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. | Lecture Strength of Materials I: Chapter 4 - 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 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 => The body is deformed =>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 .
