ACRONYM
STM is the acronym for “Strut “ Strut and Tie Models” Models” or “Strut “Strut and Tie Methods “. It is a design method of reinforced concrete structures by idealizing structural components as truss models which are composed of axially loaded members, including compression bearing members strut ! and tension bearing members tie tie!. !. B REGION
The word “B “B region” region” is short for “Bernoulli “ Bernoulli region” region” or “Beam “Beam region “. "ccording "ccording to #ernoulli #ernoulli hypothesis Plane Plane sections remain plane after bending…!, bending… !, the strains in concrete structures follow a linear distribution. This is the theoretical basis for flexural design of concrete components. Those regions which follow #ernoulli hypotheses belong to # regions. They could be designed by simple calculations. CORBEL
$orbel is an example which does not follow the #ernoulli hypotheses. It is discontinued in geometry. %r we can say the stress and strain in corbel is disturbed. D REGION
&xamples of ' regions ' region means “discontinued “ discontinued region” region” or “disturbed “disturbed region “, such as as corbel. These ' regions do not follow #ernoulli hypothesis. Thus, they could not be designed or analyzed by simple calculations. The solution is either empirical approximation or (ery complicated computations such as )&" methods. EXAMPLES
#esides corbels, there are many other types of ' regions, such as deep beams, pile caps, beams with opening holes, and beam*column +oints. FLEXURE
Tae the design of pile caps as an example. In many cases, pile caps are designed by beam theory. They are assumed to fail in flexure, which is a ductile brea and has warning cracs. -owe(er, according to se(eral research wors, the failure modes of most of them are brittle shear failures.
GRAPHICAL PROCEDURE
' and /' graphic of STM 0ie Maxwell method for analyzing trusses, STM is also a graphical procedure. It is based on graphics of structures, either two*dimensional or three*dimensional. The angles, dimensions, and areas of struts and ties could be obtained by graphical methods. HISTORY
STM was presented by Schlaich et al. in the year 1234. %ther research wors include $ollins and Mitchell 1221! and Mac5regor 122!. It has been adopted by many codes or standards, such as ""S-T% 06)' Specifications, "$I /13, $S" Standard, )I7 6ecommendations, and &uropean $ode. INCLINED ANGLE
%ne of the definitions in these codes for STM is the geometric rules in creating a proper STM model. )easible inclined angle between strut and tie members is an important factor. There are different pro(isions in different codes. "pproximately, the inclined angle is limited between 89 and :;9. )or example, in the "$I /13M*;8, the pro(ision is “ The angle between the axes of any strut and any tie entering a single node shall not be taken as less than 25 degrees ” JOINT
STM of beam*column +oints The common beam*column +oints in moment frame structures are examples of ' regions. They could be analyzed by STM models. KIT
LOAD PATH
5ood and poor load paths of the same deep beam %ne characteristic of a proper STM model is that the load path is simple and direct. There are se(eral possible load paths in reinforced concrete structures since there are se(eral possible reinforcement arrangements.
The basic method for STM is showed in this flow chart $. $. )u, ;;1!.
)low chart of the method of STM NODE
'ifferent types of
Since there are se(eral possible models, we should use the most ideal model in our analysis. 5enerally, the common criterion is the amount of reinforcement. " model with the minimum amount of reinforcement is usually the optimal model. POTENTIAL
STM could pro(ide relati(ely easy and accurate analysis for ' regions in reinforced concrete. It is also useful in the shear design of structural members. Thus, it has a great potential in the field of concrete structures. QUANTITATIVE
"lthough STM is a graphical procedure, >uantitati(e method is still re>uired. The calculation of the amount of ties and the checing of nodes and struts all need >uantitati(e procedures. ?e can see the detailed procedure in the following example. REINFORCEMENT
STM of +oint and the corresponding reinforcement 'etailed reinforcement could be arranged by following the location and distribution of idealized ties in the STM models. 7ay attention to the anchorage. %therwise, brittle anchorage failures might
happen. STRUT
#asically, there are three types of struts@ prism, fan, and bottle. They ha(e different factors in the calculation of compression strengths. TIE
Ties are tension members in the STM models. They should ha(e ade>uate anchorage in the nodes. UNIFIED APPROACH
The tile of the paper of Schlaich et al. in the year 1234 is Toward a !onsistent "esign of Structural !oncrete. Since STM considers all load effects simultaneously, it is a unified approach for concrete structures. VERTICAL REINFORCEMENT
STM for shear design of beams %ne of the usages of STM is the shear design of concrete components. The (ertical reinforcement stirrups! in beams could be decided by STM analysis. WALL
0ie deep beams, load bearing walls could also be analyzed by STM. X-RAY
“
A*ray” of pier cap
Sometimes, STM models of concrete structures could be regarded as the x*ray pictures of the structure members, such as this STM model of a pier cap. YIELD
In order to guarantee the safety of structural members, reinforcement should yield before the brittle crush of concrete. ZUM BEISPIEL
(FOR EXAMPLE)
STM and )&" analysis of a deep beam 7rof. ?right pro(ided an example of STM in his wor published in the year ;;/. I con(erted it into metric units and tried another (ersion of STM model. "lso, I compared it with the calculation based on beam theory in $hinese code 5# 8;;1; and the results of )&" analysis. 7lease clic this web lin to see the detailed graphics and calculations of this example@
[email protected];1B1B;1Bstm*deep*beamB 6eferences@
•
"$I $ommittee /13, Building code re#uirements for structural concrete and commentary $%!&
'()M*+5,, ;;8 •
$. $. )u, Ceynote “The Strut*and*tie model of concrete structures “, ;;1
•
de Souza 6", Cuchma '", 7ar D?, et al. “ -onlinear finite element analysis of four*pile caps
supporting columns sub.ected to generic loading “, $omputers and concrete, Eol. F, Iss. 8, ;;4, pp. /:/*/4: •
Schlaich, D.G SchHfer, C.G and Dennewein, M., “ Toward a !onsistent "esign of structural !oncrete”,
7$I Dournal, E. /,
?ight, D.C., and 7arra*Montesinos, 5. “Strut*and*tie model for deep beam design “, "$I $oncrete
International, Eol. 8,
?ight, D.C. Ceynote “"e/elopment of the Strut*and*Tie Method for %ppendix % of the Building !ode
$%!& '()*+), “, ;;3
