tailieunhanh - Lecture Strength of Materials I: Chapter 7 - PhD. Tran Minh Tu

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. | Lecture Strength of Materials I: Chapter 7 - PhD. Tran Minh Tu 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 => Pure Bending Segments AB,CD: Mx≠0, Qy≠0 => 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