Chapter 8 Internal Forces in Structural Memberscac542/L18.pdf1 MEM202 Engineering Mechanics -...
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1 MEM202 Engineering Mechanics - Statics MEM Chapter 8 Internal Forces in Structural Members • Axial Force and Torque in Bars and Shafts • Axial Force, Shear Force, and Bending Moments in Multiforce Members
Transcript of Chapter 8 Internal Forces in Structural Memberscac542/L18.pdf1 MEM202 Engineering Mechanics -...
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MEM202 Engineering Mechanics - Statics MEM
Chapter 8 Internal Forces in Structural Members
• Axial Force and Torque in Bars and Shafts
• Axial Force, Shear Force, and Bending Moments in MultiforceMembers
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in A General 3-D Body
0=∑Fr
0=∑Fr
0=∑Fr
0=∑Fr
0=∑Fr
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural Members
x
y
z
xF( )xMT =
zV
yV
yMzM
( )
axis-about moment Bending:aixs-about moment Bending:
Torque :direction- in forceShear :direction- in forceShear :direction)- (in force Axial :
zMyM
MTzVyVxF
z
y
x
z
y
x
=
FV
M T
3-D
Torque :moment Bending:
forceShear :force Axial :
TMVF
2-D
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersAxial Forces
P P2
P
P
PF =
PF 2=
P
P
P
P P
P
P
PF =
PF =
PP2P2
PP
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersAxial Forces
N 10
N 10=ABF
N 15=BCF
N 10
N7N5 N 8
N 7=CDF
N 10
N 10
N 10
N5
N5 N 8
N 10N 15 N 15
N7 N7
A B C D
A B C D
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersAxial Forces
N 10
N 10=ABF
N 5−=BCF
N 10
N 3N 15 N 8
N 3=CDF
N 10
N 10
N 10
N 15
N 15 N 8
N 10
N5−
N 3 N 3
A B C D
AB C
DN5−
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersTorque
mN 10 ⋅
mN 10 ⋅=ABT
mN 5 ⋅−=BCT
mN 10 ⋅
mN 3 ⋅mN 15 ⋅ mN 8 ⋅
mN 3 ⋅=CDT
mN 15 ⋅
mN 15 ⋅ mN 8 ⋅
mN 10 ⋅
mN5 ⋅−
mN 3 ⋅
A B C D
AB C
DmN5 ⋅−
=
mN 10 ⋅
mN 10 ⋅
mN 10 ⋅
mN 3 ⋅
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersF, V, and M in Multiforce Members
Example 8-3 FBD of member ABC
( ) ( )( ) 050055
0500sin
0cos
=−−=
=−+=
=−=
∑∑∑
yB
BDyy
BDxx
AM
FAF
FAF
θ
θ
Internal forces at cross section a-a.
lb 8.1600lb 500lb 1250 === BDyx FAA
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersF, V, and M in Multiforce Members
a
a
( )( ) 05002
0500
01250
=−=
=+−=
=−=
∑∑∑
− MM
VF
PF
aa
y
x
lb-ft 1000lb 500lb 1250
===
MVP
( )( ) ( )( ) 05008sin8.16003
0500sin8.1600
0cos8.1600
=−+=
=−+−=
=−=
∑∑∑
− θ
θ
θ
MM
VF
PF
aa
y
x
lb-ft 1000lb 500lb 1250
===
MVP
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersF, V, and M in Multiforce Members
a
a
( )( ) 0500
0500
01250
=+=
=−−=
=+=
∑∑∑
− xaa
xy
xx
MxM
VF
FF
lb-ft 500lb 500
lb 1250
xMVF
x
x
x
−=−=−=
( )( ) ( )( ) 066.38sin8.16005500
066.38sin8.1600500
066.38cos8.16001250
=+−−=
=−+−=
=+−=
∑∑∑
− xbb
xy
xx
MxxM
VF
FF
o
o
o
xxF
xV
xM
xF
xV
xM
b
b
a
a
( ) lb-ft 5000500lb 500
lb 0
−===
xMVF
x
x
x
lb 0.500
lb 0.1250
lb 8.1600o66.38
b
b
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersF, V, and M in Multiforce Members
( ) lb-ft 5000500 lb, 500 lb, 0 :105For lb-ft 500 lb, 500 lb, 1250 :50For
−===≤≤−=−=−=≤≤
xMVFxxMVFx
xxx
xxx
x
lb 1250−
lb 500−
lb 500
lb 1250−
lb 500
lb 500−
lb-ft 2500−
Axial Force
Shear Force
Bending Moment
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MEM202 Engineering Mechanics - Statics MEM
Internal Forces in Structural MembersF, V, and M in Multiforce Members
lb 0770 =⇒=∑ DF FM
Example 8-5 Internal forces at a-a and b-b.
E
D Xb
YbMb
F.B.D. for member EDF
Section a-a Section b-b
D
