. The compression strut that developed in the concrete as a result of shear deflection can be seen in this figure. The increase in the shear strength of the concrete shown in Figure 3.36 is because of the development of such a diagonal compression strut. The length of shear span affects the strength of this strut. Figure 3.40 shows Von-Mises stress contours on the surface of the steel tube at the maximum positive displacement. The shear force carried by each part that was shown in Figure 3.36 is compared to the shear strength values that were calculated using the AASHTO BDS (2014) and the WSDOT BDM (2016) equations in Figure 3.41. As shown in Figure 3.41a, the shear strength of steel tube given by the AASHTO BDS (2014) matches the first yield strength obtained from finite element analy- sis. Also, it is observed that the shear strength given by the AASHTO BDS (2014) for the concrete part does not consider the effect of the compression strut discussed above and only considers the material based (cross-section) shear strength of the concrete. This can be seen by comparing the shear strength values given by AASHTO BDS (2014) with the shear force at the concrete at the unloading branches in Figure 3.41a. As shown in Figure 3.41b, the shear strength of the steel tube given by WSDOT BDM (2016) is about two times the shear force in the steel tube at the first yield point obtained from finite element analysis. Figure 3.37. Von-Mises stress contours on the steel tube of Specimen SH4 at first yield point.

Findings and Applications 143 Figure 3.38. Von-Mises stress contours on the steel tube of Specimen SH4 at maximum experimental strength point. Figure 3.39. Principal stress vectors on the concrete at the middle of the cross-section of Specimen SH4 at maximum experimental strength point.

144 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance 3.3.5. Proposed Shear Strength for RCFST Shafts As shown in the previous section, the shear strength values calculated using the WSDOT BDM (2016) equation for the tested RCFST shear specimens were close to the test results. However, the break-down of the total shear strength into the relative contributions of the steel tube (Vst) and concrete (Vc) components shows that the WSDOT BDM (2016) equation underestimates the shear strength of the concrete part and overestimates the shear strength of the steel tube. An alternative shear strength equation for composite RCFST members is proposed below by considering the developed compressive diagonal strut in the concrete and its interaction with the steel tube. The accuracy of the proposed equation is evaluated by comparing the values obtained with that equation with the experimental shear test results obtained as part of this project and from other researchers. Figure 3.40. Von-Mises stress contours on the steel tube of Specimen SH4 at the maximum positive drift. (a) (b) Shear span displacement, in. Sh ea r f or ce , k ip s -1.5 -1 -0.5 0 0.5 1 1.5 -300 -200 -100 0 100 200 300 FEA Concrete part FEA tube part FEA First yield Maximum exp. strength Vs AASHTO Vc AASHTO Shear span displacement, in. Sh ea r f or ce , k ip s -1.5 -1 -0.5 0 0.5 1 1.5 -300 -200 -100 0 100 200 300 FEA Concrete part FEA tube part FEA First yield Maximum exp. strength Vs WSDOT 2016 Vc WSDOT 2016 Figure 3.41. Comparison of component shear forces with (a) AASHTO BDS (2014) and (b) WSDOT BDM (2016).

Findings and Applications 145 In order to investigate the effect of the compressive shear strut in the concrete that develops in RCFST members under shear deformation, a series of supplementary finite element analyses were performed. Figure 3.42 shows a schematic view of the finite element models developed for the supplementary analyses. The boundary conditions were defined to simulate a double curva- ture setup. The supplementary finite element analyses that were conducted on the RCFSTs with different shear spans and boundary conditions showed that the development of the compression strut typically depends on the shear span and the composite action of the RCFST. According to the finite element analyses, three different behaviors can be attributed to the developing compression strut with respect to the RCFST’s shear span-to-concrete diameter (a/D) ratios. For a/D < 0.25, the strut size is governed by the length of the shear span a, while for 0.25 < a/D < 0.5, it will be governed by the diameter of the concrete core. For a/D of greater than 0.5, the strength of the compression strut was not significant and shear-flexural failure type was observed. Figures 3.43 to 3.48 show the typical finite element analyses results for the shear response and the three dimensional illustrations of the developing compression strut at various defor- mations for 12 in. diameter RCFSTs for three different a/D values that each falls in one of the three different a/D ranges discussed in the previous paragraph. For each a/D value, the first figure shows the relative contribution of the steel and concrete to the total shear strength and identifies the twelve drift values for which three-dimensional illustrations of iso-surfaces of the minimum principal stresses in the concrete core are presented in a sec- ond figure. The minimum principal stress represents the compression field in the concrete. Z X Y H a Figure 3.42. Loading and boundary conditions for the finite element models. Displacement, in Sh ea r fo rc e, ki p 0.05 0.1 0.15 0.2 0.250 0 50 100 150 200 250 300 350 Total RCFST Steel tube Concrete Steps of the 3D illustrations H=10in., a/D=0.4 1 2 3 4 5 6 7 8 9 10 11 12 Figure 3.43. Shear response of 12OD RCFST with a/D = 0.4.

