__Determination of Young’s modulus__

__(Mild steel-simply supported beam)__

**Aim:**

To determine the Young’s modulus of given mild steel section of simply supported beam.

**Apparatus required:**

1. Digital displacement meter

2. Experimental set up of cantilever beam

3. Weights

4. Stands

5. Vernier caliper

**Formula used:**

in N/mm

^{2 }^{}

Where,

l = length of beam in mm

I = moment of beam in mm

^{4}^{ }= Stiffness (from graph) in N/mm

**Theory:**

Within the elastic limit, the stress is directly proportional to strain. The constant of proportionality is known as Young’s modulus. The moment of inertia of any material depends on nature of the material.

**Tabulation:**

Sl.No | Loadin g | Deflection at C in mm | Deflection in mm | Young’s modulus | ||

Loading | Unloading | Average | ||||

| | | | | | |

Mean=

**Procedure:**

1) The cantilever beam made of Al is fixed at one end and other being free provided with long hanger.

2) The experimental arrangement are made as follows. The weight is 193 gms(including the weight of hanger) is provided at free end.

3) The corresponding reading of displacement meter and weights are added with increase of 100 gms each displacement is measured using displacement meter based on strain rosette gauges forming different resistance for different deflection of beam and calibrated correspondingly time and corresponding displacement readings are noted and tabulated.

4) Repeat steps till the total weight is 893 gms. Plot a graph of load against displacement. This formula gives a linear graph. The slope of line gives directly the stiffness value P/δ

**Result:**

The Young’s modulus of given mild steel section of simply supported beam is………………………

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