BENDING. 



25 



We have thus three co-efficients of elasticity E, G, and 

 K, and their mutual relations are expressed by the 

 equation just deduced. 



13. Bending. A full investigation of the stresses and 

 strains in bending will not be possible here. It is a large 

 subject, and the reader is referred to one of the many books 

 on applied mechanics for a full and sufficient treatment. 

 It will only be possible here to deal with the main facts. 



In testing, only the simpler and more straightforward 

 cases are dealt with, beams being generally tested when 

 resting upon two end supports, and with the load applied 

 centrally and at right angles to the axis of the beam. In 

 some cases the ends may be fixed, and the load may be 

 applied in a distributed form, but this is unusual. In the 

 matter of form of cross-section, this may vary considerably, 

 and every conceivable section may be tested. Thus the 

 beams tested may be simple rectangular ones, beams of \-\, 

 T, and built-up sections, or they may be less symmetrical, 

 as in the case of tram rails. Let us, then, take the 

 simplest case first, namely, a uniform rectangular beam 

 supported at the two ends, and loaded in the middle. 



The beam is supposed to be elastic and weightless. The 

 distance between the supports, or the span, is I (inches) 



FIG. 11. 



and a load W (Ibs.) is supported at the centre. The effect 

 of this load is to impose pressures HI and R 2 upon the 

 supports, such that 



W 



RI = R 2 = - j . 