146 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Figure 3.44. Three-dimensional illustrations of iso-surfaces of the minimum principal stresses in the concrete core at the steps marked in Figure 3.43. Displacement, in Sh ea r f or ce , k ip 0 0.02 0.04 0.06 0.08 0 50 100 150 200 250 300 350 400 Total RCFST Steel tube Concrete Steps of the 3D illustrations H=3in., a/D=0.12 1 2 3 4 5 6 7 8 9 10 11 12 Figure 3.45. Shear response of 12OD RCFST with a/D = 0.12.

Findings and Applications 147 Displacement, in Sh ea r fo rc e, ki p 0 0.05 0.1 0.15 0.2 0.25 0 50 100 150 200 250 Total RCFST Steel tube Concrete Steps of the 3D illustrations H=20in., a/D=0.8 1 2 3 4 5 6 7 8 9 10 11 12 Figure 3.47. Shear response of 12OD RCFST with a/D = 0.8. Figure 3.46. Three-dimensional illustrations of iso-surfaces of the minimum principal stresses in the concrete core at the steps marked in Figure 3.45.

Figure 3.48. Three-dimensional illustrations of iso-surfaces of the minimum principal stresses in the concrete core at the steps marked in Figure 3.47.

Findings and Applications 149 To clearly illustrate the development of the compression strut, principle stresses lower than 2.5 ksi are not shown in these figures. The range of the plotted minimum principal stress is shown on the right side of each figure. Based on the finite element results, a significant compression strut develops in Figures 3.44 and 3.46 for the a/D values of 0.4 and 0.12, which fall within the 0.25 < a/D < 0.5 and a/D < 0.25 ranges, respectively. Clearer illustrations of the strut developing in these models are shown in Figures 3.49 and 3.50. For both ranges, the centerplane of the compression strut passes through the intersection line of a horizontal plane at member’s mid height and vertical centerplane that is perpendicular to the direction of the shear loading. This is illustrated in Figures 3.49 and 3.50 for the specific examples. The crossing angle is 45°. As shown in these figures, under this assumption the cross-sectional area of the strut is at its maximum at the middle of the height Developing shear strut in the concrete core H Min. Prin. Stress/f’c Critical cross-section Figure 3.49. Definition of diagonal compression strut in RCFST with 0.25 < a/D <0.5. DC > 2H Figure 3.50. Definition of diagonal compression strut in RCFST with a/D < 0.25.

150 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance of the member (middle of the free span) and reduces toward both ends of the shear span. Also, the stress distribution throughout the strut is not uniform. In fact the compressive stresses are higher at both ends of the strut compared to its middle. This could be attributed to development of higher confining stresses at both ends of the shear member. The critical cross-section over which the force developed by the concrete strut can be assumed to be located at the mid length of the strut; a uniformly distributed stress equal to f c′ was assumed to develop in that cross-section, based on observation of the magnitude of the compressive stresses obtained from the finite element analyses. Figure 3.51 shows the defini- tion of the critical cross-section. This cross-sectional area of the strut (AStrut), from geometry, as shown in Figure 3.51, can be calculated by Equation 3.23. An approximate simpler formula for the strut cross-sectional area, which was developed based on a lower-bound approach, is also given in Equation 3.24. 2 2 4 asin 2 4 (3.23)2 2 2A R b R b R bStrut exact =     + −    ( ) where b D H b H R D c c 2 , 0 2 2 = − ≤ ≤ = and Dc = is the concrete core diameter, and H = is the height of the specimen in double curvature shear setup, which is equal to 2a. A b R bStrut approx 2 4 (3.24). 2 2= −( ) The strut force (FStrut) is calculated by multiplying the uniaxial unconfined compressive strength of the concrete by AStrut (Equation 3.25). The resulting strut force can be decomposed Assuming a uniform distribution of the strut cross-section Strut Width2b 2 Strut Width2b 2 2b 2 4R2 – b2 Dc Dc 2 2 H 2 h b 2 b Figure 3.51. Cross-sectional area of the diagonal compression strut at the critical location.

