91影视

Forces that aim to distort an object are referred to as tension and compression. The primary distinction between tension and compression is that tension describes forces intended to lengthen a body, whereas compression describes forces intended to shorten a body.

Here we have two uniform identical beams.

Weigh on both beams is $\mathrm{W}=260\text{鈥塏}$.

The angle between two beams is $\mathrm{胃}=53.0掳$

(a)

Tension in each beam is equal to the magnitude of the weight of the wire but in opposite direction.

So,$\mathrm{T}=\mathrm{W}=260\text{鈥塏}$

The angle between the two beams is $\mathrm{胃}=53.0掳$ and the force of the crossbar is${\mathrm{F}}_{\mathrm{C}}$ .

As the system is at equilibrium, therefore the torque is zero.

$\begin{array}{c}鈭�\mathrm{蟿}=0\\ \mathrm{TLsin}\left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)鈭�{\mathrm{F}}_{\mathrm{C}}\left(\raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\cos \left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)鈭�\mathrm{W}\left(\raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\sin \left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)=0\end{array}$

$\begin{array}{c}{\mathrm{F}}_{\mathrm{C}}=\frac{\mathrm{TLsin}\left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)鈭�\mathrm{W}\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\sin \left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}{\left(\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\cos \left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}\\ =(2\mathrm{T}鈭�\mathrm{W})\tan \left(\raisebox{1ex}{$\mathrm{胃}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\\ =(2\left(260\text{鈥塏}\right)鈭�260\text{鈥塏})\tan \left(\raisebox{1ex}{$53掳$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)\\ =130\text{鈥塏}\end{array}$

Hence, the force that the crossbar exerts on each beam is $130\text{鈥塏}$

(b)

Due to their connection and the fact that their angles are less than $90.0掳$, the two beams exert force in the same direction on the crossbar. As a result of both beams holding the crossbar to each other, the crossbar is under compression.

Hence, the crossbar is under or compression

(c)

The hinge keeps the two beams separated from one another by applying force to keep them horizontal. Because the hinge's force is solely horizontal, it acts on the center of each beam rather than the point$A$. Consequently, the force at the position$\mathrm{A}$that the hinge zero applied.

${\mathrm{F}}_{\mathrm{h}}=0$.

Hence, the force the hinge at point A exerts on each beam is zero.