Unformatted text preview: Sec_3.8.qxd 9/27/08 1:13 PM Page 303 303 SECTION 3.8 Statically Indeterminate Torsional Members Solution 3.8-2 Circular bar with fixed ends
(a) ANGLE OF TWIST AT SECTIONS B AND C
φB φ max 0 fB From Eqs. (3-46a and b): fAB L/A TAx
GIP TA T0 LB
GIPL TB T0 LA
dx 0; L APPLY THE ABOVE FORMULAS TO THE GIVEN BAR: L
4 or x x L/2 T0
GIPL 2x)(x) 4x)
4x 0 ; (b) MAXIMUM ANGLE OF TWIST
L TA x) T0x
L 2x) TD (fB)max (fB)x T0L
4 ; TA Problem 3.8-3 A solid circular shaft AB of diameter d is fixed against rotation at
both ends (see figure). A circular disk is attached to the shaft at the location shown.
What is the largest permissible angle of rotation max of the disk if the allowable
shear stress in the shaft is allow? (Assume that a b. Also, use Eqs. 3-46a and b of
Example 3-9 to obtain the reactive torques.) Disk
A d B a b Solution 3.8-3 Shaft fixed at both ends
Assume that a torque T0 acts at the disk.
The reactive torques can be obtained from Eqs. (3-46a
Since a b, the larger torque (and hence the larger
stress) is in the right hand segment.
TA L a a b b ...
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