I have a problem while solving 1-d tapered bar(cantilever) problem

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SUMMARY

The discussion centers on solving a one-dimensional tapered cantilever bar problem subjected to an axial load of 4000 N. The bar's cross-sectional area decreases from 10 sq cm to 5 sq cm over a length of 75 cm. The governing differential equation is given as - d/dx(EA du/dx) + P(at x) = 0, with boundary conditions specified at x=0 (u=0) and x=75 (du/dx=0). Participants are seeking assistance in deriving the equations for displacement (u) and its derivative (du/dx).

PREREQUISITES
  • Understanding of differential equations, particularly in the context of structural mechanics.
  • Familiarity with cantilever beam theory and its boundary conditions.
  • Knowledge of material properties, specifically Young's modulus (E) and cross-sectional area (A).
  • Basic principles of axial loading and its effects on structural elements.
NEXT STEPS
  • Study the derivation of solutions for differential equations in structural mechanics.
  • Learn about the application of the method of separation of variables in solving boundary value problems.
  • Research the impact of varying cross-sectional areas on stress and strain in beams.
  • Explore numerical methods for solving differential equations, such as the finite element method (FEM).
USEFUL FOR

Structural engineers, mechanical engineers, and students studying mechanics of materials will benefit from this discussion, particularly those focused on analyzing tapered beams under axial loads.

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I have a problem while solving 1-d tapered bar(cantilever) problem with one end fixed and other free with an axial load of 4000 N outwards from the free end.
Area decreases from10sqcm to 5sqcm over a length of 75 cm.

Differential equation is - d/dx(EA du/dx) + P(at x) =0

Boundary Conditions - at x=0 u=0
at x=75 du/dx=0

Please help in finding the equations for u and du/dx

Thank you.
 
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some1 please answer this question...


date.chinmay said:
I have a problem while solving 1-d tapered bar(cantilever) problem with one end fixed and other free with an axial load of 4000 N outwards from the free end.
Area decreases from10sqcm to 5sqcm over a length of 75 cm.

Differential equation is - d/dx(EA du/dx) + P(at x) =0

Boundary Conditions - at x=0 u=0
at x=75 du/dx=0

Please help in finding the equations for u and du/dx

Thank you.
 

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