to Transverse Strain in Beams. 413 



the moment of LHM is 



1 . 2 b <P a 3 



and the moment of LCDM is 



Therefore the total moment of stress is 



S "6"V 2a + ¥ +3(l + ^^- N /a-)(l-V^)) 



ha 12 

 = S— (3-2^0-) (1) 



Now if Si be the maximum stress which would have existed 

 in consequence of the loading at the lower side of the section 

 if the elasticity had been perfect, the total moment of stress 



31 



will be represented by S x ^- ; 



S(3-2 v /o-) = S 1 . 



Let ~ =r y then 



(3 — r\ 2 



And the strain at half the depth of section below the neutral 

 axis is 



s _ s / 2 V ,™ 



the maximum tensile strain at C D represented by EF is 



2eh _ 2S + 2 - s/a _ S 4 + Q-l) 2 {0 . 



ei ~ d ~ E a- ~E (3-r) 2 ; * ' W 



the maximum compressive strain at A B is 



_ 2e(d-h) _ S 2 N /o-<r _ S 1 + r ( . 



* 2 ~ d ~E er ~E3~r ; * * W 



and the maximum compressive stress is 



6-r 



(5) 



The amount of displacement of the neutral axis from the 

 Phil. Mag. S. 5. Vol. 33. No. 204. May 1892. 2 F 



