To solve this problem using the Finite Element Method (FEM), we'll follow these general steps:

Steps for Analysis

1. Define Structural Geometry and Elements

   • Identify the frame elements and their connectivity (node and element assignments).
   • Use the dimensions and properties of each group provided in the table.

2. Assign Material and Section Properties

   • Use modulus of elasticity $E = 30 \, \text{GPa}$.
   • Calculate the area $A$ and moment of inertia $I$ based on the given section dimensions $b$ and $h$.

3. Set Up Load Cases

   • Distribute the given uniform load $q$ on the top beam as shown.
   • Assign fixed supports at nodes 1, 2, and 3.

4. Finite Element Discretization

   • Discretize the members into beam elements.
   • Use stiffness matrices for beams (considering axial, shear, and bending effects).

5. Form Global Stiffness Matrix

   • Assemble the local stiffness matrices of individual elements into a global stiffness matrix.

6. Apply Boundary Conditions

   • Incorporate the fixed support conditions (displacements and rotations at nodes 1, 2, and 3 are zero).

7. Solve for Displacements

   • Solve the linear system $\mathbf{K} \cdot \mathbf{U} = \mathbf{F}$, where:
     • $\mathbf{K}$ = global stiffness matrix
     • $\mathbf{U}$ = nodal displacement vector
     • $\mathbf{F}$ = force vector

8. Calculate Reactions and Internal Forces

   • Use the displacements to compute reaction forces at supports and member forces (bending moment $M$, axial force $N$, and shear force $T$).

9. Plot Diagrams

   • Draw the bending moment $M$, shear force $T$, and axial force $N$ diagrams for each element.

10. Verification Using Software

    • Cross-check results with a structural analysis program (e.g., SAP2000 or ANSYS).

Next Steps

I can help calculate specific parameters (e.g., stiffness matrices, displacements, etc.). Do you want me to work on the general case for one group, or specify which group (e.g., Group 1, 2, etc.)? Let me know your preference.

Follow-Up Questions

1. Do you want detailed calculations for a specific group from the table?
2. Should I compute section properties (e.g., moment of inertia $I$) for a sample beam?
3. Would you like to see the global stiffness matrix formulation?
4. Do you want me to guide you through the use of SAP2000/ANSYS for this frame?
5. Should I explain how to draw the bending moment, axial force, and shear force diagrams?

Tip

When working with FEM problems, ensure all units are consistent (e.g., convert $E$ from GPa to $kN/m^2$, and lengths to meters if using SI units).