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Ebook Mechanics of materials: Part 2

(BQ) Part 2 book "Mechanics of materials" has contents: Shearing stresses in beams and thin walled members, transformations of stress and strain, principal stresses under a given loading, deflection of beams, columns, energy methods. | bee29389_ch06_371-421 03/16/2008 9:17 am Page 371 pinnacle MHDQ:MH-DUBUQUE:MHDQ031:MHDQ031-06: C H A P Shearing Stresses in Beams and Thin-Walled Members T E 6 A reinforced concrete deck will be attached to each of the steel sections shown to form a composite box girder bridge. In this chapter the shearing stresses will be determined in various types of beams and girders. R bee29389_ch06_371-421 03/16/2008 9:17 am Page 372 pinnacle MHDQ:MH-DUBUQUE:MHDQ031:MHDQ031-06: 372 6.1. INTRODUCTION Shearing Stresses in Beams and Thin-Walled Members You saw in Sec. 5.1 that a transverse loading applied to a beam will result in normal and shearing stresses in any given transverse section of the beam. The normal stresses are created by the bending couple M in that section and the shearing stresses by the shear V. Since the dominant criterion in the design of a beam for strength is the maximum value of the normal stress in the beam, our analysis was limited in Chap. 5 to the determination of the normal stresses. Shearing stresses, however, can be important, particularly in the design of short, stubby beams, and their analysis will be the subject of the first part of this chapter. y y M xydA xzdA V xdA x x z z Fig. 6.1 Figure 6.1 expresses graphically that the elementary normal and shearing forces exerted on a given transverse section of a prismatic beam with a vertical plane of symmetry are equivalent to the bending couple M and the shearing force V. Six equations can be written to express that fact. Three of these equations involve only the normal forces sx dA and have already been discussed in Sec. 4.2; they are Eqs. (4.1), (4.2), and (4.3), which express that the sum of the normal forces is zero and that the sums of their moments about the y and z axes are equal to zero and M, respectively. Three more equations involving the shearing forces txy dA and txz dA can now be written. One of them expresses that the sum of the moments of the shearing .