The deflection (d) of a cantilever beam subject to a uniformly distributed load w is given by δ ພາ 2 24 EI (x²+6L²-4Lx) which is also shown in the attached file. x is the distance along the beam, Ę is the modulus of elasticity, I is the second moment of area and L is the beam length. Using MATLAB, plot the deflection of the beam along its length using: ⚫ w = 85900 N/m ⚫ E = 200 GPa I=21.2 x100 mm^4 • L = 9.2 m Answer: APPENDIX D Shear, Moment, and Deflection Equations for Beams Appendix D-1 Shear, Moment, and Deflection Equations for Cantilever Beams Slope at Free End Maximum Deflection Deflection & at Any Point x 1. Concentrated load at end PL² PL P 8= 2E1 8x= 8 = ЗЕ 681 (34-x) V-P M M--PL 2. Concentrated load at any point M Pa 0-> Вак 2E1 Pa² = (3L-a) 6E1 For a M--Ps 3. Uniform load 6E1 8E1 V 0 ° M M-12 4. Moment load at free end MyL Mel El 8x= 2E1 V ° M F My -My Px² 8-> (3x) 6E1 For a SSL 8 = Pa (3x-a) 6E1 8-241(x²+61²-4x) 8 = Mast 2E1
The deflection (d) of a cantilever beam subject to a uniformly distributed load w is given by δ ພາ 2 24 EI (x²+6L²-4Lx) which is also shown in the attached file. x is the distance along the beam, Ę is the modulus of elasticity, I is the second moment of area and L is the beam length. Using MATLAB, plot the deflection of the beam along its length using: ⚫ w = 85900 N/m ⚫ E = 200 GPa I=21.2 x100 mm^4 • L = 9.2 m Answer: APPENDIX D Shear, Moment, and Deflection Equations for Beams Appendix D-1 Shear, Moment, and Deflection Equations for Cantilever Beams Slope at Free End Maximum Deflection Deflection & at Any Point x 1. Concentrated load at end PL² PL P 8= 2E1 8x= 8 = ЗЕ 681 (34-x) V-P M M--PL 2. Concentrated load at any point M Pa 0-> Вак 2E1 Pa² = (3L-a) 6E1 For a M--Ps 3. Uniform load 6E1 8E1 V 0 ° M M-12 4. Moment load at free end MyL Mel El 8x= 2E1 V ° M F My -My Px² 8-> (3x) 6E1 For a SSL 8 = Pa (3x-a) 6E1 8-241(x²+61²-4x) 8 = Mast 2E1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The deflection (d) of a cantilever beam subject to a uniformly distributed load w is given by
δ
ພາ 2
24 EI
(x²+6L²-4Lx)
which is also shown in the attached file. x is the distance along the beam, Ę is the modulus
of elasticity, I is the second moment of area and L is the beam length.
Using MATLAB, plot the deflection of the beam along its length using:
⚫ w = 85900 N/m
⚫ E = 200 GPa
I=21.2 x100 mm^4
• L = 9.2 m
Answer:
Transcribed Image Text:APPENDIX D
Shear, Moment, and Deflection
Equations for Beams
Appendix D-1 Shear, Moment, and Deflection Equations for Cantilever Beams
Slope at
Free End
Maximum Deflection
Deflection &
at Any Point x
1. Concentrated load at end
PL²
PL
P
8=
2E1
8x=
8 =
ЗЕ
681 (34-x)
V-P
M
M--PL
2. Concentrated load at any point
M
Pa
0->
Вак
2E1
Pa²
= (3L-a)
6E1
For a
M--Ps
3. Uniform load
6E1
8E1
V
0
°
M
M-12
4. Moment load at free end
MyL
Mel
El
8x=
2E1
V
°
M
F
My
-My
Px²
8-> (3x)
6E1
For a SSL
8 =
Pa
(3x-a)
6E1
8-241(x²+61²-4x)
8 =
Mast
2E1
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