Third Edition CHAPTER 9 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Deflection of Beams 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 Deformation of a Beam Under Transverse Loading • Relationship between bending moment and curvature for pure bending remains valid for general transverse loadings. 1 M ( x) EI © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading • Cantilever beam subjected to concentrated load at the free end, 1 Px EI © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-4 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-5 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9-6 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9-7 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Equation of the Elastic Curve • Substituting and integrating, 1 d2y EI EI 2 M x dx x dy EI EI M x dx C1 dx 0 x x 0 0 EI y dx M x dx C1x C2 © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-8 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Boundary Conditions for Beams © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-9 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 10 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 11 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 12 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 13 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 14 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 15 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 16 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 17 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 18 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 19 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 20 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 21 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 22 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 23 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 24 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 25 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Statically Indeterminate Beams © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 26 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Statically Indeterminate Beams © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 27 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 28 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 29 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 30 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 31 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Statically Indeterminate Beams © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 32 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Statically Indeterminate Beams © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 33 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 34 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 35 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 36 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 37 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 38 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 39 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 40 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 41 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 42 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 43 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 44 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 45 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Problems 9.4, 9.6, 9.9, 9.10, 9.15, 9.20, 9.25, 9.29, 9.30, 9.31 © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 46 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Method of Superposition © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 47 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 48 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 49 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 50 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 51 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 52 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 53 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 54 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 55 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 56 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Alternative Solution © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 57 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 58 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 59 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 60 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 61 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 62 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 63 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 64 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 65 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 66 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 67 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 68 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 69 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 70 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 71 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 72 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 73 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 74 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 75 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 76 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 77 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 78 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 79 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 80 Third Edition MECHANICS OF MATERIALS © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Beer • Johnston • DeWolf 9 - 81 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Problems 9.67, 9.73, 9.74, 9.77, 9.78, 9.81, 9.82, 9.83, 9.84, 9.85 © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9 - 82
