CVEN444 HW11 SOLUTIONS

CVEN444 HW11 SOLUTIONS - , , .u. ,. I § ‘ I 1 ‘ ‘...

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V _. . , '1: if? _fff;__A_Z_ * CfEEff1.7.2::5.1:;12I: f' , If}:_.L:_:;f:LL).:3: :i' f , _ , , i, ' ‘ fl ,_ ,___, 1,; A .7 ,, Lozwgrwgkg, _Z_.;j 7 -. f:f¢2ggzizsz¢3;; ,stiéfilééiéc} . .. mug—nog‘ ‘ 035,; ‘ ,A;....._:__:2;afléZLQXéjéfig-é gm j; f .jj.,j:_if.;:~._:-jf l J ‘ill I; 5m_€.,.éié\:;5.531512%}.45.4;I;ZiiiZiLEéiébfi EDZLSQ2313769915.;51:23; 7' 7. . _ W i . . “ , : fl “96.337;.='773.,._.7thSméé'o‘fig)»1 ; V ’ 7 7 7777. 7 ,5, 7 7 > ‘77.._____L_,.:.__7..__7,;__.7..._.7.7f-7 7,7,7,“ 7777.777 “47777777.. __,?.,_.7-.‘77.7____ _ _. .777! .L, -77. _ # iwfsifal77€i 777,- 7 77; 7 7 7 _ 77. 7 7, 7 77 7‘ 7777777177 7,777,777.77- 77 7, 77 -7777._.7777.7 777 7 77777.77 7 7 7- 7 7L 7, 7 777 _ 717 -7 7, 7 .__,‘...,,7_7.777.77C ‘ .71.77177777777..777777. 77.7.7777,177.7777777 777-777.77.777777777.‘7.7.‘_7777.§.77777 77-. .,7.7 77'..7_ 7- 7 7 _. _ 7 77::77A7fi‘5axtala745l2778479 7747),;‘5777; . 7 .7 7 " ‘; l3'1‘ *-_1_74¥7 - 77,7.7___.7_.._.._- __7_..7.. 77.77.77.777. 77.7.7.77777777777-7.7777 ‘ 7 7 =7As777-10765f7 7 77 7 ‘ 7 777 7 77.47%77 _.., .77f’éfwiiflfisb711'7.o.2:o.8; 741%,,771777/7937327/471 73.717 _ _ _ _ f :11::::.::. 7:7,: if. 7 V; 7_ 7 777777 77-77.77/,7sa7(zpo)..7 717747475 751/75 7 7 7 7 7 7 7 77 7 7 7 7 7 7 7 7 [4.42) Concrete Column Interaction Curve By Successive Values of c Axial Reduction Factor = 0.80 AS = 1.58 fc' = 4 (0.80 tied and 085 spiral) A; = 1.58 y = 60 d= 11.5 B] = 0.85 Po= 655 d' = 2.5 Pn = 524 b = 10 h = 14 c (in.) a (in.) as fS 65' fs' Pn Mn 6 T CS Cc inches inches in./in. ksi in./in. ksi kips kip-fl inches kips kips kips l 0.85 0.03150 60.0 -0.00450 -60.0 -161 16 -l.18 95 -95 29 2 1.70 0.01425 60.0 -0.00075 -21.8 -71 52 -8.79 95 -34 58 3 2.55 0.00850 60.0 0.00050 14.5 9 83 106.15 95 18 87 4 3.40 0.00563 60.0 0.00113 32.6 67 104 18.62 95 46 116 5 4.25 0.00390 60.0 0.00150 43.5 113 118 12.53 95 63 145 6 5.10 0.00275 60.0 0.00175 50.8 153 128 10.00 95 75 173 7 5.95 0.00193 55.9 0.00193 55.9 197 132 8.05 88 83 202 8 6.80 0.00131 38.1 0.00206 59.8 260 125 5.78 60 89 231 9 7.65 0.00083 24.2 0.00217 60.0 311 117 4.50 38 89 260 10 8.50 0.00045 13.1 0.00225 60.0 358 107 3.61 21 89 289 11 9.35 0.00014 4.0 0.00232 60.0 401 97 2.92 6 89 318 12 10.20 -0.00013 -3.6 0.00238 60.0 436 88 2.43 0 89 347 13 11.05 -0.00035 -10.0 0.00242 60.0 465 80 2.06 0 89 376 14 11.90 -0.00054 -15.5 0.00246 60.0 494 69 1.67 0 89 405 15 12.75 -0.00070 -20.3 0.00250 60.0 523 56 1.29 0 89 434 16 13.60 -0.00084 -24.5 0.00253 60.0 552 41 0.90 0 89 462 17 14.45 -0.00097 -28.1 0.00256 60.0 581 24 0.50 0 89 491 18 15.30 -0.00108 -31.4 0.00258 60.0 610 5 0.11 0 89 520 19 16.15 -0.00118 -34.3 0.00261 60.0 639 -16 -0.29 0 89 549 20 17.00 -0.00128 -37.0 0.00263 60.0 667 -39 -0.70 0 89 578 21 17.85 -0.00136 -39.4 0.00264 60.0 696 -64 -1 . 