CVE 230 Mechanics of Materials

Lab Report #4

Christopher Calderón

April 2, 2012

The relationships between load and the angle of twist, compared to shear stress and

strain are demonstrated in the data from this experiment based on the submission of

a rubber tube to a torsion test consisting of increasing loads. The purpose of this

investigation was to plot the shear stress-strain curve for rubber in order to then

show their relationship and to obtain the modulus of rigidity for rubber. In this

experiment, the experimental value of the modulus of rigidity was compared to the

theoretical value found in literature. The results in this experiment failed to prove

the ability of estimating the value of the modulus of rigidity accurately with an

approximate graph in order to obtain the same/similar given value from literature.

But the results do in fact show how the shear stress and strain are positively

correlated due to the positively correlated relationship between the load applied to

an object and its angle of twist.

LAB REPORT #4

Torsion Testing

Introduction:

Rubber can be made naturally or through synthetic processes, approximately 40 percent is made naturally from rubber trees (Hevea brasiliensis). The majority of this material is used to make rubber tubes and tires, the rest of it can be made to make consumer goods such as boots and gloves. Rubber is a material that is both highly elastic and waterproof.

In this experiment, the value of rubber’s modulus of rigidity will be attempted to be estimated. The modulus of rigidity, or the shear modulus, is the degree of elasticity a material displays under shear stress. This is important to many engineering applications due to it representing how much the material will yield under a given load.

Materials and Methods:

Materials used in this experiment include a rubber tube and a torsion testing apparatus, along with an assortment of weights.

The length of the rubber tube, the inside radius, and the outside radius were measured prior to submitting the rubber tube to a torsion test. The torsion test consisted of increasing amounts of loads applied at regular intervals. For every load, the torsion and corresponding angle of twist were both calculated and recorded (units for torsion were in pounds per inch and the units for the angle of twist were in radians).

The polar moment of the rubber tube was determined by using its relationship with the outside and inside radii and the torsion was determined by using its relationship with the applied load and the outside radius. The polar moment and the angle of twist were then used in order to calculate shear stress and strain and results were used to plot a graph of shear stress versus shear strain. The plot was then used in order to determine the modulus of rigidity.

Results and Discussion:

The purpose of this experiment was to plot the shear stress-shear strain curves for rubber in order to then use it to calculate the modulus of rigidity of rubber.

The relationship the data demonstrates for load and the angle of twist is that of a positive correlation, the more load is applied to an object, the larger the resulting angle of twist will be. Therefore, the increasing stress that exists as the applied force increases is related positively with

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LAB REPORT #4

Torsion Testing

the strain of the material because of its increasing angle. This relationship is supported by the data that has been collected from the torsion tests.

Based solely on this investigation, the modulus of rigidity for the rubber is approximately 19600 pounds per square inch. This value was obtained by selecting the first linear portion of the shear stress versus strain graph and finding the average slope of the linear portion selected.

Information Recorded Prior to Torsion TestLength 15 in

Inside Radius 0.375 inOutside Radius 0.626 in

Moment of Inertia 0.2102 in⁴

Results of Torsion TestLoad (lbs) Angle (degrees) Torsion (lb-in) Shear Stress (psi) Shear Strain (Rad)

4.060 93 6.4856 19.315 0.06774

10.060 95 16.0703 47.859 0.0692014.060 97.5 22.4601 66.889 0.0710216.060 101 25.6550 76.403 0.0735718.098 105 28.9105 86.099 0.0764819.128 106 30.5559 90.999 0.07721

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LAB REPORT #4

Torsion Testing

0.00219 0.00364 0.00546 0.00801 0.01093 0.011650.000

10.00020.00030.00040.00050.00060.00070.00080.00090.000

100.000

Shear Stress vs. Strain

Shear Strain (Rad)

Shea

r Str

ess

(psi

)

Conclusion:

The torsion test conducted on the rubber tube was the focal point of this experiment. The results from this test were meant to demonstrate the relationship that exists between the shear stress and strain of an object, to prove the ability of estimating the modulus of rigidity of a material just as the modulus of elasticity was calculated in prior experiments, and to show the accuracy of torsion testing with respect to demonstrating the abilities of a certain material.

The theoretical value for the modulus of rigidity for rubber, from literature, is between 30 and 200 pounds per square inch. This can be compared to the value obtained from this experiment in order to determine the accuracy of the overall torsion test. The experimental value was 19600 pounds per square inch. This indicates that the modulus of rigidity obtained from this investigation is far from the ideal range which was expected to be somewhat close. This demonstrates that the calculations failed to show the ability of taking the information from an approximated graph and estimating the modulus of rigidity accurately.

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