Question

6. The bending moment (M) along a beam is M = WLx/2 -Wx2/2 kNm where x is the distance of a beam length L from the left hand end. W is the weight per unit length.
(a) Shear force is calculated as the differential of bending moment. Find an expression for shear force and determine the value of shear force at x = L/4 from the left hand end.

Answer 1

If you want to draw it it is a seesaw with no one on it
w pounds per foot of weight down (+)
and a force up of wL = total weight at center :) Note that moment must be zero at both ends and will be maximum at the middle changing signs instantaneously

M = w L (x/2) - w x^2/2
S = w L/2 - 2 w x/2
S = w (L/2 - x)
at L/4
S = w (L/2 - L/4)
= w L/4 (the weight to the left of it :)

Answer 2

the shear, not the moment, changes instantly at the center

Answer 3

thanks alot!

Answer 4

You are welcome.