TAILIEUCHUNG - Ebook Mechanics of materials (7th edition): Part 2
(BQ) Part 2 book "Mechanics of materials" has contents: Stresses in beams (advanced topics), applications of plane stress (pressure vessels, beams, and combined loadings), analysis of stress and strain, statically indeterminate beams, deflections of beams, columns, review of centroids and moments of inertia. | A more advanced theory is required for analysis and design of composite beams and beams with unsymmetric cross sections. 6 Stresses in Beams (Advanced Topics) CHAPTER OVERVIEW In Chapter 6, we will consider a number of advanced topics related to shear and bending of beams of arbitrary cross section. First, stresses and strains in composite beams, that is beams fabricated of more than one material, is discussed in Section . First, we locate the neutral axis then find the flexure formula for a composite beam made up of two different materials. We then study the transformed-section method as an alternative procedure for analyzing the bending stresses in a composite beam in Section . Next, we study bending of doubly symmetric beams acted on by inclined loads having a line of action through the centroid of the cross section (Section ). In this case, there are bending moments (My, Mz) about each of the principal axes of the cross section, and the neutral axis is no longer perpendicular to the longitudinal plane containing the applied loads. The final normal stresses are obtained by superposing the stresses obtained from the flexure formulas for each of the separate axes of the cross section. Next, we investigate the general case of unsymmetric beams in pure bending, removing the restriction of at least one axis of symmetry in the cross section (Section ). We develop a general procedure for analyzing an unsymmetric beam subjected to any bending moment M resolved into components along the principal centroidal axes of the cross section. Of course, symmetric beams are special cases of unsymmetric beams, and therefore, the discussions also apply to symmetric beams. If the restriction of pure bending is removed and transverse loads are allowed, we note that these loads must act through the shear center of the cross section so that twisting of the beam about a longitudinal axis can be avoided (Sections and ). The distributions of shear stresses in the .
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