Strut and Tie Model

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28/2/2014 Strut-and-Tie Model of a deep beam | Note of Studying Structural Engineering

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Note of Studying Structural Engineering

Strut-and-Tie Model of a deep beam

01 Saturday Dec 2012

P

OSTED

BY

N

AN

G

AO

IN

C

ASE

S

TUDIES

≈ 4 C

OMMENTS

concrete structure, geometric method, SAP2000, Strut-and-Tie, truss

As I discussed in this blog article Strut-and-tie A to Z, 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.

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Compared with former STM model, the longitudinal reinforcement is a bit larger, 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

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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.

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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.

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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

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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. “Strut-and-tie model for deep beam design“, ACI Concrete

International, Vol. 25, No. 5, 2003, pp. 63-70

Wight, J.K. Keynote “Development of the Strut-and-Tie Method for Appendix A of the Building Code

(ACI 318-08)

“, 2008

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Strut and Tie Model

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Note of Studying Structural Engineering

Strut-and-Tie Model of a deep beam

01 Saturday Dec 2012

P

OSTED

BY

N

AN

G

AO

IN

C

ASE

S

TUDIES

≈ 4 C

OMMENTS

concrete structure, geometric method, SAP2000, Strut-and-Tie, truss

As I discussed in this blog article Strut-and-tie A to Z, 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.

Compared with former STM model, the longitudinal reinforcement is a bit larger, 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.

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.

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

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. “Strut-and-tie model for deep beam design“, ACI Concrete

International, Vol. 25, No. 5, 2003, pp. 63-70

Wight, J.K. Keynote “Development of the Strut-and-Tie Method for Appendix A of the Building Code

(ACI 318-08)

“, 2008

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thoughts on “Strut-and-Tie Model of a deep beam”

1.

Manuel Álvarez

2012-12-01 at 19:39

Great work, thanks for sharing.

I have some information about structures, foundations and geotechnical works:

http://manuelalvarezlopez.blogspot.com.es/p/estructuras.html

REPLY

2. Pingback: Strut-and-tie A to Z « Note of Studying Structural Engineering

3.

Nurzhan

2013-05-09 at 23:37

Great work. Thank you. It is really helpful.

REPLY

4.