586 ACI Structural Journal/September-October 2002
ACI Structural Journal, V. 99, No. 5, September-October 2002.MS
No. 01-236 received August 6, 2001, and reviewed under Institute
publication
policies. Copyright 2002, American Concrete Institute. All
rights reserved, includingthe making of copies unless permission is
obtained from the copyright proprietors.Pertinent discussion will
be published in the July-August 2003 ACI Structural Journal
ifreceived by March 1, 2003.
ACI STRUCTURAL JOURNAL TECHNICAL PAPER
The strut-and-tie method (STM) is gaining recognition as a
code-worthy and consistent methodology for the design of D-
(discontinuity)regions in structural concrete. Unfortunately, the
development ofcode provisions for the STM has been hampered by
uncertainties indefining the strength and dimensions of the
idealized load-resistingtruss (or strut-and-tie model). In
addition, the has been encumberedby an iterative and time-consuming
design procedure in whichmany geometric details need to be
considered. To overcome thisproblem, researchers are developing
computer-based design tools,including the authors computer-aided
strut-and-tie (CAST) designtool. CAST provides a graphical working
environment for allaspects of the design process, including
definition of the D-region,selection of the strut-and-tie model,
truss analysis, memberdefinitions, and creation of a design
summary. This study reportson the STM, the barriers to its
advancement, the capabilities ofcomputer-based design tools, and
the CAST program. It alsomakes suggestions for future STM
research.
Keywords: structural concrete; strut; tie.
INTRODUCTIONIn selecting the appropriate design approach for
structural
concrete, it is useful to classify portions of the structure
aseither B- (beam or Bernoulli) regions or D- (disturbed
ordiscontinuity) regions. B-regions are those parts of a
structurein which it is reasonable to assume that there is a linear
variationin strain over the depth of the section. D-regions are
theremaining parts of the structure in which there is a
complexvariation in strain, occurring near abrupt changes in
geometry(geometrical discontinuities) or concentrated forces
(staticaldiscontinuities). Based on St. Venants principle, the
extentof a D-region spans approximately one section depth of
theregion on either side of the discontinuity. The
distinctionbetween B- and D-regions is illustrated in Fig. 1.
Most design practices for B-regions are based on a modelfor
behavior. For example, the design for flexure is based
onconventional beam theory while the design for shear is basedon
the well-known parallel chord truss analogy. In contrast,the most
familiar types of D-regionssuch as deep beams,corbels, joints, and
pile capsare principally designed byempirical approaches, such as
those given in ACI 318-99,1or by using common detailing practices.
For most other typesof D-regions, code provisions provide little
guidance todesigners. Not surprisingly, most structural problems
occurin D-regions.
The strut-and-tie method2-4 (STM) is emerging as a code-worthy
methodology for the design of all types of D-regionsin structural
concrete. Unfortunately, this conceptuallypowerful method can be
complicated by the need to performtime-consuming calculations and
graphical procedures. It isfor this reason that computer-based
graphical design aids arebeing developed.
Beginning with a brief description of the STM, this
paperdiscusses complications in the STM design process and therole
that computer-based tools can serve in overcoming theseobstacles.
Then, a summary of the capabilities of a fewcomputer-based STM
design tools is presented, with emphasison the features that
distinguish one tool from another. Thisincludes work at Purdue
University, the Swiss Federal Instituteof Technology (ETH), the
University of Stuttgart, andothers. Following this, the
computer-aided strut-and-tie(CAST) design tool that is being
developed by the authors ispresented. The study concludes with a
summary of thechallenges that lie ahead for the STM and
associatedcomputer-based design tools.
RESEARCH SIGNIFICANCEBecause of the inadequacy of traditional
code provisions
and detailing practices, most structural problems occur
inD-regions. The STM has the potential to provide a
consistent,well-founded, and widely applicable design
methodologyfor D-regions, but it is marred by a cumbersome
hand-baseddesign process. To overcome this problem,
computer-baseddesign and analysis tools that bring simplicity and
transparencyto the STM design process, and thus can improve how
D-regionsare designed, are being developed. This paper presents the
roleand capabilities of these programs, summarizes uncertaintiesin
the STM design methodology, and suggests directions forfuture
research.
