Computing Beam Deflection Using Castiglianos' Theorem

Click For Summary

Discussion Overview

The discussion revolves around calculating the deflection of a cantilever beam subjected to a downward load using Castigliano's theorem. Participants are exploring the conditions and calculations that lead to different deflection results at a specific point along the beam.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents two different deflection formulas, 27QL^3/128EI and 11QL^3/384EI, derived from different moment calculations.
  • Another participant requests clarification on the support conditions of the beam to better understand the problem.
  • A third participant expresses confidence in the first formula being correct and asks for the working steps behind the calculations.

Areas of Agreement / Disagreement

There is no consensus on which deflection formula is correct, as participants have differing views based on their calculations and interpretations of the problem.

Contextual Notes

The discussion lacks details on the specific loading conditions and the method of moment calculation used by the participants, which may influence the results. Additionally, the assumptions regarding the beam's material properties and boundary conditions are not fully explored.

Juggler123
Messages
80
Reaction score
0
I am trying to find the deflection of the beam as described below,

The beam has an overall length L and a load Q acting downwards at this point, the question is asking for the deflection of the beam at the point three quarters of the way along the beam. The beam has constant flexural rigidity EI.

I have tried this problem a number of times and keep coming up with two different solutions, depending from which side of the beam I take my moments. The solutions I have are;

27QL^3/128EI and 11QL^3/384EI

Could someone please tell me which one is correct? I think it's the first answer but I'm not 100%.
Thanks.
 
Engineering news on Phys.org
It would help to know the support conditions.
 
The beam is a cantilever beam so is supported just at one end.
 
Well I make your first go to be correct.

Can you show some working?
 

Similar threads

Simply supported beam with a spring support in the middle - deflection
  • · Replies 6 ·
Replies
6
Views
4K
Cantilever beam deflection with point mass and point load at the end
  • · Replies 3 ·
Replies
3
Views
3K
Choosing correct steel beam for a span
  • · Replies 8 ·
Replies
8
Views
3K
Castigliano's method for the deflection of a cantilevered beam
  • · Replies 4 ·
Replies
4
Views
7K
Shock absorber forces
  • · Replies 4 ·
Replies
4
Views
2K
What is the best beam design for my aluminum tandem axle trailer?
  • · Replies 33 ·
2
Replies
33
Views
6K
Castigaliano's Theorem for cantilever beam
  • · Replies 2 ·
Replies
2
Views
2K
Engineering Deflection and Slope of a Simply Supported Beam
  • · Replies 8 ·
Replies
8
Views
3K
How does counter rotation control work for a tail sitter drone?
  • · Replies 15 ·
Replies
15
Views
3K
Need a Hand Calculating the Maximum Load on a Structure
  • · Replies 5 ·
Replies
5
Views
6K