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Unformatted text preview: Sec_3.8.qxd 9/27/08 1:13 PM Page 307 SECTION 3.8 Statically Indeterminate Torsional Members Combine Eqs. (2) and (5) and solve for T0:
(T0)CB SEGMENT AC GOVERNS LBIPA
pd 3 t
16 B allow
(T0)CB (6) Substitute numerical values:
(T0)CB 240.0 N m a LA dB
LB dA which can be used as a partial check on the results. Problem 3.8-7 A stepped shaft ACB is held against rotation at ends dA A and B and subjected to a torque T0 acting at section C (see figure).
The two segments of the shaft (AC and CB) have diameters dA and dB,
respectively, and polar moments of inertia IPA and IPB, respectively.
The shaft has length L and segment AC has length a. A a T0
b ; TB
LBIPA + LAIPB (a) EQUAL SHEAR STRESSES
CB or TAdA
IPA T0 a LAIPBdB
IPB LBdA LAdB dA
dA + dB a
L a)IPA Solve for a/L:
(Eq. 1) adB (b) EQUAL TORQUES
TA TB or LBIPA
or (L TB(dB/2)
IPB or a)dA Solve for a/L: LAIPB
LBIPA + LAIPB Substitute TA and TB into Eq. (1):
IPA L or (L SEGMENT CB: dB, IPB LB L a
REACTIVE TORQUES (from Eqs. 3-45a and b) AC C Stepped shaft SEGMENT AC: dA, IPA LA T0 a dB IPA (a) For what ratio a/L will the maximum shear stresses be the same
in both segments of the shaft?
(b) For what ratio a/L will the internal torques be the same in
both segments of the shaft? (Hint: Use Eqs. 3-45a and b of
Example 3-9 to obtain the reactive torques.) TA ; 150 N m NOTE: From Eqs. (4) and (6) we find that 4
pdBt allow a 1 +
LAdB Solution 3.8-7 307 or a
L LAIPB aIPB
dA + dB IPA
IPA + IPB ; ; IPB B ...
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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