1. Shear Stress Shear stress is defined a the component of force that acts parallel to a surface area Shear stress is defined a the component of force that acts parallel to a surface area Shear stress is a stress state where the shape of a material tends to change (usually by "sliding" forces – torque by transversely-acting forces) without particular volume change. Shear stress is a stress state where the shape of a material tends to change (usually by "sliding" forces – torque by transversely-acting forces) without particular volume change. The shape change is evaluated by measuring the change of the angle's magnitude (shear strain). The shape change is evaluated by measuring the change of the angle's magnitude (shear strain).

2. Examples of Shear Stress Structural members in pure shear stress are the torsion bars and the driveshafts in automobiles. Structural members in pure shear stress are the torsion bars and the driveshafts in automobiles. Riveted and bolted may also be mainly subjected to shear stress. Riveted and bolted may also be mainly subjected to shear stress.

3. Shear Stress Formula

4. Shear Strain Shear strain is the displacement that occurs in a body that is parallel to the forces applied. Shear strain is the displacement that occurs in a body that is parallel to the forces applied.

5. Shear Strain Formula Shear strain is the displacement that occurs in a body that is parallel to the forces applied. Shear strain is the displacement that occurs in a body that is parallel to the forces applied. Shear Strain = DL / L Shear Strain = DL / L Where: Where: –DL = Horizontal Displacement from Vertical –L = Original Length

6. Modulus of Rigidity (G) Also referred to as the Shear Modulus Also referred to as the Shear Modulus Ratio of shear stress to shear strain Ratio of shear stress to shear strain G = Shear Stress Shear Strain

7. Bearing Stress Bearing stress is the stress caused by one part acting directly on another. Bearing stress is the stress caused by one part acting directly on another. Bearing stress is a compressive stress and is equal to the bearing force divided by the bearing area. Bearing stress is a compressive stress and is equal to the bearing force divided by the bearing area.

8. Bearing Stress Bearing stress is a compressive stress and is equal to the bearing force divided by the bearing area. Bearing stress is a compressive stress and is equal to the bearing force divided by the bearing area.  (bearing) = Compressive Forces/Area  (bearing) = Compressive Forces/Area

9. Torque Torque is a measure of how much a force acting on an object causes that object to rotate. Torque is a measure of how much a force acting on an object causes that object to rotate. The object rotates about a pivot point. The object rotates about a pivot point. A force is applied at a distance from that pivot point. A force is applied at a distance from that pivot point. The distance from the pivot point to the point where the force acts is the moment arm. The distance from the pivot point to the point where the force acts is the moment arm.

10. Torsion Torsion occurs when an external torque is applied and an internal torque, shear stress, and deformation (twist) develops in response to the externally applied torque. Torsion occurs when an external torque is applied and an internal torque, shear stress, and deformation (twist) develops in response to the externally applied torque. There is a corresponding deformation (angle of twist) which results from the applied torque and the resisting internal torque causing the shaft to twist. There is a corresponding deformation (angle of twist) which results from the applied torque and the resisting internal torque causing the shaft to twist.

11. Torsion and Shearing Stress There is also an internal shear stress which develops inside the shaft. There is also an internal shear stress which develops inside the shaft. This shearing stress on the cross sectional area varies from zero at the center of the shaft linearly to a maximum at the outer edge. This shearing stress on the cross sectional area varies from zero at the center of the shaft linearly to a maximum at the outer edge. This may be thought of as being due to the adjacent cross sectional areas of the shaft trying to twist passed each other. This may be thought of as being due to the adjacent cross sectional areas of the shaft trying to twist passed each other.

12. Torsion The angle of twist can be found by using: The angle of twist can be found by using: Where: Where: –Theta is the angle of twist in radians –T is the torque ( N * m or ft * lbs ). –L is the length of the object the torque is being applied to or over. –G is the shear modulus or more commonly the modulus of rigidity –J is the polar moment of inertia

13. Torsion Example A steel, cylindrical bar has a 20,000 in-lb torque applied to it. A steel, cylindrical bar has a 20,000 in-lb torque applied to it. The radius of the bar is.5 inches and it is 5 feet in length The radius of the bar is.5 inches and it is 5 feet in length The steel used in this example has a shear modulus of 11 X 10 6 psi The steel used in this example has a shear modulus of 11 X 10 6 psi The polar moment of inertia for a circular object is calculated using: The polar moment of inertia for a circular object is calculated using: –J = (  r 4 )/ 2 =.10 in 4 The torsion can be calculated using: The torsion can be calculated using: –  (20,000 in-lb)(60 in)/(.10 in 4 )(11 X 10 6 psi) = 1.09 radians –Angle in degrees = Angle in Radians * 180 / Pi –Converting radians into degrees, the steel bar is expected to twist 62.5 degrees