Frame Structures including sap2000

FRAME 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+Building+Su
pport+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,
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

Structure Systems & Structure Behavior
INTRODUCTION TO STRUCTURAL CONCEPTS
SKELETON STRUCTURES
• Axial Systems
• Beams
• Frames
• Arches
• Cable-supported Structures
SURFACE STRUCTURES
• Membranes: beams, walls
• Plates: slabs
• Hard shells
• Soft shells: tensile membranes
• Hybrid tensile surface systems: tensegrity
SPACE FRAMES
LATERAL STABILITY OF STRUCTURES

LINEELEMENTSSURFACEELEMENTS
FLEXURAL STRUCTURE
SYSTEMS
FLEXURAL-AXIAL STRUCTURE SYSTEMS
TENSILE MEMBERS
COMPRESSIVE
MEMBERS
BEAMS
BEAM-COLUMN
MEMBERS
FRAMES
TENSILE MEMBRANES
PLATES
MEMBRANE FORCES
SOFT SHELLS
SLABS, MEMBRANE BENDING and TWISTING
AXIAL STRUCTURE
SYSTEMS
SHELLS RIGID SHELLS

FRAMES are flexural-axial systems in contrast to hinged trusses, which
are axial systems, and isolated beams, which are flexural systems. Continuos
frames are flexural-axial systems as identified by beam-column behavior that
includes the effects of biaxial bending, torsion, axial deformation, and biaxial
shear deformations.
Here, two-dimensional skeleton structures composed of linear elements
are briefly investigated. The most common group of planar structure systems
includes
post-beam structures,
bent and folded beams,
rectangular portal frames,
cantilever frames,
braced frames,
pitched frames,
arches,
and so on.

These structures may form
short-span or long-span,
single-story or multi-story,
single-bay or multi-bay systems.
They range from low-rise to
single, open, large volume buildings
cellular massive buildings
skyscrapers.
Frames may be of regular or irregular geometry
Primary emphasis here is on the investigation of simple, but common single-story
enclosure systems to develop a feeling for the behavior of structures under gravity
and lateral loads. Investigated are the
• response and effect of the frame profile on uniform gravity action
and on lateral loading.
• the magnitude of the internal member forces is determined so that the computer
results can be checked.

Typical examples of frame architecture
are shown on the following slides.
First some historical important cases
are shown.

Glass House,, New Caanan, Con., 1949, Philip Johnson

Frame Structures including sap2000

Barcelona Coffee Table,
1929, Mies van der Rohe

Barcelona Chair, 1929, Mies van der Rohe

mr side chair, 1927, Ludwig Mies
van der Rohe

Wassili Chair, Bauhaus School,
Weimar/Dessau, Germany, 1925, Marcel
Breuer Designer

Paimio chair, 1931, Alvar Aalto Arch

Flamingo sculpture, Chicago Federal Center
Stabile, 1974, Alexander Calder Artist (Chicago
Federal Center by Mies van der Rohe)

Cummins Engine Component Plant ,
Columbus, IN, 1965, Roche & Dinkeloo

Reliance Controls factory,
Swindon, 1967, Team 4,
Anthony Hunt Struct. Eng

Athletics Building, Phillips
Exeter Academy, Exeter, NH,
1970, Kallmann & McKinnel
Arch, Le Messurier Struct. Eng.

Facep constructive
system, Fiat car distributor,
Bussolengo, 1976, Italy,
Angelo Mangiarotti Arch

Municipal Stadium, Florence,
1932, Pier Luigi Nervi

St Alexander's
Church,
Morrisonville, New
York, Jeremiah
Oosterbaan Arch

Lake Shore Drive Apts, Chicago, 1951,
Ludwig Mies van der Rohe Arch

Economist Building,
London, England,
1962, Alison and Peter
Smithson Arch

Museum of Modern Art, Rio de Janeiro, Brazil, 1958, Alfonso Eduardo Reidy

Richard J. Klarchek Information
Commons, Loyola University Chicago,
2007, Solomon Cordwell Buenz Arch,
Halvorson and Partners Striuct.

Richard J. Klarchek Information
Commons, Loyola University Chicago,
2007, Solomon Cordwell Buenz, Halvorson
and Partners Striuct.

Ningbo downtown, 2002,
Qingyun Ma Arch

Richard J. Klarchek
Information
Commons, Loyola
University Chicago,
2007, Solomon
Cordwell Buenz,
Halvorson and Partners
Striuct.

