Chapter 4: Parametric Study of the EN 1992-1-1 & 3 and Corresponding Codes BS 8007 & BS
4.4 Influence of cover versus φ/ρ p, eff
The modelling of crack spacing model is an aspect of crack estimation that differs most across design codes (Beeby & Narayanan, 2005). Such a vast set of possible ways in which crack spacing may be determined is cause for an investigation. This is particularly of interest here where the crack spacing equations adopted by BS 8007 and EN 1992-1-1 have some noticeable differences.
An investigation into the influence of cover and the φ/ρp,eff ratio on crack spacing had been undertaken.
4.4.1 Influence of Cover on Crack Spacing
The first part of this exploration involved assessing the influence of cover on the crack spacing in the EN 1992-1-1: 2004 equation. To examine the influence of cover on crack spacing, the cover was varied and its effect compared against a comparable set of φ/ρp, eff ratios. The section thickness was kept constant at 250 mm and the reinforcing bar diameter remained 16 mm throughout the analysis. The reinforcing bars were assumed to be spaced at 250 mm centre to centre. A section width (b) of 1000 mm was selected for this analysis. The φ/ρp, eff ratio is limited by the effective tension area and only those ratios that were close in value were included in the study. Given the concrete covers chosen and the choice of bar diameter (parameters onto which the effective tension area depends) it was determined that the φ/ρp, eff ratio became constant after the cover value of 50 mm since the limiting effective depth from a 50 mm cover onwards was limited to 2.5(c + ϕ/2). Hence, the ratio developed from concrete cover values greater than 50 mm was compared against a constant φ/ρp, eff ratio and the subsequent findings (as presented in Table 4.1) were made:
Table 4.1: Influence of Cover on EN 1992 Crack Spacing Model
he,eff (mm)
cover (mm)
bar dia.
(mm)
As/face (mm2)
h/2 2.5(c + φ/2) ρp,eff φ/ρp,eff
(mm)
Sr,max
(mm)
Term
‘X’ %
Term
‘Y’ %
40 16 804 125 120 0.0067 2387 948 14 86
50 16 804 125 145 0.0064 2487 1016 17 83
60 16 804 125 170 0.0064 2487 1050 19 81
70 16 804 125 195 0.0064 2487 1084 22 78
80 16 804 125 220 0.0064 2487 1118 24 76
100 16 804 125 270 0.0064 2487 1186 29 71
Notes:
Cover varied as presented whilst only the shaded values considered in study
Reinforcement spacing was set at 250 mm centre to centre
he, eff is limited to the lesser of h/2 or 2.5(c + φ/2). The value for he, eff stabilised after cover = 50 mm and so values φ/ρp, eff became constant thereafter.
Term ‘X’ = 3.4c
Term ‘Y’ = 0.425k1k2ϕ/ρp, eff
If one were to consider the two terms (the cover and effective reinforcement ratio term) in the EN 1992-1-1: 2004 crack spacing model separately, an estimation of either one’s influence may be more clearly assessed. Considering that the crack equation is Sr, max = 3.4c + 0.425k1k2ϕ/ρp, eff, it may be separated such that the cover term is represented by term ‘X’ = 3.4c and the second half of the crack spacing which deals with the effective reinforcement ratio is represented by term ‘Y’
= 0.425k1k2ϕ/ρp, eff, then the influence held by each term on the overall crack spacing may be assessed. It is evident from the results that an increase in the concrete cover term ‘X’ value brings about an increase in crack spacing calculated, although this increase in crack spacing is marginal.
For cover values 50 and greater used in the assessment presented in Table 4.1, the limiting effective depth was h/2 meaning that the concrete cover had no influence on term ‘Y’ since it did not feature. It is evident from results that concrete cover makes a relatively small contribution on the crack spacing in the EN 1992 crack spacing model. The second term of the crack spacing formula, term ‘Y’, carries a greater influence on the crack spacing model.
A graphical representation of this data is displayed in Figure 4.1. Here, the estimation of crack spacing as done under both EN 1992 and BS 8007 was included. Since BS 8007 does not include the cover variable, it was independent of this variable and thus remained constant as the concrete cover value varied. It can be seen, in the EN 1992 case that increasing the cover resulted in an increase in crack spacing. However, this increase in crack spacing was gradual. It may also be deduced from Figure 4.1 that the EN 1992 crack spacing model predicts larger crack spacing as compared to those calculated from BS 8007. The difference between the predicted crack spacing as calculated from EN 1992 and BS 8007, of course, would increase with an increase in cover value.
