Question

Determine the reactions at the smooth support A and the pin support B. The connection at C is fixed.

Answer 1

The Cantilever beam is loaded upon by Uniformly Distributed Load with free end resting on a wedge of 60 degrees.

The intensity of UDL, w = 150 lb/ft.

The length of the beam, l = 10 ft.

Lets assume fixed end to be x = 0 and free end to be x = l

Consider any cross-section XX which is at a distance of x from the fixed end. If we just take the resultant of all the forces on the right of the X-section, then

S.F_xx = -W(l-x) for all values of ‘x'. ---------- (1)

S.F_{xx at x=0} = -Wl

S.F_{xx at x=l} = 0

So if we just plot the equation No. (1), then it will give a straight line relation. Bending Moment at X-X is obtained by treating the load to the left of X-X as a concentrated load of the same value acting through the centre of gravity.

Therefore, the bending moment at any cross-section X-X is

B.M_xx = -Wl * (l-x)/2

B.M_{xx at x =0} = -Wl²/2

B.M_{xx at x =l} = 0

So, the reaction at point B i.e. the fixed end will be equal to the shear force, -Wl = -(150)*10=-1500 lb.

The reaction (shear force) at free end will be zero and hence reaction at point A i.e. the frictionless smooth point will also be zero.

X-X x-0