Deflection in a simply supported beam with a rigid arm underneath

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Discussion Overview

The discussion revolves around calculating the deflection of a simply supported beam subjected to a uniformly distributed load (UDL) and influenced by a rigid arm underneath. Participants explore methods for analyzing the system, including the use of free body diagrams and moments.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem, suggesting that moments might be relevant but is unsure if that method will work.
  • Another participant points out that the question tests knowledge of where the additional load acts, specifically at 0.5m or 1.0m.
  • A third participant recommends starting with a free body diagram of the beam and resolving the UDL into a point force, indicating that this will help in analyzing the moments created by the load on the arm.
  • This participant also mentions the importance of drawing shear force and bending moment diagrams to find the maximum deflection, questioning if the maximum deflection correlates with the greatest shear force.
  • A later reply clarifies that the value of E=4*10^-6 refers to the product of Young's modulus and the moment of inertia (E*I), and expresses gratitude for the confirmation of using moments to determine deflection.

Areas of Agreement / Disagreement

Participants generally agree on the need to use free body diagrams and moments in the analysis, but there remains uncertainty regarding the specifics of the load's application and the relationship between shear force and maximum deflection.

Contextual Notes

There are limitations regarding assumptions about the load's position and the completeness of the information provided in the question. The discussion does not resolve these uncertainties.

Who May Find This Useful

This discussion may be useful for students or professionals interested in structural analysis, particularly those dealing with beam deflection problems in engineering contexts.

cjh200
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The attached question shows a simply supported beam with a UDL of 30kN/m and has a rigid arm underneath with a load. This question was a research one but unfortunately I have had no luck.

I thought that this could be solved by doing moments for the arm but am unsure on whether that would work for this question. If anyone can point me in the right direction would be much appreciated.
 

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The question is testing to see if you know if the additional load acts at 0.5m or 1.0m.
 
Have you drawn a free body diagram of the beam yet? That would be my starting point.

Firstly, resolve the UDL into a point force, acting equidistant between the points where the UDL is applied. force on the arm will create a moment where the arm is attached to the rigid beam, which is approximate to the force applied on the arm multiplied by the horizontal length of the arm. Once you have resolved the forces into a free body diagram, you can then draw a shear force diagram and a bending moment diagram.

That's about as far as I can get you right now off the top of my head. Conceptually, shear force and bending moment diagrams should help, as the maximum deflection should occur where the shear force is at its greatest (can someone check me on that please?). by doing a piecewise analysis of the shear force diagram you could easily find its horizontal distance (x), and being a uniformly distributed load, the shear force diagram will act linearly.

I'm guessing that that E=4*10^6 is some kind of young's modulus or something? Is there more to this question that is missing?
 
Thanks for the fast response. The 4*10^-6 was E*I (youngs modulus*Inertia) and your response that.kid reconfirmed my idea of using moments to figure out the deflection. Once again thanks
 

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