The lecture is in support of: (1) The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016: chapter 4. (2) Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller: chapter 13.

1. LATERAL STABILITY OF
STRUCTURES
including SAP2000
Prof. Wolfgang Schueller

2. For SAP2000 problem solutions refer to “Wolfgang Schueller: Building
Support Structures – examples model files”:
https://wiki.csiamerica.com/display/sap2000/Wolfgang+Schueller%3A+Build
ing+Support+Structures+-
See also,
Building Support Structures, Analysis and Design with SAP2000 Software,
2nd ed., eBook by Wolfgang Schueller, 2015.
The SAP2000V15 Examples and Problems SDB files are available on
the Computers & Structures, Inc. (CSI) website:
http://www.csiamerica.com/go/schueller
If you do not have the SAP2000 program get it from CSI. Students should request technical support from their professors, who can contact CSI if necessary, to obtain the latest lim
If you do not have the SAP2000 program get it from CSI. Students should request technical
support from their professors, who can contact CSI if necessary, to obtain the latest limited capacity (100
nodes) student version demo for SAP2000; CSI does not provide technical support directly to students.
The reader may also be interested in the Eval uation version of SAP2000; there is no capacity limitation,
but one cannot print or export/import from it and it cannot be read in the commercial version.
(http://www.csiamerica.com/support/downloads)

3. The Leaning Tower of
Pisa (54 m), Italy, 1174

4. LATERAL STABILITY

5. The primary lateral loads are caused by wind pressure
and seismic excitation. However, lateral loads may also
be generated by lateral soil pressure and liquid pressure as
well as by gravity loads in cantilevering structures and
irregular structures.

6. Wind pressure distribution as related to ordinary building shapes

7. WIND
PRESSURE

9. Seismic force action

10. Fig. 2.6 USGS National Seismic Hazard Map (courtesy of the U.S. Geological Survey)
Fig. 2.6 USGS National Seismic Hazard Map (courtesy of the U.S. Geological Survey)

11. EFFECT OF BUILDING FORM ON WIND AND SEISMIC
LOAD DISTRIBUTION

12. A typical building can be visualized as consisting of
HORIZONTAL PLANES or floors and roofs, as well as the
supporting
VERTICAL PLANES of walls and/or frames
The horizontal planes tie the vertical planes together to
achieve a box effect. In other words, floors act as
diaphragms that connect the walls or frames in two layers.

13. The Vertical and Horizontal Building Planes

14. Shear-wall frame

15. BUILDING STRUCTURES
• GRAVITY STRUCTURES
• LATERAL-FORCE RESISTING STRUCTURES
• NON-LOADBEARING STRUCTURES

16. The Behavior of Building Structure
Every building consists of the load-bearing structure and the non-load-bearing structure.
• The main load-bearing structure, in turn, is subdivided into the
gravity load resisting structure, which carries primarily gravity loads
lateral load resisting structure, which supports gravity and lateral loads, hence
must also provide lateral stability to the building.
For the condition, where the lateral bracing only resists lateral forces, but does not
carry gravity loads with the exception of its own weight, it is considered a
secondary structure.
• The non-load-bearing structure includes the curtains, ceilings, and
partitions that cover the structure and subdivide the space.

17. THE LATERAL LOAD RESISTING
STRUCTURE
The lateral-load resisting structure of a building can be subdivided into vertical
and horizontal structure subsystems.
Vertical lateral-force resisting structure systems typically act like large
cantilevers spanning vertically out of the ground. Common vertical structure
systems that are frameworks and walls.
The horizontal structure systems. called diaphragms, resist horizontal
forces induced by wind or earthquake and transfer these forces to the vertical
systems, which then take the forces to the ground. DIAPHRAGMS are like
large beams (usually horizontal beams). Diaphragms typically act like large
simply supported beams spanning between vertical systems.

18. Vertical Lateral-Force Resisting Structure Types
The primary lateral loads are caused by wind pressure and seismic
excitation. However, lateral loads also may be generated by lateral soil
pressure and liquid pressure, as well as by gravity loads in cantilevering
structures and irregular structures. These loads are resisted by the vertical
lateral-force resisting structures, which can be of the following typical
types:
Moment-resisting frames
Braced frames (concentrically, eccentrically, buckling restrained)
Shear walls
Combination of above, e.g. Dual systems, e.g., shear wall + frames
Of these structure systems, the frame is the most flexible structure. It is quite
apparent that bracing the flexible rigid frame results in extensive reduction of
the lateral building sway. A frame braced by trussing or shear walls is a
relatively stiff structure compared to the frame, where the lateral deflection
depends on the rigidity of beam-column and slab joints.

