Software Verification

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Noel Henderson
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Sotware Veriiation EXAMPLE CSA A23.3-04 RC-BM-00 Flexural and Shear Beam Deign PROBLEM DESCRIPTION The purpoe o thi example i to veri lab lexural deign in.

1 Sotware Veriiation EXAMPLE CSA A RC-BM-00 Flexural and Shear Beam Deign PROBLEM DESCRIPTION The purpoe o thi example i to veri lab lexural deign in. The load level i adjuted or the ae orreponding to the ollowing ondition: The tre-blok extend below the lange but remain within the balaned ondition permitted b CSA A The average hear tre in the beam i below the maximum hear tre allowed b CSA A , requiring deign hear reinorement. A imple-pan, 6-m-long, 300-mm-wide, and 500-mm-deep T-beam with a lange 00 mm thik and 600 mm wide i modeled uing. The beam i hown in Figure. The omputational model ue a inite element meh o rame element, automatiall generated b. The maximum element ize ha been peiied to be 200 mm. The beam i upported b olumn without rotational tinee and with ver large vertial tine ( 0 20 kn/m). The beam i loaded with mmetri third-point loading. One dead load ae (DL30) and one live load ae (LL00) with onl mmetri third-point load o magnitude 30, and 00 kn, repetivel, are deined in the model. One load ombination (COMB00) i deined uing the CSA A load ombination ator o.25 or dead load and.5 or live load. The model i analzed or both o thee load ae and the load ombination. The beam moment and hear ore are omputed analtiall. The total atored moment and hear ore are ompared with the reult. Thee moment and hear ore are idential. Ater ompleting the anali, deign i perormed uing the CSA A ode in and alo b hand omputation. Table how the omparion o the deign longitudinal reinorement. Table 2 how the omparion o the deign hear reinorement. EXAMPLE CSA A RC-BM-00 -

2 Sotware Veriiation 600 mm 75 mm 00 mm 500 mm 75 mm 300 mm Beam Setion 2000 mm 2000 mm 2000 mm Shear Fore Bending Moment Figure The Model Beam or Flexural and Shear Deign EXAMPLE CSA A RC-BM-00-2

3 Sotware Veriiation GEOMETRY, PROPERTIES AND LOADING Clear pan, l = 6000 mm Overall depth, h = 500 mm Flange thikne, d = 00 mm Width o web, bw = 300 mm Width o lange, b = 600 mm Depth o tenile rein., d = 75 mm Eetive depth, d = 425 mm Depth o omp. rein., d' = 75 mm Conrete trength, ' = 30 MPa Yield trength o teel, = 460 MPa Conrete unit weight, w = 0 kn/m 3 Modulu o elatiit, E = 25x0 5 MPa Modulu o elatiit, E = 2x0 8 MPa Poion ratio, v = 0.2 Dead load, Pd = 30 kn Live load, Pl = 00 kn TECHNICAL FEATURES OF TESTED Calulation o lexural and hear reinorement Appliation o minimum lexural and hear reinorement RESULTS COMPARISON Table how the omparion o the total atored moment in the deign trip with the moment obtained b the analtial method. The math exatl or thi problem. Table alo how the deign reinorement omparion. Table Comparion o Moment and Flexural Reinorement Reinorement Area (q-m) Method Moment (kn-m) A Calulated A,min = q-m EXAMPLE CSA A RC-BM-00-3

4 Sotware Veriiation Table 2 Comparion o Shear Reinorement Reinorement Area, (q-m/m) A v Shear Fore (kn) Calulated COMPUTER FILE: CSA A RC-BM-00.FDB CONCLUSION The reult how an exat omparion with the independent reult. EXAMPLE CSA A RC-BM-00-4

5 Sotware Veriiation HAND CALCULATION Flexural Deign The ollowing quantitie are omputed or all the load ombination: φ = 0.65 or onrete φ = 0.85 or reinorement A,min = 0.2 bw h = q-mm α = ' 0.67 = β = ' 0.67 = b = d = mm ab = βb = mm A = min[a,min, (4/3) A,required] = min[357.2, (4/3)2445] = q-mm COMB00 P = (.25Pd +.5Pt) =87.5kN Pl 3 * M = = 375 kn-m M = 375 kn-m The depth o the ompreion blok i given b: ( ) ( ) C = α b bw min h, ab = kn Thereore, b: C φ A = and the portion o M that i reited b the lange i given φ EXAMPLE CSA A RC-BM-00-5

6 Sotware Veriiation C φ A = = q-mm φ M = C min d 2 ( h, a ) b φ = kn-m Thereore, the balane o the moment, M to be arried b the web i: Mw = M M = kn-m The web i a retangular etion with dimenion bw and d, or whih the deign depth o the ompreion blok i realulated a: a 2M 2 w = d d = mm α ' φ b I a ab, the area o tenion reinorement i then given b: w A 2 = M w a φ d 2 = q-mm A = A + A2 = q-mm Shear Deign The bai hear trength or retangular etion i omputed a, φ = 0.65 or hear λ = {. 00, or normal denit onrete d v i the eetive hear depth. It i taken a the greater o 0.9d or 0.72h = mm (governing) or 360 mm. S ze = 300 i minimum tranvere reinorement M dv + V + 0.5N ε x = and ε x ( E A ) EXAMPLE CSA A RC-BM-00-6

7 Sotware Veriiation β = ( + 500ε ) ( S ) x ze = V V = φ λβ bd = kn w v = 0.25 ' b d = kn r, max φ θ = 50 ( V V ) t v w Av tanθ = =.2573 mm 2 /mm = m 2 /m. φ d EXAMPLE CSA A RC-BM-00-7

Software Verification

Software Verification Sotare Veriiation EXAMPLE NZS 3101-06 RC-BM-001 Flexural and Shear Beam Deign PROBLEM DESCRIPTION The purpoe o thi example i to veriy lab lexural deign in. The load level i adjuted or the ae orreponding