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Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347

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Section
BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.2.22P
Textbook Problem
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Solve the preceding problem for the element shown in the figure.

  Chapter 7, Problem 7.2.22P, Solve the preceding problem for the element shown in the figure.

To determine

The normal stresses acting on the element.

The shear stresses acting on the element.

Explanation of Solution

Given information:

The normal stress acting on the element in x −direction is 18MPa , the normal stress acting on the element in y -direction is 55MPa , the shear stress acting on the element is 27MPa , the angle subtended from x-axis is 50° .

The figure below shows the stresses acting on the element.

Figure-(1)

Write the expression for normal stress acting along x-direction.

σx=σx+σy2+σxσy2cos(2θ)+τxysin(2θ)    ...... (I)

Here, normal stress acting on the element is σx , normal stress acting on the element is σy , shear stress acting on the element is τxy and the angle subtended from x-axis is θ .

Write the expression for normal stress acting on the body along y-direction.

σy=σx+σy2σxσy2cos(2θ)τxysin(2θ)  ...... (II)

Here, normal stress along y direction is σy .

Write the expression for shear stress.

τxy=σxσy2sin(2θ)+τxycos(2θ)  ...... (III)

Here, shear stress is τxy .

Calculation:

Substitute, 18MPa for σx , 55MPa for σy , 27MPa for τxy and 50° for θ in Equation (I).

σx=[ 18MPa+55MPa2+[ ( 18MPa55MPa ) 2×cos( 100°)]+( ( 27MPa )×sin( 100° ))]=18.5MPa+(36.5MPa×(0.1737))+((27MPa)×sin(0

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Chapter 7 Solutions

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