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Mechanical Engineering
Date
Apr 3, 2024
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10
Uploaded by truongpha212
3/28/23, 9:53 PM
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1.
Award: 0 out of 10.00 points
Three wooden beams and two steel plates are securely bolted together to form the composite member shown. Using
the data given in the table, determine the largest permissible bending moment when the member is bent about a
horizontal axis. Take x = 9 in.
The largest permissible bending moment when the member is bent about a horizontal axis is 357.8
kip·in.
References
Numeric
Response
Difficulty: Medium
Three wooden beams and two steel plates are securely bolted together to form the composite member shown. Using
the data given in the table, determine the largest permissible bending moment when the member is bent about a
horizontal axis. Take x = 9 in.
3/28/23, 9:53 PM
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3/11
The largest permissible bending moment when the member is bent about a horizontal axis is 271.3966 ± 5%
kip·in.
Explanation:
Use wood as the reference material.
For wood,
For steel,
Designate steel as 1 and wood as 2.
For the transformed section,
For wood,
For steel,
3/28/23, 9:53 PM
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Choose the smaller value.
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5/11
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A copper strip (
E
c
= 105 GPa) and an aluminum strip (
E
a
= 75 GPa) are bonded together to form the composite beam
shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N·m, determine the
maximum stress in the aluminum strip and in the copper strip.
The maximum compressive stress in the aluminum strip is n/r
MPa (include a negative sign).
The maximum tensile stress in the copper strip is n/r
MPa.
References
Numeric
Response
Difficulty: Medium
A copper strip (
E
c
= 105 GPa) and an aluminum strip (
E
a
= 75 GPa) are bonded together to form the composite beam
shown. Knowing that the beam is bent about a horizontal axis by a couple of moment M = 35 N·m, determine the
maximum stress in the aluminum strip and in the copper strip.
The maximum compressive stress in the aluminum strip is -56 ± 5%
MPa (include a negative sign).
The maximum tensile stress in the copper strip is 66.4 ± 5%
MPa.
Explanation:
3/28/23, 9:53 PM
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6/11
Use aluminum as the reference material.
n
= 1.0 for aluminum.
n
= E
c
/
E
a
= 105 GPa/75 GPa = 1.4 for copper.
For the transformed section,
A
nA
1
144 mm
2
144 mm
2
9 mm
1296 mm
3
2
144 mm
2
201.6 mm
2
3 mm
604.8 mm
3
Σ
345.6 mm
2
1900.8 mm
3
is taken from the bottom section.
The neutral axis lies 5.50 mm above the bottom.
Aluminum:
Copper:
3/28/23, 9:53 PM
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7/11
A steel bar (
E
s
= 210 GPa) and an aluminum bar (
E
a
= 70 GPa) are bonded together to form the composite bar shown.
References
Section Break
Difficulty: Medium
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8/11
3.
Award: 0 out of 10.00 points
Determine the maximum stress in aluminum when the bar is bent about a horizontal axis, with M
= 64 N
⋅
m.
The maximum stress in aluminum is n/r
MPa.
References
Numeric
Response
Difficulty: Medium
Determine the maximum stress in aluminum when the bar is bent about a horizontal axis, with M
= 64 N
⋅
m.
The maximum stress in aluminum is 55.3277 ± 5%
MPa.
Explanation:
Use aluminum as the reference material.
For aluminum,
For steel,
For the transformed section, 1
and 2 are areas of aluminum and 3 is the area of steel.
A
, mm
2
nA
, mm
2
1
192
192
4
768
2
128
128
12
1536
3
64
192
12
2304
∑
512
4608
The neutral axis lies 9 mm above the bottom.
3/28/23, 9:53 PM
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For aluminum,
3/28/23, 9:53 PM
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10/11
4.
Award: 0 out of 10.00 points
Determine the maximum stress in steel when the bar is bent about a horizontal axis, with M
= 64 N
⋅
m.
The maximum stress in steel is −
n/r
MPa.
References
Numeric
Response
Difficulty: Medium
Determine the maximum stress in steel when the bar is bent about a horizontal axis, with M
= 64 N
⋅
m.
The maximum stress in steel is −
129.0979 ± 5%
MPa.
Explanation:
Use aluminum as the reference material.
For aluminum,
For steel,
For the transformed section, 1
and 2 are areas of aluminum and 3 is the area of steel.
A, mm
2
nA, mm
2
1
192
192
4
768
2
128
128
12
1536
3
64
192
12
2304
∑
512
4608
The neutral axis lies 9 mm above the bottom.
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11/11
For steel,
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