APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS ARCH 631 DR. ANNE NICHOLS SPRING 2018 lecture five trusses

& columns www.nyc-architecture.com

Columns & Trusses 1 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Calibrated Peer Review / Turnitin

Cables & Arches 2 Applied Architectural Structures S2018abn Lecture 6 ARCH 631 Trusses • ancient (?) wood • 1800’s analysis • efficient • long spans

Columns & Trusses 3 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Trusses • comprised of straight members • geometry with triangles is stable • loads applied only at joints

http://nisee.berkeley.edu/godden

Columns & Trusses 4 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Trusses • 2 force members – compression – tension

• 3 members connected by 3 joints

• 2 more members need 1 more joint b  2 n  3 ( n  2 j  3)

Columns & Trusses 5 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Analysis • visualize compression and tension from deformed shape

http://nisee.berkeley.edu/godden Columns & Trusses 6 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Analysis • Method of Joints –  F  0 • Method of Sections –  F  0

–  M  0 http:// nisee.berkeley.edu/godden • Graphical Methods • all rely on equilibrium – of bodies – internal equilibrium

Columns & Trusses 7 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Connections • “pins” – can’t resist rotation

http:// nisee.berkeley.edu/godden

Columns & Trusses 8 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Trusses http:// nisee.berkeley.edu/godden • require lateral bracing • consider buckling • indeterminate trusses – extra members – solvable with statics • cables can’t hold compression – displacement methods • elastic elongation – too few members, unstable

Columns & Trusses 9 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Space Trusses • pyramid • tetrahedron

http:// nisee.berkeley.edu/godden

Columns & Trusses 10 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Space Trusses • connections • supports

Columns & Trusses 11 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Crystal Cathedral, Johnson 1980

http:// nisee.berkeley.edu/godden Columns & Trusses 12 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Expo 70 Festival Plaza

• Tange & Kamiya 1970

Columns & Trusses 13 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Jacob K. Javits Convention Center • I.M. Pei 1980

Columns & Trusses 14 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Jacob K. Javits Convention Center

Columns & Trusses 15 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Louvre Museum Addition, Pei 1989

Columns & Trusses 16 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Louvre Museum Addition, Pei 1989

Columns & Trusses 17 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Design • variables – spans – depths – length of members – spacing – transverse beam spacing – pattern – materials; size & strength efficiency

Columns & Trusses 18 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Trusses • common designs

Columns & Trusses 19 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Trusses • common designs

Columns & Trusses 20 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Configurations • external factors – roof form – openings • basic forms – symmetrical loading – maximum bending – cables in tension only

Columns & Trusses 21 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Configurations • parallel chords – verticals common – longer members in tension – often cross members - indeterminate • funicular shapes – efficient – similar sized forces – some zero force

Columns & Trusses 22 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Truss Configurations • special shapes – Vierendeel – “frame” • depth – depends on loads, span http:// nisee.berkeley.edu/godden – rules of thumb, charts • structurally – tension members can have holes! – compression members can buckle – 3D trusses stable

Columns & Trusses 23 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Tools – Multiframe • in classrooms and open access labs

Columns & Trusses 24 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Tools – Multiframe • frame window – define truss members • or pre-defined truss – select points, assign supports – select members, assign section & assign pin ends • load window – select points, add point load

Columns & Trusses 25 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Tools – Multiframe • to run analysis choose – Analyze menu • Linear • plot – choose options • results – choose options

Columns & Trusses 26 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns • compression members • column behavior is length dependent – short: crush – long: buckle (sudden) in slender direction – end restraints • bearing walls – continuous in one direction – can resist lateral forces

Columns & Trusses 27 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns • column buckling crushing

Columns & Trusses 28 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns • stability – stable equilibrium

• P < Pcr

– neutral equilibrium

• P = Pcr

– unstable equilibrium

• P > Pcr

Columns & Trusses 29 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Buckling Load • related to deflected shape (P) • shape of sine wave • Euler’s Formula • I minimum  2 EI P  min critical L2

• stiffness related to E, I, & L

Columns & Trusses 30 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Critical Stress • short columns P f  actual  F critical A a

• slenderness ratio = Le/r (L/d) I • radius of gyration = r  A weak axis 2 2 2 2 Pcritical  EAr  E  EA fcritical   2  2 Pcritical  2 A AL e   L   L   e   e   r   r  Columns & Trusses 31 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Critical Stresses

• when a column gets stubby, Fy will limit the load • real world has loads with eccentricity • buckling for steel

when Fe < 0.44Fy KL E  4.71 r Fy

Columns & Trusses 32 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns • end conditions affect shape • effective length factor, k

Columns & Trusses 33 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Bracing • bracing affects shape of buckle in one direction • both directions should be checked!

Columns & Trusses 34 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns and Walls • bearing & shear

Columns & Trusses 35 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Columns • typical cross sections

Columns & Trusses 36 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Centric & Eccentric Loading • centric – allowable stress from strength or buckling • eccentric – combined stresses

Columns & Trusses 37 Applied Architectural Structures S2018abn Lecture 5 ARCH 631 Combined Stresses – axial + bending P Mc f   max A I M  P  e – design f f  F  cr max cr F .S.

Columns & Trusses 38 Foundations Structures S2018abn Lecture 5 ARCH 331 Column Materials • wood • steel – W sections can buckle about both axes • concrete & masonry – compression Trans primarily in concrete – reinforcement for bending

Columns & Trusses 39 Applied Architectural Structures S2018abn Lecture 5 ARCH 631