Principles of Strut-and-Tie Modelling

Strut-and-Tie Model (STM) design method has never been favoured by most of our local engineers, primarily due to the lack of coverage in the previous design standards (such as BS 8110 or BS 5400). However, with Malaysia embarking on the use of Eurocode 2 (EC 2) for design of concrete structures and EC 2 includes STM. Therefore, a revisit on this design method is essential. This article provides a general overview on the principles of STM and I hope you will find it useful. Please feel free to leave any comments at the end of this article.

Strut-and-Tie Model (STM) is a simple, rational and powerful design tool for modelling and detailing of non-standard structural concrete members. It is used commonly in the regions where conventional flexural beam theory does not apply, i.e. where plane section does not remain plane, or in other words, a highly disturbed non-linear strain distribution. The disturbed region or usually known as D-region arise at geometrical discontinuities, supports and concentrated loads. Examples of D-regions include pile caps, dapped-end beams, corbels, deep beams, walls with openings and connections.

The concept of STM has been around for quite some time now. It’s history can be dated back as early as 1900’s with the introduce of truss analogy originally proposed by Ritter (1899) and Mörsch (1909). But it is not until the 80’s and 90’s by the work of Schlaich and Schäfer (1987, 1991) where STM received widespread attention and acceptance. For some, STM is even considered to be the pioneer in the development of a unified design approach for structural concrete.

B-Regions and D-Regions

Concrete structures can be divided into two primary regions; namely B-regions (or “beam” regions) and D-regions (or “disturbed” regions). B-regions is where the Bernoulli hypothesis of linear strain distribution (assumption of that plane sections remain plane) is valid and can be designed with standard design code methods. On the other hands for D-regions, the strain distribution is non-linear. STM design is best to use for this localised D-regions. Although generalised STM can be used to model the whole structural concrete members, but STM is found to popularise specifically on the D-regions only.

The classification of these two distinct regions can be easily identified by Saint-Venant’s principle, where the discontinuities are assumed to extend a distance “h” from the effect of concentrated load or abrupt change in geometry. Figure 1 shows examples of discontinuities with the resulting D-regions shaded.

Development of Strut-and-Tie Model

STM is a method of design that idealised the complex states of stress within a D-region of a concrete member into a statical force system that comprised of struts, ties and nodes elements. The struts represent the concrete compression stress fields, and ties represent the internal tensile reinforcement or occasionally can also represent concrete tensile tie for members without shear reinforcement such as slab. Both struts and ties are positioned as closely to the direction and centroid of its respective internal stress fields. According to Schlaich et al. (1987), the position of struts and ties should not deviate ±15° from the main direction of the internal stress fields. All struts and ties are connected at the nodes or nodal zones, where all forces are transferred . These regions are subject to a multi-directional state of stress, that is biaxial state of stress for 2-D model and triaxial state of stress for 3-D model.

STM is basically a lower bound method of limit analysis. The main requirements are to ensure that equilibrium condition is satisfied and to proportion the cross sectional areas of struts and ties such that all their stresses must be below defined code limits. The STM design process can be summarised in the following:

1. Define the boundaries of the D-regions and then calculate the sectional forces that act on the boundaries;
2. Outline the strut-and-tie model layout in relation to the internal stress fields and solve the truss member forces;
3. Provide the required tensile reinforcement for the tie capacity and ensure sufficient anchorage is available in the nodal zones for force transfer;
4. Dimensioning the struts and nodes, and check their capacity in relation to the design forces;
5. Detailing on the reinforcement to ensure sufficient ductility.

I hope this brief overview on the principle of strut-and-tie model is useful for you. In my next article, I will explain more on the STM design provisions. Stay tuned 🙂 , feel free to leave any comments on this article. Thank you so much.

References

1. Ritter W., “Die Bauweise Hennebique”, Schweizerische Bauzeitung, Vol. 33, No. 7, Feb 1899, pp. 59-61.
2. Mörsch E., “Concrete-Steel Construction”, E. P. Goodrich, Translation, McGraw Hill, New York, 1909, 368 pp.
3. Schlaich J., Schäfer K. and Jennewein M., “Toward a Consistent Design of Structural Concrete”, PCI Journal, Vol. 32, No. 3, May-June 1987, pp. 74-150.
4. Schlaich J. and Schäfer K., “Design and Detailing of Structural Concrete Using Strut-and-Tie Models”, The Structural Engineer, Vol. 69, No. 6, Mar 1991, pp. 113-125.