Problems on Torsion

Problems on Torsion, weight ratio of solid to hollow shaft, weight saving %

1. Problems on Torsion By Mrs. Venkata Sushma Chinta

2. Q1. Determine the diameter of a solid shaft which will transmit 300 kW at 250 r.p.m; The maximum shear stress should not exceed 30 N/mm 2 angle of twist should not be more than 1 o in a shaft length of 2 m. Take modulus of rigidity = 1 x 10 5 N/mm 2 .

3. So, D= 107.5 mm is not recommended

4. Q2. A 500 mm long solid steel [G = 80 GPa] shaft is being designed to transmit a torque T = 20 Nm. The maximum shear stress in the shaft must not exceed 70 MPa, and the angle of twist must not exceed 3° in the 500 mm length. Determine the minimum diameter d required for the shaft.  

6. Q3. Determine the diameter of solid steel shaft which will transmit 90 kW at 160 r.p.m; Also determine the length of the shaft if the twist must not exceed 1 o over the entire length. The maximum shear stress is limited to 60 N/mm 2 . Take the value of modulus of rigidity = 8 x 10 4 N/mm 2

7. Q4. A hollow cylindrical steel shaft is 1.5 m long and has inner and outer diameters respectively equal to 40 and 60 mm (a) What is the largest torque that can be applied to the shaft if the shearing stress is not to exceed 120 MPa? (b) What is the corresponding minimum value of the shearing stress in the shaft? A hollow cylindrical steel shaft: length = 1.5 m inner diameter D i = 40 mm outer diameters D o = 60 mm What is the largest torque= ? shearing stress is not to exceed 120 MPa

8. What is the largest torque= ? shearing stress is not to exceed 120 MPa Simple Torsion Equation =>   => T= Z p T = = = 4084070.45 N-mm =4.08 kN-m   (b) What is the corresponding minimum value of the shearing stress in the shaft? q= . r q= q = 80 MPa  

9. Q5. Two shafts of the same material and of same lengths are subjected to the same torque, if the first shaft is of a solid circular section and the second shaft is of hollow circular section, whose internal diameter is 2/3 of the outside diameter and the maximum shear stress developed in each shaft is the same, compare the weights of the shafts.

10. Q6. A solid circular shaft and a hollow circular shaft whose inside diameter is ( ) of the outside diameter, are of the same material, of equal lengths and are required to transmit a given torque. Compare the weights of these two shafts if the maximum shear stress developed in the two shafts are equal.  

11. Q7. A solid cylindrical shaft is to transmit 300 kW power at 100 r.p.m. If the shear stress is not to exceed 80 N/mm 2 , find its diameter. (b) What percent saving in weight would be obtained if this shaft is replaced by a hollow one whose internal diameter equals to 0.6 of the external diameter, the length, the material and maximum shear stress being the same

12. Q8. The final drive to a conveyor that feeds coal to a railroad car is a solid shaft loaded in pure torsion and carrying 800 Nm of torque if the acceptable shear stress is 39MPa, find its diameter What percentage saving in weight would be obtained if this shaft is replaced by a hollow shaft whose outside diameter of 60 mm is available in the same material as specified for the solid shaft. Compute what maximum inside diameter the hollow shaft can have that would result in the same stress in the solid shaft. The length , material are being the same.

13. T orque T= 800 Nm = 8*10 5 N-mm A cceptable shear stress = 39MPa If Solid shaft finding diameter: T= Z p Z p =   d 3 = ( ) d 3 = ( ) => d= 47.09 m m