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 to the olloing ondition: The tre-blok extend belo the lange but remain ithin the balaned ondition permitted by NZS 3101-06. The average hear tre in the beam i belo the maximum hear tre alloed by NZS 3101-06, requiring deign hear reinorement. A imple-pan, 6-m-long, 300-mm-ide, and 500-mm-deep T beam ith a lange 100 mm thik and 600 mm ide i modeled uing. The beam i hon in Figure 1. The omputational model ue a inite element meh o rame element, automatially generated by. The maximum element ize ha been peiied to be 200 mm. The beam i upported by olumn ithout rotational tinee and ith very large vertial tine (1 10 20 kn/m). The beam i loaded ith ymmetri third-point loading One dead load ae (DL50) and one live load ae (LL130) ith only ymmetri third-point load o magnitude 50, and 130 kn, repetively, are deined in the model. One load ombination (COMB130) i deined ith the NZS 3101-06 load ombination ator o 1.2 or dead load and 1.5 or live load. The model i analyzed or both o thee load ae and the load ombination. The beam moment and hear ore are omputed analytially. The total atored moment and hear ore are ompared ith the reult. Thee moment and hear ore are idential. Ater ompleting the analyi, deign i perormed uing the NZS 3101-06 ode in and alo by hand omputation. Table 1 ho the omparion o the deign longitudinal reinorement. Table 2 ho the omparion o the deign hear reinorement. EXAMPLE NZS 3101-06 RC-BM-001-1
Sotare Veriiation 600 mm 75 mm 100 mm 500 mm 75 mm 300 mm Beam Setion 2000 mm 2000 mm 2000 mm Shear Fore Bending Moment Figure 1 The Model Beam or Flexural and Shear Deign EXAMPLE NZS 3101-06 RC-BM-001-2
Sotare Veriiation GEOMETRY, PROPERTIES AND LOADING Clear pan, l = 6000 mm Overall depth, h = 500 mm Flange Thikne, d = 100 mm Width o eb, b = 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, y = 460 MPa Conrete unit eight, = 0 kn/m 3 Modulu o elatiity, E = 25x10 5 MPa Modulu o elatiity, E = 2x10 8 MPa Poion ratio, v = 0.2 Dead load, Pd = 50 kn Live load, Pl = 130 kn TECHNICAL FEATURES OF TESTED Calulation o lexural and hear reinorement Appliation o minimum lexural and hear reinorement RESULTS COMPARISON Table 1 ho the omparion o the total atored moment in the deign trip ith the moment obtained by the analytial method. They math exatly or thi problem. Table 1 alo ho the omparion o deign reinorement. Table 1 Comparion o Moment and Flexural Reinorement Method Moment (kn-m) Reinorement Area (q-m) A + 510 35.046 Calulated 510 35.046 + A,min = 535.82 q-m EXAMPLE NZS 3101-06 RC-BM-001-3
Sotare Veriiation Table 2 Comparion o Shear Reinorement Reinorement Area, (q-m/m) A v Shear Fore (kn) Calulated 255 14.962 14.89 COMPUTER FILE: NZS 3101-06 RC-BM-001.FDB CONCLUSION The reult ho an aeptable loe omparion ith the independent reult. EXAMPLE NZS 3101-06 RC-BM-001-4
Sotare Veriiation HAND CALCULATION Flexural Deign The olloing quantitie are omputed or the load ombination: φb = 0.85 α 1 = 0.85 or 55MPa β 1 = 0.85 or 30, b ε = ε + E y d = 240.56 mm amax = 0.75β1b= 153.36 mm A, min A = 535. 82 4 y = max q-mm A 1. 4 = 136. 96 y = 535.82 q-mm COMB130 N = (1.2Nd + 1.5Nt) = 255 kn Nl M = = 510 kn-m 3 The depth o the ompreion blok i given by: 2 M = 2 ' α1 φbb = 105.322 mm (a > D) a d d The ompreive ore developed in the onrete alone i given by: C i given by: ( ) C = α b b h = 765 kn 1 EXAMPLE NZS 3101-06 RC-BM-001-5
Sotare Veriiation Thereore, A1 = by: M A1 = = C C y C y and the portion o M that i reited by the lange i given d d φb = 243.84375 kn-m 2 = 1663.043 q-mm Thereore, the balane o the moment, M, to be arried by the eb i: M = M M = 510 243.84375 = 266.15625 kn-m The eb i a retangular etion ith dimenion b and d, or hih the depth o the ompreion blok i realulated a: a d d 2 1 = 2 M α φ b 1 b = 110.7354 mm amax I a1 amax (NZS 9.3.8.1), the area o tenion reinorement i then given by: A2 = M = 1841.577 q-mm a1 φb y d 2 A = A1 + A2 = 3504.62 q-mm Shear Deign The bai hear trength or retangular etion i omputed a, νb = A.07 + 10 bd 0 50 MPa, and = 0.3834 0.08 = 0.438 MPa νb 0.2 ν = kd ka νb = 0.438 here (kd =1.0, ka=1.0) = 1.095 MPa The average hear tre i limited to a maximum limit o, vmax = min{ 0.2, 8 MPa} = min{6, 8} = 6 MPa EXAMPLE NZS 3101-06 RC-BM-001-6
Sotare Veriiation The hear reinorement i omputed a ollo: I ν φ ( 2) v or h max(300 mm, 0.5b) A v = 0 (NZS 9.3.9.4.13) v 2 < ν φν, I φ ( ) A v 1 = 16 b yt (NZS 9.3.9.4.15) I φν < ν φνmax, (NZS 9.3.9.4.2) A v = ( v φ v ) φ yt d I ν > νmax, a ailure ondition i delared. For the load ombination, the N and V are alulated a ollo: N = 1.2Nd + 1.5N1 V = N ν = V b d (COMB130) ν = Nd = 50 kip Nl = 130 kip V = 255 kn V = 2.0 MPa (φν < ν φνmax) b d ( φ ) A v v v b = = 1.489 q-mm/mm = 1489 q-mm/m φ yt EXAMPLE NZS 3101-06 RC-BM-001-7