Each pin-jointed member contributes a local 4×4 stiffness block, built from its axial stiffness EA/L and its orientation cosines, into a global stiffness matrix K. Solving K·u = F for nodal displacements u by Gaussian elimination gives every member's axial force from its change in length:
k_local = (EA/L) · [ c², cs, −c², −cs;
cs, s², −cs, −s²;
−c², −cs, c², cs;
−cs, −s², cs, s² ]
F_member = (EA/L) · Δ(along member axis)
Pin and roller supports are enforced with a large penalty stiffness added to the corresponding diagonal entries. Reactions follow from simple statics for a simply-supported span: R_A = P(1 − x/L), R_B = P·x/L.
- Ghost outline — the undeformed geometry, for reference.
- Solid members — the deformed shape (exaggerated by the scale slider), coloured blue for tension and red for compression.
- Pratt vs Howe — same geometry, opposite diagonal slope: Pratt diagonals go into tension under a central load, Howe diagonals go into compression.