Engineering Bucket supported by wood frame and tension wire

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The discussion centers on a structural engineering problem involving a bucket supported by a wood frame and tension wire. The original poster questions the omission of the horizontal force component from the diagonal support "G-H" in the solution provided in a YouTube video. They emphasize the importance of analyzing the entire system and isolating irrelevant portions when solving problems. The poster seeks clarification on how to properly analyze the forces at play, particularly the compressive force on "G-H." The inquiry highlights a need for a comprehensive understanding of force interactions in structural systems.
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Homework Statement
A 160-lb bucket is suspended from a cable on the wooden frame.

Determine the magnitude of the resultant internal normal force acting on the cross section at E
Determine the magnitude of the resultant internal shear force acting on the cross section at E
Determine the magnitude of the resultant internal bending moment acting on the cross section at E
Relevant Equations
Sum of forces (x and y)
Moment about "E"
Attached is an image of the HW problem, included is a YouTube video I found for a solution.
Assuming the solution shown is correct my question is about the rest of the system. I always approached problems from a top down "total system" perspective. Then try to isolate the portions of the system that are irrelevant for what I am solving. In this problem, the diagonal support for the cantilevered beam "G-H" would carry and transmit a resultant horizontal force into the main vertical member "A-B". Yet this solution and consequently the homework does not address this force. Why is the "x" component of the G-H force ignored?
 

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Let's see how you would analyze the problem, including the compressive force on GH?
 
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