10 0 89 607 22 18.70 -0.00143 -41.5 0.00266 60.0 725 -91 -1.51 0 89 636 -|l—3'(4.¢z) 2 a «5:5 2 9: com com oov 930'] IBEXV ‘ d " ‘ 22: ' "W, . ,, 2,227-”. 12-..“.5 5 . , .. N I _‘. ,. W ‘ L 43.25;. ,t20.1(12>.2-:7-24Q1111.2 ,f 2“. 4.217-121, 4’; £1 .11."; 7, . ,7 7 4%-}- I. s c =1 1:441.-sz _, ., ,. ,, J 7 I 1 2,4 1 .. "7,7,, , .27,” fl, , ,.. _ 2., ,,,,.,,, ,.-A , ,, W... ,fi __ , 7 7, w 7- *— ~ ' 7 Concrete Column Interaction Curve V I 7—9 - ; By Points - “j " Axial Reduction Factor = 0.80 ‘ 1" As = 3-81 fc' = 9 (0.80 tied and 0.85 Spiral) " " AS' = 3.81 fy= 60 = 17 13. = 0.65 P0 = 2235 i 7 f 7 d' = 3 Pn = 1788 -2. , b = 12 h = 20 _____ ,, c(in.) a(in.) 85 f5 85' fs' Pn Mn e T CS Cc ,2. . 7. inches inches in./in. ksi in./in. ksi kips kip-ft inches kips kips kips '* , ,, , Pt A (Zero Moment) ” 2235 0 0 199 - 199 1836 ~17 Pt_B (Zero Tension) 20.00 13.00 0.00045 13.05 0.00255 60 1413 452.4 3.84 21 199 1193 '1’ M (Balanced) 4: 10.06 6.54 0.00207 60.00 0.00211 60.00 571 586.4 12.32 229 199 600 774-7 E D (Tension Controlled) _._. 6.38 4.14 0.005 60.00 0.00159 46.06 298 470.0 18.92 229 146 380 »- A? 5 H2 m (Flexure) 7 _ 3.51 2.28 0.01153 60.00 0.00044 12.66 0 299 229 19 210 E a 25:52 com- com com oomfi oowfi comm comm PBO’I IBEXV ‘ «I Concrete Column Interaction Curve By Successive Values of c Axial Reduction Factor = 0.80 As = 3.81 c' = 9 (0.80 tied and 085 spiral) A; = 3.81 y = 60 ‘ d= 17 [31= 0.65 Po= 2235 d' = 3 Pn = 1788 b = 12 h = 20 c (in.) a (in.) as f5 85' fs' Pl1 MI1 e T C5 C0 inches inches in./in. ksi in./in. ksi kips kip-ft inches kips kips kips 1 0.65 0.04800 60.0 -0.00600 -60.0 -398 48 -1.45 229 -229 60 2 1.30 0.02250 60.0 -0.00150 -43.5 -275 130 -5.66 229 -166 119 3 1.95 0.01400 60.0 0.00000 0.0 -79 251 -38.25 229 -29 179 4 2.60 0.00975 60.0 0.00075 21.8 64 338 63.52 229 54 239 5 3.25 0.00720 60.0 0.00120 34.8 173 402 27.85 229 103 298 6 3.90 0.00550 60.0 0.00150 43.5 266 453 20.44 229 137 358 7 4.55 0.00429 60.0 0.00171 49.7 349 496 17.03 229 160 418 8 5.20 0.00338 60.0 0.00188 54.4 427 532 14.95 229 178 477 9 5.85 0.00267 60.0 0.00200 58.0 500 562 13.48 229 192 537 10 6.50 0.00210 60.0 0.00210 60.0 568 585 12.38 229 199 597 11 7.15 0.00164 47.5 0.00218 60.0 675 573 10.19 181 199 