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Lecture Mechanics of materials (Third edition) - Chapter 9: Deflection of beams

The following will be discussed in this chapter: Deformation of a beam under transverse loading, equation of the elastic curve, direct determination of the elastic curve from the load di, statically indeterminate beams, application of superposition to statically indeterminate, moment-area theorems,. | Third Edition CHAPTER 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 Deflection of Beams Deformation of a Beam Under Transverse Loading Equation of the Elastic Curve Direct Determination of the Elastic Curve From the Load Di. Statically Indeterminate Beams Sample Problem 9.1 Sample Problem 9.8 Moment-Area Theorems Application to Cantilever Beams and Beams With Symmetric . Bending Moment Diagrams by Parts Sample Problem 9.11 Sample Problem 9.3 Application of Moment-Area Theorems to Beams With Unsymme. Method of Superposition Maximum Deflection Sample Problem 9.7 Use of Moment-Area Theorems With Statically Indeterminate. Application of Superposition to Statically Indeterminate . © 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 • Relationship between bending moment and curvature for pure bending remains valid for general transverse loadings. 1 ρ = M ( x) EI • Cantilever beam subjected to concentrated load at the free end, 1 ρ =− Px EI • Curvature varies linearly with x 1 • At the free end A, ρ = 0, A • At the support B, © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 1 ρB ρA = ∞ ≠ 0, ρ B = EI PL 9-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading • Overhanging beam • Reactions at A and C • Bending moment diagram • Curvature is zero at points where the bending moment is zero, i.e., at each end and at E. 1 ρ = M ( x) EI • Beam is concave upwards where the bending moment is positive and concave downwards where it is negative. • Maximum curvature occurs where the moment magnitude is a maximum. • An .