eighteen steel construction: column design Cor-Ten Steel Sculpture - PowerPoint PPT Presentation

E LEMENTS OF A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN ARCH 614 D R. A NNE N ICHOLS S PRING 2019 lecture eighteen steel construction: column design Cor-Ten Steel Sculpture By Richard Serra Museum of Modern Art Fort Worth, TX (AISC - Steel Structures of the Everyday) Steel Columns 1 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Structural Steel • standard rolled shapes (W, C, L, T) • tubing • pipe • built-up Steel Columns 2 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Design Methods (revisited) • know – loads or lengths • select – section or load – adequate for strength and no buckling Steel Columns 3 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Allowable Stress Design (ASD) • AICS 9 th ed  2 f 12 E     critical F a 2 F . S . Kl 23 r Kl • slenderness ratio r – for kl/r  C c = 126.1 with F y = 36 ksi = 107.0 with F y = 50 ksi Steel Columns 4 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

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 5 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

C c and Euler’s Formula Steel Columns 6 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Short / Intermediate   • L e /r < C c   2 Kl F   r   y F 1   a 2 2 C F . S .    c  – where     3 Kl Kl 3 5 r r    F . S . 3 3 8 C 8 C c c Steel Columns 7 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Unified Design P  • limit states for failure P n  a      P P 0 . 90 P F A u c n c n cr g KL E   1. yielding 4 71 0 44 . or F . 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 8 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Unified Design • P n = F cr A g   F y – for KL E     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 9 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Procedure for Analysis 1. calculate KL/r • biggest of KL/r with respect to x axes and y axis (see Note) from appropriate equation 2. find F cr • tables are available Note: text uses F c and old  = 0.85 3. compute P n = F cr A g 4. is P a  P n /  ? or is P u   P n ? • yes: ok • no: insufficient capacity and no good Steel Columns 10 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

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 (see Note) from appropriate 3. find F a or F cr equations Note: text uses F c • or find a chart and old  = 0.85 4. compute P n = F cr A g Steel Columns 11 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Procedure for Design (cont’d) 5. is 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 12 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Column Charts,  F cr Steel Columns 13 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Column Charts Steel Columns 14 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Beam-Column Design • moment magnification (P-  ) C   M B M m B  u 1 max factored 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 1 e 2 Kl  - 1.00 (LRFD), 1.60(ASD) r Steel Columns 15 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

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   P P M M – for       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  c – resistance factor for bending = 0.9 Steel Columns 16 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

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 17 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

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 18 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614

Rigid Frame Design (revisited) • column effective length, k A B Steel Columns 19 Elements of Architectural Structures S2019abn Lecture 18 ARCH 614