1.24 As depicted in Fig. Pl.24, the downward deflection y (m) of a cantilever beam with a uniform load w (kg/m) can be computed as -(x* - 4Lx + 6Lr) 24EI where x = distance (m), E = the modulus of elasticity = 2 x 10" Pa, I = moment of inertia = 3.25 x 10 m", w = 10,000 N/m, and L = length = 4 m. This equation can be differentiated to yield the slope of the downward deflection as a function of x: dy (4x - 12L + 12L²X) 24EI dx If y = 0 at.x 0, use this equation with Euler's method (Ar = 0.125 m) to compute the deflection from.x 0 to L. Develop a plot of your results along with the analytical solution computed with the first equation. x= 0 x=L FIGURE P1.24 A cantilever beam.
1.24 As depicted in Fig. Pl.24, the downward deflection y (m) of a cantilever beam with a uniform load w (kg/m) can be computed as -(x* - 4Lx + 6Lr) 24EI where x = distance (m), E = the modulus of elasticity = 2 x 10" Pa, I = moment of inertia = 3.25 x 10 m", w = 10,000 N/m, and L = length = 4 m. This equation can be differentiated to yield the slope of the downward deflection as a function of x: dy (4x - 12L + 12L²X) 24EI dx If y = 0 at.x 0, use this equation with Euler's method (Ar = 0.125 m) to compute the deflection from.x 0 to L. Develop a plot of your results along with the analytical solution computed with the first equation. x= 0 x=L FIGURE P1.24 A cantilever beam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Provide solution in analytical method and also in numerical method please. And if you can graph then graph
Transcribed Image Text:1.24 As depicted in Fig. P1.24, the downward deflection y (m) of a
cantilever beam with a uniform load w (kg/m) can be computed as
-(x* – 4Lx° + 6L?x²)
24EI
where x = distance (m), E = the modulus of elasticity = 2 x 10"
Pa, I = moment of inertia = 3.25 x 10* m*, w = 10,000 N/m, and
L = length = 4 m. This equation can be differentiated to yield the
slope of the downward deflection as a function of x:
dy
(4x- 12Lr + 12Lx)
dx 24EI
If y = 0 at.x = 0, use this equation with Euler's method (Ar = 0.125 m)
to compute the deflection from.x 0 to L. Develop a plot of your results
along with the analytical solution computed with the first equation.
x= 0
x=L
FIGURE P1.24
A cantilever beam.
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