REINFORCED CONCRETE STRENGTH OF BEAMS. 



649 



in place at £16 per ton, the cost of a cubic foot is 70s. Concrete niaj 

 be estimated at '2s. per cubic foot, including- labour and forms, so that 

 the ratio of cost is 35 to 1. 



A curve may be drawn showing relative cost for various reinfoi'oo- 

 ments. The table below is calculated for a beam of constant 'width 

 (12 in.) to carry 700 lb. per lineal foot over a sp;in of 10 ft., and tlie 

 curve in Fig. 2 drawn from it. Two inches of concrete is allowed 

 below the reinforcement. 



From this it will be seen that from '006 to '008 is the most 

 economical proportion of reinforcement for these particular costs of 

 steel and concrete. The cui-ve also shows that if for any reason it is 

 desirable to reduce the thickness of concrete it may be done without 

 much extra cost by increasing the reinforcement up to, say, 1'2 per 

 cent. 



On the other hand, it is clearly an extravagance to reduce the 

 steel much below 0'6 per cent. 



To show that it is not obvious what percentage of reinforcement 

 is the most economical, I have plotted a curve where ratio of steal 

 cost to concrete cost is 20: 1, from which it appears that 0'9 per cent, 

 reinforcement is then the most economical. 



In an}- case if the percentage at intersection of curves for R^ and 

 E^ is adopted, it will be usually the most economical, or very nearly 

 so. 



Having determined the necessai-y dimensions at centre of span, 

 the shearing stresses should, in case the beam' may fail under them 

 before developing the strength at the centre of span, be examined. 

 There is considerable difficulty in this owing- to the uncertainty as to 

 the actual distribution of stress in the beam, and especially in the 

 neighbourhood of the reinforcement. Although it is a safe thing to 

 neglect the tensile strength of the concrete in calculating the moment 

 01 resistance at the centre of span, we must recognise the tensile 

 resistances if we wish to know something of the real stresses in the 

 beam. 



I have endeavoured to investigate the stresses in a beam 10 ft. 

 long, 10 in. wide, and 12 in. deep, with horizontal reinforcement of 

 1 sq. in. at 10 in. from upper surface. The load to be 700 lb. per 

 lineal foot. 



