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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 (- 4Lx + 6L?) 24EI where x = distance (m), E = the modulus of elasticity = 2 x 10" Pa, / = 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 24E1 (4x' - 12Lxr + 12L²x) 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.

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 (- 4Lx + 6L?) 24EI where x = distance (m), E = the modulus of elasticity = 2 x 10" Pa, / = 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 24E1 (4x' - 12Lxr + 12L²x) 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.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Solve using analytical method. Input in the table. Please provide solutions

Solution: Euler's method Analytical method Deflection, y Length, x Deflection, y 1 0.125 1.86353E-05 2 0.25 5.47417E-05 3 0.375 0.000107192 4 0.5 0.000174898 5 0.625 0.000256807 m with a unifrom load is given as: 0.75 0.000351905 7 0.875 0.000459216 0.006 1 0.000577801 0.005 1.125 0.000706759 10 1.25 0.000845225 0.004 11 1.375 0.000992373 12 1.5 0.001147415 0.003 13 1.625 0.001309599 14 1.75 0.001478212 0.002 15 1.875 0.001652578 16 2 0.001832058 0.001 17 2.125 0.002016051 18 2.25 0.002203995 19 2.375 0.002395362 20 2.5 0.002589665 21 2.625 0.002786453 22 2.75 0.002985314 23 2.875 0.00318587 24 3 0.003387785 25 3.125 0.003590758 26 3.25 0.003794526 27 3.375 0.003998863 28 3.5 0.004203583 29 3.625 0.004408534 30 3.75 0.004613604 31 3.875 0.004818718 32 4 0.005023838
Transcribed Image Text:Solution: Euler's method Analytical method Deflection, y Length, x Deflection, y 1 0.125 1.86353E-05 2 0.25 5.47417E-05 3 0.375 0.000107192 4 0.5 0.000174898 5 0.625 0.000256807 m with a unifrom load is given as: 0.75 0.000351905 7 0.875 0.000459216 0.006 1 0.000577801 0.005 1.125 0.000706759 10 1.25 0.000845225 0.004 11 1.375 0.000992373 12 1.5 0.001147415 0.003 13 1.625 0.001309599 14 1.75 0.001478212 0.002 15 1.875 0.001652578 16 2 0.001832058 0.001 17 2.125 0.002016051 18 2.25 0.002203995 19 2.375 0.002395362 20 2.5 0.002589665 21 2.625 0.002786453 22 2.75 0.002985314 23 2.875 0.00318587 24 3 0.003387785 25 3.125 0.003590758 26 3.25 0.003794526 27 3.375 0.003998863 28 3.5 0.004203583 29 3.625 0.004408534 30 3.75 0.004613604 31 3.875 0.004818718 32 4 0.005023838
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.
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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