Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length L. It is subjected to a distributed torque of intensity t per unit distance. The intensity varies linearly from t = 0 at the free end to a maximum value t = to at the support. Express your answer in terms of maximum value zo , length L, shear modulus G and polar moment of inertia Ip . U =

Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length L. It is subjected to a distributed torque of intensity t per unit distance. The intensity varies linearly from t = 0 at the free end to a maximum value t = to at the support. Express your answer in terms of maximum value zo , length L, shear modulus G and polar moment of inertia Ip . U =

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Concept explainers

Members with compression and bending

Compression members are structural elements that carry compressive axial force. They are the vertical members of a building that support beams and their design, which is governed by buckling and strength. Columns are known as struct or compression members, which are subjected to compressive forces. These members provide stiffness to the building and avoid any imperfection regarding the transfer of axial load. For instance, webs in a truss, braces in a framed structure, tiers, and so on.

Question

Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross
sections and length L. It is subjected to a distributed torque of intensity t per unit distance. The intensity
varies linearly from t = 0 at the free end to a maximum value t = to at the support. Express your answer in
terms of maximum value zo , length L, shear modulus G and polar moment of inertia Ip .
U =

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