Blog and Article

Blog and Article

New Strut-and-Tie-Models for Shear Strength Prediction and Design of RC Deep Beams

posted Aug 12, 2014, 12:33 AM by Domain Admin   [ updated Aug 12, 2014, 12:34 AM ]

A journal paper titled, “New Strut-and-Tie-Models for Shear Strength Prediction and Design of RC Deep Beams” was recently accepted for publication in Computers and Concrete (Vol. 13, No.7, 2014). Mr. Panatchai Chetchotisak (a PhD student at the Department of Civil Engineering, Khon Kaen University, Thailand), Prof. Jaruek Teerawong (Department of Civil Engineering, Khon Kaen University, Thailand), Dr. Sukit Yindeesuk (Department of Highways, Ministry of Transport, Thailand) and Prof. Junho Song at SSRG co-authored the paper.

This paper proposes a new Strut-and-Tie-Model (STM) for deterministic and probabilistic prediction of the shear strength of reinforced concrete deep beams, and develops corresponding limit-state design formula and reduction factors for a reliable design of reinforced concrete deep beams. A Bayesian parameter estimation method was used to reduce the bias and quantify uncertain errors of the proposed model based on a large database of experimental results. Seven different deterministic models which were selected from code of practices and literatures were compared with the proposed models. The abstract of the paper is given below.

Abstract : Reinforced concrete deep beams are structural beams with low shear span-to-depth ratio, and hence in which the strain distribution is significantly nonlinear and the conventional beam theory is not applicable. A strut-and-tie model is considered one of the most rational and simplest methods available for shear strength prediction and design of deep beams. The strut-and-tie model approach describes the shear failure of a deep beam using diagonal strut and truss mechanism: The diagonal strut mechanism represents compression stress fields that develop in the concrete web between diagonal cracks of the concrete while the truss mechanism accounts for the contributions of the horizontal and vertical web reinforcements. Based on a database of 406 experimental observations, this paper proposes a new strut-and-tie-model for accurate prediction of shear strength of reinforced concrete deep beams, and further improves the model by correcting the bias and quantifying the scatter using a Bayesian parameter estimation method. Seven existing deterministic models from design codes and the literature are compared with the proposed method. Finally, a limit-state design formula and the corresponding reduction factor are developed for the proposed strut-and-tie model.

One can download this paper as Author’s Accepted Manuscript Version from the following URL:

The DOI number of the paper (permanent link) is:

(The full reference information of the paper will be updated at the Publications webpage.)

Strut-tie model for simply supported deep beam

STM Resources: D-Regions Example 02

posted Mar 18, 2014, 9:15 AM by Domain Admin   [ updated Jul 6, 2015, 11:04 PM ]

D-regions example 02

In this example, D-regions define as portion of discontinuity of geometry; for examples, changing from small to larger cross section regions or changing from solid section to opening section. These are clearly illustrated in Fig. (a). 
D-regions can be defined as portions (Fig. (b)) near supports and under pointed load where the non smooth stress field due to the force transfer mechanism occurs. 

Using the concept of D-Regions due to discontinuity of geometry and force transfer mechanism, the examples of D-Regions in a portal frame are illustrated in Fig. (c).  

For the subsequent examples, I will collect tons of D-Regions examples to illustrate how challenging engineers can define this complex state of stress and strain regions when designing a structure.

STM Resources: D-Regions Example 01

posted Mar 8, 2014, 11:27 PM by Domain Admin

To develop understanding of designers in defining the portion of structures as B- or D- regions, tons of examples of D-Regions are provided in this blog. 

D-Regions example 01

This example illustrates D-Regions defined as the followings:

 1)  corbel of a column with transition of cross section 

 2) knee joint connection of a reinforced concrete frame 

 3) dapped ends or half joint of a reinforced concrete girder including the opening inside the girder. 

The concept of defining those D-Regions is to adopt the discontinuity of dimensions or cross section. 

STM Resources: What are B- and D-Regions?

posted Feb 20, 2014, 10:04 PM by Domain Admin

B- (Beam or Bernoulli) Regions or D- (Disturbed or Discontinuity) Regions. B-Regions are parts of a structure in which Bernoulli's hypothesis of straight-line strain profiles applies. D-Regions, on the other hand, are parts of a structure with a complex variation in strain. D-Regions include portions near abrupt changes in geometry (geometrical discontinuities) or concentrated forces (statical discontinuities). Based on St. Venant's principle, the extent of a D-Region spans about one section depth of the region on either side of the discontinuity.

In the figures for buildings and bridges, the unshaded area with a notation B indicates B-Region, and the shaded area with a notation D is used to indicate D-Region. The notations h1, h2, h3, ... are used to denote the depth of structural members. The notations b1 and b2 denote the flange width of structural members.

The examples of B and D Regions in a Building.

The examples of B and D Regions in a Bridge.


