Respuesta :
The equations of the electric curve using the coordinates x₁ and x₂ are:
For AB:
y₁= (1/EI) [-M₀x₁³/6L + M₀ Lx₁/6]
For CB:
y₂= (1/EI) [-M₀x₂²/2 + 3M₀Lx₂/2 - M₀L]
The elastic curve of a beam is the curve formed by the intersection of the neutral surface and the side of the beam when the longitudinal stresses on the fibers.
An Elastic curve is flatter, resembling the horizontal lines in the letter E. Price elasticity of demand, also known as demand elasticity, relates to the degree of responsiveness in demand quantity with respect to price.
For AB:
= - x₁
By using double integration method,
EI y₁"== - x₁
EI y₁'=- (x₁)²/2 +C₁ -------(1)
EI y₁=- (x³/6)+C₁ x +C₂ -------(2)
The boundary conditions are:
At x₁=0, y₁=0
At x₁=L, y₁=L
y₁=0,
=- (0)+C₁ (0) +C₂
Then, C₂=0
y₁=L,
=- (L³/6)+C₁ (L) +0
Then, C₁= (L²/6)
C₁=M₀L/6
EIy₁'= -M₀L((x₁)²/2) ------(3)
EIy₁ = -M₀L((x₁)³/6)+(M₀L/6)x₁ -----(4)
For CB:
Mₓ= -M₀
x₂ is in opposite direction to x₁
So the integration with respect to x₂ will be alternately signed.
EI y₂"=Mₓ= -M₀
EI y₂'= -(-M₀x₂)+C₃
EI y₂'=M₀x₂+C₃ ------(5)
EI y₂= -M₀((x₂)²/2)-C₃x₂+C₄ ------(6)
The boundary conditions are;
x₂=L, y₂'=y₁'
y₂=y₁=0
At x₂=L,
y₂'= M₀L²+C₃
y₂'= y₁'= -M₀L/2
C₃= -3M₀L/2
y₂= -M₀L₂/2-(-3M₀L/2)+C₄
C₄= -M₀L
The equation of the electric curve is,
For AB:
y₁= (1/EI) [-M₀x₁³/6L + M₀ Lx₁/6]
For CB:
y₂= (1/EI) [-M₀x₂²/2 + 3M₀Lx₂/2 - M₀L]
To know more about Elastic Curve:
brainly.com/question/24230581
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