Strut-and-Tie Model of a deep beam

By Nan Gao.

STM is a useful method in the analysis of the D regions in concrete structures. Today’s case study is using STM to design a deep beam. This case is from Prof. James K. Wight’s paper “Strut-and-tie model for deep beam design“. First of all, I repeated the STM model of Prof. Wight, but converted all the English units into metric units. It is a practice for me. Secondly, I choose a different STM model and try to figure about whether this simpler triangle STM model could work. Thirdly, I used traditional beam theory to design this deep beam and compared the result with the STM models. The calculation is based on Chinese code GB 50010-2010. Finally, I used SAP2000 to analyze the same deep beam and made a comparison with results of STM.

1. REPEAT PROF. WIGHT’S STM MODEL IN METRIC UNITS

2. TRY ANOTHER VERSION OF STM MODEL

Compared with former STM model, the longitudinal reinforcement is the same, but the vertical reinforcement in this model is much small. However, there are some issues. The inclined angle is very small and is very near to the lower limit. Considering the decrease in the amount of reinforcement and the smaller inclined angle, maybe a better solution is to make the height of the beam a little higher. Thus, the angle could be a bit bigger and the amount of reinforcement will not increase significantly.

3. DESIGN THE SAME DEEP BEAM FOLLOWING CHINESE GB 50010-2010

Compared with STM models, the longitudinal reinforcement is similar. However, the required amount of vertical reinforcement is much larger. The traditional beam theory is much more conservative in the shear design of STM models.

4. ANALYZE THE SAME DEEP BEAM WITH SAP2000

The required amount of longitudinal reinforcement in the left part is larger than the right part. Only the first STM model reflects this characteristic. The second STM model and the calculation based on GB 50010-2010 has the same required amount of reinforcement in the whole span. Thus, Prof. Wight’s STM model is more rational.

In this image, we can see the two zones which required larger amount of vertical reinforcement. They are the locations of Struts in STM models. Also, the Tie 3-4 in Prof. Wight’s model is reflected in this image.

We can see the two bottle-shaped concrete struts very clearly. The stress in the left strut is larger than the right strut. This corresponds with the analysis of the STM model.

References:

• Wight, J.K., and Parra-Montesinos, G. (2003). “Strut-and-tie model for deep beam design“, ACI Concrete International, Vol. 25, No. 5, pp. 63-70
• Wight, J.K.(2008). Keynote “Development of the Strut-and-Tie Method for Appendix A of the Building Code (ACI 318-08)”

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