Question

Problem 2. Plot (Excel plot) the nominal capacity interaction diagram of the column shown below by calculation (hand calculation) of the following points on the diagram and connecting them with straight lines. A) Pure compression, Mn=0 B) No tension in tension steel, fs=0 C) Balance point, Ec= ecu and €5=ey D) Tension controlled section limit, ec= ecu and es= 0.005 E) Pure bending, Pn=0 F) Pure tension, Mn=0 b f'c = 4 ksi fy = 60 ksi b = h = 16 in #4 ties 6 #10 rebar 1.5in clear cover h

Answer 1

23 24 25 26 27 SEPTEMBER 14 2019 SATURDAY bearing [1.5 16 fle=4801 Ry = 6opsi 6# 10 jebay 1.5 in clear cover. 13 B = 0.85-8.05(ple-4ksi) -0.85 0.65 Pore compression. EC -0.003. 0-85P'C EST s's cs. Cc ES Sc. no 11 C's = A's py Cs = ASRY. (c = 0.85 f'c (Ag-Astot) Astot - 6xTx(107.36 Capacity in pure compression, N=0.85 (FO CAg-Astot) + Astotary N = 0.85 x 4 (16 x 16 GTX/100)?) +7.86X60 N. 128 6.98 2019 S S T NOVEMBER M TW F 2019 SS 5 6 F T 4 1 2 3 2 3 9 10 5 2 8 5 7 12 5 16 13 4 11 17 18 9 10 16 17 19 20 13 14 15 11 12 18 19 25 26 20 21 31 22 23 24 29 30 27 28

SEPTEMBE 8 21 201 SEPTEMBE SATURDAY 2019 C's: 0.003 A'S Es (crd ) Cone C-1.5 = 0.003 * 7.36 x 29 000 X 2 320:16 ( [-2.5 Tot Ce = 085 ß fc b = 0.8 5x0.8 584 x 6 x 16 46.24 C. Tension steel , Ts = Aspy = 220.8 R N=EF 46.240 +26 320.16 - 321 - 220.8 -0. M 46.240 - 220.8C + 32o. 16 C - 480.24 46.240²t 99.86 C - 480.24 = 0 C = 2.82" Concrete lever force. Cc = 0.85 Bip'cCb 0.85x0.85x4X16 C = 46.240. 107.28 K AUGUST M T 2019 S S w T F SEPTEMBER M T w 30 2019 S - F F S 1 8 2 9 3 10 1 5 6 7 2 3 10 5 6 12 13 14 15 9 11 16 23 17 18 24 25 12 13 19 20 22 16 17 21 28 18 19 7 8 14 15 21 28 29 20 26 27 29 30 31 23 24 25 26 27

Tension Controlled CEU = 0.005, ECE EA SEPTEMBE 19 6 2011 THURSDAY NA S ed ( d = 1415 ed 0.00 3 + 0.005 5.487" 0.003 a Calculate the compression steel strain Els = 0.003 fc-d" 2.17 X10-3. Compression steel stress f'&= 29000ksi X 2.17x10-3- 62.93KSI Compression steel. cs = 7.36 x 62.93K. = 281.58 K [cs = Asf's] Concrete Ce = 0.85 x 0.85 X 4 X 5.437 x 16 251.4LR Tension steel Is = Asry 220.8 K M = EFE17013. Ignk AUGUST M T W 2019 S S T F SEPTEMBER M T w 20 T 1 F 2 3 4 S 5 30 6 7 8 9 10 11 2 12 13 14 15 16 3 10 4 5 9 19 20 6 13 21 17 18 24 25 22 12 11 18 23 26 27 16 17

0.00257 18 SEPTEMBER 2019 WEDNESDAY Is = As Ry 220.8 K. 785.7 g R 6.5-0.85x7.66 N= 120.87 354.19 4220.8 = 0 to concrete lever arm. ya = y pt - Bic = 8245-4.745 Tot steel lever arm. y cs= 8.5-1.5 -6.511. Bottom Steel - 11 - yts = 14.5-88 = 8 6.500 OLX 8. Codec M = 6.5 x 220.8 6.5 X 220-8 t 4.745 x 854.19 t. = 4551.032 kin OCTOBER M T 2019 S S NOVEMBER M TW 2019 S S TF w T F 1 2 3 1 2 3 4 6 5 8 7 9 10 6 5 7 10 11 4 12. 13

SEPTEMBER 23 2019 MONDAY Moment [kipin)/ axial- (kip Point A Pure compressim Bizero tersim Balance point D Tensim control Pure moment Pure tension O 2662.178 4551032 4368.47 2928.3 O 1286.98 891.28 795.79 262:19 C E - 441.6 1400 ooo 8 600 400 200 D Doo 500 1000 1800 2900 2500 3000 3500 4008 4500 M. 400 foo AUGUST M T w 2019 S S SEPTEMBER M T W T F T 20 S 1 F 2 3 30 5 6 4 11 7 8 9 10 12 4 13 15 16 6 14 21 2 3 9 10 16 17 5 12 19 20 17 18 24 25 31 7 1 22 23 11 18 13 26 27 28 29 19 30 20 26

