Question

Consider the pin-jointed truss as shown in figure below.


$\text{For all the members,}\frac{AE}{L}\text{is the same . The stiffness coefficient}{K}_{11}=X\frac{AE}{L}\text{then the value of X is}$ ________.

• A. 1.5

Answer 1

The correct option is A 1.5
$K_{11}=\sum \left(\frac{AE}{L}\right)co{s}^2\theta ={\left[\frac{AE}{L}(cos{60}^0{)}^2\right]}_{OD}+{\left[\frac{AE}{L}\right(cos{90}^0{)}^2]}_{OC}+{\left[\frac{AE}{L}\right(cos{135}^0{)}^2]}_{OB}+{\left[\frac{AE}{L}\right(cos{150}^0{)}^2]}_{OA}=\frac{AE}{L}\left(1.5\right)=X\frac{AL}{L}So,X=1.5$