Torsional Stress Hand-out PDF

BECC1103 (MECHANICS OF DEFORMABLE BODIES): Chapter IV: Torsional Stress TORSIONAL STRESS -- is a form of shear stress experienced by a body when a twisting force (TORQUE) is applied. Typical cases involve a “shaft/ shafting”, a power transmitting element which rotates w...

BECC1103 (MECHANICS OF DEFORMABLE BODIES): Chapter IV: Torsional Stress TORSIONAL STRESS -- is a form of shear stress experienced by a body when a twisting force (TORQUE) is applied. Typical cases involve a “shaft/ shafting”, a power transmitting element which rotates while transmitting motion/ power and whose tendency is to “shear/ cut” the shaft/ shafting into two (2) portions. Thus, TORSIONAL STRESS may also be referred to as SHEARING STRESS, Ss. FORMULAS: 1_TORSIONAL STRESS, Ss: Where: T -- Torque/ rotational work (energy) possessed by the rotating shaft/ shafting. Joule (N-m); Kgf-m; Lbsf-ft c -- Distance from the outermost fiber towards the shaft center (shaft radius). m; cm; mm; ft; in. J -- Polar moment of inertia (figure dependent) For typical shafts, Area is cylindrical: For Solid Shafts: For Hollow Shafts: *For Solid Shafts: **For Hollow Shafts: 2_ANGLE OF TWIST, Ø: Where: Ø -- Angle of twist (must be converted into radian value from degrees to be used). O (degree value); Radian value T -- Torque/ rotational work (energy) possessed by the rotating shaft/ shafting. Joule (N-m); Kgf-m; Lbsf-ft L -- Shaft length m; cm; mm; ft; in. J -- Polar moment of inertia (figure dependent) For typical shafts, Area is cylindrical: For Solid Shafts: For Hollow Shafts: G -- Modulus of Rigidity (material dependent but that steel is normally used). 83 GPa (for steel only) 3_POWER TRANSMITTED, P: Where: P -- Power transmitted by the shaft kW; hp T -- Torque/ rotational work (energy) possessed by the rotating shaft/ shafting. Joule (N-m); Kgf-m; Lbsf-ft N -- Rotative or synchronous speed of the electric motor (prime mover). Rpm; Rps SAMPLE PROBLEMS: 1. For a hollow cylinder with Do = 100mm and Di = 90mm, determine the torque, T which causes a maximum shearing stress of 24 MPa. Using the same torque, what maximum stress is there should this hollow cylinder become a solid cylinder? Consider diameter of the solid cylinder equal to the outside diameter of the hollow cylinder. 2. A steel marine propeller is to transmit 4.5 MW of power at 3 rps without exceeding a shearing stress of 50 MPa or twisting through no more than 1o in a length 25 times its diameter. With the given data, what should be the proper steel propeller diameter with Gsteel = 83 GPa? 3. A solid steel shaft 5m long is stressed to 60 MPa when twisted through 4o. Using G = 83 GPa (for steel), compute the power that can be transmitted by the shaft at 20 rps. 4. A stepped steel shaft (shafting having two differing cross-sectional areas) consists of a hollow shaft 2m long (Do = 100mm; Di = 70mm) rigidly attached to a solid shaft 1.5m long and 70 mm in diameter. Determine the maximum torque which can be applied without exceeding a shearing stress of 70 MPa or a twist of 2.5o in the 3.5m length. Use Gsteel = 83 GPa. 5. Two steel shafts of the same diameter measuring 50mm has their ends built into a rigid support have flanges that are rigidly attached to their free ends. The shafts are to be bolted by 8mm diameter bolts on four (4) bolt holes of their flanges. However, there is initially a 6o mismatch in the location of their bolt holes. A_What torsional stress exists on both shafts? Gsteel bolts = 83 GPa B_If one (1) bolt has a 10mm diameter, how much stress are there per bolt? Neglect deformation on the bolts and flanges while assuming that the necessary torque to fix both shafts from the 6o mismatch to be the same. Bolts 2m 1m Flange Coupling Steel shafts