Text book for the mechanics of materials Static Equilibrium ・Static Equilibrium ・Reaction Force & Moment ・Equation of Equilibrium Note: Your feedback is welcome!

1. Static Equilibrium
1. Static Equilibrium
2. Reaction Force & Moment
3. Equation of Equilibrium
Goal
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2. Static Equilibrium
Force
No translation
Moment
No rotation
Staying at rest
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3. Equilibrium of Force
F1
F2
F3
F1 F2 F3+ + = 0
ΣFi
＝
i
0
Vector
Component
ΣFij
＝
i
0 ( j = x, y, z )
F1x + F2x + F3x = 0
F1y + F2y + F3y = 0
F1z + F2z + F3z = 0
F1
F1x
F1y
F1z
= F2
F2x
F2y
F2z
= F3
F3x
F3y
F3z
=
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4. Reaction Force
F
Constraint Constraint
R1
R2
N1
Constraints may derive Reaction force
x
y
Up & Down
left& Right
Up & Down
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5. Equation of Equilibrium of Force ?
F
R1
R2
N1
x
y
x component y component
R1 + R2 + ( -F ) = 0
Note: positive or negative direction
N1 = 0
R1 + R2 - F = 0
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6. Equilibrium of Moment
M1
M3
M2
M1 M2 M3+ + = 0
ΣMi
＝
i
0
Vector
Component
M1x + M2x + M3x = 0
M1y + M2y + M3y = 0
M1z + M2z + M3z = 0
ΣMij＝
i
0 ( j = x, y, z )
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7. Reaction Moment
x
y
F
R1
Axis
N1
M1
r
rF
Constraint
left& Right
Up & Down
Rotation
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8. Equilibrium Equation of Moment？
F
R1
Axis
N1
M1
r
rF
M1 + ( -rF ) = 0
rFM1 - = 0 8/9

9. Summary
1. Static Equilibrium
2. Reaction Force
3. Equation of Equilibrium
Staying at rest
Constraints may derive
Reaction force
ΣMi
＝
i
0ΣFi
＝
i
0
No rotationNo translation
Constraint
left& Right
Up & Down
Rotation
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Force Moment