Torsion in a hollow beam cross-section

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Discussion Overview

The discussion revolves around the analysis of torsion and shear in a hollow beam cross-section, specifically addressing a homework problem related to calculating shear stresses and axial forces. Participants are exploring the appropriate equations and methods for analyzing closed sections under various loads.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the use of the equation τ = VQ/It for computing shear stresses in closed sections, suggesting that it may not be applicable without proper understanding of shear analysis for such sections.
  • Another participant indicates that the axial force is applied along the longitudinal axis of the beam and prompts the original poster to recall the basic stress formula for axially loaded members.
  • A participant expresses uncertainty about the correct approach to find the moments Mx and My, indicating they have values for N, A, Ix, and Iy but lack Mx and My.
  • There is a discussion about the appropriateness of examples used for reference, with one participant noting that the example cited may not accurately represent the problem due to differences in shear connections.
  • Another participant raises a question regarding the relevance of torsion and bending in the context of the problem, suggesting that the loads may be eccentrically applied.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct method for analyzing the hollow beam, with multiple viewpoints on the applicability of the shear stress equation and the relevance of bending and torsion in the problem.

Contextual Notes

Some participants express limitations in their understanding due to a lack of clear resources and guidance from their university, which may affect the accuracy of their claims and assumptions.

beamsandthangs
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Homework Statement



The problem is regarding the question on the attached file called 'QUESTION3.png' This is urgent so please reply if you can.

Homework Equations



The attempt is in the file attached. Is my procedure correct? Am I missing something or is something wrong?

Also, how do I find the compressive axial force if N- = 20kN? What equation do I use?

The Attempt at a Solution



Attempt is attached.

Thanks.
 

Attachments

  • Torsion Attempt.pdf
    Torsion Attempt.pdf
    659.8 KB · Views: 364
  • QUESTION 3.png
    QUESTION 3.png
    14 KB · Views: 453
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1. Your section is closed. You are using τ = VQ/It to compute the shear stresses in the walls. This is incorrect. Have you studied how to analyze closed sections in shear?

2. The axial force is applied along the longitudinal axis of the beam. How do you calculate stress in axially loaded members? (Hint: it was probably the first stress formula you learned.)
 
SteamKing said:
1. Your section is closed. You are using τ = VQ/It to compute the shear stresses in the walls. This is incorrect. Have you studied how to analyze closed sections in shear?

I've done some research but couldn't find any clear information to learn from. I only have one example of the same question, which is from a friend and he uses the same equation : VQ/It (where t includes the wall thickness of both the left and right side. If you could give me a link explaining the equation for shear stress in hollow beams or just give me the equation that would be great. The information my lecturer gives me on the university website is very limited. This is a repeat exam and I'm currently outside the country my uni is in so I don't have any lecturers to explain this.

2. The axial force is applied along the longitudinal axis of the beam. How do you calculate stress in axially loaded members? (Hint: it was probably the first stress formula you learned.)

Oh. I assume it is the SigmaZ= N/A + Mx(Y)/Ix - My(X)/Iy equation.
If so, I have the values of N, A, Ix, Iy, but not Mx and My. How do I obtain the M values?
I assume after obtaining the Mx and My values, I replace the X and Y values for the top and bottom of the beam to find the normal force?

Reply is above in Bold

Edit:

In this example I found through google, the person uses VQ/It to find the shear at N.A :
http://faculty.ksu.edu.sa/modar/CE%20302%20Solved%20Problems/Solved%20Problems%20on%20Ch6.pdf
 
Last edited by a moderator:
1. No mention is made of any bending in your problem, so Mx = My = 0.

2. In your example, there is no shear connection between the sides of the wooden box and the top and bottom plates except be the nails which connect them. This is not a good example to use on your problem, since you have a full shear connection at all four corners.

3. The attached example is for a beam which does have a thicker top plate than your problem.
http://www.engr.colostate.edu/~thompson/hPage/CourseMat/Tutorials/Solid_Mechanics/shear.pdf
On reading their description, it appears that if all plates are the same thickness, one can assume equal shear flow in the sides, and thus τ = VQ/It may be valid for your problem after all. I apologize for the earlier confusion. However, the attached method should also work for more general problems, as well as this one.
 
What happened to the Torsion and Bending part? The loads appear to be eccentrically applied?? Is this correct?
 

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