House II (Falk House),
Hardwick, Vermont, 1969,
Peter Eisenman Arch

Shipping Container Restaurant,
Seguin Island, Paris, France,
2013, Jean Nouvel Arch

Uniform Loading on Inclined Members
Simple Folded and Bent Beams
Single-bay Frames
Three-Hinged Frames
Indeterminate Frames
Cantilever Frames
Braced frames
Pitched Frames
Multi-bay Frames
Multi-bay, Single-Story Frames
Multi -Story Frames
Vierendeel Trusses
The following sequence of topics is used:

The loading on a simply supported inclined beam is investigated in with a pin support at the
base and a roller support at the top, which however may have different orientations.
The typical gravity loading of an inclined member consists of the dead load wD acting along
the structure, and the live load wL, which is usually given by codes on the horizontal
projection of the structure (a). To determine the maximum moment, it is convenient to
transfer the dead load to the horizontal projection of the beam (b), since the maximum
moment of a simply supported inclined beam is equal to that for an equivalent beam
on the horizontal projection carrying the same loading as the inclined beam. In other
words, the moment is independent of beam slope and support conditions.
The shear depends on the beam inclination but not on the orientation of the top support. It is
equal to the shear of the beam on the horizontal projection multiplied by cosθ. The parallel
load components cause axial forces along the beam and are equal to the load on the
horizontal projection multiplied by sinθ. The axial force flow depends on the beam inclination
and on the reaction condition of the top support.
The uniform lateral loading case is analogous to the uniform gravity loading case; just
visualize the span L and height h to be exchanged. For example, the maximum moment due
to the wind pressure q on the vertical projection of the beam is,
The fact that the moment is independent of the geometry of the bent or folded beam for
vertical support conditions, is demonstrated in the drawing.
Various folded beam systems are investigated in the following drawing ranging from a simple
inclined beam (B), a stair (E.), to other roof frame shapes.
Notice SAP automatically transfers the loads from the projection to an equivalent load along
the member!

wD
wL + wD/cosθ
wD + wLcosθ
wD cos θ + wLcos2θ
L/cosθ
wL
h
L
θ
The parallel load component causes axial force action in the member: (wD + wLcosθ) sinθ
and from the perpendicular load component the shear is determined: (wD + wLcosθ) cosθ

50 ft-k
50 ft-k
50 ft-k
49.70 ft-k
34.46 ft-k
-7.94 ft-k
wcosθ = 0.93 k/ft

-5.76 ft-k
37.69 ft-k
54.11 ft-k
53.85 ft-k
53.85 ft-k
53.85 ft-k
1 k/ft

8 ft-k
8 ft-k
8 ft-k
7.94 ft-k
13.61 ft-k
15.87 ft-k
wsinθ = 0.37 k/ft

Folded Beam Structures
The magnitude of the maximum moment for simple folded or bent beams
under uniform vertical loads does not change when the load is applied on
the horizontal projection of the beams. Naturally, the magnitude of the
axial forces will change.
a
c
e
b
d
f
g

a
c
e
b
d
f
g
a
c
e
b
d
f
g
Mmax = wL2/8

Each part of the structure (e.g. joint,
element) has its own LOCAL
coordinate system 1-2-3.
The joint local coordinate system is
normally the same as the global X-Y-Z
coordinate system.
For the elements, one of the element
local axes is determined by the
geometry of the individual element;
the orientation of the remaining two
axes is defined by specifying a single
angle of rotation.
For frame elements, for example, the
local axis 1 is always the longitudinal
axis of the element with the positive
direction from I to J. The default
orientation of the local 1-2 plane in
SAP is taken to be vertical (i.e.
parallel to the Z-axis). The local 3-axis
is always horizontal (i.e. lies in the X-Y
plane).
MEMBER ORIENTATION
Is defined by local coordinate system

If the roller in the simple folded beams is replaced by a pin support,
horizontal thrust or kickout forces are generated by the gravity loads at the
base (since the boundary conditions do not allow outward displacement),
which in turn cause bending of the columns and beam.
By providing two pin supports, the structure is once indeterminate and
cannot be solved directly with the equations of equilibrium as is discussed
further in the next section of this book. But when an internal hinge is
introduced somewhere along the frame one more known condition is
introduced because the moment must be zero at this point, so the frame can
be solved by statics.
Quite common are three-hinged frame systems where the hinge is placed
at mid-span of the beam as demonstrated in the following drawing for
various one-story, single-bay frame shapes.

