Unsymmetrical Bending

When the plane of loads acting transversely on a beam does not contain any of the beams axes of symmetry, the loads may tend to produce twisting as well as bending. Figure 3.53  shows a horizontal channel twisting even though the vertical load H acts through the centroid of the section.

The bending axis of a beam is the longitudinal line through which transverse loads should pass to preclude twisting as the beam bends. The shear center for any section of the beam is the point in the section through which the bending axis passes.
For sections having two axes of symmetry, the shear center is also the centroid of the section. If a section has an axis of symmetry, the shear center is located on that axis but may not be at the centroid of the section.

Figure 3.54 shows a channel section in which the horizontal axis is the axis of symmetry. Point O represents the shear center. It lies on the horizontal axis but not at the centroid C. A load at the section must pass through the shear center if twisting of the member is not to occur. The location of the shear center relative to the center of the web can be obtained from

y1 and y2
vertical distance from the angles centroid to the centroid of parts 1 and
2
Substitution in Eq. (3.88) gives
Æ’
= 6.64x  5.93y
This equation indicates that the maximum stresses normal to the cross section occur at the corners of the angle. A maximum compressive stress of 25.43 ksi occurs at the upper right corner, where x
0.1 and y
4.4. A maximum tensile stress of 22.72 ksi occurs at the lower left corner, where x
1.1 and y
2.6. (I. H. Shames, Mechanics of Deformable Solids, Prentice-Hall, Inc., Englewood Cliffs, N.J.; F.R. Shanley, Strength of Materials, McGraw-Hill, Inc., New York.)