19. Braced Frames have much better strength and stiffness. Bracing is a much
effective than rigid joints at resisting racking deformation of the frame. Efficient and
economical braced frames use less material and have simpler connections than
moment-resisting frames. Compact braced frames can lead to lower floor-to-floor
heights, which can be an important economic factor in tall buildings, or in a region
where there are height limits. Visual braces can be used as a strong visual element.
Obstructive. Braces can interfere with architectural requirements for doors, windows,
and open floor area. Braced frames have low ductility characteristics under cyclic
loading, which is important for seismic design. Brace buckling is not a good energy
dissipation mechanism (not such bad news for wind design).
Moment Frames provide a great deal of flexibility in planning: no braces. They can
have good ductility, if detailed properly (Special Moment Resisting Space Frame =
SMRF = "smurf"). The performance is very sensitive to the detailing and workmanship
at connections. The bad aspect of moment frames are expensive lots of material
plus labor-intensive connections. Low stiffness (large deflections) can lead to high
non-structural damage in earthquakes (i.e. undamaged structure will all glass broken
and finishes cracked). The 1994 Northridge earthquake revealed unforeseen problems
with conventional details and weld procedures.
Eccentric Braced Frames combine properties of moment and braced frames;
braces provide stiffness in elastic range, links control strength and provide ductility.

20. The classification for common high-rise building structure systems is as follows, taking into account special
framing types when ductility considerations for seismic design must be considered:
BEARING WALL SYSTEMS
Reinforced or plain concrete shear walls (ordinary, special)
Reinforced or plain masonry shear walls (ordinary, special)
Light frame walls with shear panels
Steel-braced frames in light frame construction
Prestressed masonry shear walls (ordinary, special)
etc.
BUILDING FRAME SYSTEMS
Steel eccentrically braced frames with moment or hinged beam-column connections
Concentrically braced frames (ordinary, special)
Reinforced or plain concrete shear walls (ordinary, special)
Composite eccentrically braced frames
Ordinary composite braced frames
Composite steel plate shear walls
Light frame walls with shear panels
Reinforced or plain masonry shear walls (ordinary, special)
Prestressed masonry shear walls (ordinary, special)
etc.
MOMENT-RESISTING FRAME SYSTEMS
Steel moment frames (ordinary, special)
Reinforced concrete moment frames (special, ordinary)
Composite moment frames (ordinary, special)
Composite partially restrained moment frames
Special steel truss moment frames
Masonry wall frames
etc.
DUAL SYSTEMS WITH MOMENT FRAMES
Combination of the above
INVERTED PENDULUM SYSTEMS
Cantilevered column systems
Steel moment frames (ordinary, special)
Special reinforced concrete moment frames

21. VERTICAL BUILDING STRUCTURE SYSTEMS

22. Structure systems

23. Vertical force flow

24. BUILDING RESPONSE TO LATERAL FORCE ACTION

25. Vertical lateral-force
resisting structure systems

26. hx
LUMPED
MASS
MODEL
LINEAR APPROXIMATION
OF FIRST THREE MODES
OF VIBRATION
ACTUAL
Fx
Wx
H = hn
D
V
H/3
H/3
H/3
H/5
H/5
H/5
H/5
H/5
1st 2nd 3rd
V
STORY SHEARS
Vx
Equivalent lateral seismic load distribution

27. THE EFFECT OF SEISMIC INTENSITY

28. Diaphragm Action of Floor and Roof Planes
The lateral forces are delivered as story forces at each floor
level and are transmitted along the horizontal floor planes and
horizontal or inclined roof planes, which act as deep beams,
called diaphragms that span between the vertical structure
systems. As the lateral wind forces strike the building façade,
curtain panels are assumed to act similar to one-way slabs
spanning vertically between the floor spandrel beams, from
where the lateral loads, in turn, are carried along the floor
diaphragms and distributed to the vertical structure systems.
Similarly, the seismic base shear is considered to be
distributed as story forces at each floor level.

