Question

The hollow steel construction auger in Figure 4 has an outer diameter d2 = 140 mm and thickness of t = 8 mm. The steel has a shear modulus of elasticity E = 200 GPa and v = 0.3. For an applied torque of 35 kN m, determine the following quantities: a) Shear stress at the mid-center of the thickness t of the shaft. [2] b) Shear stress on the outer surface. [1] c) Shear stress in the inner surface, [1] d) Rate of twist (degrees per unit of length). [2] e) Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section. [4] O Figure 4: Steel Hollow Drill

Answer 1

given cuta diameter d₂ = 140mm thickness t=8mm So inne chiamete, di- d₂-2t =140 28) di=124 mm applied torque T= 3SEN- E=2006pa, V-0.3. SO Shean modulas G- E 2/4) 200 2(103) Cross Section of hollow ی 6-76-923 apal 7 auger shaft Potter moment of Inentia J = 7 2 1 (di-di) J= .(1904—1240) di = 124 mm d₂=140mm J = 145042050494 mm panta) Shear stress at the mid centar of thickness to radial distance of mid center ro= 0% = } = (1404124 2 2 ro= 132 2 U Shear stress Tie -(3SNOʻN-m) (66mm) 7 80=66mm Taniel lusoy 208,494 mmt trip = 159.26 N/mm2 part by Shear stress on outy surface @salf) a at/ Tauty = 168.916 MPa 14504205.494 140 Tody = T(22) J port(c) Shear stress at inne surface Timma = The (3519) Y(121 tinnes = 149.61 Mpq J 14504205.494

parted, for Im Length Rate of twist per unit Lergty oz TL ng o 35 x 10 mm (100mm) 76.923/10*Xar) (14504205.484 mm) O=0.03137 sad per mety O=8-03137X 180 degree per meter रा o=1.7974° per meter. partce Shear stress distribution - 168 916 MP3 0 - Elmery atong ordial distance 149-61 MPa
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