2009+12+Bending

2009+12+Bending - Introduction to Solid Mechanics-Vm211...

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1 SJTU Introduction to Solid Mechanics -Vm211 Chapter 12 Bending Chapter 12 Bending SJTU Introduction to Solid Mechanics -Vm211 SJTU Introduction to Solid Mechanics -Vm211 SJTU Introduction to Solid Mechanics -Vm211 SJTU Introduction to Solid Mechanics -Vm211 SJTU Introduction to Solid Mechanics -Vm211 APPLICATIONS

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2 SJTU Introduction to Solid Mechanics -Vm211 APPLICATIONS Wood specimen failed in bending Fibers being crushed Fibers being torn apart SJTU Introduction to Solid Mechanics -Vm211 CHAPTER OUTLINE 1. Shear and Moment Diagrams (Review) 2. Bending Deformation of a Straight Member 3. The Flexure Formula 4. Unsymmetrical Bending SJTU Introduction to Solid Mechanics -Vm211 ± Members that are slender and support loadings applied perpendicular to their longitudinal axis are called beams SHEAR AND MOMENT DIAGRAMS SJTU Introduction to Solid Mechanics -Vm211 ± In order to design a beam, it is necessary to determine the maximum shear and moment in the beam SHEAR AND MOMENT DIAGRAMS ± Express V and M as functions of arbitrary position x along axis. These functions can be represented by graphs called shear and moment diagrams ± Engineers need to know the variation of shear and moment along the beam to know where to reinforce it SJTU Introduction to Solid Mechanics -Vm211 ± Shear and bending-moment functions must be determined for each region of the beam between any two discontinuities of loading SHEAR AND MOMENT DIAGRAMS SJTU Introduction to Solid Mechanics -Vm211 Beam sign convention ± Although choice of sign convention is arbitrary, in this course, we adopt the one often used by engineers: SHEAR AND MOMENT DIAGRAMS
3 SJTU Introduction to Solid Mechanics -Vm211 Procedure for analysis Support reactions ± Determine all reactive forces and couple moments acting on beam ± Resolve all forces into components acting perpendicular and parallel to beam’s axis SHEAR AND MOMENT DIAGRAMS SJTU Introduction to Solid Mechanics -Vm211 Procedure for analysis Shear and moment functions ± Specify separate coordinates x having an origin at beam’s left end, and extending to regions of beam between concentrated forces and/or couple moments, or where there is no discontinuity of distributed loading SHEAR AND MOMENT DIAGRAMS x x 1 x 2 x 3 0 0 x x 1 x 1 x x 2 x 2 x x 3 x 3 x L SJTU Introduction to Solid Mechanics -Vm211 SHEAR AND MOMENT DIAGRAMS Procedure for analysis Shear and moment functions ± Section beam perpendicular to its axis at each distance x ± Draw free-body diagram of one segment ± Make sure V and M are shown acting in positive or negative sense, according to sign convention SJTU

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2009+12+Bending - Introduction to Solid Mechanics-Vm211...

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