Confused on Calculating Deflection and Rotation for Non-Prismatic Beam?

  • Thread starter Thread starter Fat Ryan
  • Start date Start date
  • Tags Tags
    Beam
Click For Summary
SUMMARY

The discussion focuses on calculating deflection and rotation for a non-prismatic beam under uniform loading conditions. The user initially applied the deflection equations for a prismatic beam, specifically dmax = -wL^4/(8EI) and thetamax = -wL^3/(6EI), but encountered discrepancies in results. After integrating the moment of inertia I(x), the user achieved reasonable deflections but faced inconsistencies in shear force calculations, indicating a potential error in the application of equilibrium equations. The user clarified that the modulus of elasticity E is 5000 ksi, which is critical for accurate calculations.

PREREQUISITES
  • Understanding of beam theory and mechanics of materials
  • Familiarity with deflection and rotation equations for beams
  • Knowledge of integration techniques for variable moment of inertia
  • Proficiency in equilibrium equations for static systems
NEXT STEPS
  • Review the derivation of deflection formulas for non-prismatic beams
  • Study the application of the moment-curvature relationship in beam analysis
  • Learn about calculating shear forces and bending moments in beams
  • Explore numerical methods for solving beam deflection problems
USEFUL FOR

Engineering students, structural analysts, and professionals involved in beam design and analysis, particularly those working with non-prismatic beams and complex loading conditions.

Fat Ryan
Messages
48
Reaction score
0

Homework Statement


COMP1beam.jpg



Homework Equations


[k]{delta}=F


The Attempt at a Solution


I found I(x) and confirmed it manually. Basically, I think my confusion comes when finding delta. Delta is a 2X1 array of -d and -theta, respectively. I used equations for deflection and rotation for a prismatic beam that's uniformly loaded...

dmax=-wL^4/(8EI)
thetamax=-wL^3/(6EI)

initially, i integrated the above equations WRT x, along the length 0-->L (with I=I(x) of course), but that gave me absurdly large answers. So then I used the above equations with I=integral(I(x)dx). This gave me reasonable deflections, but it left me with a resulting shear force of only 0.2kip on the right. equating vertical forces to 0 leaves me with a shear of 59.8kip on the left. This cannot be correct.

I can't seem to figure out what I am doing wrong, but once i get it, i shouldn't have a problem calculating the FEFs for w2. can someone please take a look, and let me know where I am going wrong? Thanks!
 
Physics news on Phys.org
Ha, I meant E=5000ksi in the problem statement; my apologies.
 
Tried doing it a different way and got it to work
 

Similar threads

Engineering Deflection and Slope of a Simply Supported Beam
  • · Replies 8 ·
Replies
8
Views
2K
Mechanical - Deflection and Slope, cantilever beam
  • · Replies 5 ·
Replies
5
Views
4K
Engineering Calculating shear center for a "skewed" I beam
  • · Replies 1 ·
Replies
1
Views
2K
Solving Beam Deflection with Singularity Equations
  • · Replies 2 ·
Replies
2
Views
2K
A beam: need to calculate its max moment and deflection
  • · Replies 1 ·
Replies
1
Views
2K
Beam with two supports + spring
  • · Replies 1 ·
Replies
1
Views
3K
Integration method (Navier) calculating deflection
  • · Replies 7 ·
Replies
7
Views
3K
Calculate the maximum vertical point force P that this beam can sustain
  • · Replies 1 ·
Replies
1
Views
2K
Calculating Deflection and Stress in a Tapered Cantilever Beam
  • · Replies 3 ·
Replies
3
Views
13K
Engineering Statics, Finding Reaction forces for A and H
  • · Replies 6 ·
Replies
6
Views
2K