274 Prof. J. Perry on Struts and 



the greatest bending-moment, then in struts, if A is the 

 area of cross section, 



i*+5=A (") 



f*»-5=/*j < 12 > 



and in tie-rods 7 



i--J=/« ( 13 > 



1^+5 =A (i*) 



where f e and/; are the maximum compressive and tensile 

 stresses to which any part of the strut or tie-rod is subjected. 

 In many practical cases z e = z t , and then I/z e is called Z, the 

 strength-modulus of the section. 



We can therefore find the strength and stiffness of any 

 strut of uniform section fixed or free at either or both ends 

 when loaded laterally in any way whatever. 



When, as in many practical cases, it is allowable to take an 

 approximate value for <j>(%), and especially when the lateral 

 loading and initial shape are such that the strut is symme- 

 trical about the axis of y, the w T ork can be greatly simplified 

 by not introducing such terms as r and t. In the symmetrical 

 cases such terms as hi and /3 t - are absent from the expressions y 

 and M = Mj. If the ends are not fixed, M = M!= — Fh. 



Examples. 



I. A uniform straight strut has a lateral load W uniformly 

 distributed. It will be found that in this case we have 

 very nearly 



0(.r)=i"W7cos^* (15) 



Then, if F is the resultant of the pushing forces, (8) becomes 



<te* + Ei^-EI ei "a* • • (lb) 



Solving this by the rule given above and applying the con- 

 ditions that # = when # = /, and -f- = when x=0, it is easy 



