Computational & Technology Resources
an online resource for computational,
engineering & technology publications
engineering & technology publications
Civil-Comp Proceedings
ISSN 1759-3433
ISSN 1759-3433
CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 165
Strength Optimum Design of Beams with MC90
M.H.F.M. Barros+, A.F.M. Barros* and C.C. Ferreira+
+Civil Engineering Department, Faculty of Science and Technology, University of Coimbra, Portugal
*IDMEC/IST, Mechanical Engineering Department, IST, Lisbon, Portugal
Full Bibliographic Reference for this paper
M.H.F.M. Barros, A.F.M. Barros, C.C. Ferreira, "Strength Optimum Design of Beams with MC90", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 165, 2004. doi:10.4203/ccp.79.165
Keywords: reinforced concrete, beam ultimate design, MC90 equation, optimum reinforcement.
Summary
A model for the optimal design of rectangular reinforced concrete sections is
developed considering the stress strain diagram for concrete under compression
indicated in the MC90. The strain in concrete in the rupture condition is defined in
terms of the non-dimensional neutral axis position
, by the use of Heaviside
functions, as described in Barros et al. [4], with
given by:
The strain in the tension steel is defined by:
Considering the equilibrium force and bending moment equations, respectively:
the following expressions are developed: optimal area of steel and optimal steel ratio between compression and tension steel. The optimum reinforcement ratio is:
The corresponding optimum location defined by the ratio between total area of compression steel
and total area of tension steel 
is:
In these expressions
and 
are parameters obtained from the integration of
equilibrium equations, derived in the paper. A comparison is made with the present
model and the parabola-rectangle diagram provided in the EC2 for different
concrete classes exemplified in Figure 1.
, by the use of Heaviside
functions, as described in Barros et al. [4], with
given by:
 |
(55) |
The strain in the tension steel is defined by:
 |
(56) |
Considering the equilibrium force and bending moment equations, respectively:
 |
(57) |
 |
(58) |
the following expressions are developed: optimal area of steel and optimal steel ratio between compression and tension steel. The optimum reinforcement ratio is:
 |
(59) |
The corresponding optimum location defined by the ratio between total area of compression steel
and total area of tension steel is:
 |
(60) |
In these expressions
and are parameters obtained from the integration of
equilibrium equations, derived in the paper. A comparison is made with the present
model and the parabola-rectangle diagram provided in the EC2 for different
concrete classes exemplified in Figure 1.
Ackowledgment
This work is developed within the Programa Operacional do Quadro Comunitário de Apoio, Eixo 2, Medida 2.3 do POCTI, FEDER, termed POCTI/P/ECM/12126/98/2001, QCA III.References
- 1
- EC2 . PrEN 1992-1. (Final Draft). 2001.
- 2
- CEB-FIP Model Code 1990. Thomas Telford 1993.
- 3
- CEB-FIP Manual on Bending and Compression 1982. No 141.
- 4
- M.H.F.M. Barros, A.F.M. Barros and C.C. Ferreira. "Closed Form Solution of Optimal Design of Rectangular Reinforced Concrete Sections", accepted for publication, Engineering Computations, Emerald, 2004. doi:10.1108/02644400410565298
- 5
- M.H.F.M. Barros, C.C. Ferreira and A F. M. Barros. "Integração do diagrama de tensões de compressão no betão em flexão desviada usando a equação do MC90" Construlink, http://www.construlink.com, Vol.1 no3, 41-49, 2003.
purchase the full-text of this paper (price £20)
go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £135 +P&P)