The 'stiffness matrix' [K] of a beam element in the finite element method has order:
Choose the correct answer
2×2 (one node each end)
4×4 — two nodes × two DOF (deflection + rotation) per node for a beam element
6×6 for a beam element
1×1 for simple beams
Correct Answer
B. 4×4 — two nodes × two DOF (deflection + rotation) per node for a beam element
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Bernoulli-Euler beam element: 2 nodes × 2 DOF per node (deflection + rotation) = 4 DOF → 4×4 stiffness matrix [K]. K = EI/L³ × [12, 6L, -12, 6L; 6L, 4L², -6L, 2L²; -12, -6L, 12, -6L; 6L, 2L², -6L, 4L²]. For frame element: 3 DOF per node (u, v, θ) → 6×6. Assembled global [K] is sparse and banded. Assembled [K]{d}={F} solved for global displacements.
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