line in R F 0 y y http://www.physics.umd.edu R - PowerPoint PPT Presentation

E LEMENTS OF A RCHITECTURAL S TRUCTURES : Equilibrium F ORM, B EHAVIOR, AND D ESIGN ARCH 614 • balanced D R. A NNE N ICHOLS • steady S PRING 2019 • resultant of forces on a particle is 0 lecture three X equilibrium = and planar trusses X Equilibrium 1 Elements of Architectural Structures S2009abn Equilibrium 2 Elements of Architectural Structures S2006abn Lecture 3 ARCH 614 Lecture 5 ARCH 614 Equilibrium on a Point Equilibrium on a Point • analytically • collinear force system   – ex: cables  R F 0  x x  0 F    line in  R F 0 y y http://www.physics.umd.edu       R F 0 R F 0 • Newton convinces us it will stay at rest x x y y Equilibrium 6 Elements of Architectural Structures S2004abn ARCH 614 Equilibrium 7 Elements of Architectural Structures S2004abn ARCH 614 1

Free Body Diagram Equilibrium on a Point • FBD (sketch) • concurrent force system • tool to see all forces on a body or a – ex: cables    point including R F 0 x x – external forces    – weights R F 0 y y – force reactions – internal forces Equilibrium 10 Elements of Architectural Structures S2004abn Equilibrium 8 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 Free Body Diagram Free Body Diagram • determine point • sketch FBD with relevant geometry • FREE it from: • resolve each force into components – ground – known & unknown angles – name them – supports & connections – known & unknown forces – name them • draw all external forces • are any forces related to other forces? acting ON the body • for the unknowns – reactions • write only as many equilibrium – (supporting forces) = m· g equations as needed – applied forces – gravity • solve up to 2 equations Equilibrium 11 Elements of Architectural Structures S2004abn Equilibrium 12 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 2

Force Reactions Free Body Diagram • result of applying force • solve equations • unknown size – most times 1 unknown easily solved – plug into other equation(s) • connection or support type – known direction • common to have unknowns of – related to motion prevented – force magnitudes – force angles no vertical motion no translation Equilibrium 19 Elements of Architectural Structures S2004abn Equilibrium 10 Elements of Architectural Structures S2006abn ARCH 614 Lecture 5 ARCH 614 Friction Cable Reactions • equilibrium: • resistance to movement • contact surfaces determine  – more reactions (4) than equations – but, we have slope relationships • proportion of normal force (  ) – X component the same everywhere – opposite to slide direction – static > kinetic B A 4 m 6 m 2 m F  μ N C 45 kN 45 kN Equilibrium 28 Elements of Architectural Structures S2004abn Equilibrium 11 Elements of Architectural Structures S2009abn ARCH 614 Lecture 3 ARCH 614 3

Cable-Stayed Structures Patcenter, Rogers 1986 • diagonal cables support horizontal • column free space spans • roof suspended • typically symmetrical • solid steel ties • Patcenter, • steel frame supports masts Rogers 1986 Equilibrium 35 Elements of Architectural Structures www.columbia.edu S2005abn Equilibrium 36 Elements of Architectural Structures S2005abn Lecture 5 ARCH 614 Lecture 5 ARCH 614 Patcenter, Rogers 1986 Truss Structures • dashes – cables pulling • ancient (?) wood – Romans 500 B.C. • Renaissance revival • 1800’s analysis • efficient Trusses Intro10 Elements of Architectural Structures S2004abn Equilibrium 37 Elements of Architectural Structures S2005abn ARCH 614 Lecture 5 ARCH 614 4

Truss Structures Truss Structures • comprised of straight members – analogous to cables and struts • geometry with triangles is stable • loads applied only at pin joints http:// nisee.berkeley.edu/godden Trusses Intro12 Elements of Architectural Structures S2004abn Trusses Intro11 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 Truss Structures Truss Structures • 2 force members • compression and tension – forces in line, equal and opposite – compression – tension • 3 members connected by 3 joints • 2 more members need  n 2  1 more joint b 3 Trusses Intro13 Elements of Architectural Structures S2004abn Trusses Intro14 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 5

Truss Structures Trusses • statically determinate • common designs • indeterminate • unstable Trusses Intro15 Elements of Architectural Structures S2004abn Trusses Intro16 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 Trusses Trusses • common designs • uses – roofs & canopies – long spans – lateral bracing Trusses Intro17 Elements of Architectural Structures S2004abn Trusses Intro18 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 6

Truss Connections Sainsbury Center, Foster 1978 • “pins” http:// nisee.berkeley.edu/godden Trusses Intro19 Elements of Architectural Structures S2004abn Trusses Intro20 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 Sainsbury Center, Foster 1978 Truss Analysis • visualize compression and tension from deformed shape http:// nisee.berkeley.edu/godden Trusses Intro 22 Elements of Architectural Structures S2005abn Trusses Intro21 Elements of Architectural Structures S2004abn Lecture 6 ARCH 614 ARCH 614 7

Truss Analysis Method of Joints • Method of Joints • isolate each joint P • Graphical Methods • enforce C D F • Method of Sections equilibrium in A E B F x and F y • can find all forces • all rely on equilibrium P – of bodies • long – internal equilibrium • easy to mess up Trusses Intro22 Elements of Architectural Structures S2004abn Trusses Intro23 Elements of Architectural Structures S2004abn ARCH 614 ARCH 614 Joint