Unsymmetrical Beams

Flexural Stress varies directly linearly with distance from the neutral axis. Thus for a symmetrical section such as wide flange, the compressive and tensile stresses will be the same. This will be desirable if the material is both equally strong in tension and compression. However, there are materials, such as cast iron, which are strong in compression than in tension. It is therefore desirable to use a beam with unsymmetrical cross section giving more area in the compression part making the stronger fiber located at a greater distance from the neutral axis than the weaker fiber. Some of these sections are shown below.
 

The proportioning of these sections is such that the ratio of the distance of the neutral axis from the outermost fibers in tension and in compression is the same as the ratio of the allowable stresses in tension and in compression. Thus, the allowable stresses are reached simultaneously.
 

In this section, the following notation will be use:
f_bt = flexure stress of fiber in tension
f_bc = flexure stress of fiber in compression
N.A. = neutral axis
y_t = distance of fiber in tension from N.A.
y_c = distance of fiber in compression from N.A.
M_r = resisting moment
M_c = resisting moment in compression
M_t = resisting moment in tension