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cos nL

cos nL

My nL h maximum stress owing to bending = -j- = Pe sec — x y where h is the distance from the N.A. to the highest stressed fibre.

Therefore the total maximum compressive stress owing to combined bending and thrust, assuming a ductile material^, is given by

^ For a brittle material which is relatively weak in tension it is the maximum tensile stress which becomes the criterion of failure and the bending and direct stress components are opposite in sign.

tfmaii = O

This formula is known as the Smith-Southwell formula.

Unfortunately, since a = P/A, the above equation represents a function of P (the required unknown) which can only be solved by trial and error or graphically. A good approximation however, is obtained as shown below:

Webb's approximation

From above Let Then

Now for 0 between 0 and n!2,

^max

= a

nL

_ a

~2

— v

q

0 0

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