[Statics] Determining the normal force at an internal point of a member

AI Thread Summary
To determine the normal force at point E in a frame, the correct approach involves dividing the frame into members AB and CB, solving for the reaction forces at point B, and using a free body diagram for member EB. An alternative method that treats the two members as a system and sets the sum of moments about point A can lead to discrepancies if incorrect values are used. The issue arose from using an incorrect number in the second method, which caused the different results. Ultimately, ensuring accurate values in calculations is crucial for consistent outcomes. The discussion highlights the importance of methodical problem-solving in statics.
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TL;DR Summary
A statics question regarding a two-member frame.
For this problem (see image), I get the correct answer for the normal force at point E if I:
1) divide the frame into members AB and CB,
2) solve for the x and y components of the reaction force at point B,
3) make a free body diagram with the cut at point E forming member EB and setting the sum of the x-components of the forces to 0 and solving for the normal force.

BUT

If I try to solve it by treating the two members as a system (and, thus, discount the reaction force at B), setting the sum of the moments about point A to 0 and then solving that for the x-component of the reaction force at point C which would then equal the the negative of the normal force at point E, I don't get the same answer. Why is that?
 

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I figured it out. Used a wrong number for the second method causing the answer to differ. Thank you nonetheless.
 
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