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Unformatted text preview: Sec_3.8.qxd 304 9/27/08 1:13 PM Page 304 CHAPTER 3 Torsion tmax
ad (T0)max ANGLE OF ROTATION OF THE DISK (FROM Eq. 3-49) T0 ad
2L IPt allow
ad f T0 ab
GLIp fmax ; Problem 3.8-4 A hollow steel shaft ACB of outside diameter 50 mm
and inside diameter 40 mm is held against rotation at ends A and B
(see figure). Horizontal forces P are applied at the ends of a vertical
arm that is welded to the shaft at point C.
Determine the allowable value of the forces P if the maximum
permissible shear stress in the shaft is 45 MPa. (Hint: Use Eqs. 3-46a
and b of Example 3-9 to obtain the reactive torques.) 200 mm
P 200 mm
P 600 mm
400 mm Solution 3.8-4 Hollow shaft with fixed ends
GENERAL FORMULAS: T0 P(400 mm) LB 400 mm LA 600 mm L LA d2 50 mm allow LB 1000 mm
d1 40 mm 45 MPa TA
APPLY THE ABOVE FORMULAS TO THE GIVEN SHAFT T0 LB
L P(0.4 m)(400 mm)
1000 mm 0.16 P TB T0 LA
L P(0.4 m)(600 mm)
1000 mm 0.24 P UNITS: P Newtons T Newton meters From Eqs. (3-46a and b):
TA T0 LB
L T0 LA
The larger torque, and hence the larger shear
stress, occurs in part CB of the shaft.
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.
- Fall '11