GEOMETRY - THE EFFECT OF CHANGE :
shorter column and cantilever

PRESSURE LINE RESPONSES TO VARIOUS LOAD ACTIONS:
funicular shapes

load action on triangular frame

PRESSURE LINE VS. FRAME SHAPE VS. M-diagram

THE EFFECT OF PROFILE ON
MOMENT DISTRIBUTION

Three-Hinged Frames
a
b
c
d
e
f
g
h

In general, a structure is statically determinate when the three equations of
static equilibrium are sufficient for solving the unknown forces. When, however,
the conditions of the structure are such that the three equations are not sufficient
for determining the magnitude of the force flow, additional equations related to
member properties, are required, and the structure is said to be statically
indeterminate, hyperstatic or redundant. It is apparent that the structure must
be in static equilibrium and stable, whether it is statically determinate or
indeterminate.
The degree of indeterminacy may be found by making the structure statically
determinate and stable by removing supports and/or cutting members. The
number of force-resisting conditions taken away is equal to the degree of
indeterminacy or redundancy, so named after the number of forces that are
needed to ensure static equilibrium.
Redundancy is an important phenomenon be cause it allows the force flow to
take an alternate path if the structure should be failing at a certain location, thus
not necessarily resulting in a progressive collapse of the building as for
determinate structures.

Farnsworth House, Plano, Illinois, 1950, Mies
van der Rohe

Carré d'Art Cultural
Center, Nîmes,
France, 1993,
Norman Foster
Arch, Ove Arup
Struct. Eng

Siam Center, Bangkok, elevated train
and road construction

Parc de Princes Stadium, Paris, 1972,
Roger Taillibert Arch

Sporthalle Buchholz, Ulster, 1998, S. Camenzind
& M. Graefensteiner, Geilinger Stahlbau

Deere & Company Headquarters,
Moline, Illinois, 1963, Eero
Saarinen Arch

Crown Hall, IIT, Chicago,
1956, Mies van der Rohe

Herz Jesu Kirche, Munich, 2000, Allmann,
Sattler Wappner Arch, A. Hagl Struct. Eng

United Airlines Wash Hangar, San Francisco, Calif., 1958, Myron Goldsmith (SOM)

United Airlines Maintenance Hangar, San Francisco, Calif., 1958, Myron Goldsmith
(SOM)

Herb Brooks Arena , Lake
Placid, NY, 1980, Distin &
Wilson Arch

Rosen House, Los
Angeles, California,
1962, Craigt Ellwood
Arch

Sainsbury Centre, Norwich, UK,
1978, Norman Foster Arch,
Anthony Hunt Struct. Eng.

Kemper Arena, Kansas
City, 1974, Helmut Jahn
Arch

Munson-Williams-Proctor Institute Art
Gallery, Utica, NY, 1960, Phillip Johnson
Arch, Lev Zetlin Struct. Eng

Republic Newspaper
Plant, Columbus, 1971,
Myron Goldsmith
(SOM)

THE EFFECT OF BEAM
AND COLUMN STIFFNESS
FOR CONTINUOUS
FRAMES

W24x62
W24x68
W24x76
W14x90
W14x90
W14x82
W14x82
W14x74
W14x74
1 1
1 1
1 1
Ib = 2.64Ic: k = 0.99
Ib = 2.07Ic : k = 0.78
Ib = 1.55Ic: k = 0.58
k = (I/L)b /(I/L)c
THE EFFECT OF CHANGE
OF MEMBER STIFFNESS:
conceptual drawing

When the hinge in the three-hinged portal frame is taken out, then the two-hinged
frame becomes once statically indeterminate; now the force flow cannot be found
anymore simply by statics, the bending stiffness EI of the members must be
considered. For example, the support moment Ms in the two-hinge frame of one
material (Ec = Eb) is dependent on the stiffness of the beam (Ib/Lb) and column
(Ic/Lc) that is the stiffness factor k.
MS = -[wL2/12]/[3/(3+2k)]
where, k = (I/L)b/(I/L)c = (Ib/Lb)Lc/Ic = n(Lc/Lb), where, Ib = nIc
For some typical conditions, the support or column moment Ms is,
k = 1.0 (i.e. equal beam and column stiffness): Ms = - wL2/20
k = 0.5: Ms = - wL2/16
k = 0.3 (same column and beam section, k = Lc/Lb, say 1/3): Ms ≈ - wL2/14

