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

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SUMMARY

The discussion focuses on calculating the dimensions of a beam using shear, moment, and moment of inertia principles. Key equations include the Moment of Inertia equation I=(1/12)bh^3 and stress equations Sigma= -(M*c)/I and Tao = (V*Q)/(I*t). Participants emphasize the importance of utilizing shear and moment diagrams to determine the maximum moment and subsequently the moment of inertia for cross-section dimensions. Clarifications are made regarding the type of beam, specifically distinguishing between cantilever and simply supported beams.

PREREQUISITES
  • Understanding of Moment of Inertia calculations
  • Familiarity with shear and moment diagrams
  • Knowledge of stress and strain equations
  • Ability to differentiate between cantilever and simply supported beams
NEXT STEPS
  • Study the construction of shear and moment diagrams for various loading conditions
  • Learn how to apply the Moment of Inertia equation in practical scenarios
  • Research the definitions and applications of bending moments in beam theory
  • Explore the implications of allowable bending stress in beam design
USEFUL FOR

Engineering students, structural engineers, and professionals involved in beam design and analysis will benefit from this discussion.

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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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Wouldn't you want to start by setting sigma in your equation equal to the given allowable bending stress? Give it a try.
 
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?
 
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?
 
If it is a simply supported beam, rather than a cantilever (as it says in the question !) where are the two supports?
 

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