Elasticity pp 259-268

# 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
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