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S2009abnPinned Frames 1Lecture 10
Elements of Architectural StructuresARCH 614
ELEMENTS OF ARCHITECTURAL STRUCTURES:
FORM, BEHAVIOR, AND DESIGN
ARCH 614
DR. ANNE NICHOLS
SPRING 2015
ten
other beams &
pinned frames
lecture
Pinned Frames 2
Lecture 10
Elements of Architectural Structures
ARCH 614
S2007abn
Continuous Beams
• statically indeterminate
• reduced moments than simple beam
Pinned Frames 3
Lecture 10
Elements of Architectural Structures
ARCH 614
S2007abn
Continuous Beams
• loading pattern affects
– moments & deflection
max∆
Pinned Frames 4
Lecture 10
Elements of Architectural Structures
ARCH 614
S2007abn
Continuous Beams
max∆
• unload end span
2
Pinned Frames 5
Lecture 10
Elements of Architectural Structures
ARCH 614
S2007abn
Continuous Beams
• unload middle span
max∆
Pinned Frames 6Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Moment Redistribution
• continuous slabs & beams with uniform
loading
– joints similar to fixed ends, but can rotate
• change in moment to center =
– Mmax for simply supported beam 8
2wL
S2007abnPinned Frames 7
Lecture 10
Elements of Architectural Structures
ARCH 614
Moment Distribution (a)
• no load
http:// nisee.berkeley.edu/godden
S2007abnPinned Frames 8
Lecture 10
Elements of Architectural Structures
ARCH 614
Moment Distribution (b)
• add load
http:// nisee.berkeley.edu/godden
3
S2007abnPinned Frames 9
Lecture 10
Elements of Architectural Structures
ARCH 614
Moment Distribution Method (c)
• release joint 2
http:// nisee.berkeley.edu/godden
S2007abnPinned Frames 10
Lecture 10
Elements of Architectural Structures
ARCH 614
Moment Distribution Method (d)
• release joint 3
http:// nisee.berkeley.edu/godden
S2007abnPinned Frames 11
Lecture 10
Elements of Architectural Structures
ARCH 614
Moment Distribution Method (e)
• exposure of final shape after cycles over initial shape
http:// nisee.berkeley.edu/godden
Pinned Frames 12
Lecture 10
Elements of Architectural Structures
ARCH 614
S2007abn
Analysis Methods
• Approximate Methods
– location of inflection points
• Force Method
– forces are unknowns
• Displacement Method
– displacements are unknowns
4
Pinned Frames 13Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Theorem of Three Moments
• moments at three adjacent supports
(2 spans)
• distributed load and same I:
• concentrated loads and same I:
( )44
23
22
3
112321211
LwLwLMLLMLM −−=+++
( ) =+++ 2321211 2 LMLLMLM
( ) ( )∑∑ −−−−3
22
2
22
3
11
2
11 nnLPnnLP
Pinned Frames 14Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Two Span Beams & Charts
• equal spans & symmetrical loading
• middle support as flat slope
Pinned Frames 15Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Pinned Frames
• structures with at least one 3 force body
• connected with pins
• reactions are equal and opposite
– non-rigid – rigid
Pinned Frames 16Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Rigid Frames
• rigid frames have no pins
• frame is all one body
• typically statically indeterminate
• types– portal
– gable
5
Pinned Frames 17Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Rigid Frames with PINS
• frame pieces with connecting pins
• not necessarily symmetrical
Pinned Frames 18Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Internal Pin Connections
• statically determinant
– 3 equations per body
– 2 reactions per pin + support forces
A
B
C
D
G
E F
Ax
Ay D
S2007abnPinned Frames 19
Lecture 10
Elements of Architectural Structures
ARCH 614
Arches
• ancient
• traditional shape tospan long distances
Packhorse Bridge, UK
Roman AquaductsRainbow Bridge National Monument
S2007abnPinned Frames 20
Lecture 10
Elements of Architectural Structures
ARCH 614
Arches
• primarily sees compression
• a brick “likes an arch”
6
Pinned Frames 21Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Arches
• behavior
– thrust related
to height to width
Pinned Frames 22Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Three-Hinged Arch
• statically determinant
– 2 bodies, 6 equilibrium equations
– 4 support, 2 pin reactions (= 6)
S2007abnPinned Frames 23Lecture 10
Elements of Architectural StructuresARCH 614
Beams with Internal Pins
• statically determinant when
– 3 equilibrium equations per link =>
– total of support & pin reactions(properly constrained)
• zero moment at pins
F1 F2 F1F2
not independent
R1x
R1y
MR1
R3
(internal) pin R2yR2y
R2xR2x
Pinned Frames 24Lecture 10
Elements of Architectural StructuresARCH 614
S2007abn
Procedure
• solve for all support forces you can
• draw a FBD of each member
– pins are integral with member
– pins with loads should belong to 3+ force
bodies
– pin forces are equal and opposite on
connecting bodies
– identify 2 force bodies vs. 3+ force bodies
– use all equilibrium equations