Lecture Strength of Materials I - Chapter 7: Bending. The following will be discussed in this chapter: Introduction, bending stress, shearing stress in bending, strength condition, sample problems, deflections of beam, statically indeterminate beams. | STRENGTH OF MATERIALS 1 10 2013 TRAN MINH TU - University of Civil Engineering 1 Giai Phong Str. 55 Hai Ba Trung Dist. Hanoi Vietnam CHAPTER 7 BENDING 1 10 2013 Contents . Introduction . Bending stress . Shearing stress in bending . Strength condition . Sample Problems . Deflections of beam . Statically indeterminate beams 1 10 2013 3 . Introduction In previous charters we considered the stresses in the bars caused by axial loading and torsion. Here we introduce the third fundamental loading bending. When deriving the relationship between the bending moment and the stresses causes we find it again necessary to make certain simplifying assumptions. We use the same steps in the analysis of bending that we used for torsion in chapter 6. 1 10 2013 4 . Introduction Classification of Beam Supports 1 10 2013 5 . Introduction Limitation 1 10 2013 6 . Introduction Segment BC Mx 0 Qy 0 gt Pure Bending Segments AB CD Mx 0 Qy 0 gt Nonuniform Bending 1 10 2013 7 . Introduction Pure Bending Prismatic members subjected to equal and opposite couples acting in the same longitudinal plane 1 10 2013 8 . Bending stress Simplifying assumptions 1 10 2013 9 . Bending stress The positive bending moment causes the material within the bottom portion of the beam to stretch and the material within the top portion to compress. Consequently between these two regions there must be a surface called the neutral surface in which longitudinal fibers of Neutral axis the material will not undergo a change in length. 1 10 2013 10 . Bending stress Compatibility 1 2 Consider a segment of the beam a b bounded by two cross-sections that c y d are separated by the infinitesimal distance dz. dz 2 1 Due to bending moment Mx caused d Neutral fiber by the applied loading the cross- 1 2 section rotate relatively to each other a b by the amount of d . y c d The Normal strain of the longitudinal 1 2 fiber cd that lies distance y below the neutral surface. dz c d cd y d
