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Determine the equation of the elastic curve for the beam using the x1 coordinate for 0 ≤ x1 ≤ l/2

Sagot :

The elastic curve between 0 to L/2 is a cubic curve. And the elastic curve is shown in the given diagram.

What is an elastic curve?

The flexible curve of a beam is the curve generated by the crossover of the horizontal member with the beam's side, with continuous stresses on the fibers considered to be within the elastic limit.

The slope at L/2 will be

[tex]\rm \theta _{L/2} = \dfrac{PL^2}{8EI}[/tex]

The deflection of the beam at L/2 will be

[tex]\rm y_{L/2} = \dfrac{P(L/2)^3}{3EI}\\\\\rm y_{L/2} = \dfrac{PL^3}{24EI}[/tex]

And the deflection of the beam at L will be

[tex]\rm y_{L} = \dfrac{PL^3}{24EI} + \dfrac{L}{2} \times \theta _{L/2} \\\\\rm y_{L} = \dfrac{PL^3}{24EI} + \dfrac{L}{2} \times \dfrac{PL^2}{8EI}\\\\\rm y_{L} = \dfrac{5PL^3}{48EI}[/tex]

Then the elastic curve will be shown in the diagram.

More about the elastic curve link is given below.

https://brainly.com/question/24230581

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