ABSTRACT
This study centres around the evaluation of the expected total cost of reinforced concrete beams designed to BS 8110 (1985) when gross errors are accounted for. Beam performance functions are obtained for bending, shear and torsion. The performance function for a beam performing in combined bending and torsion is adopted from CP 110 (1972), where it is explicitly given. Due to the multiplicity of uncertainties surrounding the performance of beams, they are only realistically assessed in terms of a probability. In this study, the reliability index, ft, and hence the probability of failure Pf, is used as a measure of beam performance. Consequently, the First Order Second Moment integration technique is employed to determine the values of ft or Pf implicit in the design criteria. Since it is practically impossible to quantify the whole range of human errors likely to occur in reinforced concrete beam construction, consideration is therefore limited to workmanship error involving the transverse and longitudinal positioning of beam supports. In addition, the effects of perturbations in the design values of basic variables on the performance and the expected total cost of beams are examined. The results show that the BS 8110 (1985) design criteria give fairly consistent and non-conservative designs. From structural design considerations only, the code's requirements are found to be adequate. The sensitivity analysis also shows that gross errors in the value of the effective depth, d, lead to the greatest associated failure cost among other design variables. On the other hand, the strength of concrete, fcu, is found to show very little sensitivity to gross errors as far as the design equations are concerned. Associated failure costs are thus minimal. This assessment shows that for beams failing in bending, shear, torsion and combined bending and torsion, expected failure cost surcharges do not go higher than about 13%, 47%, 36.5% and 24.4% of the initial cost respectively. The results of this investigation are only indicative trends of the BS 8110 (1985) design requirements since the scope of the work precludes experimental details that may give the actual distributions of the design parameters. It is therefore indicative from economic considerations only that the criteria for shear and torsion be reviewed.