Rectangular Concrete Beam Section Analysis

 RECTANGULAR CONCRETE BEAM/SECTION ANALYSIS Beam Torsion and Shear Per ACI 318-05 Code Input Data: Reinforcing Yield Strength, fy = ksi Concrete Comp. Strength, f 'c = ksi Beam Width, b = in. Depth to Tension Reinforcing, d = in. Total Beam Depth, h = in. Ultimate Design Shear, Vu = kips Ultimate Design Torsion, Tu = ft-kips Ultimate Design Axial Load, Pu = kips Total Stirrup Area, Av+t(used) = in.^2 Closed Stirrup Spacing, s = in. Edge Distance to Tie/Stirrup, dt = in. Results: For Shear: fVc = The ultimate shear strength provided by the concrete, 'fVc', is calculated as follows: For shear and flexure only (no axial load): fVc = 2*f*(f'c*1000)^(1/2)*b*d For shear with axial compression: fVc = 2*f*(1+Pu/(2*Ag)*(f'c*1000)^(1/2)*b*d For shear with axial tension: fVc = 2*f*(1+Pu/(0.5*Ag)*(f'c*1000)^(1/2)*b*d where: f = 0.75 Ag = b*hNote: for members such as one-way slabs, footings, and walls, where minimum shear reinforcing is not required, if fVc >= Vu then the section is considered adequate. For beams, when Vu > fVc/2 , then a minimum area of shear reinforcement is required. kips fVs = The ultimate shear strength provided by the shear reinforcing in beams, 'fVs', is calculated as follows: fVs = f*fy*d*Av/s2where: f = 0.75The required amount of shear strength to be provided by the shear reinforcing in beams is: fVs(req'd) = Vu-fVc >= 0.The required amount of shear strength to be provided must be <= fVs(max). kips fVn = fVc+fVs = fVs(max) = The maximum allowable ultimate shear strength to be provided by the shear reinforcing in beams, 'fVs(max)', is calculated as follows: fVs(max) <= 8*f*(f'c*1000)^(1/2)*b*d/1000 where: f = 0.75 Av(prov) = in.^2?? = Av+t(used) Av(req'd) = The required area of shear reinforcing, 'Av(req'd)', perpendicular to axis of the beam is calculated as follows: Av(req'd) = fVs*s/(f*fy*d) >= Av(min) where: f = 0.75Note: Av(req'd) = area of two legs of a closed stirrup. Av(min) = The minimum area of shear reinforcing, 'Av(min)', to be provided for beams is calculated as follows: Av(min) = 75*SQRT(f'c*1000)*b*s/fy but not less than: 50*b*s/(fy*1000)Note: Av(min) = area of both legs of a closed stirrup. s(max) = The maximum allowable shear reinforcing (closed stirrup) spacing, 's(max)', shall not exceed d/2, nor 24". However, when fVs > 4*f*(f'c*1000)^(1/2)*b*d, then the maximum spacing given above shall be reduced by one-half. (Note: f = 0.75) For Torsion: Tu(limit) = The effects of torsion may be neglected when the factored torsional moment, 'Tu', is less than 'Tu(limit)', which is calculated as follows: Tu(limit) = f*(f'c*1000)^(1/2)*(Acp^2/Pcp)/12000 where: f = 0.75 Acp = b*h Pcp = 2*(b+h) xo = b-(2*dt) yo = h-(2*dt) Tu(max) = The maximum allowable torsion (with or without shear), 'Tu(max)', is calculated as follows: Tu(max) = (((fVc*1000/(b*d)+f*8*(f'c*1000)^(1/2))^2-(Vu*1000/(b*d))^2)*(1.7^2*Aoh^4/Ph^2))/12000 where: f = 0.75 Acp = b*h Pcp = 2*(b+h) xo = b-(2*dt) yo = h-(2*dt) Ph = 2*(xo+yo) Aoh = xo*yo Ao = o.85*Aoh At(prov) = in.^2?? = (Av+t(used)-Av(req'd))/2 At(req'd) = The required area of transverse torsion reinforcing, 'At', perpendicular to axis of the beam is calculated as follows: At = Tu*12*s/(f*2*Ao*fy) >= At(min) where: f = 0.75 Aoh = xo*yo Ao = 0.85*AohNote: At = area of only one leg of a closed stirrup. At(prov) = (Av+t(used)-Av(req'd))/2 At(min) = The minimum area of transverse torsion reinforcing, 'At(min)', perpendicular to axis of the beam is calculated as follows: At(min) = (50*b*s/(fy*1000)-Av(req'd))/2Note: At(min) = area of only one leg of a closed stirrup. At(prov) = (Av+t(used)-Av(req'd))/2 Al(req'd) = The required area of longitudinal torsion reinforcing, 'Al(req'd)', parallel to axis of the beam is calculated as follows: Al = At(req'd)/s*Ph >= Al(min) where: xo = b-(2*dt) yo = h-(2*dt) Ph = 2*(xo+yo) Al(min) = The minimum area of longitudinal torsion reinforcing, 'Al(min)', parallel to axis of the beam is calculated as follows: Al(min) = 5*(f'c*1000)^(1/2)*Acp/(fy*1000)-At(req'd)/s*Ph where: Acp = b*h xo = b-(2*dt) yo = h-(2*dt) Ph = 2*(xo+yo) Total (Av+t) = The required total area of transverse shear and torsion reinforcing, 'Av+t', perpendicular to axis of the beam is calculated as follows: Av+t = Av+2*At >= Av+t(min)Note: Av = area of two legs of a closed stirrup. At = area of only one leg of a closed stirrup. Total (Av+t)(min) = The required total area of transverse shear and torsion reinforcing, 'Av+t(min)', perpendicular to axis of the beam is calculated as follows: Av+t(min) = 50*b*s/(fy*1000)Note: Av = area of two legs of a closed stirrup. At = area of only one leg of a closed stirrup.