Calculate Tip Deflection of Beam Under Applied Loads

  • Thread starter Thread starter wildleaf
  • Start date Start date
  • Tags Tags
    Beam Deflection
Click For Summary

Discussion Overview

The discussion revolves around calculating the tip deflection of a cantilever beam subjected to multiple applied loads, including its own weight. Participants are exploring the application of superposition and relevant equations for deflection under various loading conditions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents the problem statement, including beam specifications and relevant equations for calculating deflection under uniform loads.
  • Another participant suggests checking deflection tables for cantilever beams to calculate the deflection due to the 4000 lb and 5000 lb loads separately, emphasizing the use of superposition.
  • A third participant mentions the existence of two equations for each of the 4000 lb and 5000 lb loads, indicating that both equations should be utilized for accurate calculations.
  • A later reply clarifies the application of the equations based on the position along the beam, indicating specific ranges for the equations related to the loads.
  • One participant expresses frustration over the time spent trying to calculate the deflection, indicating the complexity of the problem.

Areas of Agreement / Disagreement

Participants generally agree on the need to use superposition and the importance of applying the correct equations for different segments of the beam. However, there is no consensus on the exact approach to calculating the deflection for the specific loads, as participants propose different methods and equations.

Contextual Notes

Participants reference specific equations and tables for deflection calculations but do not provide complete derivations or clarify all assumptions involved in their approaches. The discussion does not resolve the exact method for calculating deflection for the non-uniform loads.

wildleaf
Messages
24
Reaction score
0

Homework Statement


For the given beam (link), calculate the tip deflection for the given loadings. In addition to the applied load, the beam wt 2000 lbs/ ft.
E = 30 * 10^6 psi
I = 60 * 10^3 in^4

http://i52.tinypic.com/990xef.jpg


Homework Equations


deflection for the uniform load is: w= -p/ (24*E*I)* [(x^4) - (4*L*x^3) + (6*L^2*x^2)]

You use this to calculate the uniform load of 1000 lb/ft. I think you use this for the weight of the beam (2000 lb/ft) as well, but i am not too sure.
I have solved the deflection function by hand and have checked on sites and it is the correct case for uniform load.

The Attempt at a Solution


I know we have to use superposition, we have to separate them by uniform load of
1000 lb/ft, the 4000 lb load, 5000 lb load, and the weight of the beam itself... After I separate them, I solved for the deflection function for the uniform load of 1000 lb/ft.
I know that I need to do this for all four loads and then add them together at the end but I don't know how to calculate the deflection for the 4000 lb load, and 5000 lb load since they are not evenly spaced.
 
Physics news on Phys.org
Check your deflection tables for a cantilever beam with a single load applied away from the end. You can calculate the deflection of the 4000# load by itself, and the 5000# load by itself. The total deflection at the free end is obtained by superposition.
 
there are two equations for one load for 4000 and two equations for 5000, Do use all 4 of them.. The two equations have a limit, the first equation is from the left end to the Force/load and second is from the Force/load to the right end. Here is the link: Look at case 2:
http://www.advancepipeliner.com/Resources/Others/Beams/Beam_Deflection_Formulae.pdf

So i will have to use all 4 equations, 2 of each force, and add them?
 
If you look at Beam Type 2 and the equations for deflection y, note that each equation is applicable for a certain portion of the beam:

Eq. 1 - x is between the load P and the fixed end of the beam 0 < x < a
Eq. 2 - x is between the load P and the free end of the beam a < x < L

However, your problem asks you to calculate the tip deflection, so use the eq. in the right hand column (Max. deflection) of the table for dmax.
 
Thanks bro :)
Wasted about 4 hours trying to calculate the two load, lol.
 

Similar threads

Deflection of partially loaded cantilever beam with non-homogeneous EI
  • · Replies 3 ·
Replies
3
Views
2K
How Do You Calculate Distributed Load on a Roof Truss Due to Snow?
  • · Replies 3 ·
Replies
3
Views
5K
What is the relationship between slope and bending moment in a penstock beam?
  • · Replies 6 ·
Replies
6
Views
2K
A beam: need to calculate its max moment and deflection
  • · Replies 1 ·
Replies
1
Views
2K
Calculate deflection of rod/axlepipe due to distributed load
  • · Replies 5 ·
Replies
5
Views
2K
Simply supported beam with a spring support in the middle - deflection
  • · Replies 6 ·
Replies
6
Views
4K
Engineering Multi-point Boundary Value Problems Using Finite Difference Method
  • · Replies 3 ·
Replies
3
Views
3K
Mechanical - Deflection and Slope, cantilever beam
  • · Replies 5 ·
Replies
5
Views
4K
Maximum Deflection of Brass Beam: Troubleshooting Homework Solution
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Deflection and Stress in a Tapered Cantilever Beam
  • · Replies 3 ·
Replies
3
Views
13K