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Deflection and slope of cantilever beam

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For the cantilever beam and loading shown, determine the deflection and slope at point B. Use E = 29,000,000 psi.

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A beam under load deflects and bends. If the deflection of the beam is given by the displacement function v in terms of location x, from calculus we conclude that the curvature K of the beam is given
K ≈ (d2v/dx2)
We have to fine the deflection v(x) and the slope (dv/dx) of the cantilever beam.
From the study of pure bending we know the relation between the radius of curvature and the applied bending moment to be given by ...

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MS Word document contains detailed explanation of a cantilever beam bending problem.

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Beam deflection

Q.1 Derive an expression for the deflection due to shear for a cantilever beam of constant rectangular cross section, under action of a point load, P at free end.

Q.2 Show how the max shear stress occurs at the neutral axis and a value of 3/2 x average shear stress on the section.

Q.3 If length of cantilever is 2m, P=100KN, b=100mm, d=200mm, E=7.5 KN/mm2, calculate the shear deflection at the free end.

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