With reference to concrete with normal aggregate, the specific weight of structural elements can be assumed equal to the following nominal values:
• plain concrete 24.0 kN/m3
• reinforced concrete 25.0 kN/m3 (coefficient of variation 0.06).
Table 1.11: Concrete Production Control
The control charts and the relative diagrams of a continuing concrete production in a given plant are reported below. The charts are to be used following the indications listed below:
• each chart should refer to a homogeneous type of mix constant in time;
• the mix should be named with the class and with a market specification of the final product;
• basic data should be added (content of cement, water/cement ratio, admixture content and aggregate size);
• the type of curing should be specified, also via the evaluation of b of the hardening law (see Table1.1);
• it has to be specified whether strength measurements are referred to the reference age (28 days) for at earlier agesfj;
• 28-day tests should always be carried, tests at earlier ages only if required by early stages verifications;
• the chart is made of consecutive sheets, one for each solar month, where nor- mally each row corresponds to a day;
• one concrete sample has to be taken every production day and cured in the same environment of casting;
• a sample consists of two specimens for 28-day tests, plus two specimens for earlier ages’tests if required;
• data, written on the row of the day of sampling, should start with the date of test;
• the strength measurements of the two specimens and the mean value should then be reported;
• if measured on cubic specimens, the strength value should be reduced with a factor of 0.83 to obtain the cylinder strengthfj;
• the mean value fj should be corrected based on the age j of the specimen to deduce the reference (28 days) strength;
• the statistics should be calculated with the values of the set of n samples available in the last 21 solar days;
• for sets of n < 6 samples a conventional deviation of ks = 8 MPa should be assumed;
• for sets of 6 n 15 samples the value ofkshould be taken from the table reported further on;
• for sets of 16 n 21 samples thefixed value ofk= 1.48 is assumed;
• for thenmeasurements available, the mean valuefmand the standard deviation sare then calculated;
• the current characteristic strengthfkisfinally deduced, to be compared with one of the expected classes.
The formulas for the required calculations are (whereR1and R2are the cubic strengths of the two cubic specimens andtis the concrete age in days at the time of testing):
fj¼0:83R1þR2
2 f ¼ fj
ebð11=sÞ s¼t=28 fm¼
Pn i¼1fi
n s¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn
i¼1ðfifmÞ2 q
n1 fk¼fmks:
n 6 7 8 9 10 11 12 13 14 15
k 1.87 1.77 1.72 1.67 1.62 1.58 1.55 1.52 1.50 1.48
In any case the values of the variation coefficientss/fmshall be less than 0.15.
The following pages contain
• the template of control chart for data recording (with values shown as example);
• the diagram relative to the results of testing for the visualization of the pro- duction trend (with marks shown as example using, for decimals, the comma instead of the point following the European praxis).
CONTROL CHART FOR CONTINUING CONCRETE PRODUCTION
STANDARD ROOF ELEMENTS – CONCR. CLASS C35/43 – AGGR. ≤ 15mm FACTORY PREFAB SYSTEM - MILAN MIX DESIGN: CEMENT 3,75 q/m3- W/C RATIO 0,40 – ADDITION 2,5%
ACCELERATED CURING (ββ=0,08) - TESTS AT: 28 DAYS / DEMOULDING OCTOBER 2014 p. 076 specimens mean correlation to 28 days for the set of samples of the last 21 solar days Sample
