Deriving Mid-Span Deflection of Simply-Supported Beam

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SUMMARY

The discussion focuses on deriving the mid-span deflection of a simply-supported beam using the method of area-moments. Key properties include span (L), second moment of area (I), modulus of elasticity (E), and total uniformly distributed load (UDL) (W). Participants emphasize the importance of reading Mohr's theorems, drawing the bending moment diagram, and identifying the centroid of the moment diagram's area to facilitate accurate calculations. Multiple methods exist for solving this problem, highlighting the need for clarity in requests for assistance.

PREREQUISITES
  • Understanding of Mohr's theorems
  • Ability to draw and interpret bending moment diagrams
  • Knowledge of the method of area-moments
  • Familiarity with beam properties: span (L), second moment of area (I), modulus of elasticity (E)
NEXT STEPS
  • Study the application of Mohr's theorems in structural analysis
  • Learn how to construct and analyze bending moment diagrams
  • Explore the method of area-moments for beam deflection calculations
  • Investigate alternative methods for calculating beam deflection, such as the double integration method
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in beam design and analysis will benefit from this discussion.

thebest99
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someone please help
not sure were to start.

use the method of area-moments to derive an expression for the mid-span deflection of a simply-supported beam with the following properties:

Span= L : second moment of area of section= I : modulus of elasticitiy= E which has a total UDL along its length= W
 
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1. read Mohr's theorems
2 draw the bending moment diagram
3 cut the beam and the M diagram at the point of interest
4 interpret Mohr's theorems.

You would need to identify the position of the centroid of part of the M diagram and its area. There are more than one way to solve this. You must give a bit more to this forum of what you can do in order to draw in more help.
 

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