twenty steel construction: columns & tension members Steel - PowerPoint PPT Presentation

A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN A RCH 331 Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Structures of the Everyday) D R. A NNE N ICHOLS S PRING 2018 lecture twenty steel construction: columns & tension members Steel Columns & Tension 1 Architectural Structures S2018abn Lecture 20 ARCH 331

Structural Steel • standard rolled shapes (W, C, L, T) • tubing • pipe • built-up Steel Columns & Tension 2 Architectural Structures S2018abn Lecture 20 ARCH 331

Design Methods (revisited) • know – loads or lengths • select – section or load – adequate for strength and no buckling Steel Columns & Tension 3 Architectural Structures S2018abn Lecture 20 ARCH 331

Allowable Stress Design (ASD) • AICS 9 th ed  2 f 12 E     critical F a 2 F . S . Kl 23 r K l • slenderness ratio r – for kl/r  C c = 126.1 with F y = 36 ksi = 107.0 with F y = 50 ksi Steel Columns & Tension 4 Architectural Structures S2018abn Lecture 20 ARCH 331

C c and Euler’s Formula • Kl/r < C c – short and stubby – parabolic transition • Kl/r > C c – Euler’s relationship – < 200 preferred 2  2 E  C c F y Steel Columns & Tension 5 Architectural Structures S2018abn Lecture 20 ARCH 331

C c and Euler’s Formula Steel Columns & Tension 6 Architectural Structures S2018abn Lecture 20 ARCH 331

Short / Intermediate   • L e /r < C c   2 Kl F   r   y F 1   a 2 2 . . C F S    c  – where     3 K l K l 3 5 r r    F . S . 3 3 8 C 8 C c c Steel Columns & Tension 7 Architectural Structures S2018abn Lecture 20 ARCH 331

Unified Design P  • limit states for failure P n  a      P P 0 . 9 0 P F A u c n c n c r g KL E   1. yielding 4 . 71 or F 0 . 44 F e y r F y KL E 2. buckling   4 . 71 or F 0 . 44 F e y r F y F e – elastic buckling stress (Euler) Steel Columns & Tension 8 Architectural Structures S2018abn Lecture 20 ARCH 331

Unified Design • P n = F cr A g   F y KL E – for     F 4 . 71 F 0 . 658 F e cr y   r F   y KL E   – for 4 . 71 F 0 . 877 F cr e r F y  – where 2 E    F e 2 KL r Steel Columns & Tension 9 Architectural Structures S2018abn Lecture 20 ARCH 331

Procedure 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 P allowable = F a  A or P n = F cr A g • or find f actual = P/A 4. is P  P allowable (P a  P n /  )? or is P u   P n ? • yes: ok • no: insufficient capacity and no good Steel Columns & Tension 10 Architectural Structures S2018abn Lecture 20 ARCH 331

Procedure 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 P allowable = F a A (P n /  = F cr A g ) or P n = F cr A g • or find f actual = P/A Steel Columns & Tension 11 Architectural Structures S2018abn Lecture 20 ARCH 331

Procedure for Design (cont’d) 5. is P  P allowable (P a  P n /  )? or is P u   P n ? • yes: ok • no: pick a bigger section and go back to step 2. 6. check design efficiency P r 100  % • percentage of stress = P c • if between 90-100%: good • if < 90%: pick a smaller section and go back to step 2. Steel Columns & Tension 12 Architectural Structures S2018abn Lecture 20 ARCH 331

Column Charts, F a (pg. 461-462) Steel Columns & Tension 13 Architectural Structures S2018abn Lecture 20 ARCH 331

Column Charts,  F cr Steel Columns & Tension 14 Architectural Structures S2018abn Lecture 20 ARCH 331

Column Charts Steel Columns & Tension 15 Architectural Structures S2018abn Lecture 20 ARCH 331

Beam-Column Design • moment magnification (P-  ) C   M B M m B  u 1 m a x fa cto r ed 1   1 ( P / P ) u e1 C m – modification factor for end conditions = 0.6 – 0.4(M 1 /M 2 ) or 0.85 restrained, 1.00 unrestrained  2 EA  P e1 – Euler buckling strength   P e 1 2  - 1.00 (LRFD), 1.60(ASD) Kl r Steel Columns & Tension 16 Architectural Structures S2018abn Lecture 20 ARCH 331

Beam-Column Design • LRFD (Unified) Steel   P P 8 M M – for       r u ux ux 0 2 1 0 . : .        P P 9 M M c c n b nx b nx – for   P P M M       r u ux ux 0 . 2 : 1 . 0        P 2 P M M c c n b nx b nx P r is required, P c is capacity  c - resistance factor for compression = 0.9  b - resistance factor for bending = 0.9 Steel Columns & Tension 17 Architectural Structures S2018abn Lecture 20 ARCH 331

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 Architectural Structures S2018abn Lecture 20 ARCH 331

Rigid Frame Design (revisited) • columns in frames – ends can be “flexible” – stiffness affected by beams and column = EI/L  EI l    c G  EI – for the joint l b • l c is the column length of each column • l b is the beam length of each beam • measured center to center Steel Columns & Tension 19 Architectural Structures S2018abn Lecture 20 ARCH 331

Rigid Frame Design (revisited) • column effective length, k A B Steel Columns & Tension 20 Architectural Structures S2018abn Lecture 20 ARCH 331

Tension Members • steel members can have holes • reduced area 2 s     A A A t n g of all holes 4 g (AISC - Steel Structures of the Everyday) • increased stress Steel Columns & Tension 21 Architectural Structures S2018abn Lecture 20 ARCH 331

Effective Net Area • likely path to “rip” across • bolts divide transferred force too e  • shear lag A A U n Steel Columns & Tension 22 Architectural Structures S2018abn Lecture 20 ARCH 331

Tension Members P • limit states    P n P P  a u t n for failure    0 9 0 . P F A 1. yielding t n y g    0 . 7 5 P F A 2. rupture* t n u e A g - gross area A e - effective net area (holes 1/8” + d) F u = the tensile strength of the steel (ultimate) Steel Columns & Tension 23 Architectural Structures S2018abn Lecture 20 ARCH 331