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Software Verification PROGRAM NAME: REVISION NO.: SAFE EXAMPLE CSA A23.3-04 RC-SL-001 Slab Flexural Design PROBLEM DESCRIPTION The purpose of this example is to verify slab flexural design in SAFE A one-way, simple-span slab supported by walls on two opposite edges is modeled using SAFE The slab is 150 mm thick and spans meters between the walls To ensure one-way action, Poisson’s ratio is taken to be zero The computational model uses a finite element mesh, automatically generated by SAFE The maximum element size was specified to be 1.0 meter The slab is modeled using thin plate elements The walls are modeled as line supports without rotational stiffnesses and with very large vertical stiffness (1 × 1015 kN/m) To obtain factored moments and flexural reinforcement in a design strip, one one-meter wide strip is defined in the X-direction on the slab as shown in Figure Simply supported edge at wall Simply supported edge at wall m span Free edge m design strip Y X Free edge Figure Plan View of One-Way Slab One dead load case (DL4KPa) and one live load case (LL5KPa) with uniformly distributed surface loads of magnitudes and kN/m2, respectively, are defined in the model A load combination (COMB5kPa) is defined using the CSA A23.304 load combination factors, 1.25 for dead loads and 1.5 for live loads The model is analyzed for these load cases and load combinations The slab moment on a strip of unit width is computed analytically The total factored strip moments are compared with the SAFE results After completing the analysis, design is performed using the CSA A23.3-04 code by SAFE and also by hand computation Table show the comparison of the design reinforcements computed using the two methods EXAMPLE CSA A23.3-04 RC-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE GEOMETRY, PROPERTIES AND LOADING Thickness Depth of tensile reinf Effective depth Clear span T, h dc d ln, l1 = = = = 150 25 125 4000 mm mm mm mm Concrete strength Yield strength of steel Concrete unit weight Modulus of elasticity Modulus of elasticity Poisson’s ratio fc fsy wc Ec Es ν = = = = = = 30 460 25000 2x106 MPa MPa N/m3 MPa MPa Dead load Live load wd wl = = 4.0 5.0 kPa kPa TECHNICAL FEATURES OF SAFE TESTED ¾ Calculation of flexural reinforcement ¾ Application of minimum flexural reinforcement RESULTS COMPARISON Table shows the comparison of the SAFE total factored moments in the design strip the moments obtained by the hand computation method Table also shows the comparison of the design reinforcements Table Comparison of Design Moments and Reinforcements Load Level Reinforcement Area (sq-cm) Method Moment (kN-m) SAFE 24.991 5.528 Calculated 25.000 5.406 As+ Medium A +s ,min = 357.2 sq-mm EXAMPLE CSA A23.3-04 RC-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE COMPUTER FILE: CSA A23.3-04 RC-SL-001.FDB CONCLUSION The SAFE results show a very close comparison with the independent results EXAMPLE CSA A23.3-04 RC-SL-001 - Software Verification PROGRAM NAME: REVISION NO.: SAFE HAND CALCULATION The following quantities are computed for the load combination: φc = 0.65 for concrete φs = 0.85 for reinforcement As,min = 0.2 f ′c bw h = 357.2 sq-mm fy b = 1000 mm α1 = 0.85 – 0.0015f'c ≥ 0.67 = 0.805 β1 = 0.97 – 0.0025f'c ≥ 0.67 = 0.895 cb = 700 d = 75.43 mm 700 + f y ab = β1cb = 67.5 mm For the load combination, w and M* are calculated as follows: w = (1.25wd + 1.5wt) b wl12 Mu = As = min[As,min, (4/3) As,required] = min[357.2, (4/3)540.63] = 357.2 sq-mm = 0.22•(150/125)2•0.6•SQRT(30)/460•100•125 = 282.9 sq-mm COMB100 wd = 4.0 kPa wt = 5.0 kPa w = 12.5 kN/m Mf = 25.0 kN-m The depth of the compression block is given by: a = d − d2 − EXAMPLE CSA A23.3-04 RC-SL-001 - 2M f α f 'c φc b = 13.466 mm < amax Software Verification PROGRAM NAME: REVISION NO.: SAFE The area of tensile steel reinforcement is then given by: As = Mf a⎞ ⎛ φs f y ⎜ d − ⎟ 2⎠ ⎝ = 540.630 sq-mm > As,min As = 5.406 sq-cm EXAMPLE CSA A23.3-04 RC-SL-001 -