Figure 4.1: Influence of Cover on Crack Spacing for Both EN 1992 and BS 8007
4.4.2 Influence of the φ/ρp, eff Ratio on Cracking
To determine the influence of the φ/ρp, eff ratio, the bar diameter was varied in order to vary the φ/ρp, eff ratio. The cover was kept constant at 40 mm and the bar spacing was set at 250 mm centre to centre. The section thickness in this study was fixed at 250 mm. The results of this analysis are presented in Table 4.2. Considering the contribution the φ/ρp, eff ratio makes to the estimated crack spacing (i.e. regarding term ‘Y’ = 0.425k1k2ϕ/ρp, eff) – it can be clearly seen that this ratio is once again a sizeable contributor to the overall value of the crack spacing. Concrete cover, once again, has no impact on term ‘Y’ since the limiting effective depth was h/2 for the selection of concrete covers, bar diameters and section thickness considered in this analysis.
0 200 400 600 800 1000 1200 1400
0 20 40 60 80 100 120
Crack Spacing (mm)
Cover (mm) EN 1992 BS 8007
Table 4.2: The Influence of the φ/pρ, eff Ratio on Crack Spacing as per EN 1992
he,eff (mm)
cover (mm)
bar dia.
(mm)
As/face (mm2)
h/2 2.5(c + φ/2) ρp,eff φ/ρp,eff Sr,max
(mm)
Term
‘Y’ %
40 16 804 125 120 0.0067 2387 948 86
40 20 1257 125 125 0.0101 1989 812 83
40 25 1963 125 131 0.0157 1592 677 80
40 32 3217 125 140 0.0257 1243 559 77
40 40 5027 125 150 0.0402 995 474 71
Notes:
250 mm center to center spacing for reinforcement
Term Y = 0.425k1k2ϕ/ρp, eff
The graphical representation of the effect of the φ/ρp, eff ratio on the crack spacing is displayed in Figure 4.2. It is clear from Figure 4.2 that increases in the φ/ρp, eff brought about an increase in the predicted crack spacing, as would be expected.
The influence of the φ/ρp, eff (or φ/ρ) ratio on crack spacing for both the EN 1992 design code and BS 8007 was compared. The Figure 4.2 shows this comparison between the two codes, here the section thickness was kept constant at 250 mm and the cover to reinforcement remained 40 mm throughout the analysis. It is evident from Figure 4.2 that the crack spacing values obtained through the EN 1992 are greater than those obtained by way of BS 8007. This may be attributed to the inclusion of the cover term in the EN 1992 crack spacing estimation. For instance, considering a reinforcing bar diameter to effective reinforcement ratio of 1592 mm, EN 1992 predicted a crack spacing value of 677 mm whilst the BS 8007 crack spacing model estimated a value of 573 mm (about decrease in value of factor 1.18) – φ/ρp, eff was equal to φ/ρ in this instance since the limiting effective depth was h/2 under both EN 1992 and BS 8007 for reinforcing bar diameter 25 mm. Concrete cover plays an even greater role on the EN 1992 calculated crack spacing at lower reinforcing bar diameters (namely, the 16 and 20 mm wide bars considered in this analysis), thus the difference between the calculated crack spacing of EN 1992 and BS 8007 increases at lower reinforcing bar diameters.
Figure 4.2: The influence of φ/ρp, eff (or φ/ρ) Ratio on Crack Spacing for BS 8007 and EN 1992-1-1 (40 mm Cover and 250 mm Section Thickness).
It is clear from the analysis conducted that the influence of the bar diameter to effective steel content ratio is quite great than that of concrete cover under both codes, making up a large portion of the final crack spacing predicted. This would ultimately affect the crack widths estimated under both codes and in turn the amount of reinforcement required to maintain the stipulated rack width limit. Based on the analysis conducted above, it appears as though EN 1992 is the more conservative of the two codes, requiring more reinforcement to maintain the crack width limit.