ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Structures of the Everyday) FALL 2013 lecture twenty steel construction: columns & tension members Steel Columns & Tension 1
Structural Steel standard rolled shapes (W, C, L, T) tubing pipe built-up Steel Columns & Tension 2
Design Methods (revisited) know loads or lengths select section or load adequate for strength and no buckling Steel Columns & Tension 3
Allowable Stress Design (ASD) AICS 9 th ed F slenderness ratio a f critica l F. S. 12 23 Kl 2 for kl/r C c = 126.1 with F y = 36 ksi = 107.0 with F y = 50 ksi Kl r 2 E r Steel Columns & Tension 4
C c and Euler s Formula Kl/r < C c short and stubby parabolic transition Kl/r > C c Euler s relationship < 200 preferred C c 2 2 E F y Steel Columns & Tension 5
C c and Euler s Formula Steel Columns & Tension 6
Short / Intermediate L e /r < C c where F a F. S. 5 3 Kl r 1 2C 2 c 3 2 F y F. S. Kl Kl 8C r r 8C 3 c c 3 Steel Columns & Tension 7
Unified Design limit states for failure c 0. 90 n F cr A g a u n c n 1. yielding 2. buckling KL r KL r E 4. 71 or Fe F y E 4. 71 or Fe F F e elastic buckling stress (Euler) y 0. 44F 0. 44F y y Steel Columns & Tension 8
Unified Design n = F cr A g Fy for KL E Fe 4. 71 Fcr 0. 658 r Fy KL E for 4. 71 Fcr 0. 877 F r F where F e y 2 E KL 2 r e F y Steel Columns & Tension 9
rocedure for Analysis 1. calculate KL/r biggest of KL/r with respect to x axes and y axis 2. find F a or F cr from appropriate equation tables are available 3. compute allowable = F a A or n = F cr A g or find f actual = /A 4. is allowable ( a n /)? or is u n? yes: ok no: insufficient capacity and no good Steel Columns & Tension 10
rocedure for Design 1. guess a size (pick a section) 2. calculate KL/r biggest of KL/r with respect to x axes and y axis 3. find F a or F cr from appropriate equations or find a chart 4. compute allowable = F a A ( n / = F cr A g ) or n = F cr A g or find f actual = /A Steel Columns & Tension 11
rocedure for Design (cont d) 5. is allowable ( a n /)? or is u n? yes: ok no: pick a bigger section and go back to step 2. 6. check design efficiency percentage of stress = if between 90-100%: good r 100% if < 90%: pick a smaller section and go back to step 2. c Steel Columns & Tension 12
Column Charts, F a (pg. 361-364) Steel Columns & Tension 13
Column Charts, F cr Steel Columns & Tension 14
Column Charts Steel Columns & Tension 15
Beam-Column Design moment magnification (-) M u B M 1 m a x f a c t o r e d B 1 1 ( C u m / e1 ) C m modification factor for end conditions Steel Columns & Tension 16 = 0.6 0.4(M 1 /M 2 ) or 0.85 restrained, 1.00 unrestrained e1 Euler buckling strength e 1 2 EA Kl 2 r
Beam-Column Design LRFD (Unified) Steel for r u 8 0. 2 : 9 for r c c 0. 2 M bm r is required, c is capacity : c M M c - resistance factor for compression = 0.9 b - resistance factor for bending = 0.9 n u 2 c n M bm ux ux nx nx b M M b ux ux nx nx 1. 0 1. 0 Steel Columns & Tension 17
Design Steps Knowing Loads (revisited) 1. assume limiting stress buckling, axial stress, combined stress 2. solve for r, A or S 3. pick trial section 4. analyze stresses 5. section ok? 6. stop when section is ok Steel Columns & Tension 18
Rigid Frame Design (revisited) columns in frames ends can be flexible stiffness affected by beams and column = EI/L EI l G c EI for the joint l c is the column length of each column l b is the beam length of each beam measured center to center l b Steel Columns & Tension 19
Rigid Frame Design (revisited) column effective length, k A B Steel Columns & Tension 20
Tension Members steel members can have holes reduced area s 2 A A A n g of all increased stress holes t 4 g(aisc - Steel Structures of the Everyday) Steel Columns & Tension 21
Effective Net Area likely path to rip across bolts divide transferred force too shear lag A e A n U Steel Columns & Tension 22
Tension Members limit states for failure a n u t n 1. yielding t 0. 90 n F y A g 2. rupture* A g - gross area A e - effective net area (holes 1/8 + d) t 0. 75 F u = the tensile strength of the steel (ultimate) n F u A e Steel Columns & Tension 23