Statics - Pin & Slider Structure - Equilibrium

[raniero]

Homework Statement

Given force F (=5000N), find Moment on member 4.

I have attempted to start solving this problem by drawing the following diagram:

I added the letter 'A' to the support of member 2, and also put an angle of 7 degrees to the vertical at the support 1.

I have drawn force and moment reactions on bodies 3, 5 and 8 which are all sliders and reaction forces on pins D, F, E, G and A.

I worked out the geometry so as to be able to work out moments and components.

Homework Equations

To solve the problem I tried to use the Equilibrium equations which state that forces in all directions should equal to zero and also that all moments should equal to zero.

The Attempt at a Solution

Member 4:$$\sum{F_x} = 0: B\cos(15)+G_x-C\cos(7)=0 \\ \sum{F_y}=0: B\sin(15)-C\sin(7)-G_y=0 \\ \sum{M_G}=0: B(1.54) - C\cos(7)(6.4) -C\sin(7)(1.71) + M_3 = 0$$

Member 2:$$\sum{F_x}=0: A\sin(30) - B\cos(15) = 0 \\ \sum{F_y}=0: A\cos(30) + B\sin(15) = 0 \\ \sum{M_A}=0: B(0.8)=0$$

Problems:

Equations of member 2 get me to a conclusion that member 2 is a zero force member. Am I right?
Are my equations and diagram correct ?

 

[LightHero]

For the moment on member 4, I am getting a result of M4= -3000Nm. Is this correct or am I missing something?