3 SEPTEMBER 2019 16 MONDAY compression steel, c's Asry 7.36 x 60 = 220.8 R. 2 Concrete Cc = 0.85B, PE cb - 0.85 x 0.85 X 4 X (14.5 x 16 670.48. Tensio Steel ТcОК N - 22018 +670.48 891.28 K 18 Moment M = Yes C's t you CC + YTSTS. concrete Y ce = 4 pt - Bic/2. 8" - 0.85 x 14.5 = 183 Top sted. y's=ypt di 81- 1.5 = 6.5" Bottom steel YTS = d-gpt = 14.51- 81 6.5" M = 220.8 X 6.5 + 220.8x 0x 6.5 t 1.83 x 670.48 206 2.178 Kin. OCTOBER M T NOVEMBER M T w 2019 SS T F W T F 2019 S S 5 6 1 1 2 3 4 6 8 9 5 4 7 8 14 15 21 22 2 3 9 10 16 17 7 14 16 10 17 24 11 12 13 15 11 12 13 18 19 20 25 26 27 18 20 19 21 23 22 23 24 28 29 30 25 26 27 31 28 29 30

BER 19 SEPTEMBER 2019 20 FRIDAY -003) 231.58 + 251.41 - 220.8k 262.19 R M concrete lever arm y ce upt - Bic 2 = 8- 0-85X5-437 Top steel lever arm yt = = 5.68 18-15= 6.5 in bottom steel lever arm. YT: 14.5-8=6 sin 1 Ma 6.88 281.58 + 6.5x220.8 t 5.68 X 251.41 43 68.47. 5) Pure bending W We will find the Na depth based on eqwlibrium Els=0.003 cc-dig . Compression steel. o strain. f's = Es els ... compression steel C'S = A's P's compression steel VTC stress OCTOBER M T NOVEMBER M T w T w 019 S T 2019 S S 5 6 1 2 4 3 10 6 9 10 1 7 2019 F S S 1 2 3 8 15 16 17 22 23 24 29 30 8 9 12 13 19 20 11 18 4 11 18 5 12 7 14 13 14 16 15 26 27 21 15 21 22 19 20 26 27 25 22 28 29

SEPTEMBE 2010 SUNDAY SEPTEMBE 2019 (8 4 3 + Cc Yet C'syls 15 Moment at this point m=0 Rin Plastic centroid ERI ER COMPLE Upt = &Rily, Concre 736X Gox t 0.85 Tensit Cc = 0.85*4 (16x16 - 7.36) = 7.36 x 60 x14.5+ 845.88 x 8 + 7367 60x1.5 1286.98 Mome Concrete Y cc Top stea 2) Zero tension. Y c' Bottom c's Ts =OR. M = depth c= d = 14.51 Compression steel strain Els = 0.003 (14.5-1.57 14,5 Els = 0.003. (e-do) 2.68 X10-39 Ey. с AUGUST M т W T 2019 S S F SEPTEMBER M T W 1 2 T F 2019 SS 1 6 5 12 7 8 30 9 13 14 15 2 16 3 4 5 6 3 4 10 11 17 18 24 25 31 8 7 19 20 26 27 21 22 11 12 28 29 23 30 9 10 16 17 23 24 13 20 14 15 21 22 18 19 30 25 26 27 28 29

SEPTEMBER 2019 22 SUNDAY 10 Concrete lever arm. Yec = ypt BIL = 8 -0.85 x 2.32 C - 7.014" o ouro Top steel lever arm = y e's = 8 - 1.5-6.57 Top steel force = 0.003 A's Es (Cd) Bottom Steel 113.16 arm = 113.16* 6.5 + 7.0 14x 107.28 + 6.5X220.8 2 g 28.2 ure tension 000031 Oct 03 - T's = A's Ry tension (Mcokin Top steel Bottom steel To - As Rey N= EF T's & Tc + TS. N =-7-36 * 60 = -441.6 R. M=0 2019 S S NOVEMBER M T W T F 2019 S s OCTOBER M T 1 F T w 5 6 2 3 9 10 16 17 4 3 6 7 4 5 8 15 11 10 14 12 13 19 20 11 12 13 22 23 24 18 21 17 20 1 2 7 8 9 14 15 16 21 22 23 28 29 30 18 19 25 26 25 26 27 24 29 30 27 28 31

17 SEPTEMBE 2019 TUESDAY SE 2 3) Balance point mu NA = (= d (0003784 a C = 14,5 / 0.003 3 + 2.68x10-3 7 66 11, 14.5*(0.00 3) Compression steel E'c = 8.003 (e-d') Shain = 0.003 (7.66-), 5) 7.66 2.4 1x10 3 > Ees Compression steel cs = A's Ry 220.8 R, concrete. Cc = 0.85 XP1 Pc cb 0.85 x 0-85* 4x (7.66 ) x (16) 364.19 R. AUGUST M T w T F 2019 SS 3 4 10 11 SEPTEMBER M T w 2 T F 2019 S S 5 6 30 8 7 14 9 12 2 13 20 15 3 16 4 17 18 5 6 21 9 1 8 19 26 22 10 7 22 12 27 28 11 18 29 16 13 24 25 31 30 14 17 24 23 19 26 20 25 27 21 28