shear capacity would be uneconomical. could be increased by adding flexural reinforcement but that this approach to increasing the 1.3 Ultimate strength analysis method by ASCE-ACI Committee 326 Figure 2.2: Moment-shear interaction diagram by Zaghlool (1971) Table 2.1: Values of k,, k,, and k, (Stamenkovic, 1969) 2.1.11 Study of slab-column behaviour by Regan exceed twice the reinforcement yield stress. n 1981, Regan developed various design equations using experimental data relating to flexure, provided in Table 2.1; X, is the minimum of the top and bottom reinforcement circumference; influenced the punching capacity of slab-column connections. These parameters includec Figure 2.5: Shear capacity versus eccentricity for interior connections (Regan, 1981) Equation 2.36 using coefficients of 1.0, 1.5, and 2.0 is plotted in Figure 2.5. Considering all aforementioned effects, Regan proposed that the ultimate load for interior in Equation 2.36 could be modified to 1.0 or 2.0 to better correlate to some experimental data. Figure 2.6: Critical sections located: a) 0.5d away from column, and b) 0.5d away from are the same for both CSA A23.3-19 and ACI 318-19. a/a trom the outermost peripheral line of shear reinrorcement (secuion 42.0.4.2). Lhe Critical perimeter, b,, for Section 22.6.4.1 and Section 22.6.4.2 is presented in Figure 2.6. The dimension b, defines the length of the critical perimeter parallel to the axis of the unbalanced moment. Similarly, the dimension b, defines the critical perimeter length orthogonal to the unbalanced moment axis. This figure applies to CSA A23.3-19 as the critical section definitions ara tha anma fav hnth ICA AYNQIQ 10 any ANT 21010 inbalanced moment axis. This figure applies to CSA A23.3-19 as the critical section definition: moment. Similarly, the dimension b, defines the critical perimeter length orthogonal to the 2.2.1.2 Two-way shear strength Table 2.2: Maximum v, for two-way members with shear reinforcement (ACI Committee 318, 2019) The two-way shear strength provided by shear reinforcement is provided by Section 22.6.7.2: reinforcement. Table 2.2 presents Section 22.6.6.1 as presented in the ACI code. The polar moment of inertia, J,, is given by The required minimum amount of punching shear reinforcement is such that pressure as outlined by Section 6.1.3.3. Figure 3.1: Hognestad parabola for defining concrete compression uniaxial stress-strain data Figure 3.2: Typical concrete tensile uniaxial stress-strain data energy required for a unit area of concrete to fracture in tension. Table 3.1: Base values of fracture energy Gr as per Model Code 1990 The base value of the fracture energy, Gr, is determined using Table 3.1. size dmax, fem 18 the mean value of concrete compressive strength, and f.,, is equal to 10 MPa Figure 4.1: Boundary conditions used for FE analyses of SM specimens y 305 mm. The dimension of the slab was 1830 mm by 1830 mm. 4.4 Concrete properties Figure 4.2: Concrete mesh used for FE analyses of SM specimens Figure 4.3: Compression stress-strain data used for FE analyses of SM specimens Linear-elastic data Table 4.1: Compression reinforcement properties for FE analyses of SM specimens Table 4.2: Tension reinforcement properties for FE analyses of SM specimens Figure 4.5: Concrete material assignments for FE analyses of SM specimens Figure 4.6: Reinforcement stress-strain data used for FE analyses of SM specimens The steel reinforcement stress-strain data is shown in Figure 4.6. analysis and the experiment was 68.7-percent. analyses. However, the ultimate rotation percentage difference between the softer column Table 5.2: Specimen SM 1.0 analyses results using varying column moduli of elasticity E Figure 5.4: Specimen SM 1.0 analyses crack patterns using varying values for modulus of elasticity E The experiment and analyses crack patterns are shown in Figure 5.6. Among the top face cracl patterns, all analyses showed cracks propagating from the left, top, and right column faces Table 5.3: Specimen SM 1.5 analyses results using varying column moduli of elasticity E Table 5.4: Support lengths analysed for corner boundary condition study the experiment displaced a distance of 10.9 mm. This is a percentage difference of 10.1-percent Figure 5.10: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns for boundary condition analyses BC1 through BC4. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.11: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns for boundary condition analyses BC1 through BC4. