24 



BROOMALL : 



Assume a steel beam 6" X 6" in cross section subjected to 

 such bending moment that its outside fibre sustains a stress 

 of 30,000 lbs. / sq. in. L,et the factor of lateral deforma- 

 tion be 1/3. The unit shortening of the upper surface of 

 the beam and the unit lengthening of the lower surface are 



30,000 I 



= in. each. The lateral unit expansion of 



30,000,000 1000 



the upper surface and the lateral unit contraction of the lower 

 surface will be each 1/3 . i/iooo ^ 1/3000". The total widen- 

 ing of the upper surface and total lateral contraction of the 



^l# 



if I ^ 



FIGUR E 11 



lower surface will be, each 6 . 1/3000 =: 2/1000". This means 

 tension in the upper surface and compression in the lower sur- 

 face, both at right angles to the axis, equal to 



S = sE = 2/1000 .1/6 . 30,000,000 = 10,000 lbs. / sq. in. 

 This is one-third of 30,000 lbs., as it should be. 



A very approximate value of the shearing stress may be 

 found by assuming a trapezoidal cross section, and taking the 

 distortion to be equal to one-half the expansion on one side 

 at the top divided by the half depth of beam and multi- 



