194- WROUGHT IKON \M> STEEL BEAMS. 



be taken as the elastic limit. The stress at which this 

 occurs may be found in the usual way as follows: 

 Here, 



Where the symbols have the following meanings : 



M = the bending moment at the centre, when the limit 

 occurs. 



W.I 



4 



/ = the corresponding stress. 

 I = the moment of inertia, 



= 55 '9, as before. 

 Y = the distance from the extreme layers to 



the neutral surface, 

 = 3 in. 

 So that, 



W.I Y 

 4 1 

 18 x 60 x 3 



4 x 55-9 



= 14 '5 tons per square inch 



The value of the stress /, obtained above, is, as nearly as 

 can be determined, the stress on those fibres of the beam 

 which are first strained beyond the elastic limit. 



The loads may be carried beyond this point until 

 one is reached which the beam is no longer able to sup- 

 port, when the test is at its natural end. When this maxi- 

 mum load is approached the deflection of the beam as a 

 whole is often accompanied by a crippling of the flanges, 

 and sometimes of the web. 



It is only up to the elastic limit that the conditions 

 represented by the ordinary beam formula obtain. The 

 assumptions upon which the formula is based cease to be 

 true after the elastic limit has been passed. 



The transverse loads applied to a beam produce not 

 only deflections due to the bending stresses, but deflections 

 produced by the shearing stresses which exist on planes 

 perpendicular to the neutral surface.* In the case of 

 beams of large span and small depth this shearing strain 

 is small, and may be neglected; but where the span is 



*This point is discussed in Johnson's "Materials of Construc- 

 tion," p. 66. 



