eleven rigid frames: compression & buckling Rigid Frames 1 - 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 eleven rigid frames: compression & buckling Rigid Frames 1 Elements of Architectural Structures S2019abn http:// nisee.berkeley.edu/godden Lecture 11 ARCH 614

Rigid Frames • rigid frames have no pins • frame is all one body • joints transfer moments and shear • typically statically indeterminate • types – portal – gable Rigid Frames 2 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frames • behavior Rigid Frames 3 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frames – moments get redistributed – deflections are smaller – effective column lengths are shorter – very sensitive to settling Rigid Frames 4 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frames • resists lateral loadings • shape depends on stiffness of beams and columns • 90 ° maintained Rigid Frames 5 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frames • staggered truss – rigidity – clear stories www.arcchicago.blogspot.com Rigid Frames 6 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frames • connections – steel – concrete http:// nisee.berkeley.edu/godden Rigid Frames 7 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Braced Frames • pin connections • bracing to prevent lateral movements http:// nisee.berkeley.edu/godden Rigid Frames 8 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Braced Frames • types of bracing – knee-bracing – diagonal – X diagonal X – K or chevron – shear walls K (chevron) shear walls Rigid Frames 9 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Shear Walls • resist lateral load in plane with wall Rigid Frames 10 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Compression Members • 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 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Column Buckling • axially loaded columns • long & slender – unstable equilibrium = buckling – sudden and not good Rigid Frames 12 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Modeling • • can be modeled with a spring at mid-height • when moment from deflection exceeds the spring capacity ... “boing” • critical load P Rigid Frames 13 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Effect of Length • short & stubby • long & slender Rigid Frames 14 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Buckling Load • related to deflected shape (P  ) • shape of sine wave • Euler’s Formula • smallest I governs  2 EI  P   critical 2 L Rigid Frames 15 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Critical Stress • short columns P   actual f F critical a A • slenderness ratio = L e /r (L/d) I r  • radius of gyration = weak axis A     2 2 2 2 EA P EAr E    critical P f   critical critical 2 2 2     A A L L L     e e e     r r Rigid Frames 16 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Critical Stresses • when a column gets stubby, F y will limit the load for steel • real world has loads with eccentricity Rigid Frames 17 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Effective Length • end conditions affect shape   • effective length factor, K L e K L Rigid Frames 18 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Bracing • bracing affects shape of buckle in one direction • both should be checked! Rigid Frames 19 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Centric & Eccentric Loading • centric – allowable stress from strength or buckling • eccentric – combined stresses Rigid Frames 20 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Combined Stresses – axial + bending P Mc   f max A I   M P e – design f  cr  cr f F max F . S . Rigid Frames 21 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Stress Limit Conditions – ASD interaction formula f f f   a b a 1 . 0 F a F F a b 1 – with biaxial bending f f f f    by b a bx 1 1 . 0 F b F F F interaction diagram a bx by Rigid Frames 22 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Stress Limit Conditions – in reality, as the column flexes, the moment increases – P-  effect  f f Magnificat ion factor ( )   a b 1 . 0 F F a bx Rigid Frames 23 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frame Analysis • members see – shear – axial force – bending • V & M diagrams – plot on “outside” Rigid Frames 24 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frame Analysis – need support reactions – free body diagram each member – end reactions are equal and opposite on next member – “turn” member like beam – draw V & M Rigid Frames 25 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frame Analysis – FBD & M P • opposite end reactions at joints M+ Rigid Frames 26 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frame Design • 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 Rigid Frames 27 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Rigid Frame Design • column effective length, k A B Rigid Frames 28 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Tools – Visual Analysis (VA Edu) • in open access labs and VOAL and https://www.iesweb.com/edu/index.htm Rigid Frames 29 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Tools – Visual Analysis (VA Edu) • model view / structure tab – grid and units – define frame members • or pre-defined frames (Create) • columns “up”, beams “left - right” – select points, assign supports – select members, assign member shapes & any connection types Rigid Frames 30 Elements of Architectural Structures S2019abn Lecture 11 ARCH 614

Tools – Visual Analysis (VA Edu) • loading tab – select points, add point load – (edit load case with no self weight) • results view – status bar – results filter • member graph – choose options • report view - choose and drag options Rigid Frames 31 S2019abn Lecture 11