3 7 Torsion of statically indeterminate systems Ex

3. 7 Torsion of statically indeterminate systems Ex 3. 5) 2020 -09 -30 재료역학 3장 2

3. 8 displacement method for torsion of circular shafts • A shaft made up of segments with different length C. S(circular) material has the following properties. 2020 -09 -30 재료역학 3장 5

1) applied axial twisting moments act only at node points(i. e , at the junction of two shaft elements or at the end of the first or last shaft element)and are denoted by Qi (lb in or N m), where i can take value from i=1 to i=N 2) the shear modulus Gi and the polar moment of inertia Ji are constant in each shaft element of length Li, where i can take on values from i=1 to i=N 3) the angular displacement (the angle. of twist in radians) of each node point is denoted by i, and all applied twisting moments or torques and angular displacements are positive when they are directed in the positive x direction of the shaft. The vector twisting moments and vector angular displacements follow the right-handed rule 2020 -09 -30 재료역학 3장 6

cf eq. (2. 17) 2020 -09 -30 재료역학 3장 7

Ex 3. 7) max. ? 2020 -09 -30 재료역학 3장 8

해) i) from F. B. D of each node ③ 2020 -09 -30 재료역학 3장 9

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◎ General Case - - 2020 -09 -30 재료역학 3장 11

3. 9 computer program TORMECH Ex 3. 8) 2020 -09 -30 재료역학 3장 12

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Ex 3. 9) 2020 -09 -30 재료역학 3장 14

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3. 10 Design of circular shafts for power transmission Specify d or di/do to transmit a specific amount of power so as not to be and / or , 2020 -09 -30 재료역학 3장 16

power Ex) 10 hp at 60 rpm, T ? 2020 -09 -30 재료역학 3장 17

Ex 3. 11) A propeller shaft connected with an engine with its full power 260 hp /3800 rpm , What is the minimum d of the shaft? 2020 -09 -30 재료역학 3장 18

Ex 3. 12) A steel shaft transmitting 8 k. W at 15 Hz 해) 2020 -09 -30 재료역학 3장 20

3. 11 differential eqs. for the twisting moment and angle of twist Internal twisting moment T Radius d 2020 -09 -30 재료역학 3장 vary along the axis 21

For moment equil. Let q(x) : T per unit length -(☆1) -(☆2) (☆1) - (☆3) 2020 -09 -30 재료역학 3장 B. C 22

Ex 3. 13) a steel shaft L=1. 25 m d=50 mm G=80 GPa 2020 -09 -30 재료역학 3장 23

해) neglecting the weight of the shaft. ( 1) 2020 -09 -30 재료역학 3장 24

Ex 3. 14) 2020 -09 -30 재료역학 3장 26