Beam Reaction Force: Calculating Final Value

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Discussion Overview

The discussion revolves around calculating the final reaction force at a middle restraint of a beam when it settles by 13mm. Participants explore the implications of this settlement on the reaction forces, considering factors such as uniformly distributed loads (UDL) and concentrated loads.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that the reaction force would decrease due to the bending of the beam absorbing some of the applied force.
  • Another participant notes that neglecting the UDL complicates the situation, indicating that the initial reaction at the middle support is influenced by both the concentrated load and the UDL.
  • A participant asserts that the initial reaction already accounts for the UDL, questioning the need for its value in the calculations.
  • One participant clarifies that the center support reaction includes contributions from both the applied load and the UDL, emphasizing the need to consider both in the deflection calculation.
  • There is mention of specific deflection formulas for both concentrated loads and UDLs, indicating that both must be included to accurately assess the deflection and resulting reaction forces.

Areas of Agreement / Disagreement

Participants express differing views on the role of the UDL in the calculations, with some asserting its importance while others believe it is already accounted for in the initial reaction. The discussion remains unresolved regarding the exact impact of the UDL and the appropriate approach to calculating the final reaction force.

Contextual Notes

Participants reference specific formulas for deflection related to concentrated loads and UDLs, but there is uncertainty regarding the values of these loads and their contributions to the overall reaction forces. The discussion highlights the complexity of the problem due to the statically indeterminate nature of the system.

Ry122
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Homework Statement



http://users.on.net/~rohanlal/udl.jpg
If the middle restraint has a vertical reaction of 50kn when the structure is first built,
how do i determine what the reaction would be if the middle restraint was to settle by 13mm?

Homework Equations



Is this a simply supported beam? If so
delta=(P(L^3))/48EI


The Attempt at a Solution



Would this reduce the reaction force since the bending of the metal is sucking up some of the applied force?

So would it be Final Reaction = (Initial Reaction) - (P from above equation)
 
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At a glance, I think you have the correct line of reasoning, but that UDL of unknown value complicates the situation. If you neglect the UDL, then initially all of the P concentrated load gets supported at the middle (rigid) support. Then due to the settlement of that support, you are correct that some of that load goes to the end supports based on a simple beam between the end supports with the 13mm deflection at centerline, so that what's left goes to the middle support. But the problem does not seem solvable without a value for the UDL, because you'd have to consider it in your deflelction calculation.
 
I do know the the value for the UDL but the initial reaction takes the UDL into account already, so knowing this is what I said correct?
 
No. The center support reaction initially includes a contribution from the applied load, P, and the UDL. I assume you are given P, which must be less than 50 kN. The contribution from the UDL is statically indeterminate, but you can find it in handbook tables. Now as the middle support settles, some of the 'P' load transfers to the end supports, and some of the UDL load also transfers to the end supports. When you use the deflection formula, you must include not only the FL^3/48EI term, which is for the unit load only,
but also the UDL deflection at mid point, which, if memory serves me correctly, is wL^4/384EI. Both contribute to the 13 mm deflection.
 

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