LATERAL STABILITY OF

STRUCTURES including SAP2000

Prof. Wolfgang Schueller

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 limit

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)

The Leaning Tower of

Pisa (54 m), Italy, 1174

LATERAL STABILITY

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.

Wind pressure distribution as related to ordinary building shapes

WIND

PRESSURE

Seismic force action

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)

EFFECT OF BUILDING FORM ON WIND AND SEISMIC

LOAD DISTRIBUTION

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.

The Vertical and Horizontal Building Planes

Shear-wall frame

BUILDING STRUCTURES

• GRAVITY STRUCTURES

• LATERAL-FORCE RESISTING STRUCTURES

• NON-LOADBEARING STRUCTURES

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.

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.

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.

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.

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 etc.

VERTICAL BUILDING STRUCTURE SYSTEMS

Structure systems

Vertical force flow

BUILDING RESPONSE TO LATERAL FORCE ACTION

Vertical lateral-force resisting structure systems

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 3rdV

STORY SHEARS

Vx

Equivalent lateral seismic load distribution

THE EFFECT OF SEISMIC INTENSITY

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.

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.

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.

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.

DIAPHRAGM ACTION OF ROOF

EXAMPLE OF ROOF DIAPHRAGM ACTION

Tekla Xsteel bracing

HORIZONTAL FORCE FLOW

BASIC VERTICAL LATERAL FORCE RESISTING

STRUCTURE TYPES

Effect of structure type on cantilever action

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.

Rigid Frame Shear Core Interaction

The Building Response to Load Action

• 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

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.

Relative Stiffness of diaphragm and vertical elements

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.

16'2

0'

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

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

15'

25' 25'

20'

20'

20'

a.

b. c. d.

EXAMPLE: 13.1

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)

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

Rya = 0.15(50) = 7.50 k

ΣMa = 0 = 7.5(25) – Rxa(60)

Rxb= 3.125 k

Rxa= 3.125 k

Lateral deflection of solid walls

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

Ry ≈ 0.15(50)/3 = 2.50 k

(1) Fig. 4.21 Fig. 4.22 Example 4.7

Bracing the frame with a shear wall,

notice the effect of the wall opening

(ref: Dr Frame)

rigid vs. flexible diaphragm action vs. indeterminate force distribution

(1) Fig. 4.26 Example 4.11 and 4.12

torsion caused by eccentric core

Asymmetrically arranged lateral force resisting system

Example 13.6: Two-story rigid frame structure

12

0/2

= 6

0'

2(1

20

)/3

= 8

0'

H =

10

SP

@ 1

2' =

12

0'

Fx

hx h7 =

70

'

F7

F1

w10F

10

37 k

60 k

3 SP @ 20 = 60'

W

wx

w7

V

Multi-Bay, Multi-Story Rigid Frame

RIGID FRAME - SHEAR

WALL INTERACTION

CONCRETE FRAME - SHEAR

WALL INTERACTION

HINGED STEEL FRAME

BRACED BY CONCRETE

SHEAR WALL

Lateral stability of buildings

STEPHEN P CLARK

GOVERNMENT

CENTER, Miami, FL,

1985, Hugh Stubbins

and Assoc. Arch,

LeMessurier Assoc.

Struct. Eng.

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

Alcoa Building (6 stories), San

Francisco, 1967, SOM

Alcoa Building, San

Francisco, 1967, SOM

Turmhaus am Kant-Dreieck mit

Wetterfahne aus Blech, Berlin,

Josef Paul Kleinhues, 1994

Chulalongkorn University, Bangkok, Thailand

Taoyuan 02 Graduate Student

Dormitory, Nanjing University,

Nanjing, 2008, Zhang Lei Arch

House (World War 2 bunker),

Aachen, Germany

Triangle building,

Friedrichstr/ Mauerstr.

Berlin, 1996, Josef Paul

Kleihues Arch

Duesseldorf City Gate,

Duesseldorf, Germany, 1997,

H. Petzinka + Fink Arch

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

Samsung Jongno Tower, Seoul,

1999, Rafael Vinoly Arch

Broadgate Tower,

London, UK, 2009,

SOM Arch+Struct

Eng

Leadenhall Building, London, UK, 2014, Richard

Rogers Arch, Ove Arup Struct Eng

NEO Bankside, London, UK, 2013, Richard

Rogers Arch, Waterman Struct Eng

Dee and Charles Wyly

Theater, Dallas, 2009, Joshua

Prince-Ramus +Rem Koolhaas

Arch, Magnusson Klemencic

Struct Eng

Interdisciplinary Building,

Columbia University, New York,

2009, Rafael Moneo + Arup

http://archleague.org/site/wp-content/uploads/2009/08/Columbia002.gif

Alan House, Los Angeles, 2007,

Neil Denari (NMDA) Arch

Market Bangkok, Thailand

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

Fort School, Mumbai, India, 2005,

Chris Lee & Kapil Gupta

CDU-

Bundesgeschäftsstelle

Berlin, Berlin, Germany,

2000, Petzinka

Pink Architekten

Vertretung des Landes Nordrhein-

Westfalen beim Bund in Berlin,

2002, Petzinka Pink Arch

The two large one-bay frames at

each end of the building are

designed to resist the lateral

forces applied in the direction

indicated.

The Reliance Control

Electronic Plant,

Swindon, UK, 1966,

Team 4 (Foster/Rogers),

Tony Hunt Struct. Eng

Sainsbury Centre for Visual Arts, Norwich, UK, 1978,

Norman Foster Arch, Anthony Hunt Struct Eng

United Airlines Terminal at

O’Hare Airport, Chicago,

1987, H. Jahn Arch,

Lev Zetlin Struct Eng

Shenyang Taoxian

International Airport, 2001,

Huilai Yao architect

Toronto Pearson International Airport – Terminal 1,

Toronto, Canada, 2014, SOM/Adamson

Architects, ARUP/Yolles Struct. Eng.

Ningbo Air terminal

Cologne/Bonn Airport, Germany,

2000, Helmut Jahn Arch., Ove

Arup USA Struct. Eng

Beijing Airport, Terminal 2,1999

Hamburg Airport, Terminal

1, Hamburg, Germany,

2005, von Gerkan, Marg &

Partner Arch, Weber Poll,

Eggert Lohrmann Partner

Struct. Eng.

Arena Amazonia,

Manaus, Brazil, 2014,

von Gerkan Marg

Arch+Schlaich

Bergermann Struct Eng