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. be unloaded before photographing. Figure 5.11: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack crushing failure. Table 5.6: Specimen SM 0.5 results for analyses BC1-E through BC4-E Figure 5.13: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns for boundary condition analyses BC1-E through BC4-E. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. show the compressive support failure common to all analyses. experiment did not form among the “E” analyses. support failure counteracted the downward column displacement due to the column loading. Table 5.7: Specimen SM 1.0 results for analyses BC1 through BC4 Figure 5.16: Specimen SM 1.0 analyses crack patterns for boundary condition analyses BC! through BC4 SM 1.0 are shown in Figure 5.18. Among both top and bottom face crack patterns, the previously Table 5.8: Specimen SM 1.0 results for analyses BC1-E through BC4-E in increased angles between the diagonal cracks which form between the column and slab edges. Table 5.9: Specimen SM 1.5 results for analyses BC1 through BC4 The bottom face crack patterns of the experiment and analyses BC1 through BC4 for specimen Figure 5.21: Specimen SM 1.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns for boundary condition analyses BC1 through BC4. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Compared to analyses BC1 through BC4, analyses BC1-E through BC4-E showed similar Table 5.10: Specimen SM 1.5 results for analyses BC1-E through BC4-E [he bottom face crack patterns of the experiment and analyses BCI-E through BC4-E for Figure 5.25: Boundary conditions used for option A study of preventing support failure study Figure 5.27: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns for option A and base case analyses. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. decrease in slope due to support failure did not happen with the option A analysis. Figure 5.29: Specimen SM 1.0 analyses crack patterns for top and bottom of slab edges restrained analysis versus bottom of slab edges restrained analysis The experiment and analyses crack patterns for option A and base case analyses for specimen lable 5.13: Specimen SM 1.5 analyses results for top and bottom of slab edges restrained preventing lift of the slab edge and therefore the column d) Bottom face, top and bottom of failing slab edves restrained Figure 5.32: Typical a) material properties and b) meshing for option B analyses Figure 5.34: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns for elastic lifting slab edge analysis versus plastic lifting slab edge restrained analysis. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. the lifting slab edge. Figure 5.36: Specimen SM 1.0 analyses crack patterns for elastic lifting slab edge analysis versus plastic lifting slab edge restrained analysis Figure 5.38: Specimen SM 1.5 experiment (Ghali et al., 1976) and analyses crack patterns for elastic lifting slab edge analysis versus plastic lifting slab edge restrained analysis. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. stresses. Since concrete performs well in compression, support failure was unlikely to occur. specimen 0.5 are presented in Figure 5.41. A summary of this data is provided in Table 5.18. Figure 5.40: Specimen SM 0.5 a) moment-rotation and b) displacement-rotation data for the option C analysis was similar to the base case analysis. d) Bottom face, changing boundary conditions between loads differences in crack patterns were evident between the two analyses. for changing support boundary conditions between loads analysis versus static boundary higher for option C (4.0 mm) compared to the base case (3.5 mm). changing support boundary conditions between loads analysis versus static boundary The analyses crack patterns for option C and base case analyses for specimen SM 1.0 are shown Figure 5.43: Specimen SM 1.0 analyses crack patterns for changing support boundary conditions between loads analysis versus static boundary conditions analysis Figure 5.44: Specimen SM 1.5 a) moment-rotation and b) displacement-rotation data for option C analysis (2.7 mm versus 2.0 mm). Table 5.19: Specimen SM 1.5 analyses results for changing support boundary conditions d) Bottom face, changing boundary conditions between loads c) Top face, changing boundary conditions between loads Figure 5.45: Specimen SM 1.5 experiment (Ghali et al., 1976) and analyses crack patterns for changing support boundary conditions between loads analysis versus static boundary conditions analysis. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.47: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns for the support failure prevention options and base case. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.48: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns for the support failure prevention options and base case. Authorized reprint 0 experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.48: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack Table 5.20: Base values of fracture energy Gr, (Comité Euro-International du Béton, 1993) 5.4.1 Results of specimen SM 0.5 analyses Table 5.21: Fracture energy G, values used in analyses of SM specimens mm, the largest possible maximum aggregate size used was 19 mm. Table 5.22: Specimen SM 0.5 analyses results using MC 1990 versus MC 2010 fracture The crack patterns of the experiment as well as the MC 1990 and MC 2010 fracture energy Figure 5.50: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns using MC 1990 versus MC 2010 fracture energy models. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. are presented in Figure 5.52. As observed with the specimen SM 0.5 analyses, both specimen percentage difference of 88-percent. However, both analyses underestimated the experiment displacement at ultimate moment by a Figure 5.52: Specimen SM 1.0 analyses crack patterns using MC 1990 versus MC 2010 fracture energy models principal plastic strain magnitudes. difference of 122.9-percent. Table 5.24: Specimen SM 1.5 analyses results using MC 1990 versus MC 2010 fracture Figure 5.54: Specimen SM 1.5 experiment (Ghali et al., 1976) and analyses crack patterns using MC 1990 versus MC 2010 fracture energy models. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. 5.5.2 Results of specimen SM 1.0 analyses fhe moment-rotation and displacement-rotation data for the equivalent and as-teste d) Bottom face, equivalent reinforcement layout Table 5.26: Specimen SM 1.0 analyses results using equivalent versus as-tested reinforcement lavouts percent lower and 33-percent lower than those experimental values. Figure 5.58: Specimen SM 1.0 analyses crack patterns using equivalent versus as-tested reinforcement layouts [he crack patterns of the experiment as well as the equivalent and as-tested reinforcement layout 1) Bottom face, equivalent reinforcement layout c) Top face, equivalent reinforcement layout Figure 5.60: Specimen SM 1.5 experiment (Ghali et al., 1976) and analyses crack patterns using equivalent versus as-tested reinforcement layouts. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. 5.5.4 Conclusions and recommendations Using equivalent reinforcement layouts (i.e. changing the depths and spacings of the inner reinforcement mats to match the outer reinforcement depths and spacings) produced near Table 5.28: Specimen SM 0.5 results using varying concrete mesh sizes Gradually increasing the size of concrete elements eventually resulted in single elements that Figure 5.62: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete mesh sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. differences between the crack patterns of the four analyses. Figure 5.63: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete mesh sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. propagated further away from the column face compared to the other analyses. Table 5.29: Specimen SM 1.0 results using varying concrete mesh sizes size analyses for specimen SM 1.0 are presented in Figure 5.65. The 15 mm concrete mesh size Figure 5.64: Specimen SM 1.0 a) moment-rotation and b) displacement-rotation data using varying concrete mesh sizes same Curve. Table 5.30: Specimen SM 1.5 results using varying concrete mesh sizes Figure 5.66: Specimen SM 1.5 a) moment-rotation and b) displacement-rotation data using varying concrete mesh sizes Figure 5.67: Specimen SM 1.5 top face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete mesh sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. produced top face crack patterns that best resembled the experimental crack patterns. Figure 5.68: Specimen SM 1.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete mesh sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. was also observed in all four analyses. respectively. These two analyses also produced the largest rotations of all analyses. ind element type analyses for specimen SM 0.5 are presented in Figure 5.70. For each Figure 5.70: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns using varying reinforcement mesh types and sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.71: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns using varying reinforcement mesh types and sizes. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. observed among the photographed experiment crack patterns. Figure 5.74: Specimen SM 1.0 bottom face analyses crack patterns using varying reinforcement mesh types and sizes 0.5 and SM 1.0 analyses, the T3D2 analyses and the B31 analyses produced crack patterns similar rotations at ultimate moments between 10.8 mm and 11.7 mm. All analyses produced similar displacement-rotation data to one another. All analyses had Table 5.33: Specimen SM 1.5 results using varying reinforcement mesh types and sizes cracks as the strains were distributed over an even longer element length. crack pattern differences were observed among the analyses. used higher dilation angles. iterion. This was evident by the higher rotational stiffness and capacity of the analyses which Table 5.34: Specimen SM 0.5 results using varying concrete dilation angles Linear interpolation could be done to determine the dilation angle required to reproduce the Figure 5.79: Specimen SM 0.5 a) moment versus dilation angle and b) displacement versus dilation angle data using varying concrete dilation angles displacement versus dilation angle graph as a red triangle. Figure 5.80: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete dilation angles. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.80: Specimen SM 0.5 top face experiment (Ghali et al., 1976) and analyses crack magnitudes were not used as a criterion for determining analysis accuracy. Figure 5.81: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete dilation angles. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.81: Specimen SM 0.5 bottom face experiment (Ghali et al., 1976) and analyses crack Table 5.35: Specimen SM 1.0 results using varying concrete dilation angles Figure 5.83: Specimen SM 1.0 a) moment versus dilation angle and b) displacement versus dilation angle data using varying concrete dilation angles ultimate moments increased with increases in dilation angle. ‘he displacements at ultimate moments were the same for all analyses but the rotations at Table 5.36: Specimen SM 1.5 results using varying concrete dilation angles Figure 5.86: Specimen SM 1.5 a) moment versus dilation angle and b) displacement versus dilation angle data using varying concrete dilation angles on the vertical displacement versus dilation angle graph as a red triangle. Figure 5.87: Specimen SM 1.5 top face experiment (Ghali et al., 1976) and analyses crack patterns using varying concrete dilation angles. Authorized reprint of experiment photograph from ACI Journal, Volume 73, Issue 10, October 1976. Figure 5.89: Analysis ultimate moments minus experiment ultimate moments versus dilation angles for specimens a) SM 0.5, SM 1.0, and SM 1.5; and b) SM 0.5 and SM 1.0 result in the lowest overall error was 42.3 degrees. [he crack patterns for the specimen SM 0.5 analyses including and excluding self-weight, in produced identical crack patterns to one another. Table 5.37: Specimen SM 0.5 analyses results when including versus excluding self-weight Figure 5.92: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns when including versus excluding self-weight. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. presented in Figure 5.94. Both analyses produced identical crack patterns to one another. Figure 5.93: Specimen SM 1.0 a) moment-rotation and b) displacement-rotation data when including versus excluding self-weight pecimen SM 1.0 was not enough to affect the results. Figure 5.94: Specimen SM 1.0 analyses crack patterns when including versus excluding self- weight The crack patterns for the specimen SM 1.5 analyses including and excluding self-weight, ir produced identical crack patterns to one another. Table 5.39: Specimen SM 1.5 analyses results when including versus excluding self-weight Figure 5.96: Specimen SM 1.5 experiment (Ghali et al., 1976) and analyses crack patterns when including versus excluding self-weight. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. Table 5.40: Concrete properties of specimens tested by El-Salakawy (1998) Salakawy’s specimens. Table 5.41: Required tangent modulus of elasticity coefficients for El-Salakawy’s specimens curve compared to the classical Hognestad parabolas for these same specimens. 5.10.2 Results of specimen SM 0.5 analyses percent for the reduced and original EF, analyses, respectively. [he displacement at ultimate moment percentage difference was 108.9-percent and 123.6 The crack patterns for the specimen SM 0.5 analyses using strain-hardening versus perfectly- Figure 5.108: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns using strain-hardening versus perfectly-plastic reinforcement. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. plastic reinforcement are presented in Figure 5.110. Both analyses produced identical crack until the specimen failed. yortion of the stress-strain data was not important as the reinforcement remained linear elastic Figure 5.110: Specimen SM 1.0 analyses crack patterns using strain-hardening versus perfectly- plastic reinforcement The crack patterns for the specimen SM 1.5 analyses using strain-hardening versus perfectly- Figure 6.1: Concrete mesh used for FE analyses of SM specimens presented in Section 5.10. Figure 6.3: Tension stress-strain data used for FE analyses of SM specimens Figure 6.4: Concrete material assignments for FE analyses of SM specimens were ten times those presented in Figure 6.2. Table 6.1: Compression reinforcement properties for FE analyses of SM specimens Table 6.2: Tension reinforcement properties for FE analyses of SM specimens values (i.e. ten times the modulus of elasticity of the slab concrete). Figure 6.5: Reinforcement stress-strain data used for FE analyses of SM specimens 6.1.4 Moment versus rotation results and the experiment were 131.9 kNm and 127.1 kNm, respectively. 50-percent increase in reinforcement area, the difference in ultimate moment between specimen SM 1.0 and SM 1.5 was minimal. It was expected that the ulttmate moment of specimen SM 1.5 Figure 6.8: Specimen SM 1.5 moment-rotation results kNm and 131.5 kNm, respectively. Figure 6.9: Specimen SM 0.5 vertical displacement versus rotation results Figure 6.10: Specimen SM 1.0 vertical displacement versus rotation results its ultimate moment (i.e. for rotations between 15 mrad and 27 mrad). The vertical displacement versus rotation results for specimen SM 1.5 are presented in Figure Figure 6.11: Specimen SM 1.5 vertical displacement versus rotation results Figure 6.12: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns. Authorized reprint of experiment photographs from ACI Journal, Volume 73, Issue 10, October 1976. Figure 6.12: Specimen SM 0.5 experiment (Ghali et al., 1976) and analyses crack patterns. Figure 6.13: Specimen SM 1.0 FE analyses crack patterns patterns of specimen SM 1.0 were similar to those of specimen SM 1.5. concentrations observed during laboratory testing. Figure 6.15: Boundary conditions used for FE analyses of specimens XXX and HXXX maintaining the e = F,1/F, ratios of the experiments. 6.2.2 Concrete properties equal to 1320 mm. The magnitudes of forces F, and F, were selected arbitrarily while Figure 6.17: Compression stress-strain data used for FEA of specimens XXX and HXXX Figure 6.18: Tension stress-strain data used for FEA of specimens XXX and HXXX Table 6.3: Compression reinforcement properties for FEA of specimens XXX and HXXX Table 6.4: Tension reinforcement properties for FEA of specimens XXX and HXXX Table 6.5: Column reinforcement properties for FEA of specimens XXX and HXXX igure 6.19: Concrete material assignments for FE analyses of specimens XXX and HXXX Figure 6.20: 5M reinforcement stress-strain data used for specimens XXX and HXXX FE analyses The true stress-strain data for the 10M steel reinforcement is shown in Figure 6.21. Linear-elastic data 6.2.4 Moment versus rotation results The FEA and experiment moment versus rotation results for specimen XXX and HXXX are Figure 6.22: Moment versus rotation results for specimens XXX and HXXX Figure 6.23: Load versus displacement results for specimens XXX and HXXX specimen HXXX FE analysis and experiment were 58.5 kNm and 70.0 kNm, respectively. Figure 6.24: Top view of specimen XXX experiment (El-Salakawy, 1998) and FEA crack patterns. Photograph reprinted from Shear behaviour of reinforced concrete flat slab-column edge connections with openings (p.115), by E. El-Salakawy, 1998. Reprinted with permission. were tangential to the column faces in the vicinity of the column. Figure 6.24: Top view of specimen XXX experiment (El-Salakawy, 1998) and FEA crack column face toward the inner slab corners. Furthermore, the FEA reproduced the cracks whic Figure 6.25: Perspective view of specimen XXX experiment (El-Salakawy, 1998) and FEA crack patterns. Photograph reprinted from Shear behaviour of reinforced concrete flat slab- column edge connections with openings (p.122), by E. El-Salakawy, 1998. Reprinted with permission. Figure 6.26: Perspective view of specimen HXXX experiment (El-Salakawy, 1998) and FEA crack patterns. Photograph reprinted from Shear behaviour of reinforced concrete flat slab- column edge connections with openings (p.143), by E. El-Salakawy, 1998. Reprinted with permission. Figure 6.27: Column view of