Fortunately, not the actual stiffness but the relative stiffness is used to
determine the force flow along the members. Since the material does not
generally vary, the stiffness factor for the two-hinged portal frame can be
expressed simply in terms of nLc/Lb.
k = (I/L)b/(I/L)c = (Ib/Lb)Lc/Ic = n(Lc/Lb) where, Ib = nIc
In general, the magnitude of the frame moments in indeterminate frame
structures depends on the relative stiffness of the adjacent beams (Σ Ib/Lb )
and columns (Σ Ic/Lc). First, relative member sizes are assumed that is
member sizes are expressed in terms of each other using the default
sections in SAP and modifying the frame section to take the change of I
into account by going to the Modification Factors, and then filling in the
appropriate factor (e.g. 2, 3) for the Moment of inertia about 3 axis, for
example. Now the structure can be analyzed and can then be designed.
Then, the structure has to be reanalyzed with the new member sections
and be redesigned. Keep in mind that in the computer program design is
an iterative process, where the analysis and design must be run multiple
times to complete the design process.

Ib = 0.77Ic
k = (I/L)b /(I/L)c = 0.29 ≈ 0.3
Ib = 2.07Ic: k = 0.78
Ib = 2.64Ic: k = 0.99 ≈ 1Ib = 1.55Ic: k = 0.58 ≈ 0.6

k = 0.3 k = 0.6
k = 0.9 k = 1.0

A typical frame must support a roof area of one-half of a bay on each side; that is, the
joists on each side of the frame transmit to the frame one-half of the gravity roof load.
w = wD + wL = 40(0.025 + 0.030) = 1.0 + 1.2 = 2.2 k/ft
The curtain panels transmit the lateral wind load to the spandrel beams and roof
diaphragm, which in turn apply a single load Pw to the frame at the beam-column
intersection.
Pw = 40(15/2)0.017 = 5.1 k
Here the total beam moment to be distributed to column is,
M = wL2/8 = 2.2(40)2/8 = 440 ft-k
Checking approximately the computer solutions for equal beam and column stiffness
(k = 1), for
Ms = - wL2/20 = 2.2(40)2/20 = 176 ft-k (SAP gives 174.37 ft-k)
or the maximum girder moment of Mg = wL2/8 - Ms = 440 - 176 = 264 ft-k

Rh = P/2 = 5.1/2 = 2.55 k
Msw = 2.55(15) = 38.25 ft-k
Member stiffness does not influence lateral force distribution.

Using Modification Factors
for Analysis

k = 0.19 k = 0.38
k = 0.75 K = 1.13
Using Modification Factors
for Analysis

k = 0.19 K = 0.38
k = 0.75 K = 1.13

M-diagrams
N-diagrams
Deflection
a) settlement b) beam expansion
c) gravity load d) diagonal contraction
M-diagrams

CANTILEVER FRAMES
With increase of span the single-span concept becomes less efficient
because of the rapid increase in moment and deflection that is increase
in dead weight. The magnitude of the bending stresses is very much
reduced by the cantilever type of construction.
a b
c d
e f

International Airport, Rome, Italy, 1957, Pier Luigi Nervi

Sport- und Ausbildungszentrum Mülimatt, Windisch, Schweiz,
2010, Studio Vacchini Arch, Fürst Laffranchi Struct Eng

Entrance Hall University
Bremen, Germany, 2000,
Störmer Murphy Arch

Cristo Obrero Church,
Atlantida, Uruguay, 1960,
Eladio Dieste Arch+Struct E

San Diego Library, 1970, William L.
Pereira Arch

La Pyramide, Commercial Center
Abidjan, Ivory Coast, 1973 , Rinaldo
Olivieri Arch, Ricardo Morandi Struct.
Eng.