Strut-and-Tie (STM) Resources

posted Feb 5, 2014, 9:47 PM by Domain Admin

Strut-and-tie model (STM) has been gradually accepted as one of the practical design and analysis tools for complete structure member and also D-Regions. There are several of websites created for promoting the use of STM by providing theoretical background, code provisions, design examples, research and technical papers and reports, including softwares; for examples, the strut-and-tie resources website by Prof.Kuchma. However, the development of new resources of the method including practical design cases is very rapidly increasing and cause the needs of more updated information available to the engineers everyday.

CAST software for STM

To help promoting this powerful method and response to the huge demands from the practicing engineers, I decide to write series of short blogs relevant to hints, tips, and summary of the use of STM including some design aids, calculations, cases studies, software uses, and updated researches of the method.

If you have any comments,suggestions,or ideas to share with me, please contact me.

New IG Site

posted Dec 1, 2013, 1:51 PM by Domain Admin   [ updated Dec 1, 2013, 1:54 PM ]

During this month, I am going to introduce my new IG site for posting engineering photos taken during my work and travel around the world. The first sets of photos have been sharing gradually during my technical trip to Croatia. 

Please visit my IG  at

Construction Stage Analysis of Continuous Box Girder Constructed in Highly Horizontal Curve Alignment

posted Oct 14, 2009, 11:16 PM by Domain Admin   [ updated Sep 30, 2012, 2:55 AM ]

During The International Conference on Highway Engineering Computing, 2012, I and my colleagues-Rirattanapong T. and Chanintonleela M., published a technical paper entitled "Construction Stage Analysis And Construction of Overpass Bridge Crossing Intersection between Highway No.345 and Highway No. 3100 in THAILAND"  illustrating the application of nonlinear finite element analysis in design and analysis of continuous cast-in-situ box girder aligned in highly horizontal curve. The overpass bridge is geometrically designed to form the highly horizontal curve alignment with 2 traffic lanes composing of 7 continuous spans of 30+2x36+45+2x36+30 meters for the total length of 249 meters. Due to the highly horizontally curved geometry of the bridge, the analysis and design of the bridge are thus performed by utilizing the construction stage analysis in order to obtain the most effective and safety construction method of the bridge. To perform the construction stage analysis of the bridge, the finite element analysis (FEA) utilizing curved spine beam elements including the geometrical nonlinearity and time dependent effects for construction stage analysis is employed. Based on the FEA results, the direction of the construction of the highly horizontal curve continuous bridge alignment is a very important factor.

The uni-directional construction method using only cast-in-situ bridge segments from on side to another side of the bridge along the horizontal curve alignment could result in the overload causing distresses of the single bored piles with diameter of 1.80 meters supporting the box girder due to bi-axial bending. To be more economic and feasible to adopt the same pile diameter without any damages of the pile, bi-directional construction method incorporating both cast-in-situ and precast segments of the bridge is adopted based on FEA results. The details of the analysis and design including the achievement in the construction of the bridge can be refered to the paper.

An approach to improve the use of Strut-and-Tie Model (STM) for better structural performance design

posted Oct 14, 2009, 11:11 PM by Domain Admin   [ updated Sep 30, 2012, 3:41 AM ]

Based on several years of my practical and research experience in using Strut-and-Tie Model (STM) in design and analysis of D-regions-both simple and complex types, I found that design provisions, such as those in Appendix A of ACI318-08, CEB-FIP, AASHTO LRFD, etc., consist of rules for evaluating the capacity of the load-resisting truss that is idealized to carry the forces through the D-Region. These code rules were primarily derived from test data on simple D-Regions such as deep beams and corbels. However, these STM provisions are taken as being sufficiently general and conservative that they can be used for the design of all possible D-Regions, including those regions in which a highly statically indeterminate and complex truss is selected and designed to carry the imposed loadings. Since STM design provisions are only for capacity assessment and given the wide range of applicability of the method, members designed using these STM provision may not necessarily exhibit satisfactory performance under service load levels or during overloads.

Thus, I can simply point out more particular limitations of current STM design provisions include: (1) no methodology for satisfactorily estimating the complete load-displacement response history, cracking loads, stress and strain states in reinforcement, and failure modes; (2) a lack of guidance for selecting the shape, dimensions, and stress limits of STM components; (3) a lack of guidance for proportioning of forces in statically indeterminate STM designs; and (4) an inability to employ performance-based design concepts.

To overcome these limitations, the new approach is proposed based on an experimental and computational program conducted during my PhD research at University of Illinois. In addition, my PhD research also aimed to generate the data needed for evaluating and validating the STM approach, for advancing STM shape selection techniques, and also to develop more reliable computational models for predicting the response of cracked structural concrete. These research studies result in a new approach for design and analysis D-Regions for better structural performance of D-Regions. In addition, the approach enables automated nonlinear FEA design validation that integrates the current STM design provisions with two additional components: (1) the shape selection technique of STM based on topology optimization and (2) the new automated nonlinear FEA tool that was specialized for modeling and analyzing complex D-Regions.

For more information and details, please refer to my Ph.D. Dissertation.

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