Findings and Applications 151 into horizontal and vertical force components, as shown in Figure 3.52 and calculated in Equation 3.26. The horizontal force component (VStrut) is considered as the shear strength of the strut. F f AStrut c Strut (3.25)= ′× 2 2 (3.26a)V FStrut Strut= × 2 2 (3.26b)P FStrut Strut= × In a composite RCFST member that is under shear deformation, the vertical force compo- nent (PStrut) of the strut transfers to the steel tube as a tensile axial load, as shown in Figure 3.52. This PStrut force can be considered as a uniform axial compressive and tensile force on the con- crete core and the steel tube, respectively. The shear strength of the concrete core of the RCFST (VConc) when a strut develops is there- fore assumed to be equal to VStrut. When no strut develops, the shear strength of concrete can be calculated using the existing shear strength equations that have been developed for the shear strength of the reinforced concrete members in the absence of strut. Therefore, a lower limit of concrete shear strength (Vc) was defined here for VConc, as shown in Equations 3.27 and 3.28. In Equation 3.28, the term outside the parenthesis is the nominal shear resistance of the concrete from AASHTO BDS (2014) Article 5.8.3.3. In this equation, β is a “factor indicating the ability of diagonally cracked concrete to transfer tension and shear” and was taken equal to 2.0. The term inside the parenthesis was added to include the axial load effect on the shear resistance of the concrete. This term was adopted from ACI 318 (2011) Article 11.2.1.2. max , (3.27)V V VConc Strut c( )= where V f A P A c c c Strut c 0.0316 1 2 (3.28)= β ′ +  To calculate the nominal shear resistance of the steel tube here, it was assumed that the tube cross-section was fully yielded under combined tension and shear, and the effect of bending moment was neglected. In this case, the total shear resistance of the steel tube (Vs) can be cal- culated by integrating the maximum shear stress over the steel tube cross-section as shown in Equation 3.29. PStrut PStrut FStrut PStrut FStrut VStrut 45º Figure 3.52. Horizontal and vertical components of the strut force.

152 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Shear distribution on the steel tube cross-section 1 3 2 cos (3.29),max 2 2 ,max 2 2F T V Rt ds y s s∫ ( )τ = − → = τ φ φ−π π where ts,max = is the maximum shear stress on the steel tube cross-section, Fy = is the yield stress of the steel tube, and T = is the tensile stress on the steel tube cross-section. The resulting Vs obtained from Equation 3.29 is shown in Equation 3.30. The term under the square root shows that the shear strength of the steel tube reduces as the strut force increases, and PStrut should be less than AsFy (for a diagonal strut at 45 degrees, PStrut = VStrut). Therefore, an upper limit was introduced for FStrut, as shown in Equation 3.31. V Dt F P A s y Strut s 4 2 3 (3.30)2 2 = −   V P f A A FStrut Strut c Strut s ymin 2 2 , (3.31)= = ′×     Finally, the nominal shear capacity of the composite RCFST shaft is taken here as equal to the summation of the shear strength of the concrete core and the steel tube, as shown in Equation 3.32. V V VCFST s conc (3.32)= + In order to account for the effect of an applied external compressive axial load (Paxial) on the nominal shear strength of the composite RCFSTs, it was assumed that the external load was dis- tributed between the steel tube and the concrete core proportionally to each component’s axial stiffness. The portion of applied Paxial that goes to each component is calculated in Equation 3.33. Paxial Paxial = Ps + Pc Steel tube Concrete Pc CFST Ps (3.33a)P P Paxial s c= + (3.33b)&P P A F P P f As Strut s y c Strut c c− ≤ + ≤ ′ (3.33c)P P EA EA EA A Fs axial s s c s y ( ) ( ) ( ) = + ≤ (3.33d)P P P f Ac axial s c c= − ≤ ′ where Ps and Pc are the proportions of the external axial load that acts on the steel tube and concrete infill, respectively. Considering the applied external axial load on each component, the nominal shear strength of the steel tube and the concrete core were modified as shown in Equa- tions 3.34 to 3.36. The presence of an applied compressive axial load reduces the shear strength of the steel tube and increases the concrete shear strength. In Equation 3.36, a factor α(Pc, Ac)

