A two-layered material is made of two metal bars, each with square cross-sectional area t² and length L, fixed together in parallel along their lengths. The bars are made of different materials, with the linear coefficient of expansion of one bar being significantly larger than that of the other. When heated, the compound bar begins to bend. Show that the radius of curvature of the curved, compound bar is t/(AGAT), where t is the thickness, or smallest dimension, of a single bar, Aa is the difference between the linear expansion coefficients of the two materials and AT is the increase in temperature.

A two-layered material is made of two metal bars, each with square cross-sectional area t² and length L, fixed together in parallel along their lengths. The bars are made of different materials, with the linear coefficient of expansion of one bar being significantly larger than that of the other. When heated, the compound bar begins to bend. Show that the radius of curvature of the curved, compound bar is t/(AGAT), where t is the thickness, or smallest dimension, of a single bar, Aa is the difference between the linear expansion coefficients of the two materials and AT is the increase in temperature.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Basic Terminology in Mechanics

The area of science and mathematics concerned the motion of the objects, the relation between the force matter, and motion if specified. Forces exerted over the objects result in displacements or changes in the position of an object concerning its environment. This branch of physics keeps its roots in Ancient Greece in the form of the scripts of Aristotle and Archimedes.

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A two-layered material is made of two metal bars, each with square cross-sectional area
t² and length L, fixed together in parallel along their lengths. The bars are made of
different materials, with the linear coefficient of expansion of one bar being significantly
larger than that of the other. When heated, the compound bar begins to bend. Show
that the radius of curvature of the curved, compound bar is t/(AaAT), where t is the
thickness, or smallest dimension, of a single bar, Aa is the difference between the linear
expansion coefficients of the two materials and AT is the increase in temperature.

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