Beam deflection by superposition

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Discussion Overview

The discussion revolves around solving for the reaction force, Rb, in a beam deflection problem involving superposition. Participants explore equations related to deflection due to distributed loads and support reactions, focusing on the mathematical approach to derive the correct values.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the deflection equations for a distributed load and support, suggesting that the total deflection at Rb should equal zero.
  • The same participant calculates db1 and finds a match with the solution manual but expresses uncertainty about the calculation of db2.
  • Another participant questions the initial method and suggests that there may be a math error in the db2 equation, hinting at the need to adjust for the length conversion.
  • A later reply proposes an alternative equation for db2 using beam tables, indicating that it could yield the same result.
  • One participant acknowledges the assistance received and confirms that they arrived at the correct answer after revisiting the calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method for calculating db2 initially, but there is agreement on the correctness of the approach after further review. Disagreement exists regarding the initial calculations and potential errors.

Contextual Notes

There are indications of missing assumptions regarding the application of beam deflection equations and the specific conditions under which they are valid. The discussion also reflects uncertainty about the correct application of length conversions in the equations.

Jim Newt
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Homework Statement



In this problem, I'm trying to solve for the Reaction, Rb


Homework Equations



I believe for the distributed load, the deflection equation would be:

v = (-qx/24EI) * (L^3 - 6Lx^2 + x^3)

For the support, Rb, the deflection equation could be:

v = (-Pbx/6LEI) * (L^2 - b^2 - x^2)

where L = 3L

total deflection at Rb = db1 - db2 = 0

I could solve for Rb with the proper equations.

The Attempt at a Solution



For db1:

When I plug in x=L and L=3L, I end up with db1 = (11qL^4) / 12EI.
This answer matches the solution manual.

I can't figure out db2...I think I might be using the wrong deflection equation, but I'm not sure. The correct answer for db2 is db2 = (4RbL^3) / 9EI

How do I go about solving for db2?
 

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Ok, maybe my whole method is bunk. Given the standard beam deflection equations, how would you solve for Rb?
 
Jim Newt said:
Ok, maybe my whole method is bunk. Given the standard beam deflection equations, how would you solve for Rb?
You set up the equations perfectly! You may have made a math error in your db2 equation, perhaps forgetting to convert l to 3L. Note that in using the beam tables, you could have used db2 = (Rba2b2)/3EIl, the deflection at the point of the applied reaction load. The result is the same.
 
Hey thanks buddy! I went through it again and ended up with the correct answer. Its always the tidbit math that gets me...
 

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