How to Calculate Strain Energy for a Beam?

In summary, the conversation discusses the calculation of strain energy in a beam using the deflection method. The values of dM/dP and dU/dP are determined at points A-B, B-C, and C-D, and the total strain energy is calculated by adding the individual values. However, the resulting deflection value of 1.78m seems unusually large for a beam of 260mm long. The speaker requests assistance in completing the calculation.
  • #1
pradi4u
5
0
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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  • #2
Hi pradi4u! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
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
 

What is strain energy?

Strain energy is the potential energy stored in a material when it is deformed or strained. It is the energy that is required to deform a material from its original shape.

How is strain energy related to displacement?

Strain energy is directly proportional to the displacement of a material. The more a material is displaced, the higher the strain energy it will have.

What is the formula for calculating strain energy?

The formula for strain energy is: SE = ½ * k * x^2, where SE is strain energy, k is the material's stiffness, and x is the displacement.

Why is strain energy important in material testing?

Strain energy is important in material testing because it helps determine the material's strength and elasticity. It also allows for the comparison of different materials and their ability to withstand deformation.

How is strain energy used in engineering?

Strain energy is used in engineering to design and analyze structures and materials. It helps engineers understand how much force a material can withstand before it fails and how to design structures that can withstand certain loads and stresses.

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