date Test
date 1 2 fj age fj/f f n k fm s fk
1 2/10 30.5 30.0 25.1 0.67 0.65 38.6 15 1.48 41.5 2.37 38.0
2 3/10 32.0 31.0 26.1 0.67 0.65 40.3 15 1.48 41.3 2.35 37.8
3 6/10 39.0 39.5 32.6 3 0.85 38.3 15 1.48 41.2 2.46 37.6
4 5
6 7/10 35.0 32.0 25.9 0.67 0.65 39.9 15 1.48 41.0 2.44 37.4
7 8/10 31.0 31.5 25.9 0.67 0.65 39.9 15 1.48 40.8 2.40 37.2
8 9/10 37.5 36.0 30.5 0.67 0.65 46.9 15 1.48 41.0 2.77 36.9
9 10/10 34.0 34.5 28.4 0.67 0.65 43.7 15 1.48 40.9 2.66 37.0
10 13/10 46.0 47.0 38.6 3 0.85 45.4 15 1.48 41.0 2.78 36.9
11 12
13 14/10 33.5 34.0 28.0 0.67 0.65 43.0 15 1.48 41.1 2.82 36.9
14 15/10 34.0 35.0 28.6 0.67 0.65 44.1 15 1.48 41.3 2.93 37.0
15 16/10 33.0 34.5 28.0 0.67 0.65 43.0 15 1.48 41.3 2.93 37.0
16 17/10 31.0 31.0 25.7 0.67 0.65 39.6 15 1.48 41.2 2.95 36.8
17 21/10 42.0 43.5 35.5 4 0.88 40.3 15 1.48 41.3 2.91 37.0
18 19 20
21 22/10 35.0 35.0 29.0 0.67 0.65 44.7 14 1.50 41.9 2.76 37.8
22 23/10 29.0 30.0 24.5 0.67 0.65 37.7 14 1.50 41.9 2.75 37.8
23 24/10 30.0 30.5 25.1 0.67 0.65 38.6 14 1.50 41.8 2.96 37.4
24 27/10 45.5 44.5 37.3 3 0.85 43.9 14 1.50 42.2 2.83 38.0
25 26
27 28/10 33.0 34.0 27.8 0.67 0.65 42.7 14 1.50 42.4 2.75 38.3
28 29/10 35.0 35.0 29.0 0.67 0.65 44.7 14 1.50 42.7 2.72 38.6
29 30/10 35.0 35.5 29.3 0.67 0.65 44.9 14 1.50 42.6 2.52 38.8
30 31/10 34.0 34.5 28.4 0.67 0.65 43.7 14 1.50 42.6 2.52 38.8
31 3/11 47.0 47.0 39.0 3 0.85 44.7 14 1.50 42.5 2.28 39.1
Table 1.12: Creep: Class Coef fi cient
The following table shows, for the different strength classes of concrete, the value of the coefficientbcof the formula:
u1¼bcbhsuo
for the calculation offinal concrete creep. The values are calculated with bc¼1:673
ffiffiffic p ;
wherec=fc/10 is the class index andfcis the mean strength in MPa.
For the other coefficients of the formulas, one can refer to Tables1.13and1.14.
Ordinary fc(MPa) bc
Class
C16/20 24 1.08
C20/25 28 1.00
C25/30 33 0.92
C30/37 38 0.86
C35/43 43 0.81
C40/50 48 0.76
C45/55 53 0.73
Controlled fc(MPa) bc
Class
C30/37 35 0.89
C35/43 40 0.84
C40/50 45 0.79
C45/55 50 0.75
C50/60 55 0.71
C55/67 60 0.68
C60/75 65 0.66
C70/85 75 0.61
Table 1.13: Creep: Ambient Coef fi cient
The following table shows, for the different relative humidities RH of the ageing environment and for the different equivalent thicknesses 2Ac/u, the values of the coefficientbhsof the following formula:
u1¼bcbhsuo
for the calculation of concretefinal creep. The values are calculated with
bhs ¼0:725 1þ 1h 0:46 ffiffi
s p3
where h = HR/100 and s= (2Ac/u)/100 (Ac= cross-sectional area of concrete;
u= its perimeter).
For the other coefficients of the formula, one can refer to Tables1.12,1.13,1.14.
Relative humidity
2Ac/u(mm) Small thickness
Medium– small
Medium thickness
Medium– big
Big thickness
% 50 100 150 300 600
80 1.12 1.04 1.00 0.94 0.90
70 1.32 1.20 1.14 1.05 0.98
60 1.52 1.35 1.28 1.16 1.07
50 1.72 1.51 1.41 1.27 1.16
Table 1.14: Creep: Reference Coef fi cient
The following table shows, for the different concrete ages at loading, the values of the coefficientuoof the following formula:
u1¼bcbhsuo;
for the calculation offinal creep. The values are calculated with uo¼ 4:37
0:1þt0o:2 ðtoin daysÞ;
and should be assumed, with a coefficient of variation of about 0.20, for water/cement ratios 0:55. For higher ratios, the values are greater.
For the definition oftosee Table 1.15; for the other coefficients of the formula, see Tables1.12and 1.13.
