HOW TO CALCULATE STANDARD DEVIATION OF CONCRETE....

How to calculate standard deviation of concrete.....

For standard deviation we need minimum strength of 30 samples for accuracy  for a particaular grade of concrete..

LET START WITH ONE EXAMPLE   

GRADE OF CONCRETE M 35

Strength of samples of M 35 grade of concrete derive in lab during cube test is given below:

X                   Y           Y-X =A                 (A) 2
                   
                                 
38.77                         -1.13                         1.27                                               
39.00                         -1.36                         1.84
40.00                         -2.36                          5.56
35.00                          2.64                          6.96
32.00                          5.64                         31.80
42.00                         -4.36                        19.00
40.00                         -2.36                          5.56
35.20                         -2.44                          5.95
36.81                          0.83                          0.68
37.71                         -0.07                      0.0049
30.81                          6.83                        46.64
35.70                          1.94                           3.76
38.80                         -1.16                          1.34
43.50                         -5.86                        34.33
43.00                         -5.36                        28.89
45.00       37.64         -7.36                        54.16
37.00                           0.64                          0.40
36.00                          1.64                          2.68
38.50                         -0.86                          0.73
29.90                          7.74                         59.90
34.00                          0.64                         0.40
37.80                         -0.16                        0.025
39.90                         -2.26                         5.10
38.70                         -1.06                         1.12
37.90                         -0.26                         0.067
38.00                         -0.36                         0.129
37.20                          0.44                         0.193
36.10                          1.54                         2.37
37.10                          0.54                          0.291
38.05                         -0.41                        0.168

                                    TOTAL         =     321.31


    After this we calculate  root of    321.31   which is  17.92

    And number of samples is 30

    In which  we minus 1 from sample
    i.e  30-1   = 29

    Root of 29 is  = 5.38

Than standard deviation is   =  17.92 / 5.38  =  3.33 N/ mm 2


  co efficient  of variation =     3.33/37.64*100 =  8.84


Significance of standard deviation is given below :

1) If standard deviation is low than in this case Quality of concrete is very good and difference between mean strength to samples strength is low.

2) consistency of concrete is good regarding strength of concrete.

3) If  standard deviation is low than in this case we can minimize cement content also in mix design.

                                                

IS OUR CONCRETE FAIL ?

Is concrete fail if  strength of concrete of any particular grade less than its characteristics strength ?

No, we can't directly say that concrete fail if strength is less than characteristics strength.
As per special publication SP 23 of CONCRETE we follow the following steps if strength is less than Fck.

1) Strength  of  concrete of any sample   should  not  less  than

a) characteristics strength  minus  1.35 times of standard  deviation.

b) 0.80 times of characteristics strength of concrete.

c) And average strength of concrete sample should not less than

   fck + ( 1.65 - 1.65/(root of number of samples)* standard deviation

THE ABOVE THREE   CRITERIA    MUST BE FULL FILLED  IF ANY ONE CRITERIA  IS   FAILED THAN FORTH EQUATION IS GIVEN BELOW  :

Fck + ( 1.65 - 3/( root of samples)* standard deviation


IT   IS  ELABORATED  WITH   SIMPLE  EXAMPLE   GIVEN BELOW:

Let Grade of concrete  M35

Strength of different  samples is derive during cube test is:

39, 42, 40, 43, 32 , 40 N / mm2  respectively


1 , 2 , 3 , 4 samples are directly passed more than 35 N/ mm2

But in the case of 5th sample it is 32 N / mm2

Which is less than 35 N/ mm2


Than from 1st criteria:

 35 - 1.35 × 5 = 28.25 N/ mm2

From second criteria:

0.80 × 35 = 28 N / mm2

1st and 2nd criteria full fill  hence ok



Let come on third criteria:

Average of  sample strength
39+ 42+40+43+32= 196

196/5 = 39.2 N/ mm2

According to 3rd criteria:

35 + ( 1.65 - 1.65/ 2.23) × 5
  
     ( 2.23 is root of 5)

After calculation it is   39.5 mm2 which is greater than 39.2 N/ mm2. ( Here our concrete is fail ) but we have fouth equation
If fouth criteria meet the requirement than our concrete passed with the sole discretion of designer.


Let we are going to 4th criteria

35+( 1.65- 3/ 2.23) × 5
After calculation we get 36.5 N / mm2


Average strength 39. 2 N / mm2 is greater than 36.5 N / mm2 hence our concrete 5th sample also  passed .


