625_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 625_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 7.6 Triaxial Stress 619 Problem 7.6-7 A rubber cylinder of length and cross-sectional area is compressed inside a steel cylinder by a force that applies a uniformly distributed pressure to the rubber (see figure). (a) Derive a formula for the lateral pressure between the rubber and the steel. (Disregard friction between the rubber and the steel, and assume that the steel cylinder is rigid when compared to the rubber.) (b) Derive a formula for the shortening of the rubber cylinder. d p F S A L R L S R F S F Solution 7.6-7 Rubber cylinder (a) L ATERAL PRESSURE or 0 p a F A p b Eq. (7-53 a): â x s x E E ( s y + s z ) â x â z 0 s z p s x p s y F A (b) S HORTENING Substitute for and simplify: (Positive represents an increase in strain, that is, elongation.) (Positive represents a shortening of the rubber cylinder.) d d (1 + )(1 2 ) (1 ) a FL EA b ; d â y L â y â y F EA

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