twenty pipe built-up steel construction: columns & tension - PowerPoint PPT Presentation

A RCHITECTURAL S TRUCTURES : Structural Steel F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • standard rolled shapes Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX D R. A NNE N ICHOLS (AISC - Steel Structures of the Everyday) (W, C, L, T) S PRING 2018 • tubing lecture twenty • pipe • built-up steel construction: columns & tension members Steel Columns & Tension 1 Architectural Structures F2009abn Lecture 20 ARCH 331 Steel Columns & Tension 2 Foundations Structures F2008abn Lecture 20 ARCH 331 Design Methods (revisited) Allowable Stress Design (ASD) • AICS 9 th ed • know  2 f 12 E – loads or lengths     critical F a 2 • select F . S . Kl 23 r – section or load – adequate for Kl • slenderness ratio strength and r no buckling – for kl/r  C c = 126.1 with F y = 36 ksi = 107.0 with F y = 50 ksi Steel Columns & Tension 4 Foundations Structures F2008abn Lecture 20 ARCH 331 Steel Columns & Tension 3 Foundations Structures F2008abn Lecture 20 ARCH 331 1

C c and Euler ’ s Formula 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 Foundations Structures F2008abn Steel Columns & Tension 6 Foundations Structures F2008abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 Unified Design Short / Intermediate P  • limit states for failure • L e /r < C c   P n    2 a Kl   F      P P r   y 0 . 90 P F A F 1 u c n   c n cr g a 2 2 C F . S .    c  KL E   4 . 71 or F 0 . 44 F 1. yielding e y – where r F     y 3 KL E Kl Kl   3 2. buckling 4 . 71 or F 0 . 44 F 5 r r    e y F . S . r F y 3 3 8 C 8 C F e – elastic buckling stress (Euler) c c Steel Columns & Tension 8 Foundations Structures Su2011abn Lecture 17 ARCH 331 Steel Columns & Tension 7 Foundations Structures F2008abn Lecture 20 ARCH 331 2

Unified Design Procedure for Analysis • P n = F cr A g 1. calculate KL/r   F y • biggest of KL/r with respect to x axes and y axis – for KL E     F F 0 . 658 F e 4 . 71 2. find F a or F cr from appropriate equation cr y   r F   y • tables are available 3. compute P allowable = F a  A or P n = F cr A g – for KL E   4 . 71 F 0 . 877 F • cr e or find f actual = P/A r F y 4. is P  P allowable (P a  P n /  )? or is P u   P n ?  2 – where E    F e • yes: ok 2 KL • no: insufficient capacity and no good r Steel Columns & Tension 9 Foundations Structures Su2011abn Steel Columns & Tension 10 Foundations Structures Su2011abn Lecture 17 ARCH 331 Lecture 17 ARCH 331 Procedure for Design (cont’d) Procedure for Design 5. is P  P allowable (P a  P n /  )? or is P u   P n ? 1.guess a size (pick a section) • yes: ok 2.calculate KL/r • no: pick a bigger section and go back to step 2. • biggest of KL/r with respect to x axes and y axis 6. check design efficiency 3.find F a or F cr from appropriate equations • or find a chart P r 100  % • percentage of stress = (P n /  = F cr A g ) 4.compute P allowable = F a A P c or P n = F cr A g • if between 90-100%: good • or find f actual = P/A • if < 90%: pick a smaller section and go back to step 2. Steel Columns & Tension 11 Foundations Structures Su2011abn Steel Columns & Tension 12 Foundations Structures Su2011abn Lecture 17 ARCH 331 Lecture 17 ARCH 331 3

Column Charts,  F cr Column Charts, F a (pg. 461-462) Steel Columns & Tension 11 Foundations Structures F2008abn Steel Columns & Tension 14 Foundations Structures S2012abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 Column Charts Beam-Column Design • moment magnification (P-  ) C   m B M B M  1   u 1 max factored 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 14 Foundations Structures Su2011abn Lecture 17 ARCH 331 Steel Columns & Tension 15 Foundations Structures Su2011abn Lecture 17 ARCH 331 4

Beam-Column Design Design Steps Knowing Loads (revisited) • LRFD (Unified) Steel 1. assume limiting stress   – for M P 8 M P   • buckling, axial stress,     uy r u ux 0 2 1 . 0 . :      combined stress P P 9 M M   c n b nx b ny c – for   2. solve for r, A or S M P M P       uy u ux r 0 . 2 : 1 . 0      3. pick trial section P 2 P  M M  c c n b nx b ny P r is required, P c is capacity 4. analyze stresses  c - resistance factor for compression = 0.9 5. section ok?  b - resistance factor for bending = 0.9 6. stop when section is ok Steel Columns & Tension 16 Foundations Structures Su2011abn Steel Columns & Tension 18 Foundations Structures F2008abn Lecture 17 ARCH 331 Lecture 20 ARCH 331 Rigid Frame Design (revisited) Rigid Frame Design (revisited) • columns in frames • column effective length, k – ends can be “ flexible ” – stiffness affected by beams A and column = EI/L  EI l    c G  EI B – 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 Foundations Structures F2008abn Steel Columns & Tension 20 Foundations Structures F2008abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 5

Tension Members Effective Net Area • steel members can • likely path to “ rip ” across have holes • bolts divide transferred force too • reduced area e  • shear lag A A U 2 s n     A A A t n g of all holes 4 g (AISC - Steel Structures of the Everyday) • increased stress Steel Columns & Tension 19 Foundations Structures F2008abn Steel Columns & Tension 20 Foundations Structures F2008abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 Tension Members P    • limit states P P P n  u t n a for failure    0 . 90 P F A 1. yielding t n y g    0 . 75 P F A 2. rupture* t n u e A g - gross area A e - effective net area (holes 3/16” + d) F u = the tensile strength of the steel (ultimate) Steel Columns & Tension 22 Foundations Structures Su2011abn Lecture 17 ARCH 331 6