solutions manual Reinforced Concrete Structures: Analysis and Design David A.Fanella 2nd Edition

Chapter



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Problem 2.1
The strength test results for a normal-weight concrete mixture with a specified compressive
strength of 7,000 psi are given in Table 2.14. Strength tests were obtained from 6 × 12 in
cylinders.
1. Determine (a) the sample standard deviation and (b) the required average
compressive strength .

2. Determine if the concrete is acceptable in accordance with ACI requirements.




1

,Solution, Part (1) (all values in psi)

Specified concrete strength = 7,000 Limit per 26.12.3.1(b)(2) = 700
Test Test Test 28-day 28-day Average, 3
26.12.3.1(b)(1) 26.12.3.1(b)(2)
No. 1 2 Average, Consecutive Tests
1 7,580 7,940 7,760 258 66,564 OK
2 7,580 7,740 7,660 158 24,964 OK
3 6,670 6,880 6,775 7,398 -727 528,529 OK OK
4 7,330 7,480 7,405 7,280 -97 9,409 OK OK
5 7,710 7,600 7,655 7,278 153 23,409 OK OK
6 7,460 7,280 7,370 7,477 -132 17,424 OK OK
7 7,650 7,150 7,400 7,475 -102 10,404 OK OK
8 7,530 7,230 7,380 7,383 -122 14,884 OK OK
9 7,930 7,620 7,775 7,518 273 74,529 OK OK
10 6,970 7,030 7,000 7,385 -502 252,004 OK OK
11 7,400 7,030 7,215 7,330 -287 82,369 OK OK
12 7,400 7,340 7,370 7,195 -132 17,424 OK OK
13 8,200 7,030 7,615 7,400 113 12,769 OK OK
14 7,740 8,020 7,880 7,622 378 142,884 OK OK
15 7,620 8,030 7,825 7,773 323 104,329 OK OK
16 7,460 7,610 7,535 7,747 33 1,089 OK OK
17 7,370 7,380 7,375 7,578 -127 16,129 OK OK
18 7,280 7,770 7,525 7,478 23 529 OK OK
19 8,230 7,520 7,875 7,592 373 139,129 OK OK
20 7,760 7,350 7,555 7,652 53 2,809 OK OK
21 7,860 7,940 7,900 7,777 398 158,404 OK OK
22 7,760 7,720 7,740 7,732 238 56,644 OK OK
23 7,600 7,670 7,635 7,758 133 17,689 OK OK
24 6,720 6,620 6,670 7,348 -832 692,224 OK OK
25 6,150 6,380 6,265 6,857 -1,237 1,530,169 NG NG
26 7,990 7,710 7,850 6,928 348 121,104 NG OK
27 7,900 7,460 7,680 7,265 178 31,684 OK OK
28 8,200 8,460 8,330 7,953 828 685,584 OK OK
29 8,030 7,820 7,925 7,978 423 178,929 OK OK
30 7,030 7,210 7,120 7,792 -382 145,924 OK OK
 225,065 5,159,935


Maximum strength = 8,330
Minimum strength = 6,265
Mean strength ( ̅ ) = 7,502
Standard deviation = 422




2

,For 7,000-psi concrete:

ACI 301 Eq. (4-3): 1.34 7,000 1.34 1.00 422 7,566 psi
(governs)

ACI 301 Eq. (4-5): 0.9 2.33 0.9 7,000 2.33 1.00 422
7,283 psi

Solution, Part (2)

Check the acceptance criteria of ACI 26.12.3.1:

1. The arithmetic average of each set of three consecutive strength tests, which is given
in column 5 in the table in Part (1), is greater than 7,000 psi in all cases except for test
numbers 25 and 26…fails acceptance criterion

2. The average strength for Test 25 is below 0.10 7,000  700
6,300 psi…fails acceptance criterion




3

, Problem 2.2
Repeat Problem 2.1 using only the first 15 test records given in Table 2.14.

Solution, Part (1) (all values in psi)

Specified concrete strength = 7,000 Limit per 26.12.3.1(b)(2) = 700
28-day Average, 3
Test Test Test 28-day
Consecutive 26.12.3.1(b)(1) 26.12.3.1(b)(2)
No. 1 2 Average,
Tests
1 7,580 7,940 7,760 288 82,944 OK
2 7,580 7,740 7,660 188 35,344 OK
3 6,670 6,880 6,775 7,398 -697 485,809 OK OK
4 7,330 7,480 7,405 7,280 -67 4,489 OK OK
5 7,710 7,600 7,655 7,278 183 33,489 OK OK
6 7,460 7,280 7,370 7,477 -102 10,404 OK OK
7 7,650 7,150 7,400 7,475 -72 5,184 OK OK
8 7,530 7,230 7,380 7,383 -92 8,464 OK OK
9 7,930 7,620 7,775 7,518 303 91,809 OK OK
10 6,970 7,030 7,000 7,385 -472 222,784 OK OK
11 7,400 7,030 7,215 7,330 -257 66,049 OK OK
12 7,400 7,340 7,370 7,195 -102 10,404 OK OK
13 8,200 7,030 7,615 7,400 143 20,449 OK OK
14 7,740 8,020 7,880 7,622 408 166,464 OK OK
15 7,620 8,030 7,825 7,773 353 124,609 OK OK
 112,085 1,368,695


Maximum strength = 7,880
Minimum strength = 6,775
Mean strength ( ̅ ) = 7,472
Standard deviation = 313


For 7,000-psi concrete:

ACI 301 Eq. (4-3): 1.34 7,000 1.34 1.00 313 7,419 psi
(governs)

ACI 301 Eq. (4-5): 0.9 2.33 0.9 7,000 2.33 1.00 313
7,029 psi




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