Mechanics of Materials - Where's my mistake?

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SUMMARY

The discussion focuses on the mechanics of materials, specifically analyzing the forces acting on a steel rod subjected to three axial forces: F1 = 80 kN, F2 = 50 kN, and F3 = 30 kN. The cross-sectional area of the rod is 4 cm², and the modulus of elasticity (E) is 2 x 105 MPa. Participants clarify the calculation of forces at various points in the rod, emphasizing the importance of consistent sign conventions when summing forces to maintain equilibrium. The total expansion of the rod is calculated to be 0.425 mm at point A, with subsequent expansions at points B and C being less.

PREREQUISITES
  • Understanding of axial forces and equilibrium in mechanics
  • Knowledge of stress and strain calculations in materials
  • Familiarity with unit conversions, particularly area from cm² to mm²
  • Basic principles of graphing movement and expansion in materials
NEXT STEPS
  • Study the principles of axial loading and stress distribution in materials
  • Learn about the calculation of cross-sectional areas for different shapes
  • Explore the concept of equilibrium in static systems
  • Investigate the use of movement diagrams in structural analysis
USEFUL FOR

Students and professionals in mechanical engineering, civil engineering, and materials science who are analyzing forces and deformations in structural components.

  • #31
niece of md. said:
Hi I am the friend, just to confirm:

A= π/4*(D)^2-π/4*(D-2α)^2

Yep. That is the proper formula for the area of the cross section.
 
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  • #32
Thanks I'll change that, but I am allowed to make those mistakes since I don't really study it, I just do it for fun :)
 
  • #33
Well, I'm just doing this for fun too.
But I don't allow myself many mistakes! ;)
 
  • #34
Well, I do it for fun and for a degree! Thanks for helping out ILS :smile: we got it done, and are off to solve more complicated stuff now. Hopefully it'll go more smoothly.
 
  • #35
I was trying to solve this exercise but since it's in English I wasn't sure I understood it.

question.jpg


this is what I did:

solve.jpg


I was a little confused with +/- sings on F(bc).
 
  • #36
The signs appear to have been no problem at all and your work is neat!
I give it the ILSe Seal of Approval! :smile:
 

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