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------------------------------------------------ Locate the centroid of the beam's cross-section, which is built up from a channel and a wide-flange beam.

The centroid of the composite cross-section is located as a weighted average of the centroids of the channel and the wide-flange beam, based on their respective areas.

Explanation:

To locate the centroid of a beam's cross-section built up from a channel and a wide-flange beam, you need to determine the centroid of each individual shape and then find the combined centroid based on the areas and distances from a common reference axis.

This process involves calculating the centroids separately for the channel and wide-flange beam and then using the principle of moments to find the centroid of the composite section.

The centroid of the composite section will be a weighted average of the centroids of the individual shapes, based on their respective areas.