Question

A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length \( L \), and flexural rigidity \( EI \). Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, \( R \), is

• A. \( \frac{5FL^3}{3EI} \)
• B. \( \frac{4FL^3}{3EI} \)
• C. \( \frac{2FL^3}{3EI} \)
• D. \( \frac{FL^3}{3EI} \)

Hint:

For deflection calculations in frames, consider using the principle of virtual work or double integration methods for bending moments.

Answer 1

The Correct Option is B

For a plane frame with a horizontal load \( F \) applied at the free end, the deflection \( \delta \) at point \( R \) can be found using the method of double integration or by applying the virtual work principle. For the given frame with two members PQ and QR and using the known formulas for deflections in such frames, the deflection at the free end \( R \) is given by: \[ \delta_R = \frac{4FL^3}{3EI} \] Thus, the correct answer is (B).