twenty steel construction: columns & tension members ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS FALL 2018 lecture
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1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS Cor-Ten Steel Sulpture By Rihard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Strutures of the Everyday) FALL 2018 leture twenty steel onstrution: olumns & tension members Steel Columns & Tension 1
2 Strutural Steel standard rolled shapes (W, C, L, T) tubing pipe built-up Steel Columns & Tension 2
3 Design Methods (revisited) know loads or lengths selet setion or load adequate for strength and no bukling Steel Columns & Tension 3
4 Allowable Stress Design (ASD) AICS 9 th ed F a f ritia l F. S E Kl 2 r slenderness ratio Kl r for kl/r C = with F y = 36 ksi = with F y = 50 ksi Steel Columns & Tension 4
5 C and Euler s Formula Kl/r < C short and stubby paraboli transition Kl/r > C Euler s relationship < 200 preferred C 2 2 E F y Steel Columns & Tension 5
6 C and Euler s Formula Steel Columns & Tension 6
7 Short / Intermediate L e /r < C where F a F. S. 5 3 Kl r 1 2C F y F. S. Kl Kl 8C r r 8C 3 3 Steel Columns & Tension 7
8 Unified Design limit states for failure 1. yielding P 2. bukling n F e elasti bukling stress (Euler) F r A g P P a u P L E Fy 4.71 or 2.25 r Fy Fe L E Fy 4.71 or 2.25 r F F y e n P n Steel Columns & Tension 8
9 Unified Design P n = F r A g for for where Steel Columns & Tension 9 L r L r y E 4.71 F Fe F r Fy E 4.71 F 0.877F r Fy 2 E F e 2 L r F e y
10 Proedure for Analysis 1. alulate KL/r biggest of KL/r with respet to x axes and y axis 2. find F a or F r from appropriate equation tables are available 3. ompute P allowable = F a A or P n = F r A g or find f atual = P/A 4. is P P allowable (P a P n /)? or is P u P n? yes: ok no: insuffiient apaity and no good Steel Columns & Tension 10
11 Proedure for Design 1. guess a size (pik a setion) 2. alulate KL/r biggest of KL/r with respet to x axes and y axis 3. find F a or F r from appropriate equations or find a hart 4. ompute P allowable = F a A (P n / = F r A g ) or P n = F r A g or find f atual = P/A Steel Columns & Tension 11
12 Proedure for Design (ont d) 5. is P P allowable (P a P n /)? or is P u P n? yes: ok no: pik a bigger setion and go bak to step hek design effiieny perentage of stress = if between %: good Pr 100% P if < 90%: pik a smaller setion and go bak to step 2. Steel Columns & Tension 12
13 Column Charts, F a (pg ) Steel Columns & Tension 13
14 Column Charts, F r Steel Columns & Tension 14
15 Column Charts Steel Columns & Tension 15
16 Beam-Column Design moment magnifiation (P-) C M B M B m r 1 nt 1 1 ( P / P ) C m modifiation fator for end onditions Steel Columns & Tension 16 = (M 1 /M 2 ) or 0.85 restrained, 1.00 unrestrained L 1 effetive length in plane of bending P e1 Euler bukling strength (LRFD), 1.60(ASD) P e u e1 EI 1 2 L 1
17 Beam-Column Design LRFD (Unified) Steel for Pr P 8 r M M rx ry 0.2 : 1.0 P P 9 M x M y for Pr P r M M rx ry 0.2 : 1.0 P 2P M x M y P r is required, P is apaity M rx is required, M x is apaity M ry is required, M y is apaity Steel Columns & Tension 17
18 Design Steps Knowing Loads (revisited) 1. assume limiting stress bukling, axial stress, ombined stress 2. solve for r, A or S 3. pik trial setion 4. analyze stresses 5. setion ok? 6. stop when setion is ok Steel Columns & Tension 18
19 Rigid Frame Design (revisited) olumns in frames ends an be flexible stiffness affeted by beams and olumn = EI/L EI l G EI for the joint l is the olumn length of eah olumn l b is the beam length of eah beam measured enter to enter l b Steel Columns & Tension 19
20 Rigid Frame Design (revisited) olumn effetive length, k A B Steel Columns & Tension 20
21 Tension Members steel members an have holes redued area A A A t n g of all holes inreased stress s 2 4g (AISC - Steel Strutures of the Everyday) Steel Columns & Tension 21
22 Effetive Net Area likely path to rip aross bolts divide transferred fore too shear lag A e A n U Steel Columns & Tension 22
23 Tension Members limit states for failure 1. yielding 2. rupture* Steel Columns & Tension 23 A g - gross area A e - effetive net area (holes 1/8 + d) P F u = the tensile strength of the steel (ultimate) a 0.90 P n P P F A t n y g 0.75 P F A t n u e u t P n
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