How Should Strain Energy Be Calculated for a Short Beam?

In summary, the conversation discusses solving a problem involving a beam with no load, and the equations for calculating strain energy at different points along the beam. The conversation also addresses a discrepancy in the calculated deflection value and offers a solution to factor in the length of the beam for a more accurate result.
  • #1
pradi4u
5
0
Someone please help to solve this its urgent..

Homework Statement


Homework Equations


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The Attempt at a Solution


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
.Please guide me how i can solve this. Its urgent.The answer is not 1.78m. You have to factor in the length of the beam when calculating the strain energy. For a 260mm long beam, the strain energy will be much lower.
 

Related to How Should Strain Energy Be Calculated for a Short Beam?

1. 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 the material and is released when the material returns to its original shape.

2. How is strain energy related to displacement?

Strain energy is directly proportional to the amount of displacement in a material. The greater the displacement, the more strain energy is stored in the material.

3. What factors affect the amount of strain energy in a material?

The amount of strain energy in a material is affected by its stiffness, or Young's modulus, and the amount of force applied to it. A stiffer material will store more strain energy than a more flexible material when the same amount of force is applied.

4. How is strain energy measured?

Strain energy is typically measured in units of joules (J) or newton-meters (Nm). It can be calculated by multiplying the force applied to a material by its displacement, or by integrating the stress-strain curve for the material.

5. Why is strain energy important in engineering and design?

Strain energy is important in engineering and design because it can help predict the behavior and failure of materials under different loading conditions. It is also an important consideration in the design of structures and machines, as it can affect their durability and safety.

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