材料力学第五章弯曲应力.pdf

Chapter 5 Bending Stresses In this chapter, only members having symmetric cross sections and subjected to loads in the plane of symmetry are considered. As a consequence, the bending deflections occur in this plane known as the plane of bending. Thus the deflection curve is a plane curve lying in the plane of bending. When a segment of a beam is in equilibrium under the action of bending moments alone, such a condition is referred to as pure bending, or flexure. Studies in subsequent chapters will show that usually the bending stresses in slender beams are dominant. Therefore, the formulas derived in this chapter for pure bending are directly applicable in numerous design situations. M 5-1 Bending of beams 1. The basic assumption Consider a horizontal prismatic beam having a cross section with a vertical axis of symmetry; see Fig.5-l(a). A horizontal line through the centroid of the cross section will be referred to as the axis of a beam. The fundamental hypothesis of the flexure theory: plane sections through a beam taken normal to its axis remain plane after the beam