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

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In summary, the conversation is about a problem involving a 1-d tapered bar with one end fixed and the other free, an axial load of 4000 N, and a decrease in area from 10sqcm to 5sqcm over a length of 75 cm. A differential equation is used to solve the problem, with boundary conditions of u=0 at x=0 and du/dx=0 at x=75. The speaker is seeking help in finding the equations for u and du/dx.
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date.chinmay
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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.
 

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

What is a 1-d tapered bar cantilever problem?

A 1-d tapered bar cantilever problem refers to a specific type of structural engineering problem where a tapered bar or beam is fixed at one end (cantilever) and subjected to external loads at the other end. This problem is often encountered in the design and analysis of structures such as bridges, buildings, and supports.

What are the main challenges in solving a 1-d tapered bar cantilever problem?

The main challenges in solving a 1-d tapered bar cantilever problem lie in accurately determining the distribution of stresses and deflections along the tapered bar and at the fixed end. This requires a thorough understanding of structural mechanics and the ability to apply appropriate mathematical and computational methods.

What are the key assumptions made in solving a 1-d tapered bar cantilever problem?

Some key assumptions made in solving a 1-d tapered bar cantilever problem include: the material is homogeneous and isotropic, the bar is loaded in a plane of symmetry, and the bar is subjected to small deformations. These assumptions may not always hold true in real-world scenarios, but they are necessary for simplifying the problem and obtaining a solution.

How is a 1-d tapered bar cantilever problem typically solved?

A 1-d tapered bar cantilever problem is typically solved using analytical and numerical methods. Analytical methods involve using equations and mathematical formulas to derive a solution, while numerical methods use computational techniques to approximate the solution. Common methods used include the Euler-Bernoulli beam theory, the finite element method, and the method of virtual work.

What are some common applications of 1-d tapered bar cantilever problems?

1-d tapered bar cantilever problems have many practical applications in civil, mechanical, and aerospace engineering. They are used to design and analyze structures such as bridges, buildings, and supports, as well as components such as beams, columns, and cantilevered wings. Understanding and solving these problems is crucial for ensuring the safety and structural integrity of various engineering projects.

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