ten
play

ten moments and shear typically statically indeterminate types - PowerPoint PPT Presentation

A RCHITECTURAL S TRUCTURES : Rigid Frames F ORM, B EHAVIOR, AND D ESIGN ARCH 331 rigid frames have no D R. A NNE N ICHOLS pins S UMMER 2018 frame is all one body lecture joints transfer ten moments and shear typically


  1. A RCHITECTURAL S TRUCTURES : Rigid Frames F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • rigid frames have no D R. A NNE N ICHOLS pins S UMMER 2018 • frame is all one body lecture • joints transfer ten moments and shear • typically statically indeterminate • types rigid frames: – portal compression & buckling – gable Rigid Frames 1 Architectural Structures F2009abn Rigid Frames 2 Foundations Structures F2008abn http:// nisee.berkeley.edu/godden Lecture 10 ARCH 331 Lecture 12 ARCH 331 Rigid Frames Rigid Frames • behavior – moments get redistributed – deflections are smaller – effective column lengths are shorter – very sensitive to settling Rigid Frames 3 Foundations Structures F2008abn Rigid Frames 4 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 1

  2. Moment Redistribution Rigid Frames • continuous slabs & beams with uniform • resists lateral loadings loading • shape depends on – joints similar to fixed ends, but can rotate stiffness of beams • change in moment to center = 2 wL and columns – M max for simply supported beam 8 • 90° maintained Rigid Frames 5 Foundations Structures F2008abn Rigid Frames 6 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Rigid Frames Rigid Frames • staggered truss • connections – rigidity – steel – clear stories – concrete http:// nisee.berkeley.edu/godden www.arcchicago.blogspot.com Rigid Frames 7 Foundations Structures F2008abn Rigid Frames 8 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 2

  3. Braced Frames Braced Frames • pin connections • types of bracing • bracing to prevent lateral movements – knee-bracing – diagonal – X diagonal X – K or chevron – shear walls K (chevron) shear walls http:// nisee.berkeley.edu/godden Rigid Frames 9 Foundations Structures F2008abn Rigid Frames 10 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Shear Walls Compression Members • resist lateral load in plane with wall • designed for strength & stresses • designed for serviceability & deflection • need to design for stability – ability to support a specified load without sudden or unacceptable deformations Rigid Frames 11 Foundations Structures F2008abn Rigid Frames 12 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 3

  4. Column Buckling Modeling • axially loaded columns • • can be modeled with a spring at mid-height • when moment • long & slender from deflection – unstable equilibrium = exceeds the buckling – sudden and not good spring capacity ... “ boing ” • critical load P Rigid Frames 13 Foundations Structures F2008abn Rigid Frames 14 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Effect of Length Buckling Load • related to deflected shape (P  ) • long & slender • short & stubby • shape of sine wave • Euler ’ s Formula • smallest I governs  2 EI  P   critical 2 L Rigid Frames 15 Foundations Structures F2008abn Rigid Frames 16 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 4

  5. Critical Stress Critical Stresses • short columns • when a column gets stubby, F y will limit the P load   actual f F critical a • real world has loads A with eccentricity • slenderness ratio = L e /r (L/d) • C c for steel and I allowable stress r  • radius of gyration = weak axis A 2  2     E 2 L 2 2 2 EA P EAr E   C    e critical P f   r c F critical critical 2 2 2     A A L L L y     e e e     r r Rigid Frames 17 Foundations Structures F2008abn Rigid Frames 18 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Effective Length Bracing • end conditions affect shape • bracing affects shape of buckle in one direction • effective length factor, K   L e K L • both should be checked! Rigid Frames 19 Foundations Structures F2008abn Rigid Frames 20 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 5

  6. Centric & Eccentric Loading Combined Stresses • centric – axial + bending – allowable stress from strength or buckling P Mc   f • eccentric max A I   – combined stresses M P e – design f  cr  cr f F max F S . . Rigid Frames 21 Foundations Structures F2008abn Rigid Frames 22 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Stress Limit Conditions Stress Limit Conditions – ASD interaction formula – in reality, as the column flexes, the moment increases f f f   a a b 1 . 0 F a F F – P-  effect a b 1 – with biaxial bending  f f ( Magnificat ion factor ) f f f   f a b    1 . 0 by b a bx 1 1 . 0 F F F b F F F a bx a bx by interaction diagram Rigid Frames 23 Foundations Structures F2008abn Rigid Frames 24 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 6

  7. Rigid Frame Analysis Rigid Frame Analysis • members see – need support reactions – free body diagram each member – shear – end reactions are equal and opposite on – axial force next member – bending – “ turn ” member • V & M diagrams like beam – plot on “ outside ” – draw V & M Rigid Frames 25 Foundations Structures F2008abn Rigid Frames 26 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Rigid Frame Analysis Rigid Frame Design – FBD & M • loads and combinations P • opposite end – usually uniformly distributed gravity loads reactions at joints – worst case for largest moments... – wind direction can increase moments M+ Rigid Frames 27 Foundations Structures F2008abn Rigid Frames 28 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 7

  8. Rigid Frame Design Rigid Frame Design • frames & floors • floors – plates & slabs – rigid frame can have slab floors or slab – one-way behavior with connecting beams • side ratio > 1.5 • other • “ strip ” beam – two-way behavior – slabs or plates • more complex on columns Rigid Frames 29 Foundations Structures F2008abn Rigid Frames 30 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Rigid Frame Design Rigid Frame Design • 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 Rigid Frames 31 Foundations Structures F2008abn Rigid Frames 32 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 8

  9. Tools – Multiframe Tools – Multiframe • in OAL and VOAL • frame window – define frame members • or pre-defined frame – select points, assign supports – select members, assign section – load window – select point or member, add point or distributed loads Rigid Frames 34 Foundations Structures F2008abn Rigid Frames 33 Foundations Structures F2008abn Lecture 12 ARCH 331 Lecture 12 ARCH 331 Tools – Multiframe • to run analysis choose – Analyze menu • Linear • plot – choose options • results – choose options Rigid Frames 35 Foundations Structures F2008abn Lecture 12 ARCH 331 9

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend