tailieunhanh - 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 .