Question

In the figure, the load P = 1 N, length L = 1m Young's modulus E = 50 GPa, and the cross section of the links is a square with dimension 10 mm X 10 mm. All joints are pin joints.

The stress (in Pa) in the AB is
(Indicate compressive stress by a negative so, and tensile stress by a positive sign)

Answer 1

$\sum F_v=0$
and $\sum F_x=0\left[Atequilibrium\right]$
$F_{BC}\sin {45}^{\circ }=F_{AB}+p\sin {45}^{\circ }...\left(i\right)$
$F_{BC}\cos {45}^{\circ }=P\cos {45}^{\circ }....\left(ii\right)$
$\therefore F_{BC}=P$
$P\sin {45}^{\circ }=F_{AB}+P\sin {45}^{\circ }$
$\therefore F_{AB}=0$
${\sigma }_{AB}=0$