Normal Stress in members of a stystem

In summary, the normal stresses in the three members AB, CD, and EF are 5000 GPa, 200 GPa, and 1.2 GPa, respectively.
  • #1
RustyShackelfor
2
0
Diagram: http://i177.photobucket.com/albums/w222/77whtrocco/NORMALSTRESS.jpg

Given: members AB, CD, and EF have x-sectional area of 25 mm^2. E = 200 GPa. Neglect deformation in member GH.
Find: Normal Stresses in members AB, CD, and EF.

I know that I need to determine the axial forces in these members, but it's been a while since I took a statics class.

Isolating member GH, I have come up with...
Sum of M about G = 0 = 5000(1.6m) - AB(.4) - CD(.8) - EF(1.2)

and I have concluded that the reactions at G, A, C, and E are zero for "x" components (ie. Gx = 0, Ax = 0, Cx = 0, etc)

I should also not that AB is basically equal to reaction Ay, CD = Cy, EF = Ey. I am trying to solve for these values. Thanks.

Now I'm stumped... What else is there? I'm confident that after finding these forces I can solve for the stresses.
 
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  • #2
normal stress in a member of a system = axial force / x-sectional area. Need to determine axial forces (AB, CD, EF). Axial forces and the vertical and horizontal displacements can be related using a compatibility equation using an initial bar length (say Lab, Lcd, Lef) and change in bar length (ie "delta L"). So...
delta Lab = (EF*Lab)/(E*A), where E is the modulus of elasticity and A is cross-sectional area... my problem is that there is no specified deformation. I was given the answer, but I'm beginning to wonder if something was left out.
 
  • #3
RustyShackelfor said:
normal stress in a member of a system = axial force / x-sectional area. Need to determine axial forces (AB, CD, EF). Axial forces and the vertical and horizontal displacements can be related using a compatibility equation using an initial bar length (say Lab, Lcd, Lef) and change in bar length (ie "delta L"). So...
delta Lab = (EF*Lab)/(E*A), where E is the modulus of elasticity and A is cross-sectional area... my problem is that there is no specified deformation. I was given the answer, but I'm beginning to wonder if something was left out.
Since the beam is considered rigid, it must rotate counterclockwise about the left hinge to its equilibrium position where the deformation of each vertical member is proportional to its distance from the left end. Use similar triangles to calculate the ratio of each members deflection , and hence each member's force, to each other. This when combimed with your equilibrium equations should give you the solution.
 

1. What is normal stress?

Normal stress is a type of mechanical stress that is applied perpendicular to the cross-sectional area of a material or member. It is also known as tensile stress or compressive stress, depending on the direction of the force.

2. How is normal stress calculated?

Normal stress is calculated by dividing the applied force by the cross-sectional area of the material or member. The unit of measurement for normal stress is typically in Pascals (Pa) or pounds per square inch (psi).

3. What factors affect normal stress in a system?

The magnitude and direction of the applied force, as well as the properties of the material such as its modulus of elasticity, cross-sectional area, and shape, can all affect the normal stress in a system.

4. What are the potential consequences of high normal stress in a system?

High normal stress can cause a material or member to deform, bend, or even break. It can also lead to fatigue and failure of the system over time.

5. How can normal stress be reduced in a system?

Normal stress can be reduced by using materials with higher strength and stiffness, increasing the cross-sectional area of the member, or changing the direction of the applied force. Proper design and engineering techniques can also help to minimize normal stress in a system.

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