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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 73
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Paper 56

Analytical Solutions for Uniaxial Bending Design of Reinforced Concrete T Cross Sections according to The Eurocode 2 Standard

M. Skrinar

Faculty of Civil Engineering, University of Maribor, Slovenia

Full Bibliographic Reference for this paper
M. Skrinar, "Analytical Solutions for Uniaxial Bending Design of Reinforced Concrete T Cross Sections according to The Eurocode 2 Standard", in B.H.V. Topping, (Editor), "Proceedings of the Eighth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 56, 2001. doi:10.4203/ccp.73.56
Keywords: T cross sections, Eurocode 2, reinforced concrete, reinforcement required.

Summary
The uniaxial bending analysis of T cross sections and the bending analysis of rectangular cross sections are both based on the assumption of Bernoulli's-hypothesis (all adjacent plane cross sections remain plane during loading). However, the analysis procedures for T cross sections deviate from the analysis of a rectangular cross section due to a discrete change in the width of the web section caused by the flanges. If the neutral axis in the flexural analysis lies within the flanges, the flexural design follows the same steps as for a rectangular cross section of flange width because the area of concrete below the neutral axis is considered to be cracked and so it does not contribute to the fulfillment of static equilibrium.

If the neutral axis lies within the web, the situation changes completely and some authors suggest that just for approximate or pre-design analysis the area of the concrete under compression in the web might be conservatively ignored in the case of "high profiled" T beams. High profiled T cross sections are considered those with a large flange width to web width ratio, where the value is a usual limit. Some tables and charts found in the literature allow the inclusion of compression stresses in the concrete in the web below the flange into the analysis. These methods are usually based on the approach where the complete concrete cross section under compression is separated into two virtual rectangular parts. The required partial design parameters are afterwards obtained using either charts or equations for both virtual rectangular sections using the border strains of the two fictious parts. When implementing this approach it is necessary to evaluate the required partial characteristic values of the compression zones of both fictious sections very precisely because the final design resistance of the actual cross section in compression is the result of the difference of high values, especially for broad flanges. Although the described procedure can be practically applied in the determination of the required reinforcement in the uniaxial bending analysis of T cross sections, the separation into two virtual sections does not offer a clear insight into the computational procedure and it is thus not appropriate for programming.

To avoid this, the paper presents a detailed analysis of a T cross section with a neutral axis within the web implementing the most detailed design stress-strain relationship for the concrete: the parabola-rectangular diagram.

The paper covers all five possibilities that result from the value of the maximal strain in concrete that appears in the more strongly compressed edge of the compressive zone.

If the maximum strain in the concrete is smaller than , the stresses in the concrete are assumed to have only a parabolic distribution which represents the first case. If the compressive stresses in the top compressed edge exceed the value of , the stress-strain relation is described by the parabola for the strains below , and with a constant value for strains over . The margin between the two mathematical descriptions is thus . This is the motive to distinguish two further cases according to the position of the fibre with the strain : either within the flange or within the web.

For all five cases mentioned, the paper presents the development of the analytical expressions for coefficients (the average value of concrete stresses in the bending compression zone, related to the design value of concrete strength ) and (the related distance of the concrete compression force from the stronger compressed edge of the compressive cross section). These analytical expressions are necessary for the computation of the required cross section of the reinforcements and (if the compression reinforcement is required). The procedure for determination of required cross section, based on equations resulting from equilibrium conditions, is also briefly described.

References
1
ENV 1992-1-1: Eurocode 2: Design of concrete structures. Part 1: General rules and rules for buildings (1991).

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