# A m p st 60010 3 p br 25010 3 0 p st 041666 p br 1

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0 A M P st ×600×10 -3 -P br ×250×10 -3 =0 P st =0.41666 P br ………..(1) 600 250 st br 600 250 st st st br br br E A L P T L E A L P T L 8.333×10 -12 P st +26.666×10 -12 P br =475×10 -9 …………..(2) From equations (1) and (2) P br =15760.5 N , P st =6566.77 N br = MPa 521 . 31 10 500 5 . 15760 6 P st = MPa 267 . 26 10 250 77 . 6566 6 mm 300 st P br P y A x A A B C D E mm 250 mm 350 mm 250 br T st ) ( T br ) ( F br ) ( F st ) ( st 600 10 200 10 250 10 250 25 10 250 10 12 250 10 90 10 500 10 300 25 10 300 10 20 9 6 3 3 6 9 6 3 3 6 st br P P

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4 Torsion: T orque is a moment that tends to twist a member about its longitudinal axis. When the torque is applied, the circles and longitudinal grid lines originally marked on the shaft tend to distort into the pattern shown below. Before deformation After deformation Twisting causes the circles to remain circles and each longitudinal grid line deforms into a helix that intersects the circles at equal angles. Also, the cross sections at the ends of the shaft remain flat that is, they do not warp or bulge in or out and radial lines on these ends remain straight during the deformation. The Torsion Formula: C onsider a uniform circular shaft is subjected to a torque it can be shown that every section of the shaft is subjected to a state of pure shear. J T T T T T max r
5 : The torsional shearing stress. T: The resultant internal torque acting on the cross section. : The distance from the centre (radial position). J: The polar moment of inertia of the cross sectional area. J Tr max max : The maximum shear stress in the shaft, which occurs at the outer surface. r: The outer radius of the shaft. 4 2 r J 4 32 D J for a hollow shaft J Tr J Tr o max ) ( 32 ) ( 2 4 4 4 4 i o i o D D r r J Angle of Twist ( ): I f a shaft of length L is subjected to a constant twisting moment along its length, then the angle of twist through which one end of the shaft will twist relative to the other is: GJ TL G: The shear modulus of elasticity or modulus of rigidity. : Angle of twist, measured in rad o r i r r T T r L A

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6 If the shaft is subjected to several different torques or the cross sectional area or shear modulus changes from one region to the next. The angle of twist of one end of the shaft with respect to the other is then found from: GJ TL In order to apply the above equation, we must develop a sign convention for the internal torque and the angle of twist of one end of the shaft with respect to the other end. To do this, we will use the right hand rule, whereby both the torque and angle of twist will be positive, provided the thumb is directed outward from the shaft when the fingers curl to give the tendency for rotation.
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• Winter '15
• MAhmoudali

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