29. Typical diaphragms are as follows:
Concrete slabs
Precast concrete floor planks with concrete topping
Metal decking with concrete fill
Ring beams, horizontal framing (e.g., in masonry construction)
Roof sheathing (e.g., double-layer plywood or diagonal boarding in wood
construction)
Trussing (e.g., for roofs in wood and steel construction)
The behavior of the diaphragms depends on the layout of the vertical
lateral-force resisting structures, which can take many different forms:
In a symmetrical building with regular arrangement of vertical structures,
where the line of action of the resultant of the applied lateral loads passes
through the center of resistance, the structure deflects equally in a purely
translational manner.
Asymmetry in buildings is caused by geometry, stiffness, and mass
distribution; here, the applied resultant lateral load does not act through the
center of resistance. The floor diaphragms not only translate, but also
rotate in the direction of the lateral load action.

30. DIAPHRAGM ACTION OF TYPICAL HORIZONTAL BUILDING PLANES
The horizontal forces are transmitted along the floor and roof planes, which act as deep
beams, called diaphragms that span between the vertical lateral-force-resisting
structures as indicated in the next slide. As the lateral wind forces strike the building
façade, curtain panels are assumed to act similar to one-way slabs spanning vertically
between the floor spandrel beams, from where the lateral loads, in turn, are carried
along the floor diaphragms and distributed to the lateral-force resisting structural
systems.
The layout of the vertical lateral-force resisting systems can take many different forms,
(see next slide) varying from symmetrical to asymmetrical arrangements, or range from
a minimum of three planar structures to a maximum of a cellular wall subdivision as for
bearing wall apartment buildings. The resisting system may be located within the
building as a single spatial core unit or as separate planes.
In a symmetrical building with regular arrangement of vertical structures, where the
line of action of the resultant of the applied loads passes through the center of
resistance, the structure deflects equally in a purely translational manner.
Asymmetry in buildings is caused by geometry (e.g. Fig. 11.1B), stiffness, and mass
distribution; here, the applied resultant load does not act through the center of
resistance. The floor diaphragms not only translate, but also rotate in the
direction of the lateral load action.

31. a. b.
The lateral force distribution depends not only on the location
of the resisting structures in the building but also on the
stiffness of the diaphragms as related to the stiffness of the
vertical structure systems. Diaphragms are classified as:
flexible, rigid, or semi-rigid.

33. DIAPHRAGM ACTION OF ROOF

34. EXAMPLE OF ROOF DIAPHRAGM ACTION

35. Tekla Xsteel bracing

42. HORIZONTAL FORCE FLOW

43. BASIC VERTICAL LATERAL FORCE RESISTING
STRUCTURE TYPES

44. Effect of structure type on cantilever action

45. Of these structure systems is the frame the most flexible structure. It is quite apparent from
that bracing the flexible rigid frame results in extensive reduction of the lateral building sway.
A frame braced by trussing or shear walls is a relatively stiff structure as compared to the
frame, where the lateral deflection depends on the rigidity of beam-column and slab joints.

46. Rigid Frame Shear Core Interaction

47. The Building Response to Load Action

48. • RIGID DIAPRAGMS: rigid diaphragm action can be modeled by using,
Rigid plane with constraints of floor joints
Rigid floor membranes
RIGID MEMBRANE can be approximated for typical concrete floor slabs and concrete-topped steel deck where
the diaphragm is significantly stiffer than the vertical lateral-force resisting structure such as for frame
construction.
.
DIAGONAL BRACING of floor framing provides a large stiffness in plane of the diaphragm.
• FLEXIBLE DIAPHRAGM MEMBRANES
In a wall building with parallel floor diaphragms, the concrete floor diaphragms behave as deformable
membranes and not as rigid floors; notice how the flexible diaphragm action of the roof is expressed by the
deformed structure.
Flexible diaphragm action also applies to plywood diaphragms, where the diaphragm is very flexible relative to
the supporting vertical structure

49. The lateral force distribution does not only depend on the location of the resisting
structures in the building but also on their stiffness, as well as the stiffness of the
diaphragms. For the purpose of preliminary investigation, floor structures for
buildings are treated generally as rigid diaphragms with the exception of the
following situations, where they may be treated as flexible diaphragms for
preliminary design purposes.
• Closely spaced shear walls in relatively narrow buildings are stiffer in
comparison to the floor diaphragms.
• For low-rise buildings, the floor or roof diaphragms are often more flexible than
the supporting shear walls (e.g. light wood-framed construction).
• Floor diaphragms in long, narrow buildings with deep beam proportions of greater
than say 3:1 that span large distances across the building.
• Floor diaphragms that are weakened by cutouts and openings, unless they are
braced.
• Wood and metal deck (without concrete fill) roofs as well as prefabricated floor
systems without cast-in-place topping are to be treated as flexible, unless the
diaphragm is braced to allow truss action.

