GATE & PSUs - Mechanical Engineering (ME)

Deflection of Beams & Strain Energy question bank (Strength of Materials & Mechanics)

Practice 6 free GATE & PSUs - Mechanical Engineering (ME) Strength of Materials & Mechanics - Deflection of Beams & Strain Energy questions with answers and step-by-step solutions.

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Q1.

[Deflection of Beams & Strain Energy Concept 5] A simply supported beam of length $L$ carries a concentrated point load $W$ at its mid-span. What is the maximum bending moment and maximum downward deflection $\delta_{\max}$ of the beam (flexural rigidity $EI$)?

(A)

$M_{\max} = \frac{WL}{4}, \quad \delta_{\max} = \frac{WL^3}{48EI}$

(B)

$M_{\max} = \frac{WL}{8}, \quad \delta_{\max} = \frac{5WL^3}{384EI}$

(C)

$M_{\max} = \frac{WL}{2}, \quad \delta_{\max} = \frac{WL^3}{24EI}$

(D)

$M_{\max} = WL, \quad \delta_{\max} = \frac{WL^3}{3EI}$

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Q2.

[Deflection of Beams & Strain Energy Concept 11] A simply supported beam of length $L$ carries a concentrated point load $W$ at its mid-span. What is the maximum bending moment and maximum downward deflection $\delta_{\max}$ of the beam (flexural rigidity $EI$)?

(A)

$M_{\max} = \frac{WL}{4}, \quad \delta_{\max} = \frac{WL^3}{48EI}$

(B)

$M_{\max} = \frac{WL}{8}, \quad \delta_{\max} = \frac{5WL^3}{384EI}$

(C)

$M_{\max} = \frac{WL}{2}, \quad \delta_{\max} = \frac{WL^3}{24EI}$

(D)

$M_{\max} = WL, \quad \delta_{\max} = \frac{WL^3}{3EI}$

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