TAILIEUCHUNG - Lecture Mechanics of materials (Third edition) - Chapter 3: Torsion

The following will be discussed in this chapter: Torsional loads on circular shafts, net torque due to internal stresses, axial shear components, shaft deformations, shearing strain, stresses in elastic range, normal stresses, torsional failure modes, angle of twist in elastic range,. | Third Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Torsion Lecture Notes: J. Walt Oler Texas Tech University © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Contents Introduction Statically Indeterminate Shafts Torsional Loads on Circular Shafts Sample Problem Net Torque Due to Internal Stresses Design of Transmission Shafts Axial Shear Components Stress Concentrations Shaft Deformations Plastic Deformations Shearing Strain Elastoplastic Materials Stresses in Elastic Range Residual Stresses Normal Stresses Example Torsional Failure Modes Torsion of Noncircular Members Sample Problem Thin-Walled Hollow Shafts Angle of Twist in Elastic Range Example © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Torsional Loads on Circular Shafts • Interested in stresses and strains of circular shafts subjected to twisting couples or torques • Turbine exerts torque T on the shaft • Shaft transmits the torque to the generator • Generator creates an equal and opposite torque T’ © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Net Torque Due to Internal Stresses • Net of the internal shearing stresses is an internal torque, equal and opposite to the applied torque, T = ∫ ρ dF = ∫ ρ (τ dA) • Although the net torque due to the shearing stresses is known, the distribution of the stresses is not • Distribution of shearing stresses is statically indeterminate – must consider shaft deformations • Unlike the normal stress due to axial loads, the distribution of shearing stresses due to torsional loads can not be assumed uniform. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 3-4 Third Edition MECHANICS OF MATERIALS Beer • Johnston

• Kiến trúc - Xây dựng
• Mechanics of materials
• Cơ học vật liệu
• Lecture Mechanics of materials
• Torsional loads
• Axial shear components
• Shaft deformations
• Composite materials
• Mechanics of composite materials
• Mechanics of composite materials with MATLAB
• Effective elastic constants
• Homogenization of composite materials
• Introduction to damage mechanics
• Mechanical properties of materials
• Material impact on deformation
• Rectangular cross section
• Elastic and plastic regions
• Tension test
• Material constants
• Modulus of elasticity
• Logic in structural analysis
• Mechanics materials
• Recycling fiber reinforced composites
• Macromechanical analysis of a lamina
• Fracture mechanics
• mechanics
• racks in materials
• analytical solid mechanics
• modern materials science
• macroscopic mechanical
• Structure free body diagram
• Component free body diagram
• Method of joints
• Axial loading
• Normal strain
• Stress strain test
• Pure bending
• Symmetric member
• Bending deformations
• Beams for bending
• Bending moment diagrams
• Bending moment
• Shearing stresses in beams
• Thinwalled members
• Beam element
• Transformations of stress
• Transformation of plane stress
• Maximum shearing stress
• Principle stresses
• Transmission shaft
• Stresses under combined loadings
• Deflection of beams
• Elastic curve
• Statically indeterminate beams
• Stability of structures
• Pin ended beams
• Eccentric loading
• Energy methods
• Strain energy
• Strain energy density
• Torsion of Shafts
• Internal Torque
• Homogeneous cross section
• Concept of stress
• Stress on a surface
• Tensile stress
• Contructions of stress element
• Stress components
• Concept of strain
• Lagrangian strain
• Eulerian strain
• Preliminary definitions
• Average normal strain
• Average shear strain
• Axial members
• Prelude to theory
• Internal axial force
• Strain distribution
• Material model
• Axial formulas
• Theory for circular shafts
• Torsion formulas
• Circular cross section