656 12 7.80 0.00125 36.3 0.00225 ' 60.0 777 - 561 8.66 138 199 716 13 8.45 0.00092 26.8 0.00231 60.0 873 549 7.55 102 199 776 14 9.10 0.00064 18.6 0.00236 60.0 964 537 6.69 71 199 835 15 9.75 0.00040 11.6 0.00240 60.0 1050 524 5.99 44 199 895 16 10.40 0.00019 85.4 0.00244 60.0 1133 510 5.40 21 199 955 17 11.05 0.00000 0.0 0.00247 60.0 1214 495 4.89 0 199 1014 18 11.70 -0.00017 -4.8 0.00250 60.0 1274 488 4.60 0 199 1074 19 12.35 -0.00032 -9.2 0.00253 60.0 1333 478 4.30 O 199 1134 20 13.00 -0.00045 -13.1 0.00255 60.0 1393 464 4.00 0 199 1193 21 13.65 -0.00057 -16.6 0.00257 60.0 1453 448 3.70 0 199 1253 22 14.30 -0.00068 -19.8 0.00259 60.0 1512 428 3.40 0 199 1313 23 14.95 -0.00078 -22.7 0.00261 60.0 1572 405 3.09 0 199 1372 24 15.60 -0.00088 -25.4 0.00263 60.0 1632 379 2.79 0 199 1432 25 16.25 -0.00096 -27.8 0.00264 60.0 1691 349 2.48 0 199 1492 26 16.90 -0.00104 -30.1 0.00265 60.0 1751 317 2.17 0 199 1551 27 17.55 —0.001 11 -32.2 0.00267 60.0 1811 281 1.86 0 199 1611 28 18.20 -0.00118 -34.2 0.00268 60.0 1870 242 1.55 0 199 1671 29 18.85 -0.00124 -36.0 0.00269 60.0 1930 199 1.24 0 199 1730 30 19.50 -0.00130 -37.7 0.00270 60.0 1990 154 0.93 0 199 1790 31 20.15 -0.00135 -39.3 0.00271 60.0 2049 105 0.61 0 199 1850 32 20.80 -0.00141 -40.8 0.00272 60.0 2109 53 0.30 0 199 1909 33 21.45 -0.00145 -42.2 0.00273 60.0 2169 -3 -0.01 0 199 1969 34 22.10 -0.00150 -43.5 0.00274 60.0 2228 -61 -0.33 0 199 2029 35 22.75 -0.00154 -44.7 0.00274 60.0 2288 -123 -0.64 0 199 2088 (4,7 2 a 25:52 com com oomfi oowfl comm comm PBO'I IBEXV ‘ (I Appendix A Tables and Nomograms 787 I ; INTERACTION DIAGRAM L4-60.7 f’c=4ksi ; fy=60|si : v=o-7 Kn=Pn If’cA9 0.8 0.6 0.4 0.2 R,,=Pnelf'cAgh Figure A.15 Rectangular column nominal load-moment strength interaction diagram: fc' = 4000 psi. fy= 60,000 psi, 'y = 0.7 (ACl-SP17 and Refs. 9.8, 9.10, 9.11). i . ,_z,o,.;.,_ ;___'_- __:.w.‘ ,_ ‘,,, \W r, ."WWEWW. “-777 N k... '__2;x_;ew_g:§oo Wm, , ..;-, 4,; = mi”- WM-71-,__7‘_,T____V45:Q_. Mm... .__ Q.fie§_}___gw,1 ,7___ ; W, _ ,1 _ W # d _ ,7 A , i , n ’ ' i ‘ i ‘ g, ,. .. _. - “A __ __ H Dig-QEEESWJ": A3 = .1905) 5, ,z-sQo m3 ,lVéQNfiPJD ‘ g _ , ,_ _ , W, , l.- , figllogza N , , , , _ , , __ ,_ M V, _ _ fl. _ L , _- W ,# ,A __. :1.iiljéééiiilfl:Liéfzgai; WW « __ w ,_ _ - - fl __ _ ~ _ -7 __ - # ,, V, H; i, ; . 7 1 i -. __ , 2' “g _ , y . _ t v, ; - _ - _ -_ - m ?- _ _ _ ~ _. , fl :_.j,.;3fl;a§[Zigifff3:31,, 7, - _ - # , M, ,-.__ {9‘74 7, ,, . Mg," , 7, , , 5»! , '4“, i, u , , ~ i Lyflbé #éibasésif: ; m # , _ H fl ‘ ,._.__,~;_ _ _ _ M _ _‘ _. _ - _ V- _, M _ :f.