**Concrete Mix Design**

- Requirements:

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: Normal conditions, using giant panels.

5. Transport and placement
of concrete: Transit mix trucks and concrete pumps (2N)

6. Moisture content in
aggregates:

- F.A. (fine
aggregates) (0-7 mm): u_{s} == 2%;

- C.A. (coarse aggregates) (7 - 71 mm): u_{g} = 1%.

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 I-4 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 10-15%
we chose 13%;

sieve
0,2 - 1mm recommended 30 - 40% we chose
34%;

sieve
1-3 mm recommended 50 -
60% we chose 54%;

sieve
3-7 mm recommended 70 -
80% we chose 76%;

sieve
7-20 mm recommended 95 -
100% we chose 100%;

4. Cement:

According to environment conditions
(marine environment) results the type of cement form table I-11, conditioned by
the type and section of concrete element (structural wall) and concrete class
(C 20/16). Recommended cement type I -
32,5.

5. Water-cement maximum
ratio:

From table
I-3, according to the type of concrete (reinforced) and the exposure conditions
(4.b.1) results the water-cement 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 I-13 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. Water-cement 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 air-entrained
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';

pi-l= percent passing by
mass through sieve 'i-1';

First correction (iteration):

sieve 0 - 0,2 mm; 13/100 x 1658 = 216 kg/m^{3};

sieve 0,2 - 1mm; (34-13)/100 x 1658 = 348 kg/m^{3}
;

sieve 1 - 3mm; (54-34)/100 x 1658= 331 kg/m^{3};

sieve 3 -7mm; (76-54)/100
x 1658 = 365 kg/m^{3};

sieve 7 - 20mm; (100-76)/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