Rigid Bodies and Supports 1
Lecture 5
A
ARCHITECTURAL STRUCTURES I:
STATICS AND STRENGTH OF MATERIALS
five
rigid body
equilibrium
lecture
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Rigid Body - Architectural Structures - Lecture Slides, Slides of Structural Design and Architecture
Rigid Body, Coplanar Force Systems, Free Body Diagram, External Forces, Force Reactions, External Moments, Moment Reactions, Internal Forces, Applied Forces, Relevant Geometry. Its lecture of Architectural Structures. A complete lecture series is in my files.
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2011/2012
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Rigid Bodies and Supports 1Lecture 5
A
ARCHITECTURAL
S^ TRUCTURES
I:
STATICS AND
STRENGTH OF
MATERIALS
lecture five rigid bodyequilibrium
Rigid Bodies and Supports 2Lecture 5
A
Equilibrium •^ rigid body^ –
doesn’t deform – coplanar force systems
-^ static:
C^ A
B
(^0) =
=^ ∑
x
x^
F R
(^0) =
=^ ∑
y
y^
F R
(^0) =
=^ ∑
M M
Free Body Diagram •^ determine body •^ FREE it from:^ – Rigid Bodies and Supports 4Lecture 5
ground – supports & connections
-^ draw all external forcesacting ON the body^ –
reactions – applied forces – gravity
100 lb + weight 100 lb^ m⋅g
Rigid Bodies and Supports 5Lecture 5
A
Free Body Diagram •^ include relevant geometry^ –
guidelines helpful to see moment arms
-^ name and/or color the unknown^ –
forces – moments – angles
-^ solve up to 3 equations
- Supports and ConnectionsRigid Bodies and Supports 7Lecture
Rigid Bodies and Supports 8Lecture 5
A
Supports and Connections
Rigid Bodies and Supports 10Lecture 5
A
Moment Equations •^ sum moments at intersection where themost forces intersect •^ multiple moment equations may not beuseful •^ combos:
0 F=x^ ∑
0 F=y^ ∑
0 M^ =∑^1
(^0) F = ∑^
0 M=^1 ∑
0 M^ =∑^2
0 M=^1 ∑
0 M^ =^2 ∑
0 M^ =∑^3
Recognizing Reactions Rigid Bodies and Supports 11Lecture 5
F^
F unknowns
weight^
m⋅g^
3 unknowns
Constraints •^ completely constrained^ – Rigid Bodies and Supports 13Lecture 5
doesn’t move – may not be statically determinate
-^ improperly or partially constrained^ –
has
≤^ unknowns
-^ can’t solve
Constraints •^ overconstrained^ – Rigid Bodies and Supports 14Lecture 5
won’t move – can’t be solved with statics – statically indeterminate to n
th^ degree A
C
B
200 lb-ft 60 lb 55 °
A 5’^
C
B
200 lb-ft 60 lb 55 °
Ax
Ay^
Cy
MRA
Rigid Bodies and Supports 16Lecture 5
A
Two Force Rigid Bodies •^ equilibrium:^ –
forces in line, equal and opposite^ A
B^
C
A F 2
F B
1 d^
A
F^2
F B
1 d^
A F 2
F^1 B
α
Rigid Bodies and Supports 17Lecture 5
A
Three Force Rigid Bodies •^ equilibrium:^ –
concurrent or parallel forces
A^
B^
C
F^1
F^2
A
B C
F^3
F^2
A F 1
F^3 Bd^1 Cd^2
F^2
A F 1
B C
F^3 α