Lateral Stability of Building Structures (rev. ed.)

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LATERAL STABILITY OF

STRUCTURES

including SAP2000

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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+-

,

(1)The Design of Building Structures (Vol.1, Vol. 2), rev. ed.,

PDF eBook

by Wolfgang Schueller, 2016, published originally by Prentice Hall,

(2)Building Support Structures, Analysis and Design with SAP2000

Software, 2

nd

_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.

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

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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

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WIND

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

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EFFECT OF BUILDING FORM ON WIND AND SEISMIC LOAD DISTRIBUTION

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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

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BUILDING STRUCTURES

• GRAVITY STRUCTURES

• LATERAL-FORCE RESISTING STRUCTURES

• NON-LOADBEARING STRUCTURES

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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.

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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.

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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.

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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.

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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.

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Vertical lateral-force

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h_x

LUMPED MASS MODEL

LINEAR APPROXIMATION OF FIRST THREE MODES

OF VIBRATION ACTUAL F_x W_x H = h_n D V H/3 H/3 H/3 H/5 H/5 H/5 H/5 H/5 1st 2nd 3rd V STORY SHEARS V_x

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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.

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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.

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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.

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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:

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Mill Street Lofts building, Bozeman, Montana, 2015, Comma-Q Arch, Nishkian

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BASIC VERTICAL LATERAL FORCE RESISTING

STRUCTURE TYPES

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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.

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• 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

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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.

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Relative Stiffness of diaphragm and vertical elements

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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.

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16' 2 0 ' 12_' P = 1 k P = 1 k a b c d e f g h x y

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ARRANGEMENT OF LATERAL FORCE RESISTING STRUCTURES

a. b. c. d. e. f. g. h. e P a a P P/2 P/2 P P/2 _P/2 P P e b M_t/b = Pe/b

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15' 25' 25' 20' 20' 20'

a.

b.

c.

d.

EXAMPLE: 13.1

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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

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R_ya = 0.15(50) = 7.50 k

ΣM_a = 0 = 7.5(25) – R_xa(60) R_xb= 3.125 k

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Bracing the frame with a shear wall,

notice the effect of the wall opening

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The School of Architecture, Lyon, France, 1988, Jourda

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Wilkhahn Factory, Bad Münder, Germany, 1992,

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1 2 0 /2 = 6 0 ' 2 (1 2 0 )/ 3 = 8 0 ' H = 1 0 S P @ 1 2 ' = 1 2 0 '

F

_x h x h 7 = 7 0 '

F

₇

F

₁

w

₁₀

F

₁₀ 37 k 60 k 3 SP @ 20 = 60'

W

w

_x

w

₇

V

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RIGID FRAME - SHEAR WALL INTERACTION

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CONCRETE FRAME - SHEAR WALL INTERACTION

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HINGED STEEL FRAME BRACED BY CONCRETE SHEAR WALL

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STEPHEN P CLARK GOVERNMENT CENTER, Miami, FL, 1985, Hugh Stubbins

and Assoc. Arch, LeMessurier Assoc.

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Alcoa Building (6 stories), San Francisco, 1967, SOM

Alcoa Building, San

Francisco, 1967, SOM

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Turmhaus am Kant-Dreieck mit Wetterfahne aus Blech, Berlin,

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

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House (World War 2 bunker), Aachen, Germany

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Triangle building,

Friedrichstr/ Mauerstr. Berlin, 1996, Josef Paul

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Duesseldorf City Gate, Duesseldorf, Germany, 1997,

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Samsung Jongno Tower, Seoul, 1999, Rafael Vinoly Arch

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Broadgate Tower, London, UK, 2009,

SOM Arch+Struct Eng

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Leadenhall Building, London, UK, 2014, Richard

Rogers Arch, Ove Arup Struct Eng

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NEO Bankside, London, UK, 2013, Richard

Rogers Arch, Waterman Struct Eng

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Dee and Charles Wyly Theater, Dallas, 2009, Joshua Prince-Ramus +Rem Koolhaas

Arch, Magnusson Klemencic Struct Eng

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Interdisciplinary Building,

Columbia University, New York,

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

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Sobek House, Stuttgart, Germany, 2000, Werner Sobek Arch + Struct Eng

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Fort School, Mumbai, India, 2005,

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CDU-Bundesgeschäftsstelle Berlin, Berlin, Germany,

2000, Petzinka Pink Architekten

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Vertretung des Landes Nordrhein-Westfalen beim Bund in Berlin,

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

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The Reliance Control Electronic Plant, Swindon, UK, 1966, Team 4 (Foster/Rogers),

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

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United Airlines Terminal at O’Hare Airport, Chicago,

1987, H. Jahn Arch, Lev Zetlin Struct Eng

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Shenyang Taoxian

International Airport, 2001, Huilai Yao architect

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Toronto Pearson International Airport – Terminal 1, Toronto, Canada, 2014, SOM/Adamson

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Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove

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Hamburg Airport, Terminal 1, Hamburg, Germany, 2005, von Gerkan, Marg &

Partner Arch, Weber Poll, Eggert Lohrmann Partner

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Arena Amazonia, Manaus, Brazil, 2014,

von Gerkan Marg Arch+Schlaich

Lateral Stability of Building Structures (rev. ed.)