Finding the stress of a rigid beam

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    Beam Stress
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Discussion Overview

The discussion revolves around calculating the stress in a rectangular beam that is freely supported at both ends with a load applied at the center. Participants explore the relevant equations and concepts related to bending stress, moment, and the beam's geometry.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant states that stress can be calculated using the formula stress = moment / inertia, while another corrects this to sigma = M*c/I, prompting further clarification on how to proceed with the calculations.
  • There is a discussion about the forces acting on the beam, with one participant noting that there are two vertical forces acting upwards, each equal to F/2.
  • Participants discuss how to determine the maximum moment, suggesting that it can be found by multiplying the reaction force by the half-span of the beam.
  • Clarification is sought regarding the variable 'y', with one participant indicating that it represents the distance from the neutral axis to the point where stress is being calculated, which is typically at the top or bottom edge of the beam.
  • Another participant emphasizes that the maximum moment and stress occur at the midpoint of the beam, but notes that 'y' is a coordinate within the cross-section, not related to the beam's overall dimensions.
  • Visual aids are referenced to illustrate the stress distribution within the beam's cross-section.

Areas of Agreement / Disagreement

Participants express differing views on the correct formulation for calculating stress and the interpretation of variables involved. There is no consensus on the approach to take, and the discussion remains unresolved regarding the best method for calculating stress in the beam.

Contextual Notes

Some participants mention the need for additional resources, such as textbooks or online searches, to clarify the calculations involved in determining the moment and stress. There may be assumptions regarding the beam's material properties and loading conditions that are not explicitly stated.

ethan118
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The question is simple.

i want to find the stress of a rectangular beam freely supported at both ends. A load F is acting in the middle.

I know that stress = moment / inertia

also inertia = (b h ^3 ) / 12
 
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I think you have your equation wrong. I think what you want is
sigma = M*c/I
so, figure out M, c, and I and go to it.
 
can you explain please how to proceed with that. i have been struggling for days
 
i know that both sides there are 2 vertical forces acting upwards F/2
 
You'd have to find out the maximum moment which is at the middle, by multiplying either reaction by the half-span (distance from end to middle).

As Dr. D said, the maximum (bending) stress is My/I.
M has already been determined above, you'd need to determine for the beam cross section
y = distance between the neutral axis and the distance at which stress is required (usually top or bottom edge)
I = second moment of area.

You only have to do a little google search to find out how these quantities are calculated, if you missed your class and do not have a textbook on Strength of Materials.
 
if the length is L and the load is at the middle.

The moment, M is L/2 x F /2 ?

is y also L/2 ?
 
Look at what mathmate said about y. The neutral axis is a horizontal line (for a horizontal beam). Do you want the bending stress at a point L/2 above the neutral axis, which in this case is the midplane?
 
The maximum moment and hence highest stress is indeed situated at x = L/2, however the flexure formula above is used to calculate the stress distribution within a certain cross-section, as such the y is a coordinate within this cross-section. It has nothing to do with the dimensions of the beam itself. The distribution will look like this:

http://en.wikivisual.com/images/3/3a/Internal_Forces_and_Stresses_from_Bending.png

If your goal is to calculate the maximum stresses then the above equation may be used whereby y is the largest distance from the neutral axis (as already stated), and would in this case be h/2.
 
Last edited:

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