Tham khảo tài liệu 'sổ tay tiêu chuẩn thiết kế máy p20', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | _CHAPTER 16 CURVED BEAMS AND RINGS Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor Michigan BENDING IN THE PLANE OF CURVATURE CASTIGLIANO S THEOREM RING SEGMENTS WITH ONE SUPPORT RINGS WITH SIMPLE SUPPORTS RING SEGMENTS WITH FIXED ENDS REFERENCES NOTATION A Area or a constant B Constant C Constant E Modulus of elasticity e Eccentricity F Force G Modulus of rigidity I Second moment of area Table K Shape constant Table or second polar moment of area M Bending moment P Reduced load Q Fictitious force R Force reaction r Ring radius r Centroidal ring radius T Torsional moment U Strain energy V Shear force W Resultant of a distributed load w Unit distributed load X Constant STANDARD HANDBOOK OF MACHINE DESIGN Y Constant y Deflection Z Constant y Load angle Span angle or slope a Normal stress 0 Angular coordinate or displacement Methods of computing the stresses in curved beams for a variety of cross sections are included in this chapter. Rings and ring segments loaded normal to the plane of the ring are analyzed for a variety of loads and span angles and formulas are given for bending moment torsional moment and deflection. BENDING IN THE PLANE OF CURVATURE The distribution of stress in a curved member subjected to a bending moment in the plane of curvature is hyperbolic and is given by the equation My ----T 16-1 Ae r -e-y v where r radius to centroidal axis y distance from neutral axis e shift in neutral axis due to curvature as noted in Table The moment M is computed about the centroidal axis not the neutral axis. The maximum stresses which occur on the extreme fibers may be computed using the formulas of Table . In most cases the bending moment is due to forces acting to one side of the section. In such cases be sure to add the resulting axial stress to the maximum stresses obtained using Table . CASTIGLIANO S THEOREM A
