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Mechanics Of Materials Stress Problem

  • Thread starter Baumer8993
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  • #1
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Homework Statement


Here is a link to a picture of the problem:
http://imgur.com/5nOnpJE Click on the picture to make it bigger, and readable!


I need to find the angle that the two rods will have the same stress. We are talking about normal stress here!

Homework Equations



[itex]\sigma[/itex] = Force / Area

The Attempt at a Solution



I am using the method of joints to solve for the internal force because they are both two force members. I have the equations for x, and y.

X:
-AB + BC cos(θ) = 0

Y:
-50 + BC sin(θ) = 0

Where do I go from here? I want to start solving in terms of something to be able to put them into the stress formula.
 

Answers and Replies

  • #2
SteamKing
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In order to find the axial stress in each rod, you must first determine the axial force in each rod.
 
  • #3
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Steam is correct. However, does the load of 50 kN really matter if you want the stress to be the same? (just use F)
Draw a "joint diagram" and then find the force in BC as a function of theta, then the force in AB as a function of theta. Then continue.
 
  • #4
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I am using the method of joints to solve for the internal force because they are both two force members. I have the equations for x, and y.

X:
-AB + BC cos(θ) = 0

Y:
-50 + BC sin(θ) = 0

Where do I go from here? I want to start solving in terms of something to be able to put them into the stress formula.

You already practically have it solved. Solve your two equations for AB and BC in terms of θ. The tensile stress in each of these members is equal to its tension divided by its cross section area. Set the two stresses equal to one another, and you will get an equation for θ.
 

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