Hyatt Regency, San
Francisco, CA, 1973,
John Portman Arch

EU Hémicycle
Office Building,
Kirchberg, City
of Luxembourg,
1979, Pierre
Bohler Arch

BMW Plant Leipzig, Central Building, 2005, Zaha
Hadid Arch, Anthony Hunt Struct. Eng

BMW Plant Leipzig, Central Building, 2004, Zaha Hadid

Ciudad de las Artes.
Valencia, Spain, 2002,
Santiago Calatrava

Stadelhofen Station, Zurich,
Switzerland, 1990, Santiago Calatrava

10' 3'
3.5'
Stadelhofen Station, Zurich, Switzerland,
1990, Santiago Calatrava

BRACED FRAMES
Frames can be braced in a concentric or eccentric manner as indicated for portal
bents. Cases A. and B. are concentrically braced, while cases C. and D. are
eccentrically braced, and cases E. and F. have knee bracing. In the symmetrical
post-beam structures (A., C., and E.) the braces change from K-bracing, to
eccentric bracing to knee bracing. In the asymmetrical frames (B. and D.) the
change is similar from diagonal bracing to the beam-column intersection, to a
single eccentric bracing, and then to knee bracing for the post-beam structure.
The knee braces as often found in wood construction, do not provide a rigid
support to the beam; the support settlement is a function of the column stiffness.
The knee-braced corners of frames can be visualized as rigid frame connections.
In earthquake regions the use of eccentric bracing should be considered. While
the conventional concentrically braced frames are very stiff because the forces
are transmitted directly in axial fashion, under severe cyclic loading the braces
may buckle because of the lack of ductility and cause an unbalance of loading,
which may result in failure. However, when the brace is connected eccentrically to
the beam, rather than concentrically to the beam-column intersection, then the
diagonal force is transmitted in shear and bending along the beam segment,
forming a ductile link, where the plastic deformations prevent the brace from
buckling.

Pitched Frames
The pitched frame concept ranges from residential roof construction to the folded
frame for industrial buildings. Several typical examples are shown in Fig. 7.7.
Case (A.) is basic triangular truss unit; when the tie is taken out and the roller support
is replaced by a pin support, then the structure forms a three-hinge A-frame. In wood
construction the inclined beams are called rafters. A statically indeterminate collar
frame is shown in case (C.), where the simple A-frame is internally braced by a collar
strut to reduce the bending in the beams, w. For the strut to be truly effective, floor
decking or horizontal bracing should connect the various collar ties together to form a
horizontal deep beam, which must be supported by shear walls or vertical trussing.
For this method of construction, the collar strut provides a rigid support to the beams;
otherwise, a flexible support would only be available under unsymmetrical load action,
requiring much larger member sizes.
Case (B.) represents a post-beam structure as is typical for residential construction. In
contrast to A-frame construction, where the beams support each other at the crown to
form a continuous frame, in the post-beam structure the inclined beams or joists (if
they are closely spaced) function independently as inclined simple bending members,
supported on ridge beams. For the post-beam structure there are no ties at the base
support required because there is no thrust under gravity action. In case (D.)
intermediate beam supports are introduced to reduce bending and deflection.
Case (E.) is a three-hinge gable frame whereas in case (F.) a tie rod is added to
frame knees to reduce the thrust and thus reduce bending in the frame.
The critical moment for the gable frame is at the knee, the field moments along the
inclined frame beam are rather small when compared with the support moments so
they do not play an important role during the preliminary design process.

Xiangguo Si
temple complex,
Kaifeng, China

Da Qingzhen Si (Great
Mosque) originially built in
742 and then rebuilt in the
Qing dynasty, Xi’an, China

Carl-Zeiss Planetarium
Stuttgart, Germany,
1977, Wilfried Beck-
Erlang Arch

St. Albert, Saarbrücken, Germany,
1955, Gottfried Böhm Arch

Hotel Maritim, Cologne,
Germany, 1989,
Gottfried Böhm Arch

St. Anna in Köln-Ehrenfeld,
1956, Dominikus
Böhm+Gottfried Böhm
Arch

Airport Madrid,
Spain, 2005,
Richard Rogers
Arch, Anthony
Hunt Struct. Eng

Swissbau 99, Basel, Switzerland

Factory 798 , art district, Beijing northeast Dashanzi area, previously factory
buildings buit by East German architects in the 1950’s

Schwebebahnhof Ohligsmühle, Wuppertal-
Elberfeld, Germany, 1982, Wolfgang Rathke Arch

Schwebebahnstation Kluse,
Wuppertal-Elberfeld, 1999, Bernward
von Chamier+Francisco Molina Arch,
Ralf-Harald von Felde Struct. Eng

Multi-Bay, Single-Story Frames
post-beam structure
rigid frames
combinations of the above
a
b
c
d
e
f

a
b
c
d
e
f
10' 10' 10' 10'
10'

