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HW 8 formulas

# HW 8 formulas - BRAE 433 A B C D E F G H I J K L 1 Given...

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BRAE 433 HW 8 10/7/2011 Bryce DaFonte 1 1) Given: Concrete with unit weight from 80 lb/ft^3 to 150 lb/ft^3 and f'c from 3000 psi to 7000 psi. Required: Develop a spreadsheet that will display in a table the values of Ec. Round Ec to the nearest ksi. Ec = modulus of elasticity of concrete in compression (psi) w 80 f'c 3000 w = unit weight of concrete (lb/ft^3) Ec 1293.3305841895 f'c = compressive strength of concrete (psi) f 'c (psi) 1293 3000 3500 ### 4500 5000 5500 6000 6500 7000 80 1293 1397 ### 1584 1670 1751 1829 1904 1976 85 1416 1530 ### 1735 1829 1918 2003 2085 2164 90 1543 1667 ### 1890 1992 2090 2182 2272 2357 95 1674 1808 ### 2050 2161 2266 2367 2464 2557 100 1807 1952 ### 2214 2333 2447 2556 2661 2761 f 'c fr b = widthh=depth c Z = (2/3 T = 1/2(fr)(width)(depth/2) 105 1945 2101 ### 2382 2511 2633 2750 2863 2971 3000 411 6 14 7 9.33 Weight (lb/ 110 2085 2252 ### 2554 2692 2823 2949 3069 3185 3500 444 7 15 7.5 10.00 115 2229 2408 ### 2730 2878 3018 3152 3281 3405 4000 474 8 16 8 10.67 120 2376 2566 ### 2910 3067 3217 3360 3497 3629 4500 503 9 17 8.5 11.33 125 2526 2728 ### 3094 3261 3420 3572 3718 3859 5000 530 10 18 9 12.00 130 2679 2894 ### 3281 3459 3628 3789 3944 4092 5500 556 11 19 9.5 12.67 135 2835 3062 ### 3472 3660 3839 4010 4173 4331 6000 581 12 20 10 13.33 140 2994 3234 ### 3667 3865 4054 4234 4407 4574 6500 605 13 21 10.5 14.00 145 3156 3409 ### 3865 4074 4273 4463 4645 4821 7000 627 14 22 11 14.67 150 3321 3587 ### 4067 4287 4496 4696 4888 5072 7500 650 23 11.5 15.33 8000 671 24 12 16.00 Values in table are the calculated Ec values in ksi 25 12.5 16.67 26 13 17.33 2) Given: b 6 in Vary width from 6 inches to 14 inches (by 1 inch increments) and the depth from 14 inches t h 14 in I 1372 in^4 26 inches (by 1 inch increments). Also f'c from 3000 psi to 8000 psi. h depth Required: 1372 14 15 16 17 18 19 20 21 22 23 24 25 26 Develop a spreadsheet that calculates the cracking moment assuming no rebar. b width 6 1372 1688 2048 2457 2916 3430 4000 4631 5324 6084 6912 7813 8788 Note: Print the solution and a separate page with the formu 7 1601 1969 2389 2866 3402 4001 4667 5402 6211 7097 8064 9115 10253 8 1829 2250 2731 3275 3888 4573 5333 6174 7099 8111 9216 10417 11717 Cracking Moment Mcr = CZ fr = 7.5 * lambda * (f 'c^.5) 9 2058 2531 3072 3685 4374 5144 6000 6946 7986 9125 10368 11719 13182 C = 1/2(fr)(width)(depth/2) 10 2287 2813 3413 4094 4860 5716 6667 7718 8873 10139 11520 13021 14647 I-values M=CZ 11 2515 3094 3755 4504 5346 6287 7333 8489 9761 11153 12672 14323 16111 12 2744 3375 4096 4913 5832 6859 8000 9261 10648 12167 13824 15625 17576 b (width) = 6 in 13 2973 3656 4437 5322 6318 7431 8667 10033 11535 13181 14976 16927 19041 h (depth) = 14 in 14 3201 3938 4779 5732 6804 8002 9333 10805 12423 14195 16128 18229 20505 l (length) = 1 ft f'c = 3000 psi (compressive strength) c 7 fr = 411 psi (modulus of rupture) fr 411 fr/c 58.7 Z = 9.33333 in fr Specific Wt = 150 lb/ft3 - pcf 58.7 411 444 474 503 530 556 581 605 627 650 671 DL (dead Load) = 87.5 lb/ft 7 59 63 68 72 76 79 83 86 90 93 96 LL (live Load) = 0 lb/ft 7.5 55 59 63 67 71 74 77 81 84 87 89 C = 8626.63 lb c = h/2 8 51 55 59 63 66 70 73 76 78 81 84 Mcr = 6709.6 ft-lb 8.5 48 52 56 59 62 65 68 71 74 76 79 9 46 49 53 56 59 62 65 67 70 72 75 Width (in) 9.5 43 47 50 53 56 59 61 64 66 68 71 fr/c values ### 6 7 8 9 10 11 12 13 14 10 41 44 47 50 53 56 58 60 63 65 67 14 6709.6013294383 7827.87 8946 ### 11183 12300.9 13419 14537 ### 10.5 39 42 45 48 51 53 55 58 60 62 64 15 7702.3484649164 8986.07 10270 ### 12837 14121 15405 16688 ### 11 37 40 43 46 48 51 53 55 57 59 61 16 8763.5609200827 10224 11685 ### 14606 16066.5 17527 18988 ### 11.5 36 39 41 44 46 48 51 53 55 56 58 17 9893.2386949371 11542 13191 ### 16489 18137.6 19786 21435 ### 12 34 37 40 42 44 46 48 50 52 54 56 Heig 18 11091.38178948 12940 14789 ### 18486 20334.2 22183 24031 ### 12.5 33 35 38 40 42 44 46 48 50 52 54 19 12357.99020371 14418 16477 ### 20597 22656.3 24716 26776 ### 13 32 34 36 39 41 43 45 47 48 50 52 20 13693.063937629 15975 18257 ### 22822 25104 27386 29668 ### 21 15096.602991236 17613 20129 ### 25161 27677.1 30193 32709 ### 22 16568.607364531 19330 22091 ### 27614 30375.8 33137 35899 ### 23 18109.077057515 21127 24145 ### 30182 33200 36218 39236 ### 24 19718.012070186 23004 26291 ### 32863 36149.7 39436 42722 ### 25 21395.412402546 24961 28527 ### 35659 39224.9 42791 46357 ### 26 23141.278054593 26998 30855 ### 38569 42425.7 46283 50139 ### c = depth/2 7 7.5 8 8.5 9 9.5

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