Explore BrainMass

Deflection and slope of cantilever beam

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

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

See the attached file.

© BrainMass Inc. brainmass.com October 24, 2018, 9:02 pm ad1c9bdddf


Solution Preview

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 ...

Solution Summary

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

See Also This Related BrainMass Solution

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.

View Full Posting Details