Age uo
0.58 4.38
1 3.97
2 3.50
3 3.25
4 3.08
5 2.95
6 2.85
7 2.77
10 2.59
14 2.43
21 2.25
28 2.13
60 1.85
90 1.71
180 1.49
365 1.30
Table 1.15: Creep: Effect of Temperature
The following table shows, as a function of the average temperaturehof concrete in the time interval 0to, the value of the correction factorbTwith which the nominal agetocan be deduced from the effective ageto at loading:
to¼bTto
This nominal age is used in the formulauo= uo(to) of creep (see Table1.14).
The values are calculated with the following formula:
bT¼eð13:652734000þhÞ ðhin CÞ
h bT
10 0.62
15 0.79
20 1.00
25 1.26
30 1.57
(continued)
(continued)
h bT
35 1.34
40 2.39
45 2.92
50 3.55
55 4.28
60 5.14
65 6.15
70 7.30
75 8.63
Table 1.16: Creep: Nominal Coef fi cients
The nominal final values of creep coefficients are given below, for the design of ordinary and pre-stressed reinforced concrete, calculated in prevision of an envi- ronment with HR = 60% of relative humidity.
Type/thickness Concrete
class
Curing/age Calculated effect
u∞ Ordinary RC struct.
medium–big
Low Naturalto14 days
Global deformation
3.1 Ordinary RC struct.
medium–big
Medium Naturalto14 days
Global deformation
2.5 Pre-tensioned small High Accelerated
to14 h
Pre-stress losses 3.1 Pre-tensioned medium–
small
Medium Accelerated to14 h
Pre-stress losses 2.7 Post-tensioned medium Medium Naturalto14
days
Pre-stress losses 1.9
Table 1.17: Characteristics of Reinforcing Steel
B450C steel, used in reinforced concrete structures, is characterized by the fol- lowing nominal values of characteristic yield strengthfyoand ultimate strengthfto
fyo¼450 MPa fto¼540 MPa
The following table shows the requirements for the actual values of the main mechanical characteristics of B450C steel:
Characteristics Symbol Value
Characteristic yield strength (fractile 5%) fyk 450 MPa Characteristic ultimate strength (fractile 5%) ftk 540 MPa Uniform elongation (fractile 10%) (=euk) (Agt)k 7:5%
Strain-hardening ratio (ft/fy)k
Minimum (fractile 10%) 1:15
Maximum (fractile 10%) 1:35
Overstrength ratio (fractile 10%) (ft/fyo)k 1:25
Bars and wires made of B450C steel have to be bendable and weldable. Other characteristics common for all types of steel are
• specific weight densityð Þ g¼7850 kg=m3
• longitudinal elastic modulus Es¼205000 MPa
• coefficient of thermal expansion aT¼1:0105C1:
Table 1.18: Bars and Wires: Commercial Diameters
/(mm) g(kg/m) u(mm) nAs(mm2)
1 2 3 4 5 6 7 8 9
6 0.222 18.9 28.3 56.5 84.8 113 141 170 198 226 254
8 0.395 25.1 50.5 101 151 201 251 302 352 402 452
10 0.617 31.4 79.0 157 236 314 393 471 550 628 707
12 0.888 37.7 113 226 339 452 566 679 791 905 1131
14 1.208 44.0 154 308 462 616 770 924 1078 1232 1385
16 1.578 50.3 201 402 603 804 1005 1206 1407 1608 1810
18* 1.998 56.6 254 509 763 1018 1272 1527 1781 2036 2290
20 2.466 62.8 314 628 942 1257 1571 1885 2199 2513 2827
22* 2.984 69.1 380 760 1140 1521 1901 2281 2661 3041 3421
24* 3.551 75.4 452 905 1357 1810 2262 2714 3167 3619 4072
25 3.853 78.5 491 982 1473 1963 2454 2945 3436 3927 4418
(continued)
(continued)
/(mm) g(kg/m) u(mm) nAs(mm2)
1 2 3 4 5 6 7 8 9
26* 4.168 81.7 531 1062 1593 2124 2655 3186 3717 4247 4778
28 4.834 88.0 616 1232 1847 2463 3079 3695 4310 4926 5542
30 5.559 94.3 707 1414 2121 2827 3534 4241 4948 5655 6362
32 6.313 100.5 804 1608 2413 3218 4022 4827 5631 6436 7240 NoteNon-standard diameters are in italic; the diameters not normalized at European level (EN10080) are marked with a star
The table gives the weightg, the perimeteruand the cross-sectional areaAsfor the commercial diameters/of the hot-rolled ribbed wires and bars for reinforced concrete. Bars are supplied in 12-m-long bundles, wires up to diameters of 12 mm can be supplied in rolls.
