#### Some symbols and their meaning used in the numerical given below are given as,

E = Youngs modulus

b = Width of beam

h = Depth of beam

#### Strain energy formula for simply supported beam with point load used in numerical below,

**Strain Energy due to Bending**

**Strain Energy due to Shear**

**Strain Energy due to Normal thrust**

#### Numerical Example,

**Q) Calculate strain energy due to bending, shear force, and normal thrust in the frame shown. All the members of the frame are rectangular with the following data. **

E = 3.4 x 10^{4} MPa

G = 0.4 E

b = 0.5 m

h = 0.8 m.

**Solution,**

Given data are,

E = 3.4 x 10^{4} MPa

G = 0.4 E

b = 0.5 m

h = 0.8 m.

And the given frame is,

If we find all horizontal reaction, vertical reaction, and moment of the above frame, then we will get the free body diagram like below,

Here, E = 3.4 x 10^{4} x 10^{6} N/m^{2} = 3.4 x 10^{10} N/m^{2}

Therefore,

I = (b * h^{3} ) / 12 = (0.5 * 0.8^{3} ) / 12 = 0.0213 m^{4}

The bending moment expressions for various portion are calculated in tabular form below,

Portion | Origin | Limit | M^{x} | EI |
---|---|---|---|---|

DC | D | 0-2 | – 50x | 2EI |

CB | C | 0-3 | -100 | EI |

BA | B | 0-4 | 50x-100 | EI |

Now,

**A) Strain Energy due to Bending, **

Also,

**B) Strain Energy due to shear,**

**C) Strain energy due to normal thrust (Axial Force) =**

I hope this article on “**Strain energy formula for simply supported beam with point load**” remains helpful for you.

Happy Learning – Civil Concept

Read Also,

Analysis of beam by Conjugate beam method with Numerical Example

Kinematic indeterminacy and Static indeterminacy – Beam, Frame etc

Draw the Shear and Moment diagrams for the beam- With Calculation