# Unsymmetric Loading of Thin-Walled Members: Problem Solving

JoVE Core
Mechanical Engineering
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JoVE Core Mechanical Engineering
Unsymmetric Loading of Thin-Walled Members: Problem Solving
##### Vorheriges Video22.5: Unsymmetric Loading of Thin-Walled Members
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.

## Unsymmetric Loading of Thin-Walled Members: Problem Solving

The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.

To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.

Next, calculate the moments of inertia for both the web and the flange. This calculated moment of inertia is essential because it is used in the formula to find the distance from the centerline of the web to the shear center. It's important to note that the distance from the web to the shear center does not depend on the material's thickness and can vary from zero to half of the flange's width.

The final step involves calculating the distance to the shear center by substituting the known values into the equation. This systematic approach ensures an accurate identification of the shear center for the channel section, which is vital for engineering applications where understanding shear stress distribution is crucial.