The stiffness matrix of a beam is given as \(K\left[\begin{array}{cc}12 & 4 \\ 4 & 5\end{array}\right]\). Calculate the flexibility matrix.

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This question was previously asked in

BPSC AE Paper 5 (Civil) 11 Nov 2022 Official Paper

Answer 1

Explanation:

If we denote stiffness matrix as M and flexibility matrix as Δ

The flexibility matrix (F) is the inverse of the stiffness Matrix.

then flexibility matrix is: Δ = M-1

Calculation:

Δ = \(\frac{1}{{\left( {12\times5 - 4\times4} \right)}}\left[ {\begin{array}{*{20}{c}} 5&{ - 4}\\ { - 4}&{12} \end{array}} \right]\)

∴ Δ = \(\frac{1}{{44}}\left[ {\begin{array}{*{20}{c}} 5&{ - 4}\\ { - 4}&{12} \end{array}} \right]\)