Question

The first row of flexibility matrix for the co-ordinate system as shown in figure is :

• A. $[\frac{l}{EI},\frac{l^2}{3EI},\frac{-l}{2EI}]$
• B. $[\frac{l}{3EI},\frac{-l^3}{18EI},\frac{-l}{6EI}]$
• C. $[\frac{l^2}{9EI},\frac{l^3}{6EI},-\frac{l^2}{24EI}]$
• D. $[\frac{l}{3EI},\frac{l^2}{6EI},-\frac{l}{3EI}]$

Answer 1

The correct option is D $[\frac{l}{3EI},\frac{l^2}{6EI},-\frac{l}{3EI}]$

First row of the flexibility matrix is

$F_{11}=\frac{l}{3EI}$

$F_{12}=\frac{(l/3{)}^2}{2EI}+\frac{\left(l/3\right)\left(l/3\right)}{EI}=\frac{l^2}{18EI}+\frac{l^2}{9EI}$

$\Rightarrow F_{12}=\frac{l^2}{6EI}$

$F_{13}=\frac{-l}{3EI}$