Findings and Applications 153 is introduced to consider the possible increasing effect of the axial load on the strength of the compression strut, but that effect is neglected in all further calculations here (α[Pc, Ac] = 1). 4 2 3 Modified Equation (3.30) for external axial load (3.34)2 2 V Dt F P P A s y Strut s s = − −  V f A P P A c c c Strut c c 0.0316 1 2 Modified Equation (3.28) for external axial load (3.35)= β ′ + +  V f A P A A F PStrut c Strut c c s y smin 2 2 , , Modified Equation (3.31) for external axial load (3.36) ( )= ′ × α +   3.3.6. Comparison of the Proposed Shear Strength with the Experimental Data The proposed nominal shear strength for the composite RCFST shafts introduced in Sec- tion 3.3.5 was compared with the results of the shear specimens tests. The test specimens proper- ties and calculated shear strength values are presented in Table 3.9. As discussed previously, the shear specimens were tested using a pantograph that ensured pure shear at mid length under double curvature flexure and no axial load was applied to the specimens. Table 3.10 shows the comparison of the experimentally obtained shear strength of the RCFST specimens with the calculated shear strength obtained using the proposed formula, as well as using the shear strength equations provided in AASHTO BDS (2014) and in the WSDOT BDM (2016). For all the RCFST specimens, the experimental values are, on average, 55%, 7%, and 137% more than the shear strength calculated by the proposed formula, WSDOT BDM (2016), and AASHTO BDS (2014), respectively. In all the presented shear strength equations, the total shear strength of the RCFST is given in terms of summation of the shear strengths carried by the concrete, steel tube, and rebar cage parts. Sp ec im en , in , in , in , ksi , ksi , ksi , ksi , kips , kips SH2 16.0 6.5 0.41 0.233 68.8 2.9 2757 51 0 0 437 273 1.60 0.21 0.79 0.21 SH3 12.8 5.0 0.39 0.233 54.8 0.0 0 58 0 0 226 199 1.14 0.00 1.00 0.00 SH4 12.8 5.0 0.39 0.233 54.8 4.5 3434 58 0 0 396 260 1.52 0.24 0.76 0.24 SH5 12.8 5.0 0.39 0.233 54.8 4.5 3434 58 0 0 397 260 1.53 0.24 0.76 0.24 SH6 12.8 5.0 0.39 0.233 54.8 4.5 3434 58 0 0 414 260 1.59 0.24 0.76 0.24 SH7 12.8 5.0 0.39 0.233 54.8 4.5 3434 58 0 0 407 260 1.57 0.24 0.76 0.24 SH1R 12.8 5.0 0.39 0.233 54.8 4.5 3434 58 0 0 404 260 1.55 0.24 0.76 0.24 Table 3.9. Shear test specimens properties, results, and comparison with proposed formula.

