Question
Download Solution PDFA simply supported beam of span L and carrying a concentrated load of W at mid-span. The value of deflection at mid-span will be [where E = modulus of elasticity, I = moment of inertia of the section of beam]:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Moment Area Method
Mohr's Theorem No.1
Mohr's Theorem No.2
where A = Reference point where slope zero, B = Origin point where slope and deflection are to be determined.
The distance of centroid of the area should be measured from the origin.
Calculation:
As we have to find the deflection at the midpoint (C) the area of half the bending moment diagram can be considered.
Area of the bending moment diagram is given by:
Area of the
x̅ = Distance of the centroid of the Bending Moment Diagram from the origin
Additional Information
Deflection and slope of various beams are given by:
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\({\theta _B} = \frac{{w{L^3}}}{{6EI}}\) |
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Where, y = Deflection of beam, θ = Slope of beam
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