# Mm 2 m example 23 the tapered shaft g determine the

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mm 2 m

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Example 23: The tapered shaft G. Determine the angle of twist L x d d y L d d x y 2 2 1 2 1 2 d=d 1 +2y=d 1 + L x d d ) ( 1 2 4 1 2 1 4 ] ) ( [ 32 32 ) ( L x d d d d x J L L L x d d d G dx T x J G dx T 0 1 2 1 0 ) ( [ 32 ) ( 1 2 1 1 2 ] ) ( [ 1 ) ( 3 32 L x d d d d d G TL 3 1 3 2 3 2 3 1 1 2 . ) ( 3 32 d d d d d d G TL 3 1 3 2 2 2 2 1 2 1 . 3 32 d d d d d d G TL 1 d x 1 shown below is made of a material hav of its end B when subjected to the torq L L x d d d dx G T 0 4 1 2 1 4 ] ) ( [ 32 ] 3 1 3 2 1 2 0 3 1 1 ) ( 3 32 d d d d G TL L d y x ving a shear modulus que. 2 d 2 2 1 2 d d
Example 24: The gears attache shown. If the shear modulus of mm , determine the displacemen Segment AC 150-T AC =0 T AC =150 N.m Segment CD 150-280+T CD =0 T CD =130 N.m Segment DE -130-40+T DE =0 T DE =170 N.m GJ TL = TL GJ 1 = ) 10 7 ( 2 10 80 1 3 9 =-0.21211 rad 2 ed to the fixed end steel shaft are sub elasticity is G=80 GPa and the shaft nt of the tooth P on gear A . 5 . 0 170 3 . 0 130 4 . 0 150 4 bjected to the torques has a diameter of 14

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Example 25: A steel shaft ABC between gears A and B and a h between gears B and C . Both ba N.m , T 2 =540 N.m , and T 3 =300 modulus of elasticity for the sha d if the allowable shear stress in diameter d if the angle of twist b T AB =240 N.m T BC =300 N.m a) 1. For solid bar AB J= 4 32 d 4 32 2 / 2 / d d T J d T AB AB 4 6 32 2 / 240 10 80 d d 6 3 10 80 240 16 d d=0.02481 m d=24.81 mm 2. For hollow bar BC J= ] ) 25 . 1 [( 32 ] [ 32 4 4 4 4 d d d d i o ) 25 . 1 [( 32 25 . 1 2 / 25 . 1 4 d d T J d T BC BC ] ) 25 . 1 [( 32 2 / 25 . 1 300 10 80 4 4 6 d d d d=0.0255 m d=25.5 mm Answer b) 1. For solid bar AB GJ L T AB 3 connecting three gears consists of a so hollow bar of outside diameter 1.25d a ars have length 0.6 m . The gears tran 0 N.m acting in the directions shown in aft is 80 GPa . a) what is the minimum n the shaft is 80 MPa ?. b) what is the between any two gears is limited to 4 ? ] 2 / 4 d 4414 . 1 10 80 25 . 1 300 16 6 3 d solid bar of diameter d and inside diameter d nsmit torques T 1 =240 n the figure. The shear m permissible diameter minimum permissible ?.
4 4 9 32 10 80 6 . 0 240 180 4 d d=0.02263 m d=22.63 mm 2. For hollow bar BC GJ L T BC ] ) 25 . 1 [( 32 10 80 6 . 0 300 180 4 4 4 9 d d d=0.02184 m d=21.84 mm d=0.02263 m d=22.63 mm Answer Example 26: The shaft is subjected to a distributed torque along its length of t=10x 2 N.m/m , where x is in meters. If the maximum stress in the shaft is t o remain constant at 80 MPa , determine the required variation of the radius r of the shaft for 3 0 x m tdx T dx x 2 10 3 3 10 x J Tr max 3 3 6 4 3 6 3 20 10 80 2 3 10 10 80 r x r r x

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5 x x r 002982 . 0
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• Winter '15
• MAhmoudali

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