Question

For the structure shown in the figure, all of I, EI and L are of respective unit values. The equivalent stiffness constant for the structure is

• A. 1
• B. 1.5
• C. 4.5
• D. 9

Answer 1

The correct option is C 4.5



Compression in spring $={\Delta }_B-{\Delta }_C$

$\frac{R}{K}=\frac{(P-R)L^3}{3EI}-\frac{R{L}^3}{3EI}$

Given, I = EI = L = 1 unit

$\therefore R=\frac{P}{3}$

equivalent stiffness of structure

$=\frac{P}{\frac{(P-R)L^3}{3EI}}=\frac{3P}{P-\frac{P}{3}}=4.5$