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.

Find the position and value of the maximum bending moment.

3 answers

first go here

http://www.jiskha.com/display.cgi?id=1480944543
Calculus applications - Damon, Monday, December 5, 2016 at 9:24am

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

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 :)
Now you want the max moment and where
the moment will be max where its derivative, the shear, is zero
S = w (L/2 - x) = 0
so the moment is max where x = L/2, the middle of course
How much is it?
M = w (L^2/4 -L^2/8)
= wL^2/8 which is wl (L/8) which is the weight * L/8