Question
Download Solution PDFElongation of a bar of uniform cross-sectional area of A and length L due to self-weight is given as: [Consider Density of bar material = ρ, Modulus of elasticity
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The elongation of a vertically hanging bar under its own weight is calculated by integrating the elemental elongation along the bar’s length due to varying force.
Given:
Length = \( L \), Area = \( A \), Density = \( \rho \), Gravity = \( g \), Modulus of Elasticity = \( E \)
Calculation:
Elongation due to self-weight is given by:
\( \Delta L = \int_0^L \frac{\rho g A x}{A E} dx = \frac{\rho g}{E} \int_0^L x \, dx = \frac{\rho g}{E} \times \frac{L^2}{2} \)
Last updated on Jul 15, 2025
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