How to Calculate Strain Energy for a Beam?

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SUMMARY

This discussion focuses on calculating strain energy for a beam subjected to various loads. The user outlines their calculations for moments (M) and strain energy (U) across different segments of the beam, specifically from points A to D. The calculations indicate a total strain energy of -1777.78, leading to an unusually high deflection value of 1.78m for a beam length of 260mm. The user seeks assistance in resolving discrepancies in their calculations.

PREREQUISITES
  • Understanding of beam mechanics and load distribution
  • Familiarity with the concepts of moment (M) and strain energy (U)
  • Knowledge of deflection calculations in structural engineering
  • Proficiency in using the formula for strain energy: Strain energy = 1/2 x (load) x (deflection)
NEXT STEPS
  • Research the principles of beam deflection and its calculation methods
  • Study the effects of varying load conditions on strain energy in beams
  • Learn about the significance of negative strain energy values in structural analysis
  • Explore advanced topics in structural mechanics, such as the Euler-Bernoulli beam theory
USEFUL FOR

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

pradi4u
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Any one can help me solving this pleasezzzz

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http://i49.tinypic.com/2vkm2r8.jpg"

My attempt
At A-B
There is No load so dM/dP= 0 and dU/dP= 0

At B-C

M = -px - wx.x/2
dM/dP= -x
dU/dP = Wx^4/8EI

At C-D

M = -Wb + Px
dM/dP = x
dM/dP = -Wbx^2/ 2EI

When i include all vaues to compute total starin energy, (AB+BC+CD)
it shows a value of 0+ 444.44-2222.22 = -1777.78

Strain energy = 1/2 x(load.)x (deflection)
= 1/2 x 2000 x deflection.

When i equate both valuse, i get deflection value of 1.78m which looks like very big value for a beam of 260mm long
 
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Hi pradi4u! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
tiny-tim said:
Hi pradi4u! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

HI,
Thanks for the reply. Here is where i am stuck
At A-B
There is No load so dM/dP= 0 and dU/dP= 0

At B-C

M = -px - wx.x/2
dM/dP= -x
dU/dP = Wx^4/8EI

At C-D

M = -Wb + Px
dM/dP = x
dM/dP = -Wbx^2/ 2EI

When i include all vaues to compute total starin energy, (AB+BC+CD)
it shows a value of 0+ 444.44-2222.22 = -1777.78

Strain energy = 1/2 x(load.)x (deflection)
= 1/2 x 2000 x deflection.

When i equate both valuse, i get deflection value of 1.78m which looks like very big value for a beam of 260mm long

Kindly help me to complete it.
Your help is highly appreciated
 

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