Project ForgeA frame of two arms of equal length L is shown in the figure: one arm is fixed at its top end and extends vertically down a distance L to a rigid corner joint, from which the second arm extends horizontally a distance L to the point where a downward load P is applied. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is
- APL³/3EI
- B2PL³/3EI
- CPL³/EI
- 4PL³/3EI
Explanation
Using the unit-load method over both members: the horizontal arm (length L, cantilevered from the corner) contributes PL³/3EI, exactly like a simple cantilever. The vertical arm carries a CONSTANT bending moment of PL throughout its length (the load's horizontal offset from the vertical arm's own axis is always L, regardless of height), contributing ∫0^L (PL)(L)/EI dy = PL³/EI. Total: PL³/3EI + PL³/EI = 4PL³/3EI.
Source: GATE ME 2009 (2009)
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