Elasticity pp 259-268 | Cite as

Shear of a Prismatic Bar

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


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
$$V_x = \int {\int_\Omega {\sigma _{zx} dxdy} } = F_x ;{\rm }V_y = \int {\int_\Omega {\sigma _{zy} dxdy} } = F_y$$
and bending moments
$$M_x = \int {\int_\Omega {\sigma _{zz} ydxdy} } = zF_x ;{\rm }M_y \equiv - \int {\int_\Omega {\sigma _{zz} xdxdy} } = - zF_x $$
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.


Harmonic Function Shear Force Maximum Shear Stress Shear Stress Distribution Elementary Mechanic 
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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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