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Concrete Mix Design
Assume a reinforced concrete building designed with a specific grade, with bearing walls located in definite location. Design the concrete mix in accordance to the following characteristics:


1. Specified concrete (grade/class): C 16/20.
2. Characteristics of concrete element
a) type of structural member:4N structural walls
b) minimum section (dimension) of concrete element. b = 200 mm.
c) concrete cover of reinforcing bars. c == 15 mm.
d) minimum spacing of reinforcing bars. D = 75mm.
3. Conditions of exposure and environment conditions: Marine Environment (3N+1).
4. Work conditions:
5. Transport and placement of concrete: Transit mix trucks and concrete pumps (2N)
6. Moisture content in aggregates:
 F.A. (fine aggregates) (07 mm): u_{s} == 2%;

7. Grade of homogeneity: II
B. Quality mix proportions of constituents
1. Consistency of concrete:
From annex 1, in accordance with the type of structural member (structural wall), transport equipment (transit mix truck), technology of concrete placing (pump) and type of concrete (reinforced), results from item no. 3 the recommended consistency T3/T4 (slump 100 ±20 mm).
2. Minimum cement content:
From annex 2., in accordance with the environment conditions (Marine Environment), result the conditions of exposure 4b1. From annex 3, results the minimum cement content of 400 kg/m^{3}, according to the type of concrete (reinforced) and the conditions of exposure (4.b.1).
3. Aggregates:
a) Type of aggregates: In accordance with the class of concrete (C 20/16) we will use
natural riverbed aggregates with the relative density r_{ag} 2,7 kg/dm^{3} (see annexes 13) T3/T4=200.
b) Maximum size of aggregate:
Depends on the following elements: type of concrete member (structural walls), minimum length of section being formed (b = 200 mm), minimum distance between bars (D == 75 mm), transport and placement of concrete and minimum concrete cover of reinforcing bars (c = 15 mm):
Damx< 1.3xc=19.5mm
d max < 1/4 x b = 1/4 x 200 = 50 mm ;
d max < D  5 mm = 75  5 == 70 mm ;
pumpable dmax =31 mm.
According to section 2.3., because the conditions of exposure (marine environment), the concrete cover of reinforcing bars conditions the maximum size of aggregates as being 20mm( with a min air entrained of 4%). All these conditions have to be simultaneously respected, results dmax <19,5mm. We chose dmax = 20mm.
c) Gradation:
From table I4 results the grading zone (I) according to the minimum cement content
400 kg/dm^{3}. Knowing the grading zone (I) and the maximum size of aggregate 31mm, from
annex 5 results the following upper and lower grading limits:
sieve 0  0,2mm recommended 1015% we chose 13%;
sieve 0,2  1mm recommended 30  40% we chose 34%;
sieve 13 mm recommended 50  60% we chose 54%;
sieve 37 mm recommended 70  80% we chose 76%;
sieve 720 mm recommended 95  100% we chose 100%;
4. Cement:
According to environment conditions (marine environment) results the type of cement form table I11, conditioned by the type and section of concrete element (structural wall) and concrete class (C 20/16). Recommended cement type I  32,5.
5. Watercement maximum ratio:
From table I3, according to the type of concrete (reinforced) and the exposure conditions (4.b.1) results the watercement maximum ratio (A/C maximum = 0,45).
C. Quantity mix proportions of constituents
1. Water:
The estimated water quantity needed (A) is determined according to the class of concrete (C 20/16) and the consistency (T3/T4).
From table I13 results:
A=200l/m^{3}
This quantity will be adjusted with a coefficient (c= 1) determined by the maximum aggregate size 31mm, as follows:
A’ = A x c == 200 x 1.05 = 210 l/m^{3}
2. Watercement ratio:
From annex 14, according to the concrete grade (C 20/16) and cement grade (32,5), concrete homogeneity grade II, results the water: cement ratio A/C == 0,60. The value will be adjusted with a coefficient for crushed aggregates if it is necessary and the resulting value of A/C will be compared with the maximum value calculated of A/C, determined at section 2.5. From the two values the minimum one will be chosen A/C minim == 0,45.
3. Cement:
The cement quantity is calculated as follows: _{} [kg/m^{3}] > minimum cement contents 400 kg/m^{3} (see section B.2.). From the two values the maximum one will be chosen C = 467 kg/m^{3}.
4. Aggregates:
The total amount of dry aggregates will be calculated as follows:
Ag = r_{ag} x (1000  C/rc – A’/r_{a}  r) [kg/m^{3}]
Ag ^{=} 2.7 x (1000  467/3  210/1  20) = 1658 [kg/m^{3}]
Where:
r_{ag} = relative density of aggregates (2.7 kg/dm^{3});
r_{c} = relative density of cement (3.0 kg/dm^{3});
p = void parameter (approx. 20 dm^{3}/m^{3}), when using airentrained plasticizers, (see annex 13).
5. Gradation of aggregate:
According to the lower and upper limits of gradation recommended (see section 2.3.c), it can be determined the right amount of each grade of fine and coarse aggregate (this determination can be made by plotting the cumulative percent passing by mass through each sieve, see annex 5). The amount of aggregate for each grade is found as follows:
_{}
Were:
Ag = amount of aggregates (kg);
pi = percent passing by mass through sieve 'i';
pil= percent passing by mass through sieve 'i1';
First correction (iteration):
sieve mm; 13/100 x kg/m^{3}
sieve 1mm; (3413)/100 x 1658 = 348 kg/m^{3} ;
sieve 3mm; (5434)/100 x 1658= 331 kg/m^{3};
sieve 7mm; (7654)/100 x 1658 = 365 kg/m^{3};
sieve 20mm; (10076)/100 x 1658 = 398 kg/m^{3} ;
Total: 1658 kg/m^{3}
compared with the calculated value of 1658kg/m^{3}
6. Adjustment of water quantity:
The right adjustment of water will be found according to the exact free moisture of the aggregates, as follows:
_{}
Where:
Agi = amount of aggregate form sieve 'i' (kg);
ui = free moisture of sieve 'i' (%);
n = total numbers of sieves.
A* = A'  DA (l/m^{3})
The free amount of moisture form fine aggregates (2%), is calculated as follows:
_{}
The free amount of moisture form coarse aggregates (1%), is calculated as follows:
_{}
The total amount of free moisture is calculated as follows:
DA=DAn +DAp =25,2+3,98=29,18 l/m^{3}
Adjusted amount of water: A* = A'  AA = 200  27,43 = 180,82 l/m^{3}
7. Adjustment of total amount of aggregates by sieve sizes:
The of total amount of aggregates by sieve sizes, is found as follows:
_{}
Where: A_{gi}  amount of aggregate form sieve “i” (kg);
ui = free moisture of sieve 'i' (%).
sieve 0  0,2 mm; 216 x (1+ 2/100) =220 kg/m^{3};
sieve 0,2  1mm; 348 x (1+ 2/100) = 355 kg/m^{3};
sieve 1  3mm; 331 x (1+ 2/100) =338 kg/m^{3} ;
sieve 3 7mm; 365 x (1+ 2/100 ) =372 kg/m^{3 }
sieve 7  16mm; 398 x (1+ 1/100) =402 kg/m^{3};
8. Adjustment of total amount of aggregates:
The of total amount of aggregates, is found as follows:
_{} (kg/m^{3})
Where:
Ag*_{i} = adjusted amount of aggregate form sieve 'i' (kg);
_{}
8. Total weight of one cubic meter of concrete:
1687+467+210=2364 kg/m3
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