## Main Article Content

## Abstract

This paper presents a non-linear analysis of three reinforced and two partially prestressed concrete solid beams based on a 20 node isoparametric element using an in-house 3D finite element program. Anon linear elastic isotropic model, proposed by Kotsovos, was used to model concrete behaviour, while steel was modelled as an embedded element exhibiting elastic-perfectly plastic response. Allowance was made for shear retention and for tension stiffening in concrete after cracking. Only in a fixed direction, smeared cracking modelling was adopted. The beams dimensions were 300x300 mm cross section, 3800 mm length and were subjected to combined bending, torsion and shear. Experimental results were compared with the non-linear predictions. The comparison was judged by load displacement relationship, steel strain, angle of twist, failure load, crack pattern and mode of failure. Good agreement was observed between the predicted ultimate load and the experimentally measured loads. It was concluded that the present program can confidently be used to predict the behaviour and failure load of reinforced and partially prestressed concrete solid beams subjected to a combined load of bending, torsion and shear.

## Keywords

## Article Details

*How to Cite*

*The Journal of Engineering Research [TJER]*,

*5*(1), 79–96. https://doi.org/10.24200/tjer.vol5iss1pp79-96

* * References

- Alnuaimi A.S. and Bhatt, P., 2006, "Design of Reinforced Concrete Solid Beams, Structures and Buildings Journal," Thomas Telford Limited, Vol. 159(4), pp. 197-216.
- Alnuaimi, A.S., 2007, "Direct Design of Partially Prestressed Concrete Solid Beams Structural Engineering and Mechanics,” Techno-Press Ltd, Vol. 27(6), pp. 741-771.
- Bhatt, P. and Lim, B.T., 1999a, "Flat Slab-Column Junctions with Shear and Moment Transfer: A Comparison between Finite Element Predictions and Experiments," Proc. of 7th ACME Conference, University of Durham, (Ed. Bettes, P.) pp. 11 - 14.
- Bhatt, P. and Lim, B.T., 1999b, "Punching Shear Capacity of Internal Column-Flat Slab Junction with In-Plane Restraint: A Comparison between Finite Element Predictions and Experiments. Developments in Analysis and Design Using Finite Element Methods," Civil-Comp Press, (Ed. B.H.V. Topping), pp. 141 - 147.
- El-Nuonu, G. F. R., 1985, "Design of Shear Wall-Floor Slab Connections. Ph.D. thesis, University of Glasgow.
- Ibell, T.J., Morley, C.T. and Middleton, C.R., 1998, "An Upper-bound Plastic Analysis for Shear," Magazine of Concrete Research, Vol. 50(1), pp. 67-73.
- Kotsovos, M.D. and Newman, J. B., 1979, "A Mathematical Description of the Deformation Behaviour of Concrete under Complex Loading," Magazine of Concrete Research, Vol. 31(107), pp. 77-90.
- Kotsovos, M.D. and Pavlovic, M.N., 1995, Structural Concrete, Finite Element Analysis for Limit-State Design," Thomas Telford Publications, 1 Heron Quey, London E14 4JD.
- Kotsovos, M.D., 1979, "A Mathematical Description of the Strength Properties of Concrete under Generalized Stress," Magazine of Concrete Research, Vol. 31(108), pp. 151-158.
- Lim, B.T. and Bhatt, P., 1998, "Punching Shear Failure of Flat Slabs: A Comparison between Finite Element Predictions and Experiments," Advances in Civil and Structural Engineering Computing for Practice, (Ed. B. Topping), Civil Comp-Press, pp. 163 - 173.
- MacGregor, J.G. and Ghoneim, M.G., 1995, "Design for Torsion. ACI Structural Journal," Vol. 92-S20, pp. 211-218.
- Mitchell, D. and Collins, M.P., 1974, "Behaviour of Structural Concrete Beams in Pure Torsion," Publication No. 74-06, Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada.
- Ojha Surendra, K., 1974, "Deformation of Reinforced Concrete Rectangular Beams under Combined Torsion, Bending and Shear.," ACI Journal, Vol. 71- 26, pp. 383-391.
- Preston, J.I. and Austin, M.A., 1992, "Solid Modelling of RC Beams:2, Computational Environment," Journal of Computing in Civil Engineering, Vol. 6(4), pp. 404-416.
- Rabczuk, T. and Eibl, J., 2004, "Numerical Analysis of Prestressed Concrete Beams using a Coupled Element Free Galerkin/Finite Approach," Int. J. of Solid and Structures, Vol. 41(3-4), pp 1061-1080.
- Rahal, K.N., 2000, "Torsional Strength of Reinforced Concrete Beams," Canadian Journal of Civil Engineering, Vol. 27, pp. 445 - 453.
- Rahal, K.N. and Collins, M.P., 1995, "Analysis of Sections Subjected to Combined Shear and Torsion ," A Theoretical Model. ACI Structural Journal, Vol. 92(4), pp. 459-469.
- Thurlimann, B., 1979, "Torsional Strength of Reinforced and Prestressed Concrete Beams-CEB Approach," Institut fur Baustatik und konstruktion, ETH. Zurich., Vol. 92, pp 117-143. Also can be found in: American Concrete Institute, Detroit, SP59

