Reduction of a simple distributed loading problem

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SUMMARY

The discussion centers on the incompatibility of using the NOTE method from exercise 4.21 on exercise 4-156 due to differing location functions. Specifically, the location function in exercise 4.21 is quadratic (x^2), while in exercise 4-156, it is cubic (x^3). This fundamental difference in the mathematical formulation leads to distinct integral results, confirming that the NOTE method cannot be applied interchangeably between these exercises.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the NOTE method in distributed loading problems
  • Knowledge of quadratic and cubic functions
  • Experience with mathematical modeling of load distributions
NEXT STEPS
  • Study the application of the NOTE method in various loading scenarios
  • Explore integral calculus techniques for different polynomial functions
  • Review examples of distributed loading problems in structural analysis
  • Investigate the implications of varying location functions on load calculations
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Students and professionals in civil engineering, structural analysis, and applied mathematics who are dealing with distributed loading problems and integral calculus.

Renan
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Why can't we use the NOTE method (exercise 4.21) on the exercise 4-156 ?

A = ab/3 = (10.500)/3 = 1666,66 N --> this not right
 

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Renan said:
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Why can't we use the NOTE method (exercise 4.21) on the exercise 4-156 ?
Because the location function is different. In one case is goes as ##x^2## and in the other as ##x^3##. If you do the integral in each case, you will get a different answer.
 
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