Question 1

What is the Direct Stiffness Method for truss analysis?

Accepted Answer

The Direct Stiffness Method is the foundational FEM technique for structural analysis. Each truss member contributes a local stiffness matrix that is transformed to global coordinates and assembled into the global stiffness matrix [K]. Applying boundary conditions and solving [K]{u}={F} yields nodal displacements {u}, from which member axial forces are calculated.

Question 2

How is axial force calculated in a truss member?

Accepted Answer

Axial force is f = (EA/L)[(u_j - u_i)cos θ + (v_j - v_i)sin θ], where E is Young's modulus, A is cross-section area, L is member length, θ is the member angle from horizontal, and u, v are nodal displacements. Positive values indicate tension, negative values indicate compression.

Question 3

What is the difference between a Pratt truss and a Warren truss?

Accepted Answer

In a Pratt Truss the diagonal members slope toward the center, putting them in tension under downward loading while verticals are in compression — efficient for long-span bridges. A Warren Truss uses only diagonal members in a zigzag pattern (no verticals), resulting in a lighter structure. Both are widely used in bridge and roof structures.

Question 4

How can I use this tool in real structural design?

Accepted Answer

This tool is ideal for preliminary sizing of truss members in bridges, roof structures, cranes, and towers. Use it to quickly identify the most critical members (highest force) before building a full FEM model in ANSYS, Abaqus, or SAP2000. The LINK180 (ANSYS) and T2D2 (Abaqus) elements use the same Direct Stiffness formulation.

2D Truss Analyzer

Theory (Direct Stiffness Method)