LATERAL STABILITY OF STRUCTURES including SAP2000 Prof. Wolfgang 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
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+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)
See also, (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, 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
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
VERTICAL BUILDING STRUCTURE SYSTEMS
Structure systems
Vertical force flow
BUILDING RESPONSE TO LATERAL FORCE ACTION
Vertical lateral-force resisting structure systems
H/5 H/3 H/5
H = hn
Vx
H/3
H/5
Wx
Fx
H/5 hx
H/3 H/5
V STORY SHEARS
ACTUAL
V D
LUMPED MASS MODEL
1st
2nd 3rd LINEAR APPROXIMATION OF FIRST THREE MODES OF VIBRATION
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
Mill Street Lofts building, Bozeman, Montana, 2015, Comma-Q Arch, Nishkian Monks Struct Eng
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.
P=1k
16'
g
h c
d
20'
x y
b
a
12 f
'
e
P=1k
Braced Building Core – Axial Force Flow caused by lateral forces
e
b
Mt/b = Pe/b P/2
P
P/2
a.
a
e.
P
a
P
P/2
P/2
b.
e P
f.
P
c.
g.
d.
h.
ARRANGEMENT OF LATERAL FORCE RESISTING STRUCTURES
15'
a. 25'
25'
20' 20' 20'
b.
c. EXAMPLE: 13.1
d.
3.13 k Y
X
WALL
3
C
15'
5
25' 1.88 k
1.88 k 3.13 k
3.64 k (C) 1.88 k (T)
WALL
B 7.5 k
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)
The School of Architecture, Lyon, France, 1988, Jourda et Perraudin Arch
Wilkhahn Factory, Bad Münder, Germany, 1992, Thomas Herzog Arch
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
wx
Fx h7 = 70'
2(120)/3 = 80'
120/2 = 60'
60 k
F7
hx
37 k
w7
W
F1 V
3 SP @ 20 = 60'
Multi-Bay, Multi-Story Rigid Frame
H = 10 SP @ 12' = 120'
w10
F10
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
ilding (6 stories), San o, 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
Alan House, Los Angeles, 2007, Neil Denari (NMDA) Arch
Sobek House, Stuttgart, Germany, 2000, Werner Sobek Arch + Struct Eng
Market Bangkok, Thailand
Proposal for taz-Publisher, Berlin, Germany, 2017, Piet und Wim Eckert Arch
Fort School, Mumbai, India, 2005, Chris Lee & Kapil Gupta
CDUBundesgeschäftsstelle Berlin, Berlin, Germany, 2000, Petzinka Pink Architekten
Vertretung des Landes NordrheinWestfalen 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
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Ningbo Air terminal
Cologne/Bonn Airport, Germany, 2000, Helmut Jahn Arch., Ove Arup USA Struct. Eng
Beijing Airport, Terminal 2,1999
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Arena Amazonia, Manaus, Brazil, 2014, von Gerkan Marg Arch+Schlaich Bergermann Struct Eng
