Unsymmetric Loading of Thin-Walled Members: Problem Solving

Determine the shear center of the given channel section having a known uniform thickness, height, and width. 

The first step in determining the shear center is calculating the shear flow in the flange at a certain distance from an endpoint using the vertical shear and the moment of inertia.

The magnitude of the shearing force exerted on the same flange is calculated by integrating the shear flow from one end of the flange to the other.

Then, the moment of inertia for the entire channel section is calculated. This calculation includes the moments of inertia of both the web and the flange.

The calculated moment of inertia is then substituted into the equation, finding the distance from the center line of the web to the shear center.

The distance of the shear center from the web does not depend on the thickness of the material used and can vary from zero to half of the width of the flange. By substituting the known values, the distance is calculated.