Did I Make a Mistake in Solving for the Load Applied at Point D?

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SUMMARY

The discussion centers on the correct method for solving the load applied at point D in a structural analysis problem. The participant confirmed their answer was accurate but noted a discrepancy with the textbook approach. Key insights include the identification of member ACF as a 2-force member, which affects the relationship between the x and y components of pin reactions at points C and F. The recommendation is to utilize tangents instead of sine and cosine for certain calculations, although the participant's final answer remains valid.

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mingyz0403
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Homework Statement
the 48-lb load can be moved along the line of action shown and applied at a, d, or e. determine the components of the reactions at b and f if the 48-lb load is applied at d
Relevant Equations
3 reaction equation
My answer was correct, however my direction was different from the textbook. I have checked my work a few times ,but not able to find out what I did wrong. Could anyone tell me what I did wrong.

Thank you in advance for your help.
 

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I’m not sure what the textbook method was for the load applied at D. You somehow recognized that member ACF was a 2-force member. Otherwise the x and y components of the pin reactions at C and F would not be trigonometrically related . You should have used tangents instead of sin and cos, but nonetheless your answer is correct. What about the other cases? They may not give the same results.
 
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