Strain energy formula for simply supported beam with point load

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

E = Youngs modulus

G = Modulus of rigidity

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 10⁴ MPa

G = 0.4 E

b  = 0.5 m

h  = 0.8 m.

Solution,

Given data are,

E = 3.4 x 10⁴ 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 10⁴ x 10⁶ N/m² = 3.4 x 10¹⁰ N/m²

Therefore,

I = (b * h³ ) / 12 = (0.5 * 0.8³ ) / 12 = 0.0213 m⁴

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

Portion	Origin	Limit	Mx	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

Bar bending schedule of Beam | Step by Step Procedure