   # : 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 „? ### 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 counterclockwiseangles 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„? 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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