Deflection at any point in fixed beam

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SUMMARY

The discussion focuses on calculating deflection at any point in a fixed beam subjected to a couple acting at an intermediate point. The recommended resource for this calculation is "Roark's Formulas for Stress and Strain." The approach involves using singularity functions to define the loading, setting it equal to EIy'''' (where E is the elastic modulus, I is the moment of inertia, and y'''' is the fourth derivative of deflection). The process includes successive integration to derive shear force, moment, and deflection as a function of position along the beam, applying boundary conditions to determine integration constants.

PREREQUISITES
  • Understanding of beam mechanics and deflection theory
  • Familiarity with singularity functions in structural analysis
  • Knowledge of elastic modulus and moment of inertia concepts
  • Ability to perform integration and apply boundary conditions in calculus
NEXT STEPS
  • Study "Roark's Formulas for Stress and Strain" for detailed methodologies
  • Learn about singularity functions and their applications in beam analysis
  • Explore the derivation of shear force and moment equations in fixed beams
  • Investigate small deflection theory and its assumptions in structural engineering
USEFUL FOR

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

sunil.hk1
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give formula or reference for finding deflection at any point in beam (fixed at both ends) due to couple acting intermediate in the beam? its urgent...
 
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sunil.hk1 said:
give formula or reference for finding deflection at any point in beam (fixed at both ends) due to couple acting intermediate in the beam? its urgent...

I'd start with Roark's Formulas for Stress and Strain.

CS
 
I think the easiest thing is to define the loading using singularity functions, set it equal to EIy'''' (where E = elastic mod, I = moment of inertia, y'''' = fourth derivative of deflection); then successively integrate to get the shear force, moment, and finally the deflection as a function of x (the position along the beam). and determining the integration constants from the boundary conditions (such as at x = 0 and x = l, y = 0).

example of the singularity functions
http://www.roymech.co.uk/Useful_Tables/Beams/Singularity.html

(this is assuming small deflections by the way)
 
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