52. Relative Stiffness of diaphragm and vertical elements

53. Modeling Diaphragms using SAP2000
General modeling of buildings:
•Columns and beams are modeled by using frame objects.
•Slabs are modeled by using shell objects.
•Shear walls can be modeled by using one planar membrane object per wall bay when stresses are not
investigated.
Diaphragm action can be modeled as follows:
•Conceptual rigid diaphragm forming a rigid plane: a diaphragm constraint causes all of its constrained
joints to move together as a planar diaphragm (i.e., truly rigid membrane) preventing in-plane relative
displacements of the nodes at each floor. In other words, all constrained joints are connected to each other by
links that are rigid in the plane, but do not affect out-of-plane (plate) bending. All floor beams are absorbed
into the stiffness of the rigid plane. Concrete floors or concrete-filled decks typically are modeled using
diaphragm constraints. Use the following steps in SAP2000:
•Define > Joint Constraints > Choose Constraint Type to Add: select Diaphragm > click Add New Constraint
button > name DIAPH1 > select Constraint Axis: Z-Axis > click OK.
•Select the floor joints to be constrained > Assign > Joint > Constraints > select, e.g., DIAPH1 > click OK.
•Model concrete slabs (or concrete-filled decks) using shell objects. If the slab panel is used only as a
diaphragm for lateral force analysis, it is sufficient to use one membrane object per slab panel to model the
in-plane stiffness since only overall deformation is of interest and not the magnitude of the stresses along the
concrete slab. The membrane action of typical concrete floor slabs and concrete-topped steel decks is close
to the ideal behavior of rigid membranes, where the diaphragm is generally significantly stiffer than the
vertical lateral-force resisting rigid frame construction.
•Weightless rigid diagonal bracing (connected at column nodes) of floor framing in a 3D frame model
provides a large stiffness in the plane of the diaphragm..
•Model plywood diaphragms, where the diaphragm is very flexible relative to the supporting vertical
structure.

54. 16'20'
12'
P = 1 k
P = 1 k
ab
c d
e
f
g
h
x
y
Braced Building Core – Axial Force Flow caused by lateral forces

55. ARRANGEMENT OF LATERAL FORCE RESISTING STRUCTURES
a.
b.
c.
d.
e.
f.
g.
h.
e
P
a
a
P
P/2P/2
P
P/2 P/2
P
P
e
b
Mt/b = Pe/b

56. 15'
25' 25'
20'
20'
20'
a.
b. c. d.
EXAMPLE: 13.1

57. Y
X
7.5 k
WALL B
WALL C
1.88 k
3.13 k
1.88 k
3.13 k
1.88 k (T)
3.64 k (C)
25'
15'
5
3
EXAMPLE: 13.1, case (a)

58. Rxa = Rxb = 015(60)/2 = 4.50 k

60. Rya = 0.15(50) = 7.50 k
ΣMa = 0 = 7.5(25) – Rxa(60)
Rxb= 3.125 k
Rxa= 3.125 k

69. Lateral deflection of solid walls

70. (1) Fig. 4.19 Lateral deflection of walls with openings, Fig. 4.20 Example 4.6

72. Ry ≈ 0.15(50)/3 = 2.50 k

76. (1) Fig. 4.21 Fig. 4.22 Example 4.7

77. Bracing the frame with a shear wall,
notice the effect of the wall opening
(ref: Dr Frame)

78. rigid vs. flexible diaphragm action vs. indeterminate force distribution

79. (1) Fig. 4.26 Example 4.11 and 4.12

81. torsion caused by eccentric core

90. Asymmetrically arranged lateral force resisting system

91. Example 13.6: Two-story rigid frame structure

93. 120/2=60'
2(120)/3=80'
H=10SP@12'=120'
Fx
hx
h7=70'
F7
F1
w10F10
37 k
60 k
3 SP @ 20 = 60'
W
wx
w7
V
Multi-Bay, Multi-Story Rigid Frame

