1. Introduction: Modulus of Rigidity Rigidity or (Shear Modulus) which relates the components of the s hearing Stress and shearing strain, is the coefficient of elasticity for a shearing force. It is defined as "the ratio of shear stress to the displacement per unit sample length (shear strain)".
FIG 1 : Shear stress stress and and Shear Shear strai strain n Rubber, there is two type of it. The nature rubber which formed naturally as a bark of a tree , and industrial industrial rubber _which will be used in this report_ which used in wide range as a vibrations vibrations resistant in cars, engines engines ,and ,and other machines machines and it do do this by absorbing shock energy by deforming , This deformation leads to a decrease in crosssection as the block lengthens. An effect d escribed by Poisson's Ratio. Poisson’s ratio mean that when a material is stretched in one direction it tends to become thinner thinner in other two directions.
2. Objective:
Measure the shear deformation of the b lock.
To determine the variations of deflection with app lied load.
To investigate the relationship between shear stres s and shear strain.
Modulus of Rigidity Rigidity and Poisson Ratio. Determination of Modulus
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3.
Become familiar with Modulus of Rigidity, and its experiment.
Equipment:
A rubber block 150 x 75 x 25 mm is bonded bo nded to two aluminum alloy plates. One of t he plates is pined to wall. wall. And there is a weight weight hanger (which have the load). And a dial gauge to indicate the deformations in rubber block. See Fig (2) and there is some blocks used to apply forces. See Fig (3)
FIG (3): Loads
FIG (2): The Rubber Block
4. Procedure: 1. At first, adjust t he dial gauge to zero reading. To avoid Zero error. 2. Put a weights, start from 10 N to 120 N, in 10 N increments. 3. After each 10 N write down the reading of the d ial gauge (which represent the deformation of the rubber block), until the travel of the gauge is exceeded. 4. Record the reading in table (1). 5. Plot the results, and calculate the Modulus the Modulus of Rigidity G. G.
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5. Results: Table (1): Recorded Readings Load Dial Gauge Reading (N) (mm) 0 0 10 0.32 20 0.74
Deflection (mm) 0 0.38 0.81
30
1.16
1.16
40
1.60 2.01 2.38 2.82 3.22 3.62 3.91 4.36 4.78
1.60 2.01 2.45 2.86 3.26 3.63 4.06 4.42 4.85
50 60 70 80 90 100 110 120
At first place draw the relationship between load and deformation, and then draw good and suit straight line through the points. These are the mathematical equations,
ℎ
=
=
ℎ
=
() =
=
( () )
=
3750
b
(shearstress)
(Strain angle)
75
And the practical method equation,
G
W 3750
75 8
75
1
3750 graph gradient
( N / mm 2 )
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Table (2): Load & Deflection Chart
Load & Deflection 140
120
100
) N ( 80 s d a 60 o L 40
20
0 0
1
2
3
4
Deflection (mm)
5
6
Series1
Y = 24.44x + 0.3403 W =75 mm, A = 150 mm * 25 mm = 3750
Slope = Graph Gradient = 24.44, W True Value = 0.46 MPA
G=
∗
G =24.44*77/3750= 0.48 MPA
= Error =
.. .
∗ 100% = 4.348% 4.348%
6. Comments and Recommendations: Recommendations: Errors founded and may be affected on a results in the experiment due to many reasons listed below: 1. Zero error: If the dial gauge’s reading isn’t zer o at zero load. 2. Human error: if the experimenter red the dial gauge and calculate incorrectly.
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3. Environmental error: environment affects in rubber block properties, which mean that the reading of dial gauge which represent the deflection in rubber block depends on the the temperature of the lab. It is recommended to make sure that there is no zero error, and do this experiment on other materials, and take in your account the enviro nmental nmental conditions
7. References: 1. Books:
Beer, Ferdinand and other, Mechanics of Materials, 6 th edition, Mc Graw Hill, 2012. 2. Websites:
http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html http://eng.najah.edu/apparatus/2265 http://www.engineeringtoolbox.com/poissons-ratio-d_1224.html
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