25 



A W / 

 where A=area of cross section in square inches, and— = .p , -num- 



ber of feet, B. M., per linear foot of stringer. 



Let c equal the cost per foot, B. M., for height, A; then 



Ac W/c , , v 



12 _ 16 R A 



equals the cost per linear foot of this height of stringer. 



For any other height we have, as the cost per linear foot of stringer 

 of equal strength 



AV W/V M 



12 "16 RA' vw 



Dividing (1) by (2) we have 



Ac 



(3) 



12 oh' 



AV " r It 



12 



For example, the cost per linear foot of a 12-inch stringer is to the 

 cost per linear foot of a 11-inch stringer of equal strength as 8 times 14 



is to 10 times 12, equal to — . 



Having, therefore, computed the cost per linear foot for the given 

 conditions of span and load by equation (1), the cost for other heights 

 may be found by equation (3). 



COST OF STRINGERS OF EQUAL STIFFNESS. 



The modulus of elasticity * 



E = _5 W/ 3 



32 Z/ bh s 

 for uniformly distributed load. 



II" = total load on stringer in pounds. 

 J, = breadth in inches. 

 // = height in inches. 

 / = length of stringer in inches. 

 A — deflection at middle in inches. 



Ihe,W,= 82EJA ,orsincez/=^ b= 32 E A » 



or 



x A _ A _ 1,000 w? 



*See Appendix 1. 