154 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance The shear forces carried by the steel tube and the concrete core parts from the finite element analysis of the tested shear specimen SH4 were compared with AASHTO BDS (2014), WSDOT BDM (2016), and the proposed formula in Figure 3.53. As shown in this figure, at the maxi- mum experimental strength point, AASHTO BDS (2014) underestimates the shear strength contribution of both the steel and concrete. The WSDOT BDM (2016) underestimates the shear force in the concrete part and overestimates the force carried by the steel tube. As shown in Figure 3.53c, the proposed equation gives a good estimate of the shear strength respectively resisted by the steel tube and the concrete. Both the proposed method and the WSDOT BDM (2016) in particular give a good estimate of the total shear strength of the composite RCFST. However, the WSDOT BDM (2016) does not provide a correct estimate of the shear strength resisted by each individual component of the RCFST. It is important for design purposes to use an equation that provides a good estimate of the contribution of the total shear resisted by each component of RCFST, as this indicates that the design equation is more anchored in the actual physical behavior of the structural member, thus providing more confidence in the design. Overestimating the strength of one component could also result in an unexpected failure should that component become dominant in providing the total shear strength of that member. The strengths calculated using the proposed shear strength formula were also compared to the strengths developed in other shear tests reported in the existing literature. A limited number of tests have been conducted in the past to determine the shear strength of RCFST members. Table 3.11 shows a summary of the specimen diameters and test setup details of previous experiments done by different researchers. The test setups, specimen failures, test specimen properties, test results, and comparisons of the shear strengths obtained experimentally and using the proposed equation are presented in Section I.2 of Appendix I. The ratios of the shear strength obtained experimentally and using the proposed equation for all the available test data for which no axial load was applied are shown in Figure 3.54. The horizontal axis in this figure represents the shear span-to-depth ratio. The mean and standard deviation values of the results are included in the figure. As shown, on average, the experimental values are about 50% more than the values predicted by the proposed formula. The experimental-to-proposed shear strength ratios for all the available test data including the axial load are shown in Figure 3.55. As shown, on average the experimental values are about Specimen Strength ( ), kips (Experimental) AASHTO BDS (2014) ( ), kips WSDOT BDM (2016) ( ), kips Proposed , kips SH2 (16OD CFST) 437 189 401 273 2.31 1.09 1.60 SH3 (12OD Hollow) 226 154 318 199 1.47 0.71 1.14 SH4 (12OD CFST) 396 170 357 260 2.33 1.11 1.52 SH5 (12OD RCFST) 397 170 379 260 2.34 1.05 1.53 SH6 (12OD RCFST) 414 170 405 260 2.44 1.02 1.59 SH7 (12OD RCFST) 407 170 379 260 2.39 1.07 1.57 SH1R (12OD RCFST) 404 170 379 260 2.38 1.07 1.55 Table 3.10. Comparison of experimentally obtained strengths with existing shear strength equations and the proposed shear strength formula.

Findings and Applications 155 (a) (c) Shear span displacement, in. Sh ea r fo rc e, ki ps -1.5 -1 -0.5 0 0.5 1 1.5 -300 -200 -100 0 100 200 300 FEA Concrete part FEA tube part FEA First yield Maximum exp. strength V s AASHTO V c AASHTO Shear span displacement, in. -1.5 -1 -0.5 0 0.5 1 1.5 Sh ea r fo rc e, ki ps -300 -200 -100 0 100 200 300 FEA Concrete part FEA tube part FEA First yield Maximum exp. strength V s WSDOT 2016 V c WSDOT 2016 (b) Shear span displacement, in. -1.5 -1 -0.5 0 0.5 1 1.5 Sh ea r fo rc e, ki ps -300 -200 -100 0 100 200 300 Figure 3.53. Comparison of component shear forces of the 12 in. shear specimen (SH4). (a) AASHTO BDS (2014). (b) WSDOT BDM (2016). (c) Proposed.

156 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance Research Test Setup Loading type Diameter range, in. range range University at Buffalo (current research) Double curvature Cyclic pantograph 12 and 16 0.4 0 Roeder et al. (2016) Single curvature Monotonic four point bending 20 0.25 - 1.0 0 and 0.085 Ye et al. (2016) Double curvature Monotonic three point bending 4.7 0.15 - 0.75 0 - 0.73 Nakahara and Tsumura (2014) Double curvature Cyclic pantograph 6.5 0.5 0 - 0.4 Xiao et al. (2012) Single curvature Monotonic three point bending 6.5 0.14 - 1.0 0 - 0.62 Xu et al. (2009) Single curvature Monotonic three point bending 5.5 0.1 - 0.5 0 Qian et al. (2007) Single curvature Monotonic three point bending 7.7 0.1 - 0.3 0 - 0.77 a D Table 3.11. Summary of the existing test data on shear strength of RCFST members. Mean Mean+STD Mean-STD Figure 3.54. Comparison of existing test results of tests with no applied axial load and the proposed shear strength formula. 75% more than the values predicted by the proposed formula. According to Figure 3.55a, the proposed formula gives more conservative values for the cases with more than 0.5 P/P0 applied axial load. Also, Figure 3.55b shows that the predicted values using the proposed formula are more conservative for a/D ratios of less than 0.2. For the Roeder et al. (2016) tests, the specimens that reportedly had a dominant flexural failure were excluded in the calculation of mean and standard variation. These specimens are indicated in Section I.2 of Appendix I. For the Ye et al. (2016) tests, the specimens with shear span-to-depth ratio of less than 0.1 were also excluded in the evaluation of the proposed shear formula. Here, all the other available data for the variety of a/D values were used in evaluating the performance of the proposed equation. However, not all the tested specimens may have had a shear failure mode. The test results observations provided by Xiao et al. (2012) and Ye et al.

