Elasticity pp 259-268 | Cite as

# Shear of a Prismatic Bar

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## Abstract

In this chapter, we shall consider the problem in which a prismatic bar occupying the region z>0 is loaded by transverse forces F
and bending moments
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.

_{x}, F_{y}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)

$$M_x = \int {\int_\Omega {\sigma _{zz} ydxdy} } = zF_x ;{\rm }M_y \equiv - \int {\int_\Omega {\sigma _{zz} xdxdy} } = - zF_x $$

(17.2)

## 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