Chapter 4: Parametric Study of the EN 1992-1-1 & 3 and Corresponding Codes BS 8007 & BS
4.8 Parameter Sensitivities in Crack Model: Summary and Concluding Remarks
4.7.2 Influence of Section Thickness on the BS 8007 End Restraint Crack Model
The end restraint estimation in BS 8007 follows the same approach as for edge restraint. The relationship of reinforcement to crack width for various section thicknesses will be as mentioned for edge restraint (in the previous section) where a reinforcement ratio of 0.8% As was necessary for the 0.2 mm crack width to be met. This would mean that EN 1992 requires from 50% (at 500 mm) to beyond 63% (for section thickness 400 mm down to 250 mm) more reinforcement than BS 8007 to meet the 0.2 mm crack width limit. It is also evident from this result that the EN 1992 end restraint crack model requires more reinforcement to meet the crack width limit than the EN 1992 edge restraint crack model when compared against the BS 8007 crack model– indicating that it was the more conservative of the two EN 1992 models.
φ/ρp, eff ratio:
The investigation into the φ/ρp, eff ratio’s influence on the crack spacing revealed that this ratio contributes considerably to the estimated crack spacing. This, in turn, would result in φ/ρp, eff
contributing considerably to the ultimate crack model.
Effective tension area:
The effective tension area had been found to be predominately limited to 2.5(c + φ/2) for similar covers and bar diamters. In the cases where the bar diameter or the concrete cover values are increased, h/2 becomes the limiting effective tension area. For a combination of 40 mm cover and bar diameter of 16 mm or 20 mm, the effective tension area will always give 2.5(c + φ/2) for any section thickness. For a 250 mm thick concrete section, 40 mm concrete cover and 20 mm reinforcing bar diameter the effective depth for hc,eff = 2.5(c + ϕ/2) and h/2 both return a value of 125 mm. Thus this combination section thickness, cover and bar diameter will be considered in the reliability analysis; giving opportunity for the direct comparison of reliability models containing either effective depth variations. In this way, the effect of the effective tension areas may be assessed. The effective tension area has an obvious effect on the φ/ρp,eff ratio which had already been found to contribute considerably to the crack model.
Crack width limit:
The crack width limit was found to have a considerable influence on the restrained strain crack model for both EN 1992 and BS 8007 design codes. This influence applied both to the edge and end restraint conditions. Thus, as found in previous research, the adoption of the more onerous crack limits of EN 1992 would subsequently have a significantly negative financial implication in design. A decrease in the crack limit results in an increase in the demand for reinforcing (and thus an increase in the cost of construction).
Section thickness:
The section thickness has been found to have some influence on the crack model for both the end and edge restraint. A variation of the section thickness will be used in the reliability model to gauge what influence it bears on the crack model’s overall reliability level. Section thickness was found to bear more of an influence on the end restraint crack model than the edge restraint crack model. A reference value of 250 mm section thickness will be used in reliability analysis.
Bar diameter:
Increasing bar diameter, as before mentioned, resulted in h/2 being the limiting effective tension area. Little variability in the influence on the crack model was experienced where the bar
diameters were varied. This was particularly true for bar diameters beyond 20 mm where the same effective tension area is produced each time (h/2).
Reinforcement area:
There was a noticeable correlation between the EN 1992 crack model and the amount of reinforcement used. Clearly, the decline in the crack widths estimated by the crack model came with an increase in the amount of tension reinforcement used. It had been determined in past investigations on the reliability of reinforced concrete members that the failure probability is sensitive to, among other basic variables, the reinforcement ratio in the member (Holický, Retief and Wium, 2010). Therefore, it is suggested that the sensitivity of the reliability of the crack model be tested against a variation of reinforcement ratios for various basic variables. For the selected reference case of 250 mm section thickness, 40 mm cover and 20 mm rebar diameter, a reinforcement ratio of 1748 mm 2 and 2202 mm 2 per section face for edge and end restraint respectively for the 0.2 mm crack limit to be met.
Restraint degree:
The restraint degree is not a parameter used in the estimation of end restraint in EN 1992. The edge restraint crack model has been proven to be noticeably influenced by the restraint under edge restraint conditions. Historically, according to BS 8110-2, the restraint degrees (restraint factors) have been found to be greater than a value of 0.7. EN 1992 includes creep into its restraint degree, giving a value of full restraint of up to 0.5. A fully restrained member will be considered in the reliability analysis. However, much like in the parametric study, the influence of the restraint factor on the reliability of the edge restraint crack model will be investigated by varying the restraint factor from 0.1 to 0.5. Practically, this considers an array of configurations, and thus restraint conditions under which the restrained member is nearly free to move and then increasingly restricted up to full restraint.
Following after the parametric study, it was determined that the end restraint model was the most conservative of the two external restraint conditions assessed using EN 1992 (as BS 8007 modelled edge and end restraint in the same way). In other words, more reinforcement is required for a member subjected end restraint to meet the crack limit as compared to the edge restraint condition. Also, larger crack widths were determined using the end restraint model. Comparing BS 8007 and relevant parts of BS 8110-2 to corresponding codes EN 1992-3 and EN 1992-1-1, Eurocode was found to be more conservative than the British codes. From the parametric study conducted above, a reasonable selection of design variables for which the reliability analysis could be conducted may be established. It was paramount that the effect of influential parameters be tested in the reliability analysis of the EN 1992 crack model. Hence, the variables found to be
particularly influential to the EN 1992 crack model and thus potentially influential to the reliability of the crack model include the following: concrete cover, the φ/ρp, eff ratio, the effective tension area, section thickness, the reinforcement area as well as the restraint degree.