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

A RCHITECTURAL S TRUCTURES : Structural Steel F ORM, B EHAVIOR, AND D ESIGN A RCH 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 UMMER 2018 • tubing lecture seventeen • pipe • built-up steel construction: columns & tension members Steel Columns & Tension 1 Architectural Structures F2009abn Lecture 17 ARCH 331 Steel Columns & Tension 2 Architectural Structures F2008abn Lecture 20 ARCH 331 Design Methods (revisited) Allowable Stress Design (ASD) • AICS 9 th ed • know  2 – loads or lengths f 12 E     critical F • select a 2 F . S . Kl 23 r – section or load – adequate for Kl • slenderness ratio strength and no buckling 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 F2008abn Steel Columns & Tension 3 Architectural Structures F2008abn Lecture 20 ARCH 331 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 Architectural Structures F2008abn Steel Columns & Tension 6 Architectural 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  F L E or   y c 4.71 2.25 1. yielding – where r F F     y e 3 F Kl Kl L E or 3   2. buckling y c 5 4.71 2.25 r r    . . F S r F F 3 y e 3 8 C 8 C F e – elastic buckling stress (Euler) c c Steel Columns & Tension 8 Architectural Structures Su2011abn Lecture 17 ARCH 331 Steel Columns & Tension 7 Architectural Structures F2008abn Lecture 20 ARCH 331 2

Unified Design Procedure for Analysis • P n = F cr A g 1. calculate KL/r   F y L E – for • biggest of KL/r with respect to x axes and y axis     F c 4.71 F 0.658 F e cr y   2. find F a or F cr from appropriate equation r F   y • tables are available L E 3. compute P allowable = F a  A or P n = F cr A g – for   c 4.71 0.877 F F cr e • r F or find f actual = P/A y  4. is P  P allowable (P a  P n /  )? or is P u   P n ? 2 – where E  F • e yes: ok 2   L   • c no: insufficient capacity and no good   r Steel Columns & Tension 9 Architectural Structures Su2011abn Steel Columns & Tension 10 Architectural Structures F2011abn Lecture 17 ARCH 331 Lecture 17 ARCH 331 Procedure for Design (cont’d) Procedure for Design 5. is P  P allowable ? 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 P • or find a chart r 100  % • percentage of stress = 4. compute P allowable = F a A (or P n /  = F cr 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 12 Architectural Structures Su2011abn Steel Columns & Tension 11 Architectural Structures F2011abn Lecture 17 ARCH 331 Lecture 17 ARCH 331 3

Column Charts,  F cr Column Charts, F a (pg. 461-462) Steel Columns & Tension 11 Architectural Structures F2008abn Steel Columns & Tension 14 Architectural Structures F2011abn Lecture 20 ARCH 331 Lecture 17 ARCH 331 Column Charts Beam-Column Design • moment magnification (P-  ) C   m M B M B 1   r 1 nt 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 L c1 – effective length in plane of bending  2 EI P e1 – Euler buckling strength  P    - 1.00 (LRFD), 1.60(ASD) e 1 2 L c 1 Steel Columns & Tension 14 Architectural Structures Su2011abn Steel Columns & Tension 15 Architectural Structures Su2011abn Lecture 17 ARCH 331 Lecture 17 ARCH 331 4

Beam-Column Design Design Steps Knowing Loads (revisited) • LRFD (Unified) Steel 1. assume limiting stress   – for M P P 8 M • buckling, axial stress,      ry  r r rx 0.2: 1.0   combined stress P P 9 M M   c c cx cy 2. solve for r, A or S – for   M P P M      ry  r r rx 0.2: 1.0 3. pick trial section   P 2 P M M   c c cx cy 4. analyze stresses P r is required, P c is capacity 5. section ok? M rx is required, M cx is capacity 6. stop when section is ok M ry is required, M cy is capacity Steel Columns & Tension 16 Architectural Structures Su2011abn Steel Columns & Tension 18 Architectural 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 Architectural Structures F2008abn Steel Columns & Tension 20 Architectural Structures F2008abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 5

Effective Net Area Tension Members • likely path to “rip” across • steel members can have holes • bolts divide transferred force too e  • reduced area • shear lag A A U s n     A A A t n g of all holes 4 g (AISC - Steel Structures of the Everyday) • increased stress Steel Columns & Tension 20 Architectural Structures F2008abn Steel Columns & Tension 19 Architectural Structures F2008abn Lecture 20 ARCH 331 Lecture 20 ARCH 331 Tension Members P    • limit states P P P n  a u t n 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 1/8” + d) F u = the tensile strength of the steel (ultimate) Steel Columns & Tension 22 Architectural Structures Su2011abn Lecture 17 ARCH 331 6