How Do You Calculate Shear Stress in Beams with Pin Reactions?

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Discussion Overview

The discussion revolves around calculating shear stress in beams with pin reactions, focusing on determining reactions at pins and applying the shear stress formula. Participants explore the equilibrium of forces and moments in the context of a specific problem involving a beam and support rods.

Discussion Character

  • Technical explanation, Homework-related, Debate/contested

Main Points Raised

  • One participant suggests using the formula Shear Stress = F/A and mentions the need to sum forces and moments to zero, indicating a focus on equilibrium.
  • Another participant questions the acute angle used in calculations, pointing out a discrepancy between the stated angle of 37 degrees and the figure that indicates 30 degrees.
  • A participant acknowledges the error regarding the angle and seeks further assistance in finding the reactions at the pins.
  • One reply provides guidance on calculating reactions, noting that the vertical component of the force in the support rod must equal the reaction at pin B, suggesting a method to find the tension force in the support rod based on geometry.
  • There is a question about whether the Y forces at points A and C are the same, with one participant expressing uncertainty and another clarifying that the vertical forces at pins A and C are not necessarily equal due to their independence.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the angle used in calculations and the relationships between forces at different pins. There is no consensus on the correct approach to finding the reactions, and multiple viewpoints on how to set up equilibrium equations are presented.

Contextual Notes

Participants mention the need to treat the beam and support rod as separate free bodies for clarity in calculations. There are unresolved aspects regarding the setup of equilibrium equations and the relationships between forces at different points.

Mechaman
Messages
37
Reaction score
1
1. Determine average shear stress. Question attached2. Shear Stress = F/A , Sum of Forces and Moments = 0, Trig3. Attempt attached.

Having a hard time determining reaction at pins. I worked out that the opposite side is 4.5m. I assume the next step is to determine reaction then apply Shear Stress = F/A to the Y forces on the pins only??

 

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Where do you get that the acute angle is 37 degrees? The figure with the problem statement says the angle is 30 degrees, as does the sketch attached to your work.
 
SteamKing said:
Where do you get that the acute angle is 37 degrees? The figure with the problem statement says the angle is 30 degrees, as does the sketch attached to your work.
You're right, I don't know why I put 37 down. Even so, any idea of finding the reactions?
 
Mechaman said:
You're right, I don't know why I put 37 down. Even so, any idea of finding the reactions?

Yes. And you should know how, too, but you stopped your calculations for some reason.

At point B, the ΣF = 0. You have calculated RBy = 40 kN. The unknown force in the support rod BC must have a vertical component which is equal to and opposite of RBy. Based on the geometry, you can work out what the tension force in the support rod BC must be.

I noticed that in writing your equations to sum forces in the vertical direction, you included the force at Pin C. You should restrict your FBD to the beam AB and write equilibrium equations only for that member. You can always treat the support rod BC as a separate free body.
 
So is the Y force running through point A the same as point C?
 
Mechaman said:
So is the Y force running through point A the same as point C?

Beats me. But the way you had your original equilibrium equations set up, you couldn't solve them. That's why I recommended that you treat the beam AB as a separate free body and the support rod BC as another free body. The equilibrium equations you write for each free body can be solved.

Pins A and C are not connected to each other in any way, so the vertical forces in each will not necessarily be equal either.
 

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