TAILIEUCHUNG - Lecture Strength of Materials I: Chapter 6 - PhD. Tran Minh Tu

Lecture Strength of Materials I - Chapter 6: Torsion. The following will be discussed in this chapter: Introduction, torsional loads on circular shafts, strength condition and stiffness condition, statically indeterminate problem, strain energy, examples. | Lecture Strength of Materials I: Chapter 6 - PhD. Tran Minh Tu STRENGTH OF MATERIALS 1/10/2013 TRAN MINH TU - University of Civil Engineering, 1 Giai Phong Str. 55, Hai Ba Trung Dist. Hanoi, Vietnam CHAPTER 6 TORSION 1/10/2013 Contents . Introduction . Torsional Loads on Circular Shafts . Strength Condition and stiffness condition . Statically Indeterminate Problem . Strain Energy . Examples Home’s works 1/10/2013 3 . Introduction 1/10/2013 4 . Introduction 1/10/2013 5 . Introduction Torsion members – the slender members subjected to torsional loading, that is loaded by couple that produce twisting of the member about its axis Examples – A torsional moment (torque) is applied to the lug-wrench shaft, the shaft transmits the torque to the generator, the drive shaft of an automobile. • Torsional Loads on Circular Shafts: the torsional moment or couple A F x Q2 B C Q1 t z 2 T t T 1 1 2 y 1/10/2013 6 . Introduction Internal torsional moment diagram • Using method of section • Sign convention of Mz - Positive: clockwise - Negative: counterclockwise Mz > 0 M z 0 Mz = y y z z x x 1/10/2013 7 . Torsion of Circular Shafts . Simplifying assumptions 1/10/2013 8 . Torsion of Circular Shafts => In the cross-section, only shear stress exists . Compatibility • Consider the portion of the shaft shown in the figure • CD – before deformation • CD’ – after deformation - From the geometry DD ' d dz d => The Shear strain: dz - d – the angle of twist - Following Hooke’s law: d G G 1/10/2013 dz 9 . Torsion of Circular Shafts . Equilibrium d 2 d M z dA G dA G Ip A dz A dz d M z – the rate of twist dz GI p . Torsion formulas – Shearing stress Mz – internal torsional moment Mz Ip – polar moment of inertia

• Kiến trúc - Xây dựng
• Strength of Materials
• Sức bền vật liệu
• Bài giảng Sức bền vật liệu
• Torsional loads
• Circular shafts
• Strength condition
• Finite element modelling
• Rectangular concrete filled steel tube stub columns incorporating high strength
• Ultra high strength materials
• Concentric axial compression
• Axial compression
• Theory and problems of strength of materials
• Statically indeterminate force systems tension
• Direct shear stresses
• Bending moment
• Moments of inertia
• Lecture Strength of materials
• Modulus of elasticity
• Statically indeterminate systems
• Statically indeterminate
• Stress transformation
• Plane stress state
• Transformation of plane stress
• Failure theories
• Permanently distorted
• Ductile material deforms
• Properties of cross sections
• Center of gravity – centroid
• Moment of Inertia of an area
• Radius of gyration
• Beam deflection
• Beam under transverse loading
• Statically indeterminate beams
• Torsional loads on circular shafts
• Torsion of noncircular members
• Helical spring under axial load
• Combined loading
• Eccentric axial loadings
• General combined loadings
• The secant formula
• Stability of structures
• Eccentric loadings
• Cementitious materials
• high strength concrete
• Strength required
• Placing procedures
• Splitting tensile strength
• Concentrically loaded columns
• Selected topics on strength
• The strength of materials
• Basic hypothesis
• Internal forces
• Three dimensional state
• Dimensional state
• Deflection of beams
• Bending stress
• Shearing stress
• Engineering materials
• Their properties
• Price and availability
• The elastic moduli
• Yield strength
• Tensile strength
• Fast fracture
• Toughness and fatigue
• Mechanical engineering principles
• Forces acting at a point
• Forces in structures
• Analysis of stress
• The elastic limit
• Deflection of transversally leaded beams
• Statically indeterminate problems
• Energy of strain
• Combines bending
• Helical spring
• Close coiled
• Critical load
• Applied strength of materials
• Engineering stress
• Thermal expansion
• Properties of areas
• Torsion in round shafts
• Beam reactions
• Shear diagrams
• Moment diagrams
• Stresses in beams
• Combined stresses
• Visualizing stress
• Elastic deflection
• Double integration method
• Plastic deformations
• Mechanics and strength of materials
• The stress tensor
• The strain tensor
• Constitutive law
• Fundamental concepts
• Shear force
• Bending deflections
• Structural stability
• Energy theorems
• The total potential energy