S2013abn Load Tracing 1 Lecture 14 Architectural Structures ARCH 331
fourteen
system assemblies
& load tracing
lecture
reed.tamu.edu
A
RCHITECTURAL
S
TRUCTURES
:
F
ORM,
B
EHAVIOR, AND
D
ESIGN
A
RCH 331
HÜDAVERDİ TOZAN
Structural Loads
• gravity acts on mass (F=m*g)
• force of mass
– acts at a point
• ie. joist on beam
– acts along a “line”
• ie. floor on a beam
– acts over an area
• ie. people, books,
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Concentrated Loads
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Architectural Structures ARCH 331
Equivalent Force Systems
• replace forces by resultant
• place resultant where M = 0
• using calculus and area centroids
dx
w(x)
x
L
loading
loading
L
0
wdx
dA
A
W
dx
y
x
elx
Area Centroids
• Table 7.1 – pg. 242
b h3
b
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Lecture 14
Architectural Structures ARCH 331
Equivalent Load Areas
• area is width x “height” of load
• w is load per unit length
• W is total load
x
x/2
W
x/2
x
2x/3
W/2
x/3
x
x/2
W
x/6 x/3
W/2
0
W
x
w
w
w
2
2
W
x
w
w
2w
Distributed Area Loads
• w is also load per unit area
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Load Tracing
• how loads are
transferred
– usually starts at top
– distributed by
supports as actions
– distributed by
Load Tracing
• areas see distributed
area load
• beams or trusses
see distributed line
loads
• “collectors” see
forces
– columns
– supports
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Load Tracing
tributary area
Load Tracing
• tributary load
– think of water flow
– “concentrates” load of
area into center
tributary
width
area
load
w
width
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Load Tracing
Patcenter
Rogers 1986
www.columbia.eduLoad Tracing
Alamillo Bridge
Calatrava 1992
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Load Paths
Load Paths
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Load Paths
Load Paths
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Load Paths
• deep foundations
Spans
• direction
• depth
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Levels
• determine span at top level
• find half way to next element
• *include self weight
• look for “collectors”
• repeat
Levels
• two:
S2013abn
Irregular Configurations
• tracing still ½ each side
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Architectural Structures ARCH 331
Slabs
• edge support
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Lecture 14
Architectural Structures ARCH 331
Girders and Transfer
• openings
– no load & no half way
• girder actions at beam supports
+
+
+
Sloped Beams
• stairs & roofs
• projected live load
• dead load over length
• perpendicular load to beam:
• equivalent distributed load:
c o s
w
w
w
w
adj
.
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Framing Diagrams
• beam lines and “dots”
• breaks & ends
Load Tracing 27 Lecture 14
Architectural Structures ARCH 331
• purpose
– retain soil or other material
• basic parts
– wall & base
– additional parts
• counterfort
• buttress
• key
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Architectural Structures ARCH 331
Retaining Wall Types
• “gravity” wall
– usually unreinforced
– economical & simple
• cantilever retaining wall
Retaining Wall Loads
• gravity
W =
V
• fluid pressure
p =
’
h
P = ½ p h at h/3
• friction
F =
N
• soil bearing pressure, q
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Architectural Structures ARCH 331
Retaining Wall Equilibrium
• sliding - overcome friction?
• overturning at toe (o) - overcome mass?
o
P
R
W
1
5
2
g
overturnin
.
M
M
SF
resist
2
25
1
.
F
F
SF
sliding
resist
horizontal
F
resist
• want resultant of load from pressure inside
the middle third of base (kern)
• triangular stress block with p
max
• x = 1/3 x width of stress
• equivalent force location:
Pressure Distribution
3
2
3
x
x
p
x
W
max
a
W
x
W
p
max
2
3
2
a
x
when a is
fully stressed
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