Question

use (absolute volume method). Calculate the materials (type II cement, coarse aggregate, fine aggregate, and water) needed to make 16 concrete cylinders (diameter = 4", height = 8") for our compression tests. Specified compressive strength = 3000 psi at 28 days.

For coarse aggregate, please choose 3/4 in max size gravel containing some crushed particles with the following assumptions: oven-dry specific gravity of 2.68; oven-dry rodded unit weight: 100 lb per cu. ft; moisture content: 1%.

Answer 1

Ans) We know,

For ordinary concrete, slump required = 2-4 in

First lets calculate the mix design for 1 cy (27 ft³), then we can calculate any required amount .

   According to ACI Table 6.3.3 , for slump of 4 in and 3/4 in maximum aggregate size, amount of water required is 340 lb/cy

For 3000 psi , according to Table 6.3.4(a) , water cement ratio = 0.68

Amount of cement = Amount of water/ w/c ratio = 340/0.68= 500 lb/cy

Now, according to table 6.3.6 , for 3/4 in aggregate size and 2.6 fineness modulus , volume of coarse aggregate = 0.64

Amount of coarse aggregate = oven dry weight x volume = 100 x 0.64 x 27 = 1728 lb /cy³

According to absolute volume method, volume of fine aggregate = Total volume - Volume of water , cement and coarse aggregate

Volume of materials = Weight / (Specific gravity x Unit weight)

=> Volume of fine aggregate = 27 - [ (340/62.4) + (500/3.15 x 62.4) + (1728 / 2.68 x 62.4)]

=> Volume of fine aggregate = 27 - 18.32 = 8.68 ft³

=> Amount of fine aggregate = Density x Volume = 2.68 x 62.4 x 8.68 = 1451.7 lb

Since, coarse aggregate contains moisture it will provide some water to concrete so amount of water is needed to be corrected

Amount of water provided by coarse aggregate = 0.01 x 1728 = 17.28 lb

=> Correct amount of water needed = 340 - 17.28 = 322.72 lb

Total volume = Number of cylinder x Volume of one cylinder

Volume of one cylinder, V = (/4) D² H

=> V = (/4)(4)² (8) = 100.48 in³ or 0.05814 ft³

Hence, volume of 16 cylinders = 16 x 0.05814 = 0.93 ft³

Following table consist of required batch weights of components :

Component	Amount per cy (lb)	Amount for 0.93 ft3 (lb)
Cement	500	465
Water	322.72	300.13
Coarse aggregate	1728	1607
Fine aggregate	1451.7	1350