Y| A W W -L- H4² Beam and Loading Elastic Curve M B B M y A Mc A wL² ܐ ܝ a max +++ D Умах X Ymax x Bx Упах IB x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WL SEI ML² 2EI PL³ 48EI For a > b: Pb(L²-b²)³/2 9√3EIL at x = 5wL 384EI ML² 9√3EI L²-b² 3 Slope at End PL² 2EI wL³ 6EI ML ΕΙ PL² 16EI 0₁=- 0=+ ± wL³ 24EI 0₁ = + 0=- Pb (L²-b²) 6EIL Pa (L²-a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve Šm y = = 6EI y = y=- (x³ - 3Lx²) W 24EI y=. M 2EI For x ≤L: P y = (4x³ - 3L²x) 48EI For x < a: Pb y=6EIL y = For x = a: y= (x² − 4Lx³ + 6L²x²) - ·[x³ - (L²-b²)x] W 24EI M 6EIL Pa²b² 3EIL (x² - 2Lx³ + L³x) -(x³ - L²x)
Y| A W W -L- H4² Beam and Loading Elastic Curve M B B M y A Mc A wL² ܐ ܝ a max +++ D Умах X Ymax x Bx Упах IB x For the cantilever beam and loading shown, determine (a) the deflection at B, (b) the slope at B. Maximum Deflection PL³ 3EI WL SEI ML² 2EI PL³ 48EI For a > b: Pb(L²-b²)³/2 9√3EIL at x = 5wL 384EI ML² 9√3EI L²-b² 3 Slope at End PL² 2EI wL³ 6EI ML ΕΙ PL² 16EI 0₁=- 0=+ ± wL³ 24EI 0₁ = + 0=- Pb (L²-b²) 6EIL Pa (L²-a²) 6EIL ML 6EI ML 3EI Equation of Elastic Curve Šm y = = 6EI y = y=- (x³ - 3Lx²) W 24EI y=. M 2EI For x ≤L: P y = (4x³ - 3L²x) 48EI For x < a: Pb y=6EIL y = For x = a: y= (x² − 4Lx³ + 6L²x²) - ·[x³ - (L²-b²)x] W 24EI M 6EIL Pa²b² 3EIL (x² - 2Lx³ + L³x) -(x³ - L²x)
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
Using the method of superposition and the table provided, find the deflection at b, the slope at b
![ๆ |
1
2
3
5
A
Beam and Loading Elastic Curve
A
7
6
W
|-|
A
W
-L-
a
W
P
b
M
M
B
B
0
A
Mc =
A
L
L→
a
wL²
6
→ymax
L
-X
b
Lymax
X
fymax
ymax
Уmax
Ymax
Bx
Ymax
B x
For the cantilever beam and loading shown, determine
(a) the deflection at B, (b) the slope at B.
Maximum
Deflection
PL³
3EI
WLA
SEI
ML²2
2EI
PL³
48EI
For a > b:
Pb (L²-b²)³/2
9√3EIL
at x =
5wL
384EI
ML²
9√3EI
L²-b²
3
Slope at End
PL²
2EI
wL³
6EI
±
ML
EI
PL²
16EI
0₁A==
OB = +
wL³
±
24EI
0₁ = +
0B ==
OB
Pb(L²-b²)
6EIL
Pa (L² - a²)
6EIL
ML
6EI
ML
3EI
Equation of Elastic Curve
sm
y =
y =
y
y =
P
6EI
(x³ - 3Lx²)
V=
W
24EI
For x < a:
V=
M
2EI
For x ≤L:
P
y = ; (4x³ - 3L²x)
48EI
For x = a:
(x² - 4Lx³ + 6L²x²)
Pb
-[x³ - (L² - b²)x]
6EIL
W
24EI
2
M
6EIL
y =
Pa²b²
3EIL
(x² - 2Lx³ + L³x)
(x³ - L²x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b070d29-61c8-49d8-92a5-4429b5559c9e%2F8987fbba-b3b4-4b6a-afef-a5bfb27ad424%2Fpqt1xsu_processed.png&w=3840&q=75)
Transcribed Image Text:ๆ |
1
2
3
5
A
Beam and Loading Elastic Curve
A
7
6
W
|-|
A
W
-L-
a
W
P
b
M
M
B
B
0
A
Mc =
A
L
L→
a
wL²
6
→ymax
L
-X
b
Lymax
X
fymax
ymax
Уmax
Ymax
Bx
Ymax
B x
For the cantilever beam and loading shown, determine
(a) the deflection at B, (b) the slope at B.
Maximum
Deflection
PL³
3EI
WLA
SEI
ML²2
2EI
PL³
48EI
For a > b:
Pb (L²-b²)³/2
9√3EIL
at x =
5wL
384EI
ML²
9√3EI
L²-b²
3
Slope at End
PL²
2EI
wL³
6EI
±
ML
EI
PL²
16EI
0₁A==
OB = +
wL³
±
24EI
0₁ = +
0B ==
OB
Pb(L²-b²)
6EIL
Pa (L² - a²)
6EIL
ML
6EI
ML
3EI
Equation of Elastic Curve
sm
y =
y =
y
y =
P
6EI
(x³ - 3Lx²)
V=
W
24EI
For x < a:
V=
M
2EI
For x ≤L:
P
y = ; (4x³ - 3L²x)
48EI
For x = a:
(x² - 4Lx³ + 6L²x²)
Pb
-[x³ - (L² - b²)x]
6EIL
W
24EI
2
M
6EIL
y =
Pa²b²
3EIL
(x² - 2Lx³ + L³x)
(x³ - L²x)
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