Question
Download Solution PDFA column with length ‘b' and breadth 'd' is subjected to an eccentric point load 'P' (eccentric in the direction of breadth) with an eccentricity 'e'. Calculate the bending stress developed.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If the axial load P is placed eccentric in the direction of breadth with an eccentricity of 'e' as shown in Figure, then the system can be assumed to consist of
(i) a direct compressive force P acting at the centroid,
(ii) a couple of P × e, about the y-axis
Bending stress(f) is a result of the couple of P x e about y-axis only, as a load P at centroid causes direct compressive stress.
Using pure bending equation,Bending stress due to couple M = Pe can be written as
\({M\over I} = {f \over y} = {E \over R} \),
\(f = {My \over I} = {P\;e\:y \over I} = {Pe \over Z} \)
Section modulus, z = I/ymax = \( {bd^{2}\over 6}\)
Therefore, bending stress,f = 6 Pe/bd2
Last updated on Jul 1, 2025
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