STM FOR DESIGN OF D-REGIONSBackground
The idea of the STM came from the truss analogy methodintroduced
independently by Ritter and Mrsch approximately100 years ago for
the shear design of B-regions. The trussanalogy, or truss model,
was used to idealize the flow offorces in a cracked concrete beam.
In parallel with the increasingavailability of experimental results
and the development oflimit analysis in the plasticity theory, the
truss analogymethod has been validated and improved considerably in
theform of full member or sectional design procedures. Thetruss
model has also been used as a basis for torsion-designmethods. An
excellent summary of the development oftruss model for shear design
of B-regions can be found inReference 5. The STM was developed
after Schlaich, Schfer,and Jennewein3 extended the use of a truss
model to D-regions.
Title no. 99-S60
Computer-Based Tools for Design by Strut-and-Tie Method:
Advances and Challengesby Tjen N. Tjhin and Daniel A. Kuchma
587ACI Structural Journal/September-October 2002
Strut-and-tie modelsIn the STM, the complex flow of internal
forces in the
D-region under consideration is idealized as a truss carryingthe
imposed loading through the region to its supports. Thistruss is
called a strut-and-tie model. Like a real truss, a strut-and-tie
model consists of struts and ties interconnected at nodes(nodal
zones or nodal regions). A selection of strut-and-tiemodels for a
few typical D-regions is illustrated in Fig. 2.
Struts are the compression members of a strut-and-tie modeland
represent concrete stress fields whose principal compres-sive
stresses are predominantly along the centerline of thestrut. As
shown in Fig. 2, struts are usually symbolized usinga broken line.
The actual shape of a strut, however, can beprismatic,
bottle-shaped, or fan-shaped (Fig. 3). Struts can bestrengthened by
steel reinforcement and, when this is thecase, they are called
reinforced struts.
Ties are the tension members of a strut-and-tie model.Ties
mostly represent reinforcing steel, but they can
occasionallyrepresent prestressing steel or concrete stress fields
withprincipal tension predominantly in the tie direction. Ties
areusually denoted using a solid line.
Nodes are analogous to joints in a truss, and are whereforces
are transferred between struts and ties. As a result,these regions
are subject to a multidirectional state of stress.Nodes are
classified by the types of forces being connected.Figure 4 shows
basic types of nodes; in the figure, C is usedto denote compression
and T is used to denote tension.
STM design processThe STM design process involves several steps
that are
illustrated in Fig. 5 using the design example of a dapped-ended
beam, and are described as follows:
1. Defining the boundaries of the D-region and thenevaluating
the concentrated, distributed, and sectional forcesthat act on the
boundaries of this region;
2. Sketching a strut-and-tie model and solving for the
trussmember forces;
3. Selecting the reinforcing or prestressing steel that
isnecessary to provide the required tie capacity and ensuringthat
this reinforcement is properly anchored in the nodalzones (joints
of the truss);
4. Evaluating the dimensions of the struts and nodes suchthat
the capacity of these components is sufficient to carrythe design
force values; and
5. Providing distributed reinforcement to increase theductility
of the D-region.
Because equilibrium of the truss with the boundary forcesmust be
satisfied (Step 2) and stresses everywhere must bebelow defined
code limits (Steps 3 and 4), the STM is a lower-bound (static or
equilibrium) method of limit analysis.
ACI member Tjen N. Tjhin is a doctoral candidate in the
Department of Civil andEnvironmental Engineering at the University
of Illinois at Urbana-Champaign. Hisresearch interests include
nonlinear analysis and design of concrete structures.
ACI member Daniel A. Kuchma is an assistant professor of civil
and environmentalengineering at the University of Illinois at
Urbana-Champaign. He is a member ofACI Subcommittee 318-E, Shear
and Torsion; and Joint ACI-ASCE Committee 445,Shear and
Torsion.
Fig. 2Examples of strut-and-tie models.
Fig. 1Example of division of B- and D-regions in common
structure.
