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

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In summary, the problem involves determining the bending of the free end of an adjacent bar with flexural rigidity EI. The relevant equations are q = -dt/dx = -d^2M/dx^2 = d^2/dx^2(EI*d^2w/dx^2). The attempt at a solution involved setting initial values for x = 0 and x = l, and then integrating four times, but did not result in the correct answer of w = PL^3/(3EI). It is important to use boundary conditions to determine the constants of integration when solving the problem.
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Firben
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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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  • #2
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?
 

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

What is bending?

Bending refers to the deformation or change in shape of a material due to an applied force or load.

How is the bending of a bar determined?

The bending of a bar can be determined using the formula M = EI/R, where M is the bending moment, E is the modulus of elasticity, I is the moment of inertia, and R is the radius of curvature.

What factors affect the bending of a bar?

The bending of a bar is affected by the material properties, such as elasticity and strength, as well as the shape and size of the bar. The type and magnitude of the applied load also play a role in determining the bending of a bar.

How is the bending of a bar tested or measured?

The bending of a bar can be tested or measured using various methods, such as a three-point bend test or a four-point bend test. These tests involve applying a force to the bar and measuring the resulting deflection.

What are some common applications of bending in engineering?

Bending is a common phenomenon in engineering and is used in many applications, such as building structures, bridges, and machinery. It is also an important concept in the design and analysis of beams, columns, and other structural components.

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