Unit 4

Torsion, Buckling

Q1) A hollow steel shaft transmits 200 kW of power at 150 rpm. The total angle of twist in a length of 5 m of the shaft is 3o. Find the inner and outer diameters of the shaft if the permissible shear stress is 60 MPa. Take G = 80 GPa.

A1)

Q2) Compare the length of equal length of a solid and a hollow shaft to transmit a given torque for the same maximum stress if the inside diameter of shaft is three fourth of the outside.

A2)

Q3) Figure shows a stepped steel shaft. It is subjected to a torque T at the free end and a torque 2T in the opposite direction at the junction of two sizes. Determine the total angle of twist if the maximum shear stress is limited to 80 MPa. G = 80 GPa.

A3)

Q4) Figure shows a hollow shaft. Determine the maximum power transmitted by shaft at 200 rpm if the shear stress in the shaft is nit to exceed 70 MPa. Also find the lengths of the two portions if the twist produced in the two portions of the shaft are equal.

A4)

Q5) A circular steel shaft of 40 mm diameter is provided with enlarged portion of 80 mm diameters at two ends as shown in fig. On the enlarged portion a steel tube of 2 mm thickness is shrunk. During the shrunk process, the 40 mm diameter shaft is held twisted by a couple of magnitude of 800 N.m. When the tube is firmly set on the tube, the couple is removed. Determine the twisting couple left on the shaft if the tube and the shaft are made of same material.

A5)

Q6) A thin walled 800 mm long member has the cross-section as shown in the fig. Determine: i) the maximum torque if the angle carried by the section is limited to 4o and ii) the maximum shear stress induced for the maximum torque

G = 82 GPa

A6)

Q7) Using Euler’s Formula, determine the critical stresses for the strut of slenderness ratio 80,120, 160 and 200 under a condition of (a) both ends hinged and (b) both ends fixed. Take E = 205 GPa.

A7)

Q8) A 4 m long hollow alloy tube with inside and outside diameter are 36 mm and 48 mm elongates by 3 mm under a tensile force of 50 kN. Determine the buckling load for the tube when it is used as a column with both ends pinned and with factor of safety 5.

Q9) Determine the shortest length for a pin-joined steel column of cross-section 75 mm x 48 mm using Euler’s Formula. Take critical stress value as 220 MPa and E = 205 MPa.

A9)

Q10)  A 4 m log circular bar deflects 20 mm at the center when used as simply supported beam under a 200 N load at center. Determine critical load for the same bar when used as a strut which is firmly fixed at one end and pin joined at other.

A10)