Lecture Strength of Materials I: Chapter 1 - PhD. Tran Minh Tu

Lecture Strength of Materials I - Chapter 1: Introduction – Concept of stress. The following will be discussed in this chapter: Review of static, equilibrium of deformable body, concept of stress, stress under general loadings, strain, types of loading, assumptions, principle superposition.

STRENGTH OF MATERIALS STRENGTH OF MATERIALS 1/10/2013 TRAN MINH TU - University of Civil Engineering, Giai Phong Str 55, Hai Ba Trung Dist Hanoi, Vietnam GENERAL INFORMATION • Ass Prof Tran Minh Tu, PhD Eng • Mon., Fri.: 12.15 -14.45 A.M at Room 202 H1 • Office: Floor – Lab Building • E-mail: tpnt2002@yahoo.com • Tel: 04.8691 462 (off.) Handphone: 0912101173 • Course notes: • http://www.tranminhtu.com • Ref : Ferdinand P Beer, Jr J T DeWolf, D F Mazurek Mechanics of Materials Mc Graw Hill 2009 • Office hours: appointment Tuesday 8:00-11:00 A.M or by Sample reading list: Russell C Hibbeler, Mechanics of Materials, 6/E (required text) Roy R Craig, Jr (1996), Mechanics and Materials Bedford, Fowler & Liecht (2003), Statics and Mechanics and Materials Beer & Johnson, Mechanics and Materials James H Gere, Mechanics and Materials, 6th edition 1/10/2013 Strength of Materials This course discusses stress calculation due to loads Description includes stress-strain concept, tensile test, stress and strain due to axial loading, statically indeterminate case related to axial loading, introduction to plasticity and residual stress, stress and strain due to other loads, such as torsion, bending moment, and shear force, Mohr’s circle of stress, failure theory, deflection, statically indeterminate structures, and energy method 1/10/2013 GENERAL INFORMATION Princeton ： Grading: Mid Term Exam - 20% Design Project - 30% Take Home Final Exam 25% Problem set(s) - 15% Other (See Instructor) - 10% MIT： Grading Homework 25% Lab Assignments 30% Quiz 15% Case Study and Presentation 10% Final Exam 20% Class Attendance* Stanford： Grading Homework Assignments 25% Lab Reports 10% Midterm 25% Final Exam 40% Berkeley: Grading Weekly homework assignments(25%) Two Midterm Examinations(20%+20%) Final examination (35%) 1/10/2013 CHAPTER 1/10/2013 Introduction – Concept of Stress Contents 1.1 Introduction 1.2 Review of Static 1.3 Equilibrium of deformable body 1.4 Concept of Stress 1.5 Stress Under General Loadings 1.6 Strain 1.7 Types of loading 1.8 Assumptions 1.9 Principle Superposition 1/10/2013 1.1 Introduction - Consider a diving board as an example of a deformable body - From rigid-body equilibrium, given the weight of the diver, and the lengths L1, L2, we can determine the diving board support reactions at A and B Questions of the following type can only be answered by employing the principles and procedures of strength of materials 1/10/2013 1.1 Introduction 1/10/2013 1.1 Introduction 1.1.1 Strength of materials • A branch of mechanics • It studies the relationship of – External loads applied to a deformable body, and – The intensity of internal forces acting within the body • Are used to compute the deformations of a body • Strength of Materials is a field of study that determines strength, stiffness, & stability 1/10/2013 10 1.6 Strain 1.6.1 Deformation: When A force is applied to a body, it will tend to change the body’s shape and size - deformation 1.6.2 Strain: The strain is the geometrical expression of deformation caused by the action of stress on a physical body The strain is calculated by first assuming a change between two body states: the beginning state and the final state Basically Strain are of three types Longitudinal Strain: -It is defined as the increase in length (d) per unit original length (L) when deformed by the external force Longitudinal Strain = d / L 2.Volumetric Strain:-It is defined as the change in volume (v) per unit original volume (V), when deformed by external force Volume Strain = v / V 1/10/2013 49 1.6 Strain Shear Strain:-When the change takes place in the shape of the body, the strain is called a shear strain - Normal Strain (longitudinal strain) - Shear Strain 1/10/2013 50 1.7 Types of loading Mechanics of materials is a branch of applied mechanics that deals with the behaviour of solid bodies subjected to various types of loading Compression Tension (stretched) Bending 1/10/2013 Torsion (twisted) Shearing 51 1.8 Basic Assumptions • • • • • 1/10/2013 Continuous Homogeneous Isotropic Perfectly elastic Small deformation 52 1.8 Basic Assumptions • Continuous 1/10/2013 53 1.8 Basic Assumptions • Homogeneous 1/10/2013 54 1.8 Basic Assumptions • Isotropic Isotropic 1/10/2013 Anisotropic 55 1.8 Assumptions – Hooke’s Law Hooke’s Law • "Hooke's Law" is about stretching springs and wires • Hooke's Law states:- the extension is proportional to the force • the spring will go back to its original length when the force is removed • so long as we don't exceed the elastic limit 1/10/2013 56 1.8 Assumptions – Hooke’s Law s=Ee Young’s modulus 1/10/2013 t=Gg Shear modulus 57 1.9 Principle Superposition Conditions must be satisfied: 1/10/2013 58 1.9 Principle Superposition + 1/10/2013 59 1/10/2013 60 1/10/2013 61 1/10/2013 62 THANK YOU FOR YOUR ATTENTION ! 1/10/2013 63 ... relationship: s = Ee 12 1. 1 Introduction 1. 1.2 Classification of Structural element 1/ 10/2 013 13 1. 1 Introduction 1/ 10/2 013 14 1. 1 Introduction Classification of Structural elements Structural elements... procedures of strength of materials 1/ 10/2 013 1. 1 Introduction 1/ 10/2 013 1. 1 Introduction 1. 1 .1 Strength of materials • A branch of mechanics • It studies the relationship of – External loads applied... Introduction • Rods, Bars 1/ 10/2 013 17 1. 1 Introduction 1/ 10/2 013 18 1. 1 Introduction 1/ 10/2 013 19 1. 1 Introduction 1. 1.3 External loads • Surface forces – Area of contact – Concentrated force