a propped cantilever AB of span L is fixed at A and support by prop at B and is subjected to a uniformly distributed downward load of W per metre length throughout.The r action of the prop is

Hello,

Let us consider a Beam AB. As it is a Cantilever Beam, one end will be fixed. Let us assume that end A is fixed. It is given that the beam is propped cantilever. So, there will be a vertical load in upward direction at B.

So, DOSI = No. of unknown - No. of reactions

So, DOSI = 3 - 2 = 1

Since, DOSI = 1, it is a statically indeterminant system.

So, it cannot be simply solved by applying equilibrium conditions.

There are various ways to solve it, MDM, Stifffness Matrix Method, 3 Moments theorem, Flexibility Method and many more. But the simplest method to solve this problem is the constant deformation and superposition method.

Hence, solving the above numerical.

Load = UDL = W

Length = L

Prop reaction = R

First, neglecting the prop and consider the above UDL. A downward deflection will be produced at B.

The magnitude of that deflection will be equal to wL ^ 4 / 8 EI.......... ( 1 )

Now, secondly, neglect the UDL and consider the prop at B. A upward deflection will be produced at B.

The magnitude of that deflection will be -RL ^ 3 / 3EI.................. ( 2 )

So, now, as per the superposition theorem,

( 1 ) + ( 2 ) = 0

Hence, ( wL^4 /  8EI ) - ( RL^3 / 3EI ) = 0

So,  wl^4 / 8EI = RL^3 / 3EI

So, R = 3 w.L / 8

Hence, the reaction of the prop is 3.w.L / 8

Best Wishes.