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Politeknik Sultan Azlan Shah

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The force distribution acting at a point on the surfaceis unique and will have components in the normal andtangential directions called normal stress andtangential shear stress

If the direction of is outward from the surface it is

considered to be a tensile stress and is a positivenormal stress

If is into the surface it is a compressive stress andcommonly considered to be a negative quantity.

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For equilibrium condition:

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Forces acting on the end of the rod are directed along the axis . This loadingcondition is termed under axial loading

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The coefficient E is called the modulus of elasticity of the material involved, oralso known as Youngs modulus

Stress

Strain

E Young Modulus

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If the resulting axial stress =P/A does not exceed theproportional limit of the material, we may applyHookes law and write

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Where J = polar moment of inertia

For solid circular shaft:

For hollow circular shaft:

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Example

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The principal specifications to be met in the design ofa transmission shaft are the power to be transmittedand the speed of rotation of the shaft.

The role of the designer is to select the material andthe dimensions of the cross section of the shaft, so thatthe maximum shearing stress allowable in the materialwill not be exceeded when the shaft transmitting the

required power at the specified speed

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Where is the angular velocity of the body expressed

in radians per second.

f is the frequency of the rotation (number ofrevolution per second)

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Example