APPENDIX C-Continued 



content of Al.5.2.9.1 by 3 kg/m» ot concrete for each 

 1 percent by which the air content is to be increased 

 or decreased from that of the trial batch. 



Al.5.2.9.3 The re-estimaled unit weight of the 

 fresh concrete for adjustment of trial batch proportions 

 is equal to the unit weight in kg/m' measured on the 

 trial batch, reduced or increased by the percentage 

 increase or decrease in air content of the adjusted 

 batch from the first trial batch. 



APPENDIX 2 — 

 EXAMPLE PROBLEM IN METRIC SYSTEM 



A2.1 — Example 1. Example 1 presented in Section 

 6.2 will be solved here using metric units of measure. 

 Required average strength will be 250 kgf/cm^ with 

 slump of 8 to 10 cm. The coarse aggregate has a 

 maximum size of 40 mm and dry-rodded weight of 

 1600 kg/m'. As stated in Section 6.1, other properties 

 of the ingredients are: cement — Type I with specific 

 gravity of 3.15; coarse aggregate— bulk specific gravity 

 2.68 and absorption 0.5 percent; fine aggregate — bulk 

 specif ic . gravity 2.64, absorption 0.7 percent, and fine- 

 ness modulus 2.8. 



A2.2 — AU steps of Section 5.3 should be followed in 

 .sequence to avoid confusion, even though they some- 

 times merely restate information already given. 



A2.2.1 Step I. The slump is required to be 8 to 

 10 cm. 



A2.2.2 Step 2. The aggregate to be used has a 

 maximum size of 40 mm. 



A2.2.3 Step 3. The concrete will be non-air-en- 

 trained since the structure is not to be exposed to 

 severe weathering. From Table Al. 5.2.3, the esti- 

 mated mixing water for a slump of 8 to 10 cm in 

 non-air-entrained concrete made with 40-mm aggregate 

 is found to be 175 kg/m'. 



A2.2.4 Step 4. The water-cement ratio for non- 

 air-entrained concrete with a strength of 250 kgf/cm^ 

 is found from Table A1.5.2.4(a) to be 0.62. 



A2.2.5 Step 5. From the information developed in 

 Steps 3 and 4, the required cement content is found 

 to be 175/0.62 = 282 kg/m^. 



A2.2.6 Step 6. The quantity of coarse aggregate is 

 estimated from Table Al.5.2.6. For a fine aggregate 

 having a fineness modulus of 2.8 and a 40 mm maxi- 

 mum size of coarse aggregate, the table indicates that 

 0.72 ms of coarse aggregate, on a dry-rodded basis, may 

 be used in each cubic meter of concrete. The required 

 dry weight is, therefore, 0.72 x 1600 = 1152 kg. 



A2.2.7 Step 7. With the quantities of water, ce- 

 ment and coarse aggregate established, the remaining 

 material comprising tlje cubic meter of concrete must 

 consist of sand and whatever air will be entrapped. 

 The required sand may be determined on the basis 

 of either weight or absolute volume as shown below: 

 A2.2.7.1 Weight Basis. From Table Al.5.2.7.1, the 

 weight of a cubic meter of non-air-entrained concrete 

 made with aggregate having a maximum size of 40 mm 

 is estimated to be 2420 kg. (For a first trial batch, 

 exact adjustments of this value for usual differences 

 in slump, cement factor, and aggregate specific gravity 

 are not critical.) Weights already known are: 



Water (net mlxlnf ) 



179 K( 



Cement 



2S3kf 



Coarec aiiief gtc 



llUkI 



Total 



IMSkf 



The weight of sand, therefore, is estimated to be 

 2420-1609 = 811 kg 

 A2.2.7.2 Absolute volume basis. With the quan- 

 tities of cement, water, and coarse aggregate estab- 

 lished, and the approximate entrapped air content (as 

 opposed to purposely entrained air) of 1 percent 

 determined from Table Al.5.2.3, the sand content can 

 be calculated as follows: 



Volume of water 



1000 



Solid volume of c 

 Solid volurr 



"" 3.15 X 1000 

 aggregate = -^'^^ 



Volume of entrapped alr= 0.01 X 1.000 



0.17S m' 

 0.090 m' 



: 1.000 ~ 0.705 



: 0^95 X 2 M X 1000 



A2.2.7.3 Batch weights per cubic meter of con- 

 crete calculated on the two bases are compared below: 





Based on 



absolute 



estimated concrete 



volume of 





welglit, kg 



ingredients, kg 



Water (net mixing) 



175 



175 



Cement 



282 



282 



Coarse aggregate (dry) 



1152 



1152 



Sand (dry) 



811 



T79 



A2.2.« Step S. Tests indicate total moisture of 2 

 percent in the coarse aggregate and 6 percent in the 

 fine aggregate. If the trial batch proportions based on 

 assumed concrete weight are used, the adjusted ag- 

 gregate weights become 



Coarse aggregate (wet) = 1152(1.02) = 1175 kg 

 Fine aggregate (wet) = 811(1.06)= 860 kg 



Absorbed water does not become part of the mixing 

 water and must be excluded from the adjustment in 

 added water. Thus, surface water contributed by the 

 coarse aggregate amounts to 2 — 0.5 = 1.5 percent; by 

 the fine aggregate 6 - 0.7 = 5.3 percent. The estimated 

 requirement for added water, therefore, becomes 



175 - 1152(0.015) - 811(0.053) = 115 kg 



The estimated batch weights for a cubic meter of 

 concrete are: 



Water (to be added) 



115 kg 



Cement 



282 k< 



Coarse aggregate (wet) 



1179 k( 



Fine aggregate (wet) 



SSOkf 



ToUl 



2432 kf 



A2.2.9 Step 9. For the laboratory trial batch, it is 

 found convenient to scale the weights down to produce 

 0.02 tn' of concrete. Although the calculated quantity 

 of water to be added was 2.30 kg, the amount actually 

 used in an effort to obtain the desired 8 to 10 cm 

 slump is 2.70 kg. The batch as mixed, therefore, con- 

 sists of 



Water (added) 



Cement 



Coane aggregate (wet) 



rine aggregate (wet) 



ToUl 



a.TOkg 



g.Mkg 



UMkg 

 17 JO kg 

 4a.0tk( 



ACI STANDARD 



383 