#### References

Alnuaimi A.S. and Bhatt, P., 2006, "Design of Reinforced Concrete Solid Beams, Structures and Buildings Journal," Thomas Telford Limited, Vol. 159(4), pp. 197-216.

Alnuaimi, A.S., 2007, "Direct Design of Partially Prestressed Concrete Solid Beams Structural Engineering and Mechanics,” Techno-Press Ltd, Vol. 27(6), pp. 741-771.

Bhatt, P. and Lim, B.T., 1999a, "Flat Slab-Column Junctions with Shear and Moment Transfer: A Comparison between Finite Element Predictions and Experiments," Proc. of 7th ACME Conference, University of Durham, (Ed. Bettes, P.) pp. 11 - 14.

Bhatt, P. and Lim, B.T., 1999b, "Punching Shear Capacity of Internal Column-Flat Slab Junction with In-Plane Restraint: A Comparison between Finite Element Predictions and Experiments. Developments in Analysis and Design Using Finite Element Methods," Civil-Comp Press, (Ed. B.H.V. Topping), pp. 141 - 147.

El-Nuonu, G. F. R., 1985, "Design of Shear Wall-Floor Slab Connections. Ph.D. thesis, University of Glasgow.

Ibell, T.J., Morley, C.T. and Middleton, C.R., 1998, "An Upper-bound Plastic Analysis for Shear," Magazine of Concrete Research, Vol. 50(1), pp. 67-73.

Kotsovos, M.D. and Newman, J. B., 1979, "A Mathematical Description of the Deformation Behaviour of Concrete under Complex Loading," Magazine of Concrete Research, Vol. 31(107), pp. 77-90.

Kotsovos, M.D. and Pavlovic, M.N., 1995, Structural Concrete, Finite Element Analysis for Limit-State Design," Thomas Telford Publications, 1 Heron Quey, London E14 4JD.

Kotsovos, M.D., 1979, "A Mathematical Description of the Strength Properties of Concrete under Generalized Stress," Magazine of Concrete Research, Vol. 31(108), pp. 151-158.

Lim, B.T. and Bhatt, P., 1998, "Punching Shear Failure of Flat Slabs: A Comparison between Finite Element Predictions and Experiments," Advances in Civil and Structural Engineering Computing for Practice, (Ed. B. Topping), Civil Comp-Press, pp. 163 - 173.

MacGregor, J.G. and Ghoneim, M.G., 1995, "Design for Torsion. ACI Structural Journal," Vol. 92-S20, pp. 211-218.

Mitchell, D. and Collins, M.P., 1974, "Behaviour of Structural Concrete Beams in Pure Torsion," Publication No. 74-06, Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada.

Ojha Surendra, K., 1974, "Deformation of Reinforced Concrete Rectangular Beams under Combined Torsion, Bending and Shear.," ACI Journal, Vol. 71- 26, pp. 383-391.

Preston, J.I. and Austin, M.A., 1992, "Solid Modelling of RC Beams:2, Computational Environment," Journal of Computing in Civil Engineering, Vol. 6(4), pp. 404-416.

Rabczuk, T. and Eibl, J., 2004, "Numerical Analysis of Prestressed Concrete Beams using a Coupled Element Free Galerkin/Finite Approach," Int. J. of Solid and Structures, Vol. 41(3-4), pp 1061-1080.

Rahal, K.N., 2000, "Torsional Strength of Reinforced Concrete Beams," Canadian Journal of Civil Engineering, Vol. 27, pp. 445 - 453.

Rahal, K.N. and Collins, M.P., 1995, "Analysis of Sections Subjected to Combined Shear and Torsion ," A Theoretical Model. ACI Structural Journal, Vol. 92(4), pp. 459-469.

Thurlimann, B., 1979, "Torsional Strength of Reinforced and Prestressed Concrete Beams-CEB Approach," Institut fur Baustatik und konstruktion, ETH. Zurich., Vol. 92, pp 117-143. Also can be found in: American Concrete Institute, Detroit, SP59