B. ceranic, Research Fellow and C. Fryer, Head of Department
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SRO BRO DRO 
Material cost ratio q Figure 7 Percentage material costs (fy=460 N/mm2, fcu=30 N/mm2 and r=0.10) Three distinct zones are defined, depending on the beam having a singly (SRO), doubly (DRO) or boundary (BRO) reinforcement ratio as the optimum solution. The lower bound value of q for a singly reinforced section is 40. At the interface between boundary and double reinforcement the optimum reinforcement ratio for a doubly reinforced section is equal to bound plus the minimum compression steel ratio of 0.002 as specified by BS8110 (1985). For this condition, it can be calculated that the upper bound value of q is 27. It is noted that the cost of concrete compared to the total costs shows a steady decrease as the value of q increases, behaving asymptotically to the median in the zone of the singly reinforced optimum solution. To further investigate this behaviour the ratio Ctc/Ct for a singly reinforced section is re-defined by substituting (11) into (24) to give  (28)
Considering the limited practical range of fy/fcu between 5 and 25 it can be seen that 
Hence, for the practical range of q values in the singly reinforced zone it can be concluded that the material costs of the concrete will never fall below 50% of the total costs regardless of the values of fy/fcu. Download 0.68 Mb. Share with your friends:
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