Question
Download Solution PDFThe influence line for maximum bending moment in a simply supported beam is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Above is the simply supported beam AB. A section x-x is taken at x distance from left side A.
A unit load is applied and unit rotation is provided at x-x section. Then, BMs due to rolling action of load at different section is given by:
\({{\rm{M}}_{\rm{x}}} = {{\rm{R}}_{\rm{a}}} \times {\rm{x}} - 1 \times {\rm{x}} \Rightarrow {{\rm{M}}_{\rm{x}}} = \left( {{{\rm{R}}_{\rm{A}}} - 1} \right){\rm{x}}\)
\({{\rm{R}}_{\rm{A}}} = \frac{{{\rm{L}} - {\rm{x}}}}{{\rm{L}}}\)
\({{\rm{M}}_{\rm{x}}} = \frac{{{\rm{x}}\left( {{\rm{L}} - {\rm{a}}} \right)}}{{\rm{L}}}\)
X = L, Mc = 0 and at x = 0, Mc = 0
The above equation is a two degree equation in terms of x and hence and shape ILD for BM will be parabolic
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