European Court of Justice,
Luxemburg, 2008, Dominique
Perrault

Miyagi Stadium, Sendai City, Japan, 2000,
Atelier Hitoshi Abe

Gare TGV, Aix en Provence, France,
2001, Jean-Marie Dutilleul

Gare TGV, Aix en
Provence, France, 2001,
Jean-Marie Dutilleul

L = 20' L = 20' L = 20' L = 20'
H=3(10)=30"
h
h
h
LOW-RISE, MULTI-STORY, MULTI-BAY RIGID FRAME

L = 20" L = 20" L = 20"
H=3(10)=30"
h
h
h
LOW-RISE, SINGLE-BAY, MULTI-STORY FRAMES

L = 20" L = 20" L = 20"
H=3(10)=30"
h
h
h
a b c
M-diagrams for uniform gravity loads

3 Sp @ 20' = 60'
15Sp@12'=180'7Sp@25ft=175ft
180/2=90'
2(180)/3=120'
15-story planar rigid frame structure; lateral loading wind and seismic action
3 Sp @ 20' = 60'
15Sp@12'=180'

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

3 Sp @ 20' = 60'
10Sp@12'=120'7Sp@25ft=175ft
120/2=60'
2(120)/3=80'
60 k
37.83 k

Beijing Jian Wai SOHO, Beijing,
Riken Yamamoto, 2004

OCBC Center, Singapore,
1976, I.M. Pei Arch, Ove
Arup Struct. Eng

Tsinghua University
Scientific Park (Tuspark),
Beijing, China, 2006

Lehrter Bahnhof, Berlin,
2006, Gerkan, Marg & Partner
Arch, Schlaich Bergermann
und Partner Struct. Eng

Dresdner Bank, Verwaltungszentrum, Leipzig, 1997, Engel und Zimmermann Arch

Saarbrücken Schloss, Saarbrücken,
Germany, 1989, Gottfried Böhm Arch

Parkinggarage Otto
Schill Str., Leipzig,
Germany

Umspannwerk
Mediapark,
Koeln, 1996,
Sandro Graf von
Einsiedel Arch.

Ningbo downtown, Ningbo,
China, 2002, Qingyun Ma Arch

NIT, NINGBO, 2002, Qingyun Ma Arch

Residential complex, Lindenstr., Berlin,
1997, Herman Hertzberger Arch

Dokumenta Urbana
(Freiluftzikmmer), Kassel,
Germany, 1984, Herman
Hertzberger Arch

Dokumenta
Urbana, Kassel,
Germany 1984,
Otto Seidle Arch

Centraal
Beheer,
Apeldoorn, The
Netherlands,
1972, Herman
Herzberger

School of
Architecture,
Nanterre, France,
1972, J. Kalisz +
R. Salem Arch

School of Architecture,
Nanterre, France, 1972, J.
Kalisz, + R. Salem Arch

Administration Building, Ningbo Institute of Technology, Zhejiang
University, Ningbo, 2002, Qingyun Ma

WDR Arcades/Broadcasting
House, Cologne, Germany, 1996,
Gottfried Böhm Arch

Department
Store Peek &
Cloppenburg,
Berlin-
Charlottenburg,
Germany, 1965,
Gottfried Böhm
Arch

VIERENDEEL TRUSSES
same member
size
equal bay size
h=10'
a.
L = 8(10) - 80'
b.

Basic VIERENDEEL TRUSS behavior

a.
b.
EXAMPLE 8.12 axial force and moment diagrams

Gustav-Heinemann Bridge, Berlin, Germany,
2005, Max Dudler Arch, KLW Ingenieure GmbH

Chancellor's
BridgeVierendeel bridge,
Berlin, 2001

Incheon International
Airport, Seoul, 2001, Fentress
Bradburn Arch.

Landesvertretung
von Baden-
Wuertemberg,
Berlin, 2000,
Dietrich Bangert
Arch

Embassy UK, Berlin, 2000,
Michael Wilford Arch

Salk Institute, La Jolla,
California, 1966, Louis
Kahn Arch, August E.
Komendant Struct. Eng.

Salk Institute, La Jolla, California,
1966, Louis Kahn, Arch, August E.
Komendant Struct. Eng

Fuji Television Headquarters, Tokyo, 1996,
Kenzo Tange Arch, Kajima Struct. Eng

Court of Justice,
Hasselt, Belgium,
2013, J. MAYER H.
Architects

Axial Gravity Flow in Irregular Frame

Frame Structures including sap2000

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