Question
Alight truss formed from three struts lying in a plane and joined by three smooth hinge pins at their ends. The truss supports a downward force of $\overrightarrow{\mathbf{F}}=$ $1000 \mathrm{~N}$ applied at the point $B .$ The truss has negligible weight. The piers at $A$ and $C$ are smooth. (a) Given $\theta_{1}=30.0^{\circ}$ and $\theta_{2}=45.0^{\circ},$ find $n_{A}$ and $n_{C^{*}}$ (b) One can show that the force any strut exerts on a pin must be directed along the length of the strut as a force of tension or compression. Use that fact to identify the directions of the forces that the struts exert on the pins joining them. Find the force of tension or of compression in each of the three bars.
Step 1
The truss is subjected to a downward force of \(\overrightarrow{\mathbf{F}} = 1000 \, \text{N}\) at point \(B\). The reactions at the supports \(A\) and \(C\) are denoted as \(n_A\) and \(n_C\), respectively. Show more…
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Figure $\mathrm{P} 12.54$ shows a light truss formed from three struts lying in a plane and joined by three smooth hinge pins at their ends. The truss supports a downward force of $\overrightarrow{\mathbf{F}}=$ 1000 $\mathrm{N}$ applied at the point $B .$ The truss has negligible weight. The piers at $A$ and $C$ are smooth. (a) Given $\theta_{1}=$ $30.0^{\circ}$ and $\theta_{2}=45.0^{\circ},$ find $n_{A}$ and $n_{C} .$ (b) One can show that the force any strut exerts on a pin must be directed along the length of the strut as a force of tension or compression. Use that fact to identify the directions of the forces that the struts exert on the pins joining them. Find the force of tension or of compression in each of the three bars.
Consider a light truss, with weight negligible compared with the load it supports. Suppose it is formed from struts lying in a plane and joined by smooth hinge pins at their ends. External forces act on the truss only at the joints. Figure $\mathrm{P} 12.48$ shows one example of the simplest truss, with three struts and three pins. State reasoning to prove that the force any strut exerts on a pin must be directed along the length of the strut, as a force of tension or compression.
Figure $\mathrm{P} 12.56$ shows a truss that supports a downward force of 1000 $\mathrm{N}$ applied at the point $B .$ The truss has negligible weight. The piers at $A$ and $C$ are smooth. (a) Apply the conditions of equilibrium to prove that $n_{A}=366 \mathrm{N}$ and $n_{C}=634 \mathrm{N} .$ (b) Show that, because forces act on the light truss only at the hinge joints, each bar of the truss must exert on each hinge pin only a force along the length of that bar-a force of tension or compression. (c) Find the force of tension or of compression in each of the three bars.
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