Table 1.19: Bars for PC: Standard Diameters
The following table shows, for nominal diameters/normalized by the European standard EN 10138/4, the values of
g unit weight
u perimeter of the equivalent bar Ap cross-sectional area
fptk characteristic rupture strength
f0.1k characteristic strength at 0.1% residual elongation (f0.1/fpt)k hardening (reverse) ratio (=ark)
euk indicative value of ultimate elongation Fptk characteristic value of rupture load
F0.1k characteristic value of load at 0.1% residual elongation.
There are two types of steel Fe1030 and Fe1230 produced in hot-rolled bars subsequently subjected to cold-forming.
For the considered types of steel the following standard requirements are applied:
euk3:5% ark0:80:
The other general characteristics of the type of product are
• specific weight densityð Þ g¼7850 kg=m3
• longitudinal elastic modulus Ep¼205000 MPa
• coefficient of thermal expansion aT¼1:0105C1:
/ (mm)
g(kg/m) u(mm) Ap (mm2)
fptk (MPa)
f0.1k (MPa)
ark euk (%)
Fptk (kN)
F0.1k (kN) 20
20
2.47 62.8 314 1030
1230 830 1080
0.81 0.88
6.0 5.0
325 385
260 340 25
25
3.86 78.5 491 1030
1230 830 1080
0.81 0.88
6.0 5.0
505 600
416 530 26
26
4.17 81.7 531 1030
1230 830 1080
0.81 0.88
6.0 5.0
547 653
443 575 32
32
6.31 101 804 1030
1230 830 1080
0.81 0.88
6.0 5.0
830 870
670 1109 36
36
7.99 113 1018 1030
1230 830 1080
0.81 0.88
6.0 5.0
1050 1100
1208 1400 40
40
9.86 126 1257 1030
1230 830 1080
0.81 0.88
6.0 5.0
1295 1357
1050 1732
50 15.5 157 1960 1030 830 0.81 6.0 2020 1636
For the two types of steel in smooth and ribbed bars, the following table gives the values of
d¼100 fptmfptk
=fptm percent deviation
Dr fatigue limit range for 2106loading cycles.
Type d(%) Dr(MPa)
Fe1030 7.5 200 Smooth
180 Ribbed
Fe1230 6.0 200 Smooth
180 Ribbed
Table 1.20: Cold-Drawn Wire: Standard Diameters
The following table shows, for the nominal diameters / normalized by the European standard EN 10138/2, the values of
g unit weight
u perimeter of the equivalent bar Ap cross-sectional area
fptk characteristic rupture strength
f0.1k characteristic strength at 0.1% residual elongation (f0.1/fpt)k hardening (reverse) ratio (=ark)
euk indicative value of ultimate elongation Fptk characteristic value of rupture load
F0.1k characteristic value of load at 0.1% residual elongation.
There are four types of steels, namely Fe1570, Fe1670, Fe1770 and Fe1870, produced in smooth or indented wires by cold drawing and stretching.
For the considered steels the following standard requirements are applied:
euk3:5% ark0:80:
The other general characteristics of the type of products are
• specific weight densityð Þ g¼7850 kg=m3
• longitudinal elastic modulus Ep¼205000 MPa
• coefficient of thermal expansion aT¼1:0105C1:
The value of deviation d¼100ðfptmfptkÞ=fptm is for all types of steel dffi7:5%.
