A cylindrical bar, whose lateral surface is constrained so that there can be no lateral expansion, is then loaded with an axial compressive stress 01=-6. (a) Find o22 and o33 in terms of o and the Poisson's ratio v. (b) Show that the effective Young's modulus (Er)eff= o1/111 is given by: (EY)eff= E(1 - v)/(1 – v– 2v² ) where E and v are the elastic constant and Poisson's ratio in the case of isotropic elasticity.

A cylindrical bar, whose lateral surface is constrained so that there can be no lateral expansion, is then loaded with an axial compressive stress 01=-6. (a) Find o22 and o33 in terms of o and the Poisson's ratio v. (b) Show that the effective Young's modulus (Er)eff= o1/111 is given by: (EY)eff= E(1 - v)/(1 – v– 2v² ) where E and v are the elastic constant and Poisson's ratio in the case of isotropic elasticity.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

A cylindrical bar, whose lateral surface is constrained so that there can be no lateral expansion, is
then loaded with an axial compressive stress o11 =-6.
(a) Find o22 and 33 in terms of o and the Poisson's ratio v.
(b) Show that the effective Young's modulus (EY)eff = 011/ɛ11 is given by:
(EY)eff= E(1 - v)/(1 – v – 2v² )
where E and v are the elastic constant and Poisson's ratio in the case of isotropic
elasticity.

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