Do problem 12 -22 using double integration. Also find how much additional deflection is added (to the max) if we account for the beam self-weight. Find this additional deflection using the table in appendix C.     mechanics of materials chapter 12 (integration of moment)= theta, and integration of theta = v

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter9: Deflections Of Beams
Section: Chapter Questions
Problem 9.9.7P: The cantilever beam A CB shown in the hgure is subjected to a uniform load of intensity q acting...
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 Do problem 12 -22 using double integration. Also find how much additional deflection is added (to the max) if we account for the beam self-weight. Find this additional deflection using the table in appendix C.

 

 

mechanics of materials chapter 12 (integration of moment)= theta, and integration of theta = v

 

13.5
814
V
υ
v
V
L
2
01
APPENDIX
C
V
V
01
Simply Supported Beam Slopes and Deflections
Beam
Slope
-0₁
L-
-0₁
a
L
2
교
W
Omax
L
-L-
max max
02
L
L
2
P
Vmax
+-b
L
2
0₂
02
Wo
1
0₂ Mo
X
W
X
-X
X
X
X
0₁
02
02
0₁
0₂
0₁ =
Omax
0 max
=
02
=
=
0₁
=
=
=
=
SLOPES AND
=
DEFLECTIONS OF
BEAMS
=
-Pab(L + b)
6EIL
=
Pab(L + a)
6EIL
-PL²
16EI
-MOL
6EI
MOL
3EI
-wL
24EI
-3wL³
128EI
7wL³
384EI
-7woĽ³
360EI
WOL³
45EI
V
01.-0
1x=a
=
Deflection
Umax
V
Umax
- Pba
6EIL
=
-Mo L²
9√/3 EI
at x = 0.5774L
=
Vmax
|x=L/2
²([² - 6² - a²)
=
-PL³
48EI
-5wL4
384EI
=
-5wL4
768EI
SS
Vmax = -0.006563
at x = 0.4598L
Vmax = -0.00652-
at x = 0.5193L
WL4
EI
WOL4
EI
V =
- Px
48EI
0 ≤ x ≤ L/2
V =
V=
=
0≤x≤ a
V =
Elastic Curve
V=
-Pbx
6EIL
V =
V=
=
(31²
-WX
384EI
-Mox
6EIL
-WX
24EI
(L² − b² − x²)
0≤x≤L/2
-wL
384EI
-
4x²)
(x³ - 2Lx² + L²³)
L/2 ≤ x <L
(16x³ - 24Lx² +9L³)
(Ľ² - x²)
-wox
360EIL
(8x³ - 24Lx²
+17L²x-L
(3x4 - 10L²x² +
Transcribed Image Text:13.5 814 V υ v V L 2 01 APPENDIX C V V 01 Simply Supported Beam Slopes and Deflections Beam Slope -0₁ L- -0₁ a L 2 교 W Omax L -L- max max 02 L L 2 P Vmax +-b L 2 0₂ 02 Wo 1 0₂ Mo X W X -X X X X 0₁ 02 02 0₁ 0₂ 0₁ = Omax 0 max = 02 = = 0₁ = = = = SLOPES AND = DEFLECTIONS OF BEAMS = -Pab(L + b) 6EIL = Pab(L + a) 6EIL -PL² 16EI -MOL 6EI MOL 3EI -wL 24EI -3wL³ 128EI 7wL³ 384EI -7woĽ³ 360EI WOL³ 45EI V 01.-0 1x=a = Deflection Umax V Umax - Pba 6EIL = -Mo L² 9√/3 EI at x = 0.5774L = Vmax |x=L/2 ²([² - 6² - a²) = -PL³ 48EI -5wL4 384EI = -5wL4 768EI SS Vmax = -0.006563 at x = 0.4598L Vmax = -0.00652- at x = 0.5193L WL4 EI WOL4 EI V = - Px 48EI 0 ≤ x ≤ L/2 V = V= = 0≤x≤ a V = Elastic Curve V= -Pbx 6EIL V = V= = (31² -WX 384EI -Mox 6EIL -WX 24EI (L² − b² − x²) 0≤x≤L/2 -wL 384EI - 4x²) (x³ - 2Lx² + L²³) L/2 ≤ x <L (16x³ - 24Lx² +9L³) (Ľ² - x²) -wox 360EIL (8x³ - 24Lx² +17L²x-L (3x4 - 10L²x² +
for
eam's
rculars
diameter of
e sey
A
6 kN•m
A
-X
grad avand ordenio
minellet bus 900is
1.5 m
X
8 kN
C
Prob. 12-21
12-22. Determine the elastic curve for the cantilevered
W14 x 30 beam using the x coordinate. Specify the maximum
slope and maximum deflection. E = 29(10³) ksi.
9 ft
1.5 m
Prob. 12-22
B
6 kN•m
HT
3 kip/ft
B
A
12-2
load
vert
max
Transcribed Image Text:for eam's rculars diameter of e sey A 6 kN•m A -X grad avand ordenio minellet bus 900is 1.5 m X 8 kN C Prob. 12-21 12-22. Determine the elastic curve for the cantilevered W14 x 30 beam using the x coordinate. Specify the maximum slope and maximum deflection. E = 29(10³) ksi. 9 ft 1.5 m Prob. 12-22 B 6 kN•m HT 3 kip/ft B A 12-2 load vert max
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