Strain Energy Stored On Beams Due To Bending

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Beam applications are common in classical mechanics applications. Among the different applications, beams are designed to carry the bending forces which have the effect of bending on beams. Beams can be supported with different kinds of elements such as; simply supported, cantilevered, etc. 

Bending stresses on beams cause strain energy storage on beams. Here, we explain the calculation of these strain energy storage. You can find general expressions of this physical phenomenon and default formulas that are generally used in mechanics. 

Strain Energy Calculations Of Pure Bending On Beams,

Type 1: If a simple beam is simply supported from each side, and the bending force is not at the center;

The required equation to calculate strain energy storage on this beam is calculated with this formula;

The lengths are important in terms of the placement in the equation. 

Type 2: If the considered simply supported beam’s load is at the center of the beam;

So the equation to calculate the strain energy storage on this beam reduces to;

Type 3: If a simply supported beam undergoes uniformly distributed load;

The equation will be like this;

Here, ‘P’ represents the total load acting on the beam, which is ‘w*l’. 

Type 4: If a cantilevered beam from one side, carries a unitary load at the other edge; 

The equation will be like this;

Type 5: Consider the same cantilevered beam which carries a uniformly distributed load on it; 

Then the equation will be like this again;

Conclusion

These are the general formulations related to the strain energy of pure bending on beams. 

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The source of the images above: D. K. Singh – Strength of Materials-Springer, 2020, pg.417. No copyright infringement intended. This article is just for educational purposes.

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