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
For trusses with symmetric loading, the displacement is influenced by the geometry of the truss and the properties of the material, such as Young's modulus and cross-sectional area.
Step 1: Understand the system.
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).
