20KN 4 Find the load P such that all members in the followin

20KN 4 Find the load P such that all members in the following three hinged arch are in pure compression. Find the value of yi as well. Note that B and D are fixed connected joints (25 points) hingo 40kN 4 m

Solution

Let support reactions at A and E be R_A and R_E. Net downward forces should be resisted by support reactions. Hence we can equate

R_A + R_E = P+20+40

ie., R_A + R_E = 60+P----------------(Eqn. 1)

Since a hinge does not tranfer moment, we can take net moment about hinge C is zero.

Taking moments about the right side of arch,

40*6 - R_E*9 = 0

R_E = 26.67 kN ---------------(Eqn.2)

Taking moments about the left side of arch,

R_A*8 - P*4 = 0

R_A = P/4 --------------------(Eqn. 3)

Substitute Eqn. 2 and 3 in Eqn.1 to get value of P.

ie., P/4 + 26.67 = 60 + P

P = - 33.33 kN

( ie., P = 33.33kN acts in the upward direction)