Findings and Applications 157 (a) (b) Mean Mean+STD Mean-STD (Conservative approach) P0 = Ac fc′ + AsFy Figure 3.55. Comparison of all the existing test results and the proposed shear strength formula. (a) Horizontal axis shows the variations of P/P0. (b) Horizontal axis shows the variations of a/D. (2016) for tested specimens having a/D values as low as 0.1 and 0.15 suggest that some of those specimens may have had a mixed failure mode of shear combined with other local-crushing phenomena. While the results obtained with the proposed equation are safe even when includ- ing those results (as shown in Figure 3.55), by excluding the test results of a/D ≤ 0.15, the mean value of experimental-to-proposed shear strengths would improve to 1.59 with a lower standard deviation of 0.32. 3.4. Economic Impact Investigation of the economic impacts of the proposed revisions was done by performing revised designs of actual bridge structures using the proposed revisions and comparing them with the designs made by current versions. The economic impacts of the proposed revisions are presented in Appendix L.

158 Contribution of Steel Casing to Single Shaft Foundation Structural Resistance 3.5. Design Examples for the Proposed Revisions 3.5.1. Example 1: Force-Based Design of RCFST This example presents an RCFST used to support a single column bent. The plastic hinge is assumed to develop in the column, and therefore the RCFST is a capacity-protected element. This example provides all calculations to ensure transfer of these loads into the RCFST and a check of the strength of the RCFST. Use of shear rings at top of the shaft as shear transfer mecha- nisms between the concrete and steel tube and their design process is also shown. This example also provides calculations for the shear strength of the designed RCFST shaft at its top and also below the soil level at an assumed location of liquefiable layers. The outline of the calculations for the design Example 1 is as following: 1. Check of the limitations and requirements per revised AASHTO BDS (2014) Article 6.9.6.2. 2. Calculation of the nominal axial capacity per AASHTO BDS (2014) Article 6.9.6.3. 3. Calculation of the nominal flexural resistance per AASHTO BDS (2014) Article C6.12.2.3.3. 4. Generating of the material-based P-M interaction curve. 5. Calculation of the nominal and factored stability-based P-M interaction curve per AASHTO BDS (2014) Article 6.9.6.3.4. 6. Check of the factored capacity of the RCFST shaft with the design demands. 7. Calculation of the factored stability-based P-M interaction curve per AASHTO SGS (2014) Article 7.6.2 and comparison with the results of item 5. 8. Design of shear transfer mechanisms at top of the shaft per AASHTO BDS (2014) Article 6.9.6.3.5. 9. Calculation of the shear capacity of the RCFST shaft at its top (non-composite assumption) and below the soil level (composite assumption) per proposed equations for shear capacity of RCFST shafts. This process was included in Mathcad v15.0 software worksheets for design engineers. The details of the example and Mathcad worksheets are printed in Appendix K. 3.5.2. Example 2: Displacement-Based Design of RCFST This example presents an RCFST used to support a single reinforced concrete column bent of the same diameter. In this example, the plastic hinge is allowed to develop in the RCFST below ground. This example provides calculations of the displacement capacity of the RCFST shaft to compare against demand. The outline of the calculations for the design Example 2 is as following: 1. Determination of the materials stress–strain behaviors to be used in generation of moment– curvature (M-φ) curves. 2. Calculation of the effective stiffness of the cross-section per AASHTO BDS (2014) Arti- cle 6.9.6.3.2. 3. Calculation of the proposed limit states for the ultimate and damage curvatures per the pro- posed equations provided in Section 3.2.6 of the report. 4. Generating the M-φ curve by fiber-section analyses. 5. Calculation of idealized bilinear M-φ curve per AASHTO BDS (2014) Article 8.5. 6. Calculation of plastic hinge length per AASHTO SGS (2014) Article 4.11.6-4. 7. Calculation of the displacement capacity of the RCFST shaft using the equivalent cantilever model. This process was included in Mathcad worksheets for design engineers. The Mathcad work- sheets are printed in Appendix K.