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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.40P: As a designer working for a major electric appliance manufacturer, you are required to estimate the...

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