specimen HXXX experiment (El-Salakawy, 1998) and FEA crack patterns. Photograph reprinted from Shear behaviour of reinforced concrete flat slab- column edge connections with openings (p.146), by E. El-Salakawy, 1998. Reprinted with permission. Figure 6.28: Boundary conditions used for FE analysis of specimen SB1 6.3.2 Concrete properties Figure 6.29: Concrete mesh used for FE analysis of specimen SB1 The concrete compression and tension stress-strain data are presented in Figure 6.30 and Figure Note: Element length 1, is equal to 19.44 mm Figure 6.30: Compression stress-strain data used for FE analysis of specimen SB1 Linear-elastic data The concrete material assignments used for the FE analysis of specimen SB1 are shown ti Figure 6.32. The column modulus of elasticity E, was ten times the value presented in Figure Figure 6.32: Concrete material assignments for FE analysis of specimen SB1 Table 6.6: Compression reinforcement properties for FE analysis of specimen SB1 Table 6.7: Tension reinforcement properties for FE analysis of specimen SB1 Table 6.8: Column reinforcement properties for FE analysis of specimen SB1 Figure 6.33: Reinforcement stress-strain data used for specimen SB1 analysis The true stress-strain data for the steel reinforcement is shown in Figure 6.33. Figure 6.34: Specimen SB1 vertical load versus vertical displacement results analysis and the experiment were 226.3 KN and 250.4 KN, respectively. Figure 7.1: Moment-rotation results for specimen SM 0.5 subjected to varying vertical loads vertical column displacements as shown in Figure 7.2. compression flexural failure is shown in Figure 7.3. Figure 7.4: Moment-rotation results for specimen SM 1.0 subjected to varying vertical loads Figure 7.5: Moment-rotation results for specimen SM 1.5 subjected to varying vertical loads reinforcement yielding was observed for specimens with initial vertical loads less than 129 kN. Figure 7.6: Moment versus vertical load results for SM specimens 7.3 Vertical load capacity versus eccentricity failed due to punching rather than flexure. Figure 7.8: Moment-shear interaction diagram for the SM specimens Figure 8.1: Critical perimeter elements used to develop stress-based analysis method Model Code 2010 design codes. The elements studied are shown in Figure 8.1. Figure 8.2: Typical shear stress distribution at critical perimeter under only vertical load average shear stresses along the critical perimeter were nonlinear. Figure 8.4: Critical elements at additive side of critical section 8.1 Average shear stresses of critical elements versus applied moment Figure 8.5: Average shear stress versus moment for specimen SM 0.5 FE analyses Figure 8.6: Average shear stress versus moment for specimen SM 1.0 FE analyses Figure 8.7: Average shear stress versus moment for specimen SM 1.5 FE analyses s equal to V/b,d (where b, is the critical perimeter at d/2 from the column and d is the effective stress 0, was applied). The moment contribution to the average shear stress, vy, is assumed to be equal to uniaxial compressive stress Ag would be less than the change in uniaxial stress Ao, (i.e. when Figure 8.11: Values of a coefficient versus vertical loads From linear regressions, the slope of the a-V data m for all specimens is determined to be Figure 8.12: Ultimate average shear stresses versus vertical loads for SM FE analyses Figure 9.1: Average shear stress versus moment for SM specimens (V = 140 KN) Figure 9.2: Average shear stress versus moment for SM specimens (V = 160 KN) 0.30, 0.33, and 0.35, respectively. Table 9.1: Proposed values of y, for SM specimens subjected to only moments or only vertical loads Figure 9.3: Average shear stress versus moment for SM specimens (V = 180 KN) ould ensure that the specimen failed in punching shear rather than flexure under low vertica To summarize, none of the design codes’ punching shear provisions accurately predicted the Table 9.2: Experiment, FEA, and code-predicted capacities for specimen XXX he experiment, FEA, and code-predicted maximum vertical loads and moments for specimen IXXX are presented in Table 9.3. ACI 318-19 predicted a maximum vertical load closest to hat of the experiment. The next closest prediction was produced by EC2-2004 then MC 2010 LoA IV). Relative to the FEA, MC 2010 (LoA IV) was the most accurate followed by EC2- 1004 then ACI 318-19. Contrary to the specimen XXX predictions, the MC 2010 predictions ncreased in accuracy with increasing LoA level. Table 9.3: Experiment, FEA, and code-predicted capacities for specimen HXXX Table 9.4: Experiment, FEA, and code-predicted capacities for specimen SB1
