Question

The stiffness matrix of a beam element is given as $\frac{2EI}{L}$$\left[\begin{array}{cc}2& +1\\ +1& 2\end{array}\right]$ Then the flexibility matrix is

• A. $\frac{L}{3EI}$$\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$
• B. $\frac{L}{6EI}$$\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$
• C. $\frac{L}{2EI}$$\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$
• D. $\frac{L}{6EI}$$\left[\begin{array}{cc}1& -2\\ -2& 1\end{array}\right]$

Answer 1

The correct option is B $\frac{L}{6EI}$$\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$

[k]= $\frac{2EI}{L}$$\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$
[F]=$[k{]}^{-1}$
=$\frac{L}{2EI}{\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]}^{-1}$
F =$\frac{L}{2EI}\times \frac{1}{3}\times \left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$
= $\frac{L}{6EI}\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$