The fatigue limit range for 2106 loading cycles is Dr¼200 MPa for smooth wires Dr¼180 MPa for indented wires: /
(mm)
g(kg/m) u(mm) Ap (mm2)
fptk (MPa)
f0.1k (MPa)
ark euk (%)
Fptk (kN)
F0.1k (kN) 4.0
4.0
0.989 12.6 12.6 1770
1860
1520 1600
0.86 0.86
4.2 4.0
22.3 23.4
19.2 20.1 5.0
5.0
0.154 15.7 19.6 1670
1770
1440 1520
0.86 0.86
4.6 4.2
32.7 34.7
28.1 29.8 6.0
6.0
0.222 18.9 28.3 1670
1770
1440 1520
0.86 0.86
4.6 4.2
47.3 50.1
40.7 43.1
7.0 0.302 22.0 38.5 1670 1440 0.86 4.6 64.3 55.3
7.5 0.347 23.6 44.2 1670 1440 0.86 4.6 73.8 63.5
8.0 0.395 25.1 50.3 1670 1440 0.86 4.6 84.0 72.2
9.4 0.545 29.5 69.4 1570 1300 0.83 5.0 109.0 90.5
10.0 0.616 31.4 78.5 1570 1300 0.83 5.0 123.0 102
Table 1.21: Strands: Standard Diameters
The following table shows, for the nominal diameters / normalized by the European standard EN 10138/3, the values of
g unit weight
u perimeter of the equivalent bar Ap cross-sectional area
fptk characteristic rupture strength
f0.1k characteristic strength at 0.1% residual elongation (f0.1/fpt)k hardening (reverse) ratio (=ark)
euk indicative value of ultimate elongation Fptk characteristic value of rupture load
F0.1k characteristic value of load at 0.1% residual elongation.
There are strands made of three wires 3W, seven wires 7W and compacted strands of seven wires 7WC obtained from cold-drawn wires of small diameters (2.46.0 mm), in six types of steels, namely Fe1700, Fe1770, Fe1820, Fe1860, Fe1960 and Fe2060.
For the concerned steels there are the following standard requirements:
euk3:5% ark0:80
The other general characteristics of the type of products are
• specific weight densityð Þ g¼7850 kg=m3
• longitudinal elastic modulus Ep¼195000 MPa
• coefficient of thermal expansion aT¼1:0105C1:
The value of deviationd¼100ðfptmfptkÞ=fptmis for all steels 7.5%.
The fatigue limit range for 2106loading cycles is Dr¼190 MPa for smooth wires Dr¼170 MPa for indented wires: /
(mm)
g(kg/m) u(mm) Ap (mm2)
fptk (MPa)
f0.1k (MPa)
ark euk (%)
Fptk (kN)
F0.1k (kN) Strand 3W
5.2 0.107 16.3 13.6 1960 1670 0.85 4.6 26.7 22.7
5.2 0.107 16.3 13.6 2060 1750 0.85 4.2 28.0 23.8
6.5 0.166 20.4 21.2 1860 1580 0.85 4.6 39.4 33.5
6.5 0.166 20.4 21.2 1960 1670 0.85 4.6 41.5 35.3
6.8 0.184 21.4 23.4 1860 1580 0.85 4.6 43.5 37.0
7.5 0.228 23.6 29.0 1860 1580 0.85 4.6 53.9 45.8
Strand 7W
7.0 0.236 22.0 30.0 2060 1750 0.85 4.6 61.8 52.5
9.0 0.393 28.3 50.0 1860 1580 0.85 5.0 93.0 79.0
11.0 0.590 34.6 75.0 1860 1580 0.87 5.0 139 118
12.5 0.730 39.3 93.0 1860 1580 0.85 5.0 173 147
13.0 0.785 40.8 100 1860 1580 0.85 5.0 186 158
15.2 1.090 47.8 139 1770 1500 0.85 5.0 246 209
(continued)
(continued) / (mm)
g(kg/m) u(mm) Ap (mm2)
fptk (MPa)
f0.1k (MPa)
ark euk (%)
Fptk (kN)
F0.1k (kN)
15.2 1.090 47.8 139 1860 1580 0.85 5.0 258 219
16.0 1.180 50.3 150 1770 1500 0.85 5.0 265 225
16.0 1.180 50.3 150 1860 1580 0.85 5.0 279 237
18.0 1.570 56.5 200 1770 1500 0.85 5.0 354 301
Compacted 7WC
12.7 0.890 40.0 112 1860 1580 0.85 5.0 209 178
15.2 1.295 47.8 165 1820 1580 0.85 5.0 300 225
18.0 1.750 56.5 223 1700 1580 0.85 5.0 380 323