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# HW 2 - 172 CHAPTER 2 Axially Loaded Members Solution 2.12-2...

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186 CHAPTER 3 Torsion Problem 3.3-4 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see figure). The dimensions d and shear modulus of elasticity are as follows: L = 1.2 m, :T~~.;;q;~q;;;::;:;.;:q;:;:;.;;;;;;;; T d = 30mm, and G = 28 GPa. ... (a) Detennine the torsional stiffness of the bar. I I (b) If the angle of twist of the bar is 4°, what is the maximum <-. ------ L --------. shear stress? What is the maximum shear strain (in radians)? Solution 3.3-4 Aluminum bar in torsion From Eq. (3-11): T = Tr = Td = (GIpcP)(~) max I p 2I p L 2I p L = 1.2 m d = 30 mm (28 GPa)(30 mm)(0.069813 rad) G = 28 GPa 2(1.2 m) (a) TORSIONAL STIFFNESS = 24.43 MPa GI p G'TTd 4 (28 GPa) ('TT)(30 mm)4 T max = 24.4 MPa +-- kT=T= 32L 32(1.2 m) MAXIMUM SHEAR STRAIN k T = 1860 N . m +-- Hooke's Law: (b) MAXIMUM SHEAR STRESS T max 24.43 MPa cP = = (4°)( 'TT /180)rad = 0.069813 rad 'Ymax = G = 28 GPa From Eq. (3-15): 'Ymax = 873 X 10- 6 rad +-- TL cP = GI p Problem 3.3-5 A high-strength steel drill rod used for boring a hole in the earth has a diameter of 0.5 in. (see figure).The allowable shear stress in the steel is 40 ksi and the shear modulus of elasticity is II ,600 ksi. What is the minimum required length of the rod so that one end of the rod can be twisted 30° with respect to the other end without exceeding the allowable stress? ~ [c:z::::::z::::::z:::::¢rZiiz:z.Oz.·5z ... 1z'.nz· :Z::::::Z::::::Z::::::Z::::::Z::::::Z::::::Z:::::::=DO --.;:. 1--' ---L---------·I
SECTION 3.3 Circular Bars and Tubes 187 Solution 3.3-5 Steel drill rod T ~ 1=======-::1 C==+=:============TI? ~ T TL 32TL From Eq. (3-15): c/J = - = --4 Gl p GTTd GTTd 4 c/J T = ---; substitute T into Eq. (1): G = 11,600 psi 32L d = 0.5 in. T = (~)(GTTd4c/J) = Gdc/J max TTd 3 32L 2L c/J = 30° = (30 0 )(.-!!-)rad = 0.52360 rad 180 Gdc/J =-- L min Tallow = 40 ksi 2Tallow (11,600 ksi)(0.5 in.)(0.52360 rad) MINIMUM LENGTH 2( 40 ksi) 16T FromEq. (3-12): T max =--3 (1) = 38.0 in. +- L min TTd Problem 3.3-6 The steel shaft of a socket wrench has a diameter of 8.0 mm. and a length of 200 mm (see figure).

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HW 2 - 172 CHAPTER 2 Axially Loaded Members Solution 2.12-2...

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