Finding dimensions of a beam using shear, moment, and moment of Inertia

In summary, the conversation involves discussing how to find the moment of inertia and stress and strain equations for a given problem. The equations needed for this problem are the moment of inertia equation and the stress and strain equations. The conversation also includes a suggestion to start by setting the stress equation equal to the given allowable bending stress and drawing a loading diagram for the cantilever with the most stress. There is also a discussion about the definition of bending moment and whether treating the problem as a simply supported beam will work. Finally, there is a clarification about the type of beam being discussed.
  • #1
haleystew
3
0

Homework Statement



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Homework Equations



Moment of Inertia equation: I=(1/12)bh^3
Stress and Strain equations: Sigma= -(M*c)/I Tao = (V*Q)/(I*t)

The Attempt at a Solution



I know I need to use shear and moment diagrams to find the max moment so I can use the Stress diagram to find the Moment of Inertia to find the dimensions of the cross section, but I can't figure out how to get started. Any help would be great. Thank you.
 
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  • #2
Wouldn't you want to start by setting sigma in your equation equal to the given allowable bending stress? Give it a try.
 
  • #3
Can you draw a loading diagram for the cantilever you think has the most stress? Do you know a definition of bending moment that will enable you to draw the bending moment diagram?
 
  • #4
I am using the weight density to find the weight distribution over the entire area and then treating that as a simply supported beam. Will this work?
 
  • #5
If it is a simply supported beam, rather than a cantilever (as it says in the question !) where are the two supports?
 

1. What is the purpose of finding the dimensions of a beam using shear, moment, and moment of inertia?

The purpose of finding the dimensions of a beam using shear, moment, and moment of inertia is to determine the structural stability and strength of the beam. These calculations help engineers and architects design safe and efficient structures.

2. How do shear, moment, and moment of inertia contribute to finding the dimensions of a beam?

Shear, moment, and moment of inertia are all important factors in determining the internal forces and stresses in a beam. By analyzing these values, the appropriate dimensions of the beam can be determined to withstand the expected loads and maintain structural integrity.

3. What is shear and how does it affect the dimensions of a beam?

Shear is the internal force that causes one part of a beam to slide against another part. When determining the dimensions of a beam, it is important to consider the maximum shear force and ensure that the beam is strong enough to resist it.

4. What is moment and how does it impact the dimensions of a beam?

Moment is the tendency of a force to cause rotation around a specific point. In the case of a beam, it is important to consider the maximum moment and ensure that the beam is designed to withstand it without bending or breaking.

5. How is the moment of inertia used in determining the dimensions of a beam?

The moment of inertia is a measure of an object's resistance to changes in its rotational motion. In the case of a beam, it is used in calculating the amount of bending stress that the beam can withstand. The higher the moment of inertia, the stronger the beam will be.

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