TAILIEUCHUNG - Lecture Strength of Materials I: Chapter 4 - PhD. Tran Minh Tu

Chapter 4 - State of stress and strength hypothese. The following will be discussed in this chapter: State of stress at a point, plane stress, mohr’s circle, special cases of plane stress, stress – strain relations, strength hypotheses. | 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 4 State of Stress and Strength Hypothese 1 10 2013 Contents . State of stress at a point . Plane Stress . Mohr s Circle . Special cases of plane stress . Stress Strain relations . Strength Hypotheses 1 10 2013 3 . State of stress at a point External loads applied to the body gt The body is deformed gt The stress is occurred At a point K on the arbitrary section there n are 2 types of stress normal stress s and shearing stress t y K The state of stress at a point K is a set of all stresses components acting on all sections which go through this point z x The most general state of stress at a point may be represented by 6 components s x s y s z normal stresses t xy t yz t zx shearing stresses Note t xy t yx t yz t zy t zx t xz 1 10 2013 4 . State of stress at a point Principal planes no shear stress acts on Principal directions the direction of the principal planes Principal stresses the normal stress act on the principal plane There are three principal planes which are perpendicular to each other and go through a point Three principal stresses s1 s2 s3 with s1 s2 s3 Types of state of stress - Simple state of stress 2 of 3 principal stresses equal to zeros - Plane state of stress 1 of 3 principal stresses equal to zeros - General state of stress all 3 principal stresses differ from zeros 1 10 2013 5 . Plane Stress Plane Stress the state of stress in which two faces of the cubic element are free of stress. For the illustrated example the state of stress is defined by s x s y t xy and s z t zx t zy 0. State of plane stress occurs in a thin plate subjected to the forces acting in the mid-plane of the plate. y sy O sy tyx x tyx y sx sx txy txy x 6 z . Plane Stress Sign Convention Normal Stress positive tension negative compression Shear Stress positive the direction associated with its subscripts are .

• Cơ khí - Chế tạo máy
• Strength of Materials
• Sức bền vật liệu
• Bài giảng Sức bền vật liệu
• Plane stress
• Mohr’s circle
• Special cases of plane stress
• 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
• Strength condition
• Torsional loads
• Circular shafts
• 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