Discussion
The stiffness matrix of a structure is symmetric because of
Answer: D
Correct answer: Maxwell's reciprocal theorem
Maxwell's theorem states that the displacement at \( i \) due to a unit force at \( j \) equals the displacement at \( j \) due to a unit force at \( i \), for a linear elastic system.
Written in matrix terms that is \( k_{ij} = k_{ji} \) - symmetry. The property is not incidental: it halves the storage required and permits solution methods that assume symmetry, which is why the eigenvalue problem for structures is so much cheaper than the general case.
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