Question

6. Two thin-walled circular tubes, one having a seamless section, the other a split section as shown in Fig. P6, are subjected to the action of identical twiisting moments. Both tubes have equal outer diameters do, inner diameter di, and thickness t. What will be the ratio of the angles of twist bewteen the seamless tube, 0,, and that of split tube, 8z, i.e., the value of ? (a)). (b)) (c)(h), (d) }). (e) none of above 02

Answer 1

You have posted question 6 twice and hence I am writing its answer first and then for question 5 after that. Thanks.

Question 6.

For unit length of seamless sections Angle of twist, I T I cdoud; 4) G All notations are standard. Nous for split section, use reference Advanced Mechanics of materials and applied Elasticity by Aysel 0 ez Je G & Je = E { 1/3 bt3 Je = Equivalent polas MOI (do tdi) (do_dijs b= circular length t= thickness of tube

이 32 dotdi (do-di) (do ²+d; ² + dodi) 48 (do ² -d; 2) (do²+d; 2) do²+d; 2 + do di do2+di? (do since thin walled ascular tubes are given, do²+di² can be substituted by 2d² where d - mean drametes of thin section. 2 1 2d2 3 d2 x Dz 3 Ans Hence option e) None of the above

Question 5.

Given ox I For thin cantileves, dou tatay + fx=0 Jx ry Now, fx=0 and ox is given, Integrating 0 Gry - pay 2 t to Cx). 2I Now, from Boc., Exy)yah = 0 & thus, f (x) = - pach? 2 I i dłny to ay 0 - 2x²y) Txy = Hence, from Tay=-Px Ch²yz) 2 I Pxy I 0 page - a

f₂ Cx) = -ph3 Considering the y-component, +2 Try + Fy = 0 3I doy ry Hence, from Oy 2I Ph3 by ang 31 is taken =0 and Try from o 3 inoy E 4 3 I 2 doy -d an ( Px Ch² ((chat) he 2I | Jy (2²-43 l (3h²y_y (362 y = f ( 3h2y_y3 2h3) Read Answer option-b loya doy PCh² - y2) 2 he 2I Upon integration, y = P. yCh²- y 25 + £2 (4) From B.C., (y) y = h = 0 -Ph (262) hence, f₂ Cx) ZI

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