STRENGTH OF MATERIALS 287 



EXAMPLE. A wrought-iron bar 1.5 in. square has its ends 

 fastened to firm supports. What is the stress produced in 

 it by a change of 50 in its temperature? 



SOLUTION. Here, = 25,000,000; a= 1.5X1.5 = 2.25 sq. in., 

 and * = 50; and, according to the accompanying table, 

 c = .00000686. Substituting in the formula, T = .00000686 X 50 

 X 2.25X25,000,000 =19,294 Ib. 



BEAMS 



A body resting upon supports and liable to transverse stress 

 is called a beam. Beams are designated by the number and 

 location of the supports, and may be simple, cantilever, 

 fixed, or continuous. A simple beam is one that is supported at 

 each end, the distance between its supports being the span. 

 A cantilever is a beam that has one or both ends overhanging 

 the support; or a beam that has one end firmly fixed and the 

 other end free. A fixed beam is one that has both ends firmly 

 secured. A continuous beam is one which rests upon more 

 than two supports. 



Reactions. The loads acting on a beam are balanced by the 

 reactions or supporting forces; their sum must therefore be equal 



FIG. 1 FIG. 2 



to the sum of the loads. To find any reaction, as Rt, &t^B t 

 Fig. 1, take moments of all the external forces about the other 

 support A and divide their sum by the span. With reference 

 to Fig. 1, 



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