22.1 : 梁单元水平面上的剪切力

A prismatic beam's small element acted upon by vertical and horizontal shearing forces, along with normal forces, is considered for analyzing shear on a horizontal face.

Using the equilibrium equation, the balance of forces acting on this element is examined to determine the horizontal shearing force. This force is then equated to bending moments and the first moment of the cross-section.

Analyzing either the lower element or the upper element yields the same result, as the shearing forces exerted on each other are equal in magnitude but opposite in direction.

It's also observed that the first moment of the portion below a certain line in the beam is equal in magnitude but opposite in sign to the first moment of the portion above.

The first moment reaches its maximum when the distance from the neutral axis equals zero, as elements above the neutral axis positively contribute to the integration part of the horizontal shearing forces equation, while those below negatively contribute.

When horizontal shear is divided by the length of the element, the shear flow is obtained.