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: A gusset plate on a truss bridge is in plane stress with normal stresses a x and a and shear stress t , as shown in the figure. At counterclockwise angles 6 = 32° and 9 = 78° from the x axis, the normal stress is 4200 psi in tension. If the stress tr x equals 2650 psi in tension, what are the stresses cr r andT f „?

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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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BuyFindarrow_forward

Mechanics of Materials (MindTap Co...

9th Edition
Barry J. Goodno + 1 other
Publisher: Cengage Learning
ISBN: 9781337093347
Chapter 7, Problem 7.2.23P
Textbook Problem
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: A gusset plate on a truss bridge is in plane stress with normal stresses axand a and shear stress t , as shown in the figure. At counterclockwise

angles 6 = 32° and 9 = 78° from the x axis, the normal stress is 4200 psi in tension.

If the stress trxequals 2650 psi in tension, what are the stresses crrandTf„?

  Chapter 7, Problem 7.2.23P, : A gusset plate on a truss bridge is in plane stress with normal stresses axand a and shear stress

To determine

The normal stress acting on the element in the y-direction.

The shear stress acting on the element.

Explanation of Solution

Given information:

The angle for the stresses on the inclined element is 32°, the angle inclined from x-axis in counter-clockwise direction is 78°, the normal stress in tension along x-direction is 2650psi, the normal stress in tension along x-direction is 4200psi.

Write the expression for normal stress acting on the element.

σx=σx+σy2+σxσy2cos2θ+τxysin2θ...... (I)

Here, normal stresses acting on the body along x-direction is σx, normal stress acting on the body in tension is σx, normal stress in y-direction is σy, θis the angle subtended in tension and compression.

Calculation:

Substitute 4200psifor σx, 2650psifor σx, and 32°for θin Equation (I).

4200psi=2650psi+σy2+2650psiσy2cos64°+τxysin64°[1325psi+σy2+1.325psi×(0.4388)(0.2192)σy4200psi]=τxy×(0.8988)(2294.16psi+0.2808σy0.8988)=τxy...... (I)

Substitute 4200psifor σx, 2650psifor σx, and 78°for θin Equation (I).

σx=2650psi+σy2+2650psiσy2cos156°+τxysin156°4200psi=1325psi+0

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