Question

What will be the element $k_{11}$ of stiffness matrix for the system with

• A. $\frac{3EI}{16}+k$
• B. $\frac{3EI}{16}-k$
• C. $\frac{3EI}{32}+k$
  
• D. $\frac{3EI}{32}-k$

Answer 1

The correct option is C $\frac{3EI}{32}+k$


$k_{11}$ = force required in the direction of 1 to cause unit displacement in the direction of 1.

${\delta }_{net}=1$
$(P-R_B)\frac{(4{)}^3}{3E\left(2I\right)}=\frac{R_B}{k}=1\Rightarrow R_B=1$
$\Rightarrow (P-k)=\frac{6EI}{64}$
$k_{11}=\frac{3EI}{32}+k$