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

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,

Now,

A) Strain Energy due to Bending,

Also,

B) Strain Energy due to shear,

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

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