94. RIGID FRAME - SHEAR
WALL INTERACTION

95. CONCRETE FRAME - SHEAR
WALL INTERACTION

96. HINGED STEEL FRAME
BRACED BY CONCRETE
SHEAR WALL

99. Lateral stability of buildings

100. STEPHEN P CLARK
GOVERNMENT
CENTER, Miami, FL,
1985, Hugh Stubbins
and Assoc. Arch,
LeMessurier Assoc.
Struct. Eng.

101. Proposal for the new World Trade Center in New York (2002), Rafael Vinoly

102. ilding (6 stories), San
o, 1967, SOM
Alcoa Building, San
Francisco, 1967, SOM

103. Turmhaus am Kant-Dreieck mit
Wetterfahne aus Blech, Berlin,
Josef Paul Kleinhues, 1994

104. Chulalongkorn University, Bangkok, Thailand

105. Taoyuan 02 Graduate Student
Dormitory, Nanjing University,
Nanjing, 2008, Zhang Lei Arch

106. House (World War 2 bunker),
Aachen, Germany

107. Triangle building,
Friedrichstr/ Mauerstr.
Berlin, 1996, Josef Paul
Kleihues Arch

108. Duesseldorf City Gate,
Duesseldorf, Germany, 1997,
H. Petzinka + Fink Arch

110. Seoul Broadcasting Center, Seoul, 2003, Richard Rogers Arch. And Buro Happold Struct. Eng

112. Samsung Jongno Tower, Seoul,
1999, Rafael Vinoly Arch

114. Broadgate Tower,
London, UK, 2009,
SOM Arch+Struct
Eng

115. Leadenhall Building, London, UK, 2014, Richard
Rogers Arch, Ove Arup Struct Eng

116. NEO Bankside, London, UK, 2013, Richard
Rogers Arch, Waterman Struct Eng

117. Dee and Charles Wyly
Theater, Dallas, 2009, Joshua
Prince-Ramus +Rem Koolhaas
Arch, Magnusson Klemencic
Struct Eng

121. Interdisciplinary Building,
Columbia University, New York,
2009, Rafael Moneo + Arup

124. Alan House, Los Angeles, 2007,
Neil Denari (NMDA) Arch

125. Market Bangkok, Thailand

127. Proposal for taz-Publisher, Berlin, Germany, 2017, Piet und Wim Eckert Arch

128. Fort School, Mumbai, India, 2005,
Chris Lee & Kapil Gupta

129. CDU-
Bundesgeschäftsstelle
Berlin, Berlin, Germany,
2000, Petzinka
Pink Architekten

130. Vertretung des Landes Nordrhein-
Westfalen beim Bund in Berlin,
2002, Petzinka Pink Arch

131. The two large one-bay frames at
each end of the building are
designed to resist the lateral
forces applied in the direction
indicated.

132. The Reliance Control
Electronic Plant,
Swindon, UK, 1966,
Team 4 (Foster/Rogers),
Tony Hunt Struct. Eng

133. Sainsbury Centre for Visual Arts, Norwich, UK, 1978,
Norman Foster Arch, Anthony Hunt Struct Eng

134. United Airlines Terminal at
O’Hare Airport, Chicago,
1987, H. Jahn Arch,
Lev Zetlin Struct Eng

138. Shenyang Taoxian
International Airport, 2001,
Huilai Yao architect

139. Toronto Pearson International Airport – Terminal 1,
Toronto, Canada, 2014, SOM/Adamson
Architects, ARUP/Yolles Struct. Eng.

140. Ningbo Air terminal

141. Cologne/Bonn Airport, Germany,
2000, Helmut Jahn Arch., Ove
Arup USA Struct. Eng

142. Beijing Airport, Terminal 2,1999

143. Hamburg Airport, Terminal
1, Hamburg, Germany,
2005, von Gerkan, Marg &
Partner Arch, Weber Poll,
Eggert Lohrmann Partner
Struct. Eng.

144. Arena Amazonia,
Manaus, Brazil, 2014,
von Gerkan Marg
Arch+Schlaich
Bergermann Struct Eng