Combined Loading on an L-shaped beam

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    Mechanics of materials
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Discussion Overview

The discussion revolves around the analysis of combined loading on an L-shaped beam, focusing on determining the axial force (Fy) and bending moment (Fx) at various points. Participants explore the application of stress equations and the implications of loading conditions, including shear and moment diagrams.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant attempts to calculate stresses at points a and b using the relationship σ=εE, noting the presence of unknowns Fy and M in their equations.
  • Another suggests replacing the force F with its effective loading to clarify the analysis and recommends producing shear moment diagrams to identify potential errors.
  • There is uncertainty regarding the lengths of the beams, with some participants questioning whether they are the same length and noting that no measurements are provided.
  • Participants discuss the direction of moments at point B, with conflicting views on whether it should be clockwise or counterclockwise based on the applied forces.
  • One participant expresses confusion about the application of bending stress and normal stress due to the forces acting on the beam, considering multiple cutting points for analysis.
  • There is a suggestion that the internal moment should be expressed as a function of the applied forces and distances, with a participant skeptical about the assumptions regarding the beam's dimensions.
  • Concerns are raised about the number of unknowns in the problem, with one participant feeling that there are too many variables to solve definitively with the available equations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on several aspects, including the correct application of moment directions, the significance of beam lengths, and the overall approach to solving for the unknowns in the problem. Multiple competing views remain throughout the discussion.

Contextual Notes

Participants note limitations in the problem due to missing measurements and assumptions about beam dimensions. There is also uncertainty regarding the application of sign conventions in the shear and moment diagrams.

Who May Find This Useful

Students and practitioners interested in structural analysis, particularly those dealing with combined loading scenarios and beam mechanics, may find this discussion relevant.

  • #31
In order to find the bending moment at each point
 
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  • #32
morpheus343 said:
In order to find the bending moment at each point
Yes, the moment at section ##a-b## and ##c-d## are defined by ##M(x)## which is a function of ##F_x, F_y##.

Before you were applying the same moment at point ##b## and ##d##. But they are ##10 ~ \rm{cm}## apart. So they don't have the same internal moment.

You have two other points to consider, so maybe you can even solve for ##L##, I don't know...You'll have to try that out.

To me it appears as though section ##a-b## is at ##\frac{L}{2}## but that isn't specified anywhere - I'm skeptical, but who knows.

Also, it’s not clear whether or not the height of the I beam ( ##20 \rm{cm}## )is to be neglected against ##L##, that would factor into your external moment.
 
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  • #33
I see, i will work the algebra and see if i can solve it, but i think there are too many unknowns.(##F_x##, ##F_y##, ##M_B##, ##L##, ##x## distance). And i only have 4 equations, one of each of the combined stress at each point. Thank you for your time and help
 
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