Subject :- Structural Analysis II Branch :- Civil-2 —A2 Prepared By :- (1) Patel Saurabh H. ( ) Submitted to :- Mr. Kunal j Patel

1. Torque or Turning moment or twisting moment 2. Angle of twist(q) 3. Shear stress in shafts(t) 4. Strength of shafts 5. Polar moment of inertia(J) 6. Assumptions in the theory of torsion 7. Theory of torsion and torsion equation 8. Power transmitted by a shafts 9. Torsional rigidity 10. Shafts coupling 11. Principal stress in shafts subjected to combined bending and torsion without axial thrust 12. Principal stresses shafts subjected to combined bending and torsion axial thrust

(1)TORQUE OR TURNING MOMENT OR TWISTING MOMENT :- In factories and workshops, shaft is used to transmit energy from one end to the other end. To transmit the energy, a turning force is applied either to the rim of a pulley, keyed to the shafts, or to any other suitable point at some distance from the axis of the shaft. The moment of couple acting on the shafts is called torque or turning moment or twisting moment. Torque = turning force* Diameter of shaft Where, T= Torque F= Turning Force R= Radius of the shafts unit of Torque (T) is N.mm or kN.mm o F F R R T = F * 2R

( 2)Angle of twist(θ) :- When a shaft is subjected to torque (T). Point A on the surface of the shafts comes to ‘A’ position. The angle AOA’ at the centre of the shafts is called the angle of twist(θ). AOA’ = θ = Angle of twist Angle of twist(θ) is measured in radians.

(3) Shear stress in shafts(τ) When a shafts is subjected to equal and opposite end couples, whose axes coincide with the axis of the shafts, the shafts is said to be in pure torsion and at any point in the section of the shafts stress will be induced. That stress is called Shear stress in shaft.

(4) Strength of shafts Maximum torque or power the shafts can transmit from one pulley to another, is called Strength of shafts. (a) For solid circular shafts : Maximum Torque(T) is given by, T= (∏/16)* t* D³ Where, D= dia. Of the shaft t= Shear stress in shaft (b) For hollow circular shafts : Maximum Torque (T) is given by, Where, D= outer dia. Of the shaft d= inner dia. Of the shaft T= (∏/16)*t*{(D ⁴ -d ⁴ )/D}

(5) Polar moment of inertia(J) The moment of the inertia of a plane area, with respect to an axis perpendicular to the plane of the figure is called Polar moment of inertia(J). As per the perpendicular axis theorem, For hollow circular shaft, J = ( П/32)*(D ⁴ -d ⁴ ) J = (П/64)*D ⁴ +( П/64)D ⁴ = ( П/32)*D ⁴

Polar section Modulus : (Zp) : Polar section Modulus = Polar M.I. dis tance of extreme fibre from c.g. Zp = J/y = J/R For solid circular shaft, Zp = {( П/32)*D ⁴ }/D*2} = ( П/16)*D³ For solid circular shaft,Zp ={( П/32)*(D ⁴ -d ⁴ )/D*2} = {( П/16D)*(D ⁴ -d ⁴ )}

(6) Assumptions in the theory of torsion : The following assumption are made while finding out shear stress in a circular shaft subjected to torsion. 1. The material of shaft is uniform throughout the length. 2. The twist along the shaft is uniform. 3. The shaft is of uniform circular section throughout the length. 4. Cross section of the shaft, which are plane before twist remain plane after twist. 5. All radii which are straight before twist remain straight after twist.

(8) Power transmitted by a shafts (a) Power in horse power (h.p.) : P = 2ПNT h.p. Where, N = R.P.M 4500 T = Torque in kg.m (b) Power in watts : P = 2ПNT Watt where,T = Torque in N.m 60 1 kW = 1000 Watt 1 h.p. = 746 Watt 1 h.p. = kW

(9) Torsional Rigidity : Let twisting moment T, produce a twist θ radians in a length l. T = C * θ J l θ = T*l C*J For a given shaft the twist is proportional to the twisting moment T. In a beam the bending moment produce deflection, in the same manner a torque produces a twist in a shaft.

The quantity CJ in the above equation is known as Torsional Rigidity. The quantity CJ stands for the Torque required to produce a twist of 1 radian per unit length of the shaft. The quantity CJ corresponds to a similar euantity EI, in expression for deflection of beams. EI is known as flexural rigidily. The quantity CJ/l is known as Torsional stiffness. The quantity l/CJ is known as Torsional flexibility.

(11 ) Principal stress in shafts subjected to combined bending and torsion without axial thrust : We known that B.M. acting on the shaft will produce bending stress in the shaft, bending stress will be maxi. on the outermost fibre of shaft,