Question

Compute the reaction at A and B for the beam subjected to distributed and point loads as shown in fig. State what type of beam it is.

Answer 1

First change UDL in to point load. 

Resolved all the forces in horizontal and vertical direction. Since roller at B (only one vertical reaction) and hinged at point A (one vertical and one horizontal reaction). 

Let reaction at hinged i.e., point A is R_AH and R_AV, and reaction at roller support i.e., point B is R_BV 

Let ∑H & ∑V is the sum of horizontal and vertical component of the forces ,The supported beam is in equilibrium, hence Draw the FBD of the diagram as shown in fig, Since beam is in equilibrium, i.e.,

∑H = 0;

R_AH = 0

∑V = 0 ; R_AV + R_BV – P.L – W = 0 

R_AV + R_BV = P.L + W..........(i)

Taking moment about point A,

P.L × L/2 + W × 2L – RBV × 3L = 0 ........(ii)

R_BV = P.L/6 + 2W/3

Put the value of R_BV in equation (i)

R_AV = 5P.L/6 + W/3.