Question

For the truss shown in figure 4, find: (i) zero force members, if any (Justify your answer with FBD), (ii) support reactions at C and D. 

Answer 1

The member FC is a zero force member as there is no F external load on F and there are two other collinear E members.

ΣFx = 0
HD = 0

ΣFy = 0

- 20 – 50 + RC + VD = 0
L/2 L/2 L/2 RC + VD = 70 ………….(1)

`ΣMC^F = 0`

`+(V_(Dx)L) - (20 xx L/2)+(50xxL/2)= 0`

`V_D = - 15 kN`

Substituting V_D = - 15 kN in (1),
Rc = 85 kN

Zero force members – FC
The magnitude of the support reactions at C and D are, H_D = 0 V_D = -15 kN and R_C = 85 kN respectively.