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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
Related questions
Question
Solve using analytical method. Input in the table. Please provide solutions
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
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Structural Analysis (10th Edition)
Civil Engineering
ISBN:
9780134610672
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Principles of Foundation Engineering (MindTap Cou…
Civil Engineering
ISBN:
9781337705028
Author:
Braja M. Das, Nagaratnam Sivakugan
Publisher:
Cengage Learning
Fundamentals of Structural Analysis
Civil Engineering
ISBN:
9780073398006
Author:
Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:
McGraw-Hill Education
Traffic and Highway Engineering
Civil Engineering
ISBN:
9781305156241
Author:
Garber, Nicholas J.
Publisher:
Cengage Learning