Design of reinforced concrete D regions using strut and tie models and nonlinear finite element modelling
Researchers: Dr Robert Vollum, Dr Juan Sagaseta University of Surrey (former research student), Dr Hamidreza Amini (former PhD student), Libin Fang (PhD student)
All reinforced concrete structures consist of D regions in which plane sections do not remain plane unlike B regions which can be designed using standard codified methods. Typical examples of D regions are beam-column joints, deep beams and pile caps. D regions can be designed for stresses calculated with finite element analysis or alternatively with strut and tie models, in which concrete structures are represented as trusses with concrete resisting compression and reinforcement tension.
Dr Vollum is leading an on-going research programme1-17 to develop improved design methods for D regions based strut and tie analysis as well as nonlinear finite element. The aim of the strut and tie based research is to assess the accuracy of the strut and tie modelling technique and to investigate the appropriateness of its underlying assumptions.
This research has shown that strut and tie modelling is a powerful technique which tends to be more robust in its application than many nonlinear finite element based procedures which can be of very variable accuracy dependent on the modelling assumptions.
However, it can be very time consuming to develop accurate strut and tie models without some degree of automation. Therefore, research has been carried out with Amini14-17 to develop a semi-automated finite element based design method for D regions. This research into the design of D regions has resulted in three PhD theses1-3 and 16 journal articles to date.
Context and methodology
The research involves a synthesis of experimental, numerical and analytical methods. The experimental research to date has focussed on studying the behaviour of beam-column joints and short span beams loaded with up to four concentrated loads as shown in Figure 1. Particular emphasis has been placed on measuring the kinematics of the short span beams as they are loaded to failure. In depth measurements have been taken of crack opening and sliding displacements as well as the overall deformation of the beam. This enables an assessment of the contribution of aggregate interlock to shear resistance10-11.
Specialised strut and tie based models have been developed for beam-column joints and simply supported as well as continuous short span beams (see Figure 2). Amini and Vollum’s procedure3, 14-17 for the automated design of reinforcement is implemented in the computer programme NonOpt3 which operates in conjunction with the commercial finite element programme DIANA. Currently, the method makes use of the equations of the Modified Compression Field Theory (MCFT) of Collins et al19 to design the reinforcement for stresses calculated in a nonlinear finite element analysis of the structure. Importantly, the same constitutive equations are used in the nonlinear analysis and the design of the reinforcement.
The reinforcement is designed on the basis of predetermined bands as shown in Figure 3 and is subsequently assessed with nonlinear finite element analysis as shown in Figure 4. The design procedure is iterative since the stresses calculated in the nonlinear analysis depend on the reinforcement arrangement determined in the previous step. The design method works well and is a promising alternative to strut and tie based methods of design.
Vollum RL (1998) Design and analysis of reinforced concrete beam column joints, University of London.
Sagaseta J (2008) The Influence of Aggregate Fracture on the Shear Strength of Reinforced Concrete Beams. PhD thesis, Imperial College London.
Amini Najafian H. (2011) Nonlinear optimisation of reinforcement design for reinforced concrete structures loaded in plane stress. PhD thesis, Imperial College London.
- Vollum, R.L. and Newman J.B., “Towards the design of eccentric beam-column joints”, Magazine of Concrete Research, 51, (1999), 397-407.
- Vollum, R.L. and Newman J.B, “Strut and tie models for the analysis/design of external beam column joints”, Magazine of Concrete Research, 51, (1999), 415-425.
- Vollum R.L and Newman J.B, “The design of external reinforced concrete beam-column joints”, The Structural Engineer, 77(23&24), (1999), 21-27.
- Vollum R.L. and Parker D., External beam–column joints: design to Eurocode 2, Magazine of Concrete Research, 60, (2008), 511-521.
- Sagaseta J. and Vollum R.L., Non-linear finite element analysis of shear critical high strength concrete beams, ACEE, (2009), 95-106.
- Bukhari I.A., Vollum RL, Ahmad S, and Sagaseta J., “Shear strengthening of reinforced concrete beams with CFRP”, Magazine of Concrete Research, 62, (2010), 65-77.
- Sagaseta J. and Vollum R.L., “Shear design of short-span beams”, Magazine of Concrete Research, 62, (2010), 267-282.
- Sagaseta J. and Vollum R.L., “Influence of aggregate fracture on shear transfer through cracks in reinforced concrete”, Magazine of Concrete Research, 63 (2011), 119-137.
- Sagaseta J. and Vollum R.L., “Influence of beam cross-section, loading arrangement and aggregate type on shear strength”, Magazine of Concrete Research, 63 (2011), 139-155.
- Bukhari IA, Vollum RL, Ahmad S, et al, Shear strengthening of short span reinforced concrete beams with CFRP sheets, The Arabian Journal for Science and Engineering B, 38 (2013), 523-536
- Amini Najafian H, Vollum RL, Automated nonlinear design of reinforced concrete D regions, Structural Engineering and Mechanics, (2013), 46 (1), 91-110
- Authors:Amini Najafian H, Vollum RL
- Authors:Abela JM, Potts DM, Vollum RL, Izzuddin BA
- Amini Najafian H, Vollum RL, Design of planar reinforced concrete D regions with nonlinear finite element analysis, Engineering Structures, (2013) 51, 211-225
- Authors:Amini Najafian H, Vollum RL
- Vollum RL, Amini Najafian H, Optimising reinforcement design in D regions using non-linear finite-element analysis, Magazine of Concrete Research, (2013), 65, 234-247
- Amini Najafian H, Vollum RL, Fang L, (2013) Comparative assessment of finite element and strut and tie based design methods for deep beams, Magazine of Concrete Research, l:65, ISSN:0024-9831, Pages:970-986
Collins MP, Bentz EC, Sherwood EG, Xie L. (2008) An adequate theory for the shear strength of reinforced concrete structures. Magazine of Concrete Research;60(9):635–50