Figure 38 – uploaded by Mikhail Laguta

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)

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.

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

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.

Figure 5.4: Specimen SM 1.0 analyses crack patterns using varying values for modulus of elasticity E

Table 5.3: Specimen SM 1.5 analyses results using varying column moduli of elasticity E

the experiment displaced a distance of 10.9 mm. This is a percentage difference of 10.1-percent

crushing failure.

experiment did not form among the “E” analyses.

support failure counteracted the downward column displacement due to the column loading.

Figure 5.16: Specimen SM 1.0 analyses crack patterns for boundary condition analyses BC! through BC4

Table 5.8: Specimen SM 1.0 results for analyses BC1-E through BC4-E

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

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

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

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

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

stresses. Since concrete performs well in compression, support failure was unlikely to occur.

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

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).

d) Bottom face, changing boundary conditions between loads  c) Top face, changing boundary conditions between loads

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

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

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

1) Bottom face, equivalent reinforcement layout  c) Top face, equivalent reinforcement layout

Figure 5.64: Specimen SM 1.0 a) moment-rotation and b) displacement-rotation data using varying concrete mesh sizes  same Curve.

Figure 5.66: Specimen SM 1.5 a) moment-rotation and b) displacement-rotation data using varying concrete mesh sizes

respectively. These two analyses also produced the largest rotations of all analyses.

Figure 5.74: Specimen SM 1.0 bottom face analyses crack patterns 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

Figure 5.83: Specimen SM 1.0 a) moment versus dilation angle and b) displacement versus dilation angle data using varying concrete dilation angles

Table 5.37: Specimen SM 0.5 analyses results when including versus excluding self-weight

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

Table 5.39: Specimen SM 1.5 analyses results when including versus excluding self-weight

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

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

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.

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 6.11: Specimen SM 1.5 vertical displacement versus rotation results

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 6.17: 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

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 6.28: 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

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

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

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.

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