FEM 2D Truss Element

Transformation matrix T · Local → global stiffness · 2-member truss assembly · Nodal displacements · Member forces

Two-Member Plane Truss

Node 1: (0,0) pinned. Node 2 at right. Node 3 is free loaded node.

E (Pa)

A (m²)

Node 2 — x₂ (m)

Node 2 — y₂ (m) [pinned]

Node 3 — x₃ (m)

Node 3 — y₃ (m)

Fx at node 3 (N)

Fy at node 3 (N)

Element 1 length L₁ (m)—

Element 2 length L₂ (m)—

θ₁ (°)—

θ₂ (°)—

u₃ (m)—

v₃ (m)—

Member force F₁ (N)—

Member force F₂ (N)—

Cook §2.4T=[c s 0 0; 0 0 c s]; Ke_global=TᵀKe_local·T

Eq.(2.4-4)ke_global=(EA/L)·[c² cs -c² -cs; cs s² -cs -s²; ...]

Preliminary educational tool. Verify results against textbook solutions.