Question

A 200 mm x 300 The of each mm square reinforced concrete column consists of PCC and steel rebar rebar are oriented parallel to the longitudinal dimension of the column. The properties component are provided in the table below PCC (Matrix Phase 95% 20 GPa 24 Mg'm 20 MPa Material Steel Rebar 5% 200 GPa 7.8 Mg/m (Dis Phase % of Composite(by vol.) Modulus of Elasticity Density Failure Stress 250 MPa Determine the following: (a) (3%) Modulus of elasticity of the composite column under isstrainandition. (b) (3%) Density ofthe composte column. (c) (3%) Percentage of load carried by rebar under isostran condition (d) (3%) which will reach failure stress first, the steel or the PCC? Explain why and show your work. 8/12

Answer 1

Given that A 200 mm times 300 mm square Material % of composite modules of Elasticity Density Failure stress steel Rebar 5 % 200 Gpa 7.8 Ms/ms 250 mpr pcc 95% 20 Gpa 2.4 Ms/m^3 20 Mpa (a) E_c = E_s C_s + Ep Cp = (0.05 times 200) + (0.95 times 20) = 29Gpa (b) D_c = D_s C_s + D_p C_p = (0.05 times 76) + (0.95 times 24) = 2.67 Mg/m^3 (c). % of that carried by rebar = (Modules of rebar/Modules of PCC)^-1 times 100 = Es/Ec = (0.05 times 200/2g) times 100 = 34.48 % (d) fulltime stores composite = (0.05 times 250) + (0.95 times 20) = 31.5 Mpa. PCC will reach the failure stress first as its weak in Strength and has failure stress criteria similar to composite failure