CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 11: Displacement Method of Analysis:...
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CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 11: Displacement Method of Analysis: Slope-Deflection Equations
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Transcript of CIVL3310 STRUCTURAL ANALYSIS Professor CC Chang Chapter 11: Displacement Method of Analysis:...
CIVL3310 STRUCTURAL ANALYSISProfessor CC Chang
Chapter 11: Displacement Method of Analysis: Slope-Deflection
Equations
Force vs Displacement Methods• Force methods
• Choose redundant forces• Use compatibility conditions or least work principle to solve these
redundant forces
• Displacement methods• Choose degrees of freedom (DOFs: displacement or rotation
angles)• Relate internal forces to DOFs• Use equilibrium to solve DOFs• Obtain internal forces from DOFs
By
qB
Degrees of Freedom (DOFs)• Nodes, members
(elements/components) and DOFs
qB
qB
Nodes MemberDOF
C
qCDC
Degrees of Freedom (DOFs)
Beam under Loading
A
A’
B
B’L
A B
A’
B’
MAB
MBA
Assume moment/rotation +
• Choose degrees of freedom• Relate internal forces to DOFs• Use equilibrium to solve DOFs• Obtain internal forces from DOFs
How do MAB & MBA relate to deformation at A & B?
Slope-Deflection RelationshipA B
A’
B’
MAB
MBA
A B
A’
B’
MAB1
MBA1
Moments to produce such a deformation
Moments to resist loads without extra deformation
A B
A’
B’
MAB2
MBA2
MAB1+MAB2MBA1+MBA2
From Table(Fixed end moments, FEM)
Slope-Deflection Relationship
A B
A’B’
MAB1
MBA1
AB
AB
L
D
• Choose degrees of freedom• Relate internal forces to DOFs• Use equilibrium to solve DOFs• Obtain internal forces from DOFs
Slope-Deflection Relationship
M111θ 12θ
EI6
LMθ
EI3
LMθ
112
111
M2
21θ
22θ EI6
LMθ
EI3
LMθ
212
222
EI6
LM
EI3
LMθθθ
EI6
LM
EI3
LMθθθ
1212222
2112111
M1
1θ
2θ
M2
+
=
212
211
θ2θL
EI2M
θθ2L
EI2M
MAB1
A B
A’
B’
MBA1
AB
AB
L
D
ABBAABBABA2
ABBAABBABA1
ψ3θ2θL
EI2ψθ2ψθ
L
EI2M
ψ3θθ2L
EI2ψθψθ2
L
EI2M
M1 1θ
2θM2
ABψ
ABψ
A’
B’
Aθ
Bθ
ABBA1BA
ABBA1AB
ψ3θ2θL
EI2M
ψ3θθ2L
EI2M
Slope-Deflection Relationship
Moments to produce such a deformation
Moments to resist loads without extra deformation
A B
A’
B’
MAB2
MBA2
MAB1+MAB2 MBA1+MBA2
A B
A’
B’
MAB1
MBA1
ABBA1BA
ABBA1AB
ψ3θ2θL
EI2M
ψ3θθ2L
EI2M
From Table(Fixed end moments, FEM)
A B
A’
B’
MAB
MBA
Slope-Deflection Relationship
A B
A’B’
MAB
MBA
AB
AB
L
D
A
A’
B
B’L
BAABBABA
ABABBAAB
FEMψ3θ2θL
EI2M
FEMψ3θθ2L
EI2M
L
Δ=moment/rotation +
• Choose degrees of freedom• Relate internal forces to DOFs• Use equilibrium to solve DOFs• Obtain internal forces from DOFs
