tailieunhanh - Lecture Mechanics of materials (Third edition) - Chapter 5: Analysis and design of beams for bending

Lecture Mechanics of materials (Third edition) - Chapter 5: Analysis and design of beams for bending. The following will be discussed in this chapter: Introduction; shear and bending moment diagrams; relations among load, shear, and bending moment; design of prismatic beams for bending. | Third Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University Analysis and Design of Beams for Bending © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Analysis and Design of Beams for Bending Introduction Shear and Bending Moment Diagrams Sample Problem Sample Problem Relations Among Load, Shear, and Bending Moment Sample Problem Sample Problem Design of Prismatic Beams for Bending Sample Problem © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 5-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Introduction • Objective - Analysis and design of beams • Beams - structural members supporting loads at various points along the member • Transverse loadings of beams are classified as concentrated loads or distributed loads • Applied loads result in internal forces consisting of a shear force (from the shear stress distribution) and a bending couple (from the normal stress distribution) • Normal stress is often the critical design criteria σx = − My I σm = Mc M = I S Requires determination of the location and magnitude of largest bending moment © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 5-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Introduction Classification of Beam Supports © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 5-4 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Shear and Bending Moment Diagrams • Determination of maximum normal and shearing stresses requires identification of maximum internal shear force and bending couple. • Shear force and bending couple at a point are determined by passing a section through the beam and applying an equilibrium analysis on the beam portions on either side of the section. • Sign conventions for shear forces V and V’ and .