Eccentric Tension-Compression of a Rod

(the strength of materials), deformation resulting from the action upon a rod of two equal longitudinal forces of opposite directions, parallel to the axis of the rod; a form of combined strength. Eccentric tension-compression is characterized by the composition of deflections from bending and from longitudinal forces. For eccentric tension-compression at points of a cross section with flow coordinates y and z taken with respect to the principal center of axes (see Figure 1), the normal tensions are determined according to the formula

in which F is the area of the cross section, I_y and I_z are the moments of inertia of the section, i_y and i_z are the radii of gyration of the section, and y_c and z_c are the coordinates of the point of application of the longitudinal force N. The normal tensions depend linearly on the coordinates and reach maximum values at the points of the cross section farthest from the neutral line, whose position is determined by segments a_y and a_z, cut off at the coordinate axes:

If the longitudinal force is applied at the boundaries of the core of the cross section, then the neutral line either lies out-side the section or touches the profile of the section, in which case the normal stress sheet has a single value. Cases of eccentric tension-compression are often encountered in calculations for foundations, arches, and frames.

Figure 1. Eccentric tension-compression of a rod