How to Calculate the Bending of a Bar's Free End?

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SUMMARY

The discussion focuses on calculating the bending of a bar's free end, specifically using the flexural rigidity EI. The key equation involved is q = -d^2M/dx^2 = d^2/dx^2(EI*d^2w/dx^2), which relates the bending moment to the deflection of the bar. The correct solution for the deflection at the free end is w = PL^3/(3EI). Participants emphasize the importance of applying boundary conditions to determine constants of integration during calculations.

PREREQUISITES
  • Understanding of flexural rigidity (EI)
  • Familiarity with differential equations in mechanics
  • Knowledge of boundary conditions in structural analysis
  • Basic principles of beam deflection theory
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  • Study the application of boundary conditions in beam deflection problems
  • Learn about the derivation of beam deflection formulas
  • Explore advanced topics in structural mechanics, such as Euler-Bernoulli beam theory
  • Investigate numerical methods for solving differential equations related to bending
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Students in mechanical engineering, civil engineering, or anyone involved in structural analysis and beam mechanics will benefit from this discussion.

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Homework Statement


Hello, i have problem with the following:
Determine the bending of the free end of an adjacent bar. The bar have flexural rigidity EI

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Homework Equations



q = -dt/dx = -d^2M/dx^2 = d^2/dx^2(EI*d^2w/dx^2)


The Attempt at a Solution



x = 0; w = 0, d2/dx = 0
x = l, T=0, M=M0

I integrated 4 times and putted in those initialvalues but it didn't get my the correct answer.

The answer should be w = PL^3/(3EI)
 
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Well, we can't say what went wrong without seeing your work. By the way, did you use your boundary conditions to determine the constants of integration when you did your calculations?
 

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