Axially Loaded Members Question

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SUMMARY

The discussion focuses on solving a problem involving axially loaded members, specifically incorporating an angle of θ=3° into the equations. The key equations referenced include ƩMb = 0 and F = kΔ, along with the relationship ΔD/b = ΔA/a derived from similar triangles. The user has successfully identified unknown forces but struggles to integrate the angle into their calculations. A hint provided suggests using the sine function to relate the angle to the displacement and force.

PREREQUISITES
  • Understanding of static equilibrium equations, specifically ƩMb = 0.
  • Familiarity with Hooke's Law, represented as F = kΔ.
  • Knowledge of similar triangles and their application in mechanics.
  • Basic trigonometry, particularly the sine function and its application in engineering problems.
NEXT STEPS
  • Research the application of trigonometric functions in static equilibrium problems.
  • Study the principles of axial loading in structural mechanics.
  • Learn about the relationship between displacement and force in spring systems.
  • Explore examples of similar triangles in engineering contexts to solidify understanding.
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Students and professionals in mechanical engineering, structural engineering, and anyone involved in solving problems related to axially loaded members and static equilibrium.

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Homework Statement



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So I'm trying to do this problem right now. For the most part, I feel like I have 80% of the work done (in terms of finding certain unknowns etc) but I have no idea how to incorporate the θ=3°. What I mean is, what kind of equation can I set up that includes the angle in it? Apparently you don't need trig or anything, so I am a bit lost.

Homework Equations



ƩMb = 0; FA(a) + FD(b) - P(c) = 0
F = kΔ
ΔD/b = ΔA/a (I used similar triangles to achieve this for when the bar will be pulled down)

The Attempt at a Solution



At the moment, I have found all the unknowns such as the reaction and spring forces etc. I think I am on the right track, but I just have no idea how I can set up an equation using the maximum angle.

Thank you for your help!
 
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Hint 1: sin(3 deg) = delta_A/a; but delta_A = F_A/k1.
 

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