&,, 7__ V _, - 51m“ = 46276110,), =_ Hal - $ , , W ,, #5,:qu I,5,,,, _, , :' 5, J 6,1,, _ , , -. Z i 7, , , , , A, Concrete Column Interaction Curve By Successive Values of c AS = 1.58 AS' = 1.58 d = 17 d' = 3 b = 15 c (in.) a (in.) inches inches 1 0.85 2 1.70 3 2.55 4 3.40 5 4.25 6 5.10 7 5.95 8 6.80 9 7.65 10 8.50 11 9.35 12 10.20 13 11.05 14 11.90 15 12.75 16 13.60 17 14.45 18 15.30 19 16.15 20 17.00 21 17.85 22 18.70 23 19.55 24 20.40 25 21.25 26 22.10 27 22.95 28 23.80 29 24.65 30 25.50 31 26.35 32 27.20 33 28.05 34 28.90 35 29.75 85 in./in. 0.04800 0.02250 0.01400 0.00975 0.00720 0.00550 0.00429 0.00338 0.00267 0.00210 0.00164 0.00125 0.00092 0.00064 0.00040 0.00019 0.00000 -0.00017 -0.00032 -0.00045 -0.00057 -0.00068 -0.00078 -0.00088 -0.00096 -0.00104 -0.001 1 1 -0.001 18 -0.00124 -0.00130 -0.00135 -0.00141 -0.00145 -0.00150 -0.00154 6' = 4 y = 60 B1 = h = 20 f5 85‘ ksi in./in. 60.0 -0.00600 60.0 -0.00150 60.0 0.00000 60.0 0.00075 60.0 0.00120 60.0 0.00150 60.0 0.00171 60.0 0.00188 60.0 0.00200 60.0 0.00210 47.5 0.00218 36.3 0.00225 26.8 0.00231 18.6 0.00236 11.6 0.00240 5.4 0.00244 0.0 0.00247 -4.8 0.00250 -9.2 0.00253 -13.1 0.00255 -16.6 0.00257 -l9.8 0.00259 -22.7 0.00261 -25 .4 0.00263 -27.8 0.00264 -30.1 0.00265 —32.2 0.00267 -34.2 0.00268 -36.0 0.00269 -37.7 0.00270 -39.3 0.00271 -40.8 0.00272 -42.2 0.00273 -43.5 0.00274 -44.7 0.00274 fsl ksi -60.0 -43.5 0.0 21.8 34.8 43.5 49.7 54.4 58.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 60.0 Pn kips -146 -77 30 108 172 229 282 333 382 428 491 552 611 667 721 774 826 870 913 956 1000 1043 1086 1130 1173 1217 1260 1303 1347 1390 1433 1477 1520 1563 1607 Axial Reduction Factor = (0.80 tied and 085 spiral) Mn knyfi 35 81 147 192 226 254 276 293 306 315 308 298 287 274 259 242 223 205 184 161 134 104 71 35 —4 -46 -92 -140 —191 -246 -303 -364 -428 -494 -564 e inches -2.84 -12.70 58.93 21.43 15.84 13.32 11.74 10.57 9.63 8.83 7.51 6.47 5.64 4.93 4.31 3.75 3.23 2.83 2.42 2.01 1.60 1.19 0.78 0.37 -0.04 -0.46 -0.87 -1.29 -1.71 -2.12 -2.54 -2.96 -3.38 -3.80 -4.21 Pn= T kips t—‘NJBUINO\O\0\0\O\O\O\D\DVD \DOOONQUILIIMMUIUIMUIMUILII OOOOOOOOOOOOOOOOOOO 0.80 1199 959 kips kips 43 87 130 173 217 260 303 347 390 434 477 520 564 607 650 694 737 780 824 867 910 954 997 1040 1084 1127 1170 1214 1257 1301 1344 1387 1431 1474 1517 lbyféL 1/5,, 2 a E0832 com- com oov coo cow ooofi OONH oovfi coo“ oowfi 9801 [BEXV 6 d ...
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CVEN444 HW11 SOLUTIONS - , , .u. ,. I § ‘ I 1 ‘ ‘...

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