Two solid, coaxial, circular bars (each 10 in. long) are mounted into walls such

Question

Two solid, coaxial, circular bars (each 10 in. long) are mounted into walls such that their free ends arc separated by a small gap. as shown below. Rif A (I in. diameter) has a shear modulus GA - 6 times 104psi. while bar B (2 in diameter) has a shear modulus GA - 4 times106 psi. If the free end of has A is routed 2* about its axis and then the two bars are welded together. determine: The moment required to produce an angle of twist of 2? in bar A The magnitudes of the angles of twist in bars A and H after welding (The polar moment of inertia of s solid bar J = pi/2x2)

Explanation / Answer

(a) From = TL/GJ, we have

T = GJ/L = (2*/180 rad)[(6E6)(*0.54/2)/(10) = 2.056E3 lb.in = 2.056 kips.in

(b) Let the angle of twist is , Then for both shafts

= TBL/GBJB     (1)

- = TAL/GAJA    (2)

Therefore, (1)+(2) to give

= TAL/GAJA+TBL/GBJB    (3)

From the equilibrium, we also have

TA=TB                               (4)

From (4) and (3), we have

= TAL/GAJA+TAL/GBJB =TAL[1/(GAJA)+1/(GBJB)]

2/180 = TA(10)[1/(6E6**0.54/2)+1/(4E6**14/2)] We have

TA =1880 lb.in = TB

From (1), we have

= TBL/(GBJB )=(1880)(10)/[4E6* *14/2]=2.992x10-3 rad = 0.1714 degrees

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