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
Strutural Steel standard rolled shapes (W, C, L, T) tubing pipe built-up Steel Columns & Tension 2
Design Methods (revisited) know loads or lengths selet setion or load adequate for strength and no bukling Steel Columns & Tension 3
Allowable Stress Design (ASD) AICS 9 th ed F a f ritia l F. S. 12 23 2 E Kl 2 r slenderness ratio Kl r for kl/r C = 126.1 with F y = 36 ksi = 107.0 with F y = 50 ksi Steel Columns & Tension 4
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
C and Euler s Formula Steel Columns & Tension 6
Short / Intermediate L e /r < C where F a F. S. 5 3 Kl r 1 2C 2 3 2 F y F. S. Kl Kl 8C r r 8C 3 3 Steel Columns & Tension 7
Unified Design limit states for failure 1. yielding 0. 90 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
Unified Design P n = F r A g for for where Steel Columns & Tension 9 L r L r y E 4.71 F 0.658 Fe F r Fy E 4.71 F 0.877F r Fy 2 E F e 2 L r F e y
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
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
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 2. 6. hek design effiieny perentage of stress = if between 90-100%: good Pr 100% P if < 90%: pik a smaller setion and go bak to step 2. Steel Columns & Tension 12
Column Charts, F a (pg. 461-462) Steel Columns & Tension 13
Column Charts, F r Steel Columns & Tension 14
Column Charts Steel Columns & Tension 15
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 = 0.6 0.4(M 1 /M 2 ) or 0.85 restrained, 1.00 unrestrained L 1 effetive length in plane of bending P e1 Euler bukling strength 2-1.00 (LRFD), 1.60(ASD) P e u e1 EI 1 2 L 1
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
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
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
Rigid Frame Design (revisited) olumn effetive length, k A B Steel Columns & Tension 20
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
Effetive Net Area likely path to rip aross bolts divide transferred fore too shear lag A e A n U Steel Columns & Tension 22
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