A horizontal load \(F\) is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area \(A_0\), and made of the same material with Young's modulus \(E\).
The horizontal displacement of point R is:
Show Hint
- 0
- \(\frac{FL}{EA_0}\)
- \(\sqrt{2}\frac{FL}{EA_0}\)
- \(2\frac{FL}{EA_0}\)
The Correct Option is C
Solution and Explanation
We have a two-member truss where a horizontal load \(F\) is applied at point R. The two members are at \(45^\circ\) angles with respect to the horizontal. The displacement at point R depends on the deformation of the two members under the load. Step 2: Use of truss displacement formula.
For trusses with symmetrical loading and equal material properties, the displacement of point R is given by: \[ \delta_R = \frac{FL}{EA_0 \sqrt{2}}. \] Step 3: Conclusion.
Since both members are at \(45^\circ\) angles, the displacement in the horizontal direction is magnified by a factor of \(\sqrt{2}\). Therefore, the horizontal displacement of point R is: \[ \delta_R = \sqrt{2}\frac{FL}{EA_0}, \] which corresponds to option (C).
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\includegraphics[width=0.5\linewidth]{58.png} - For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is \_\_\_\_ N (answer in integer).
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