NOTE : STANDARD DEVIATION  IS 5 IN ABOVE EXAMPLE

GENERAL INFORMATION REGARDING POZZALANIC MATERIALS

Percentage of pozzalanic material used in high strength concrete as per IS 10262:2019

For flyash : 15 -30 %
Microsilica: 5-10 %
GGBFS : 25 - 50 %
Metakaoline : 5 - 15 %

Limitation of pozzalanic material used during manufacturing of cement

For PPC CEMENT  - 15 TO 35% replacement of flyash to total opc content.( IS 1489 PART FIRST)

For Psc cement - 25 To 70 % replacement of GGBFS  to total opc content.(IS 455)

Ratio of pozzalana and cement during consistency , intial and final setting time of pozzalanic material as per IS 1727

  0.2N : 0.8

where N is the ratio between specific gravity of pozzolana material to specific gravity of cement.

It is generally taken as 1 as per IS 15388.


Ratio of pozzalana , cement and standard sand during cube casting .

    0.2N :0.8: 3

where 0.2 is pozzalanic material
             0.8 is opc cement
             3.0 is standard sand ( IS 650)

and value of N is  1

For checking compressive strength after curing we need to apply load 140 KG/ CM2 / MINUTE. ( IS 1727)


Fineness of microsilica by wet seiving is not more than 10 % from 45 micron seive.


coating thickness of FBEC steel should be between 100 - 300 micron as per IS 13620

IT IS CHECKED BY ELCO METER.

HOLIDAY IN STEEL: Holiday may be defined as defects, cracks, pinholes present in steel it will be detected by holiday detector machine.

Holiday detector machine is used to detect defects in steel in which a wet spounge is used and a DC VOLTAGE of 67.5 is apply , this spounge apply on the surface of steel if any defect present in the steel water penetrate from spounge to defect ex. crack and a electric circuit complete and shows defect on this particular area.

AVERAGE HOLIDAY IS NOT MORE THAN 2 IN 300 CM LENGTH OF STEEL.

YIELD OF CONCRETE...

How to measure yield of concrete at site and plant... to measure how much actual volume of concrete dispatched and rectification if yield is minimum and maxmimum.


TO MEASURE YIELD FOLLOWING APPARATUS REQUIRE:

Cylinder - 10 ltr capacity

Tamping rod

Balace - 100 kg capacity

scoop, wheel barrow etc.

Procedure

1) Determine the actual volume of 10 ltr cylinder by filling it by distill water after taking tare wt. of cylinder, after derive water wt. by subtracting total wt. of cylinder and water with cylinder wt. devide it from density of water which is 1000 kg/ m3. Hence we get actual volume of cylinder.

2) Fill the concrete in cylinder thickness of one layer  is 50 mm and tamping must not less than 60 times in the case of 10 ltrs cylinder, fill the cylinder by repeat above procedure, strike excessive concrete from cylinder and side of cylinder must be tamped 10 to 15 times so that no large bubble appears on the surface.

3) Determine wt. of concrete in cylinder by subtracting total weight to cylinder tare weight.

4) Apply formula :
   
      density = mass of concrete / volume of            cylinder

Let mass of concrete= 24.040 kg
and volume of cylinder = 0.01 m3
  Than density of concrete
       
            24.040/ 0.01 = 2404 kg/m3

THAN YIELD OF CONCRETE

 Theoretical density/ Practical density

we derive practical density above which is
2404 kg / m3

For theoretical density we need batchsheet which is come during dispatch of concrete
Let total quantity of concrete dispatched is 5 m3 and weight of concrete is 12500 kg for 5m3 concrete as per batchsheet.

Than Theoritical density is

      12500/ 5 = 2500 kg / m3

Hence yield =  2500/2404
                       =   1.03

SO THAT OUR YIELD IS 1.03 WHICH INDICATES WE  GIVE MORE CONCRETE

AND HOW MUCH IS GIVEN BELOW

= 1.03 × 5 = 5.15 m3
i.e we produce 0.15 m3 more in the case of 5 m3 concrete.

Yield of concrete must be between
0.98  to 1.02

Cause of more volume of concrete is low specific gravity of aggregate and may also due to problem in calibration of plant.

To rectify this we can reduce quantity of aggregate in mix design .