2D truss

Support reactions

Member axial forces

Tension (+) · Compression (−)

Engine vs formula: Relative difference 1.4 × 10⁻¹³ %

N1: Engine 15 / Classical method 15 kN · 1.2 × 10⁻¹³ %

N2: Engine 15 / Classical method 15 kN · 5.9 × 10⁻¹⁴ %

N3: Engine 15 / Classical method 15 kN · 1.2 × 10⁻¹⁴ %

N4: Engine 15 / Classical method 15 kN · 1.1 × 10⁻¹³ %

N5: Engine -21.2132 / Classical method -21.2132 kN · 5 × 10⁻¹⁴ %

N6: Engine -20 / Classical method -20 kN · 0 %

N7: Engine -20 / Classical method -20 kN · 0 %

N8: Engine -21.2132 / Classical method -21.2132 kN · 1.2 × 10⁻¹³ %

N10: Engine -10 / Classical method -10 kN · 7.1 × 10⁻¹⁴ %

N12: Engine 7.07107 / Classical method 7.07107 kN · 1.4 × 10⁻¹³ %

N13: Engine 7.07107 / Classical method 7.07107 kN · 1.4 × 10⁻¹³ %

Node 1 has only truss connections and no rotational restraint — instability risk

Node 2 has only truss connections and no rotational restraint — instability risk

Node 3 has only truss connections and no rotational restraint — instability risk

Node 4 has only truss connections and no rotational restraint — instability risk

Node 5 has only truss connections and no rotational restraint — instability risk

Node 6 has only truss connections and no rotational restraint — instability risk

Node 7 has only truss connections and no rotational restraint — instability risk

Node 8 has only truss connections and no rotational restraint — instability risk

Dense solver (13 free DOFs)

Residual 4.50e-15 (13 free DOFs)

Closed form / Classical method

Method of joints: ΣFx = ΣFz = 0 at every node (determinate trusses).

Assumptions

Linear elastic, small displacements. Prismatic Euler–Bernoulli frame members; truss bars carry axial force only with ideal pin joints. Self-weight is excluded. No shear deformation, geometric nonlinearity or design checks.