8 in 6 ft 6 ft 15 in 15 in 6ft 2 Determine the stress in mem

8 in 6 ft 6 ft 15 in 1.5 in 6ft 2. Determine the stress in members CG and FG of the truss. Each steel member of the truss has a diameter of 1 in. Also, indicate all ero-force merm whether members are in tension or compress Be sure to indicate ion. 8 ft G a _ 8 ft 500 lb

Solution

There is only one zero force member in the truss and that is member DE. This is because when we consider support E, there is a roller support.From the given roller support orientation, there will be only horizontal reaction force and vertical reaction force will be zero. Therefore, considering force equilibrium of joint E in vertical direction,member force in DE will be equal to zero.

To determine member forces in members CG and FG,let us consider section a-a and solve using method of section.

From vertical force equilibrium of section, F_GCsin45-500=0

F_GC = 500/sin45 = 707.1 lb(tension)

Considering moment equilibrium about joint C, 500*16+F_FG*8 =0

F_FG = -500*16/8=-1000 lb=1000 lb(compression)

Diameter of each rod = 1 in

Area of cross section of each bar = pi*1²/4=0.785 in²

Axial stress in GC= 707.1/0.785=900.76 psi(tension)

Axial stress in FG=1000/0.785=1273.88 psi(compressive)