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Lab No 7

The document describes an experiment to determine the modulus of elasticity of a material by testing a rectangular beam under different loads. It details the theory behind flexural formulas, the apparatus used, and the procedure which involves applying loads, measuring deflection, and calculating E based on the flexural formula. The results and calculations are shown along with the conclusion stating the average E value found and comparing it to the actual value for steel.

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Zohaib Stylish
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27 views5 pages

Lab No 7

The document describes an experiment to determine the modulus of elasticity of a material by testing a rectangular beam under different loads. It details the theory behind flexural formulas, the apparatus used, and the procedure which involves applying loads, measuring deflection, and calculating E based on the flexural formula. The results and calculations are shown along with the conclusion stating the average E value found and comparing it to the actual value for steel.

Uploaded by

Zohaib Stylish
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as DOCX, PDF, TXT or read online on Scribd
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EXPERIMENT NO 7:

TO EXPERIMENTALLY DETERMINE MODULUS OF


ELASTICITY (E) OF A MATERIAL BY TESTING A
GIVEN RECTANGULAR BEAM.

OBJECTIVE:
• To find the valve of modulus of elasticity using flexural formula

THEORY:
1) SIMPLY SUPPORTED BEAM:
A simply supported beam is a type of beam that has pinned
support at one end and roller support at the other end.
Depending on the load applied, it undergoes shearing and
bending. It is the one of the simplest structural elements in
existence.

2) FLEXURAL FORMULA:
The flexure formula gives the internal bending stress caused by an
external moment to a beam or other bending member of
homogeneous material. It is derived here for a rectangular beam
but is valid for any shape.
Mathematically:
/
Once load W will be applied over the simply supported horizontal beam ,the beam
will be bending in the form of a curve.
Flexural formula or flexural bending equation for a beam which is subjected to pure
bending is as displayed in the above figure and formulated as:

Where:
M = Bending moment
I = moment of inertia for the beam

σ= flexure stress

y= Distance of layer/fiber of the beam

from the neutral axis of the beam which is

subjected to pure bending E = Young’s

modulus of elasticity of the material of the

R = Radius of curvature of the beam (in)

APPARATUS:
• Beam apparatus.
• Vernier caliper,
• Dial gauge.
PROCEDURE:
1. First of all we prepare a simply supported beam.
2. Then we measure its length, width and its height.
3. Place dial gauges along the length near midpoint and set the gauges to read
zero with no load applied.
4. Then we fixed the dial gauge on the beam in order to measure the
deflection of beam when load applied.
5. Then apply load at midpoint of the beam and record the new readings of
the gauge as well as the mass of weight.
6. Change the loads and note their corresponding mass and deflection of the
beam.
7. Take at least three different values of weights and their corresponding
deflection.

8. Calculate all the factors (except E) involve in flexural formula

9. E can be calculated as E=

OBSERVATIONS:
Length of beam (L) = 30 inches = 762mm

Width of beam (b) = 0.54 inches = 13.71mm


Thickness of beam (h) = 0.23 inches = 5.84mm

length width thickness weight Initial Final Net


value of value of deflection
deflection deflection
Δ = Δ2-Δ1
Δ1 Δ2

762mm 13.81mm 5.38m 5.9N 0 3.63mm 3.63mm

762mm 15.24mm 5.08mm 10.8N 7.6mm 12mm 4.4mm

CALCULATIONS:

1. The moment of inertia ‘I’ is calculated from formula

2. Radius of curvature ‘R’ is calculated from formula;

3- Δmax = PL^3 / 48ΔI


E = PL^3/48dI

E = (10.81)(762)^3/48(5.31)(146.315)

E = 128361 Pa or 128.36 GPa

S.No Modulus of
elasticity

01 128.36

02 136.01
CONCLUSION:

The average value of E becomes 132.18 GPa while the actual E value of steel
200GPa.

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