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Elasticity pp 259-268 | Cite as

Shear of a Prismatic Bar

  • J. R. Barber
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 172)

Abstract

In this chapter, we shall consider the problem in which a prismatic bar occupying the region z>0 is loaded by transverse forces Fx, Fy in the negative x- and y-directions respectively on the end z =0, the sides of the bar being unloaded. Equilibrium considerations then show that there will be shear forces
$$V_x = \int {\int_\Omega {\sigma _{zx} dxdy} } = F_x ;{\rm }V_y = \int {\int_\Omega {\sigma _{zy} dxdy} } = F_y$$
(17.1)
and bending moments
$$M_x = \int {\int_\Omega {\sigma _{zz} ydxdy} } = zF_x ;{\rm }M_y \equiv - \int {\int_\Omega {\sigma _{zz} xdxdy} } = - zF_x $$
(17.2)
at any given cross-section Ω of the bar. In other words, the bar transmits constant shear forces, but the bending moments increase linearly with distance from the loaded end.

Keywords

Harmonic Function Shear Force Maximum Shear Stress Shear Stress Distribution Elementary Mechanic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Applied MechanicsUniversity of MichiganAnn ArborUSA

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