Deflection by Moment Area Method

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SUMMARY

The discussion focuses on solving a cantilever beam problem using the Moment Area Method to determine the slope and deflection under a triangular uniform load. The textbook solutions provided are wl^3/8EI for slope and 11wL^4/120EI for deflection. A participant identifies that discrepancies in calculations may stem from an incorrect bending moment expression and suggests creating a shear force diagram to derive the bending moment diagram accurately.

PREREQUISITES
  • Understanding of cantilever beam mechanics
  • Familiarity with the Moment Area Method
  • Knowledge of shear force and bending moment diagrams
  • Proficiency in applying the First and Second Moment Theorems
NEXT STEPS
  • Review the derivation of the Moment Area Method for cantilever beams
  • Study the construction of shear force and bending moment diagrams
  • Practice problems involving triangular uniform loads on beams
  • Explore advanced applications of the First and Second Moment Theorems
USEFUL FOR

Engineering students, structural analysts, and professionals involved in beam design and analysis will benefit from this discussion.

obrien040362
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Homework Statement


The problem is a cantilive beam of length L with a triangular uniform load or W. The solution is to find the slope and deflection at the end by moment area method. My solution is not matching the textbook solution of wl^3/8EI and 11wL^4/120EI

Homework Equations


First Moment Theorem - Slope equal to the area under the M/EI diagram
Second Moment Therorem - Deflection is equal to the moment of the moment area about the point you want the deflection.[/B]


The Attempt at a Solution


see uploaded file[/B]
 

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I think the reason your moment-area calculations aren't working is that your bending moment expression is incorrect.

I would draw the shear force diagram and develop the bending moment diagram from it.
 

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