20.16 : 偏心轴向载荷的一般情况

Consider a member subjected to equal and opposite eccentric forces. These forces are applied at a horizontal distance of a and a vertical distance of b from the principal centroidal axis of the member.

Each eccentric force is equal to the centric force and two couple moments with moments arms being distance a and b from the principal centroidal axis of the member.

Using the Saint-Venant principle, the equivalent loadings can be used to determine the distribution of the stress at the section of the member. The analysis holds when the section is not close to either end of the member.

The superposition principle determines the stresses due to centric forces and the bending couples, and shows that the stress varies linearly along the section. 

Depending on the geometry of the member and the line of action of the eccentric loadings, the total stress may have the same or opposite sign throughout the section. The line along the section for which the stress magnitude is zero is known as the neutral axis of the section.