Mechanics of materials beam Problem

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SUMMARY

The discussion focuses on calculating the necessary cross-section of a tension rod in a 1-ton wall hoist system, supported at a 30-degree angle. The calculations utilize a factor of safety of 5 and a yield point of 30,000 PSI. The derived tension in the rod is 4,000 pounds, leading to a required area of 0.6667 square inches (2/3 square inches) based on the stress formula S=F/A. Clarifications were made regarding the distinction between tension in the rod and compression in the horizontal beam.

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  • Understanding of mechanics of materials, specifically beam and tension analysis.
  • Familiarity with stress calculations, including the formula S=F/A.
  • Knowledge of factors of safety and yield points in material design.
  • Basic trigonometry to resolve forces at angles, particularly sine and cosine functions.
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  • Study the principles of tension and compression in structural engineering.
  • Learn about calculating factors of safety in mechanical design.
  • Explore the application of trigonometric functions in engineering problems.
  • Review material properties and yield strength calculations for different materials.
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Chacabucogod
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A 1-ton wall hoist consists of a horizontal beam, supported by a tension rod at 30 deg, as shown. The rod is to be designed with a factor of safety 5 with repeat to its yield point of 30,000 PSI. Determine its necessary cross section




S=F/A



30000/5=6000PSI
-2000+Rsin(30)=0
R=4000
R_x=4000cos(30)
6000=4000cos(30)/A

The solution from the book is 2/3 which would imply that the force is 4000. Am I doing something wrong?
 

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You've just thrown some numbers down without any explanation or units. It's hard to follow what you are doing.

What is R supposed to be?

It seems like you're supposed to figure out the tension in the tension rod, which apparently is not the same as figuring out the compression load in the horizontal beam. The area 'A' should have some units attached.
 
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Never mind. It's the rod's tension, not the cantilever. Seems like I read it wrong. Thank you
 

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