Subject :- Structural Analysis II Branch :- Civil-2 —A2 Prepared By :- (1) Patel Saurabh H. (130400106094) Submitted to :- Mr. Kunal j Patel.

Slides:



Advertisements
Similar presentations
PROBLEM-1 The pipe shown in the figure has an inner diameter of 80 mm and an outer diameter of 100 mm. If its end is tightened against the support at A.
Advertisements

PH0101 UNIT 1 LECTURE 1 Elasticity and Plasticity Stress and Strain
Torsion of a Circular Cylinder A Course Project By George Kodikulam Mukesh Nagapuri Bharath Kumar Vudhamari Pradeep Kumar Bitla SriLakshmi Ganoothula Continuum.
Chapter 3 – Stress and Deformation Analysis (ref MCHT 213!!)
3 Torsion.
PH0101 UNIT 1 LECTURE 2 Shafts Torsion Pendulum-Theory and Uses
GUJARAT TECHNOLOGICAL UNIVERSITY B.E Semester: 3 Civil Engineering Structural Analysis-1 Faculty: Chandra Bhakuni
Section VI Shaft Design.
3 Torsion.
1 Classes #3 & #4 Civil Engineering Materials – CIVE 2110 Torsion Fall 2010 Dr. Gupta Dr. Pickett.
TORSION Introduction, Round bar torsion, Non- uniform torsion
2E4: SOLIDS & STRUCTURES Lecture 13 Dr. Bidisha Ghosh Notes: lids & Structures.
Torsion: Shear Stress & Twist ( )
Design of Shaft A shaft is a rotating member usually of circular cross-section (solid or hollow), which transmits power and rotational motion. Machine.
3 Torsion.
Chapter 18 Shafts and Axles Dr. A. Aziz Bazoune
Torsion Torsional Deformation of a circular shaft,
3 Torsion.
Strength of Material-5 Torsion Dr. Attaullah Shah.
DESIGNING OF SHAFTS.
Strength of Materials I EGCE201 กำลังวัสดุ 1
Topic Torsion Farmula By Engr.Murtaza zulfiqar
Chapter 5 Torsion.
BFC (Mechanics of Materials) Chapter 6: Torsion
3 Torsion.
Strengths Torsion of Circular Shafts Chapter 12. Introduction A member subjected to twisting moments (torques) is called a shaft Only solid and hollow.
CHAPTER 5 TORSION.
1 Lecture by : LT “Sayed Dawod karimi” in the name of allah For NMAA and Kardan University Faculty of Engineering.
Chapter 3 Torsion Torsion Engr. Othman A. Tayeh. DEFORMATIONS IN A CIRCULAR SHAFT Φ the angle of twist.
CTC / MTC 222 Strength of Materials Chapter 5 Torsional Shear Stress and Torsional Deformation.
Copyright © 2011 Pearson Education South Asia Pte Ltd
Torsion T T Torsional Deformation of a Circular Shaft
Combined Loadings Thin-Walled Pressure Vessels Cylindrical Pressure VesselSpherical Pressure Vessel.
CTC / MTC 222 Strength of Materials
Solid mechanics 1.1 – key points
3 Torsion.
Shear Stress Shear stress is defined a the component of force that acts parallel to a surface area Shear stress is defined a the component of force that.
PROBLEM mm x y 800 mm P = 1500 N z y 50 mm 100 mm
Plastic Deformations of Members With a Single Plane of Symmetry
Mechanics of Materials – MAE 243 (Section 002) Spring 2008
9 Torsion.
Mechanics of Materials – MAE 243 (Section 002) Spring 2008 Dr. Konstantinos A. Sierros.
MECHANICS OF MATERIALS Third Edition Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University CHAPTER.
UNIT-05. Torsion And Buckling of columns
PROBLEM-1 The pipe shown in the figure has an inner diameter of 80 mm and an outer diameter of 100 mm. If its end is tightened against the support at A.
3 Torsion.
Machine Design I (MCE-C 203) Mechatronics Dept., Faculty of Engineering, Fayoum University Dr. Ahmed Salah Abou Taleb Lecturer, Mechanical Engineering.
PROBLEMS ON TORSION.
3 Torsion.
Strain Energy Due to Shear, Bending and Torsion Lecture No-6 J P Supale Mechanical Engineering Department SKN SITS LONAVALA Strength of Materials.
Unit-5. Torsion in Shafts and Buckling of Axially Loaded Columns Lecture Number-3 Mr. M.A.Mohite Mechanical Engineering S.I.T., Lonavala.
Stress and Strain ( , 3.14) MAE 316 – Strength of Mechanical Components NC State University Department of Mechanical & Aerospace Engineering Stress.
MECHANICS OF MATERIALS Fourth Edition Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University CHAPTER.
EGM 5653 Advanced Mechanics of Materials
BME 315 – Biomechanics Chapter 4. Mechanical Properties of the Body Professor: Darryl Thelen University of Wisconsin-Madison Fall 2009.
Solid Mechanics Course No. ME213. Thin Cylinders (Examples) ME213 Solid Mechanics2 Example 1.
STRENGTH OF MATERIALS UNIT – III Torsion.
What is Moment of Inertia ( MoI )?
Longitudinal Strain Flexure Formula
Mechanical Properties of Materials
3 Torsion.
3 Torsion.
Theory of Simple Bending
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
Units of N m.
DESIGNING OF SHAFTS.
Strength of Material Torsion Dr. Attaullah Shah.
3 Torsion.
CHAPTER OBJECTIVES Discuss effects of applying torsional loading to a long straight member Determine stress distribution within the member under torsional.
Mechanics of Materials ENGR Lecture 22 Torsion 1
Presentation transcript:

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,