Solution:

Introduction:
In this problem, we are required to find the support reaction at point G. The given frame is symmetric, and all members are prismatic and have the same flexural rigidity. Also, we have been told to assume that axial deformation of any member is neglected. We will use the method of joints to solve the problem.

Method of Joints:
The method of joints is a technique used to solve problems related to trusses and frames. In this method, we consider equilibrium of forces at each joint of the truss or frame. We assume that all members are in tension and neglect the weight of the members.

Calculations:
Considering the joint F, the horizontal force H and the vertical force V can be calculated as follows:

∑H = 0
H = 0

∑V = 0
V - 2wL = 0
V = 2wL

Considering the joint E, the horizontal force H and the vertical force V can be calculated as follows:

∑H = 0
H - 2wL = 0
H = 2wL

∑V = 0
V - 2wL = 0
V = 2wL

Considering the joint G, the horizontal force H and the vertical force V can be calculated as follows:

∑H = 0
H - 2wL = 0
H = 2wL

∑V = 0
V + Fg - 2wL = 0
V = 2wL - Fg

Since we have assumed that joint F is rigid, the force in member FG is equal and opposite to the force in member EF. Also, the force in member EG is equal and opposite to the force in member FG. Therefore, we can write:

Fg = Fe
Fe = Eg

We know that all members have the same flexural rigidity. Therefore, we can assume that the angle between members EF and FG is the same as the angle between members FG and EG. Let this angle be θ.

The bending moment in member EF can be calculated as follows:

M = wL2/2

The bending moment in member FG can be calculated as follows:

M = FeLsinθ

Since members EF and FG have the same flexural rigidity, we can write:

Fe/Lsinθ = wL2/2

Fe = wL2/2sinθ

We also know that Fe = Fg. Therefore:

Fg = wL2/2sinθ

The vertical reaction at point G is given by:

V = 2wL - Fg

Substituting the value of Fg, we get:

V = 2wL - wL2/2sinθ

Therefore, the support reaction at point G is:

V = 2wL - wL2/2sinθ

Conclusion:
In this problem, we have used the method of joints to find the support reaction at point G. We have assumed that axial deformation of any member is neglected, and all members have the same flexural rigidity. We have also assumed that joint F is rigid. The support reaction at point G is given by:

V = 2wL - wL2/