The following will be discussed in this chapter: Stress & strain: axial loading, normal strain, stress-strain test, stress-strain diagram: ductile materials, stress-strain diagram: brittle materials, hooke’s law: modulus of elasticity, elastic vs. plastic behavior, fatigue, deformations under axial loading,. | Third Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Stress and Strain – Axial Loading Lecture Notes: J. Walt Oler Texas Tech University © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Contents Stress & Strain: Axial Loading Normal Strain Stress-Strain Test Stress-Strain Diagram: Ductile Materials Stress-Strain Diagram: Brittle Materials Hooke’s Law: Modulus of Elasticity Elastic vs. Plastic Behavior Fatigue Deformations Under Axial Loading Example Sample Problem Static Indeterminacy Example Thermal Stresses Poisson’s Ratio © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Generalized Hooke’s Law Dilatation: Bulk Modulus Shearing Strain Example Relation Among E, ν, and G Sample Problem Composite Materials Saint-Venant’s Principle Stress Concentration: Hole Stress Concentration: Fillet Example Elastoplastic Materials Plastic Deformations Residual Stresses Example , , 2-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Stress & Strain: Axial Loading • Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced under loading. Statics analyses alone are not sufficient. • Considering structures as deformable allows determination of member forces and reactions which are statically indeterminate. • Determination of the stress distribution within a member also requires consideration of deformations in the member. • Chapter 2 is concerned with deformation of a structural member under axial loading. Later chapters will deal with torsional and pure bending loads. © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 2-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Normal Strain σ= ε= P = stress A δ L = normal strain σ= ε= 2P P = 2A A δ L © 2002 The McGraw-Hill Companies, Inc. .
