Determine the moment at the support at A or the vertical rea

Determine the moment at the support at A or the vertical reactions at A or B as functions of the loads p_c (N/m) and M_c(N.m), applied as shown and L.

Solution

SOLUTION --

THE UNIFORMLY DISTRIBUTED LOAD Po CAN BE CONVERTED INTO POINT LOAD (Po x L) ACTING AT A DISTANCE L/2 FROM A OR FROM B.

THIS VERTICAL POINT LOAD (Po x L) IS BALANCED BY THE REACTIONS AT A AND B WHICH ARE EQUAL IN MAGNITUDE POINTING VERTICALLY UPWARDS.

VERTICAL REACTION AT A OR B IS GIVEN AS (Po x L) / 2 (N/m) (ANSWER)

THE MOMENT Mo ACTING AT B AND THE MOMENT CREATED BY POINT FORCE (Po x L) ARE BALANCE BY THE MOMENT ACTING AT A WHICH IS DETERMINED AS FOLLOWS--

TAKING MOMENT EQUILIBRIUM ABOUT A WE GET Ma = Mo - [(PoxL) x L/2] = Mo - (Po x L^2) / 2

Ma = (2Mo - PoL^2) / 2 (Nm) (ANSWER)