The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10') ksi. Assume the displacement of each end of the board relative to its center is 3 in.
The fence board weaves between the three smooth fixed posts. If the posts remain along the same line, determine the maximum bending stress in the board. The board has a width of 6 in. and a thickness of 0.5 in. E 1.60(10') ksi. Assume the displacement of each end of the board relative to its center is 3 in.
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
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![The fence board weaves between the three smooth
fixed posts. If the posts remain along the same line, determine
the maximum bending stress in the board. The board has a
width of 6 in. and a thickness of 0.5 in. E 1.60(10) ksi.
Assume the displacement of each end of the board relative
to its center is 3 in.
3 in.
Support Reactions and Elastic Curve: As shown on FBD(a).
Moment Function: As shown on FBD(b).
Slope and Elastic Curve:
d'v
dx
El
= M(x)
d'u
EI
dx2
dv
-x + C,
[1)
EI
dx
4
MCn)
El v =5+ Cx + C2
%3D
12
[2)
390625
Boundary Conditions: Due to symmetry,
dv
= 0 at x =
Also, v = 0 at x 0.
PL?
C, =
16
From Eq. [1]0 =
+ C
From Eq. [2] 0 0 +0+ C2
C = 0
The Elastic Curve: Substitute the values of C, and C, into Eq. [2].
Px
;(4x² - 3L)
[1)
48EI
Require at x 48 in., v = -3 in. From Eq.[1].
P(48)
14(48) – 3(967)]
-3 =
48(1.60)(109)(1) (6)(0.5') *
P = 16.28 lb
Maximum Bending Stress: From the moment diagram, the maximum moment is
Ma = 390.625 lb in. Applying the flexure formula,
Mc
390.625(0.25)
= 1562.5 psi = 1.56 ksi
Ans.
max
A (6)(0.5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb03011d5-e53b-48c3-9c0e-e0e3e4948fb4%2F2850ccbf-4560-40f4-a877-ee2889ed5a90%2Fr6rl4s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The fence board weaves between the three smooth
fixed posts. If the posts remain along the same line, determine
the maximum bending stress in the board. The board has a
width of 6 in. and a thickness of 0.5 in. E 1.60(10) ksi.
Assume the displacement of each end of the board relative
to its center is 3 in.
3 in.
Support Reactions and Elastic Curve: As shown on FBD(a).
Moment Function: As shown on FBD(b).
Slope and Elastic Curve:
d'v
dx
El
= M(x)
d'u
EI
dx2
dv
-x + C,
[1)
EI
dx
4
MCn)
El v =5+ Cx + C2
%3D
12
[2)
390625
Boundary Conditions: Due to symmetry,
dv
= 0 at x =
Also, v = 0 at x 0.
PL?
C, =
16
From Eq. [1]0 =
+ C
From Eq. [2] 0 0 +0+ C2
C = 0
The Elastic Curve: Substitute the values of C, and C, into Eq. [2].
Px
;(4x² - 3L)
[1)
48EI
Require at x 48 in., v = -3 in. From Eq.[1].
P(48)
14(48) – 3(967)]
-3 =
48(1.60)(109)(1) (6)(0.5') *
P = 16.28 lb
Maximum Bending Stress: From the moment diagram, the maximum moment is
Ma = 390.625 lb in. Applying the flexure formula,
Mc
390.625(0.25)
= 1562.5 psi = 1.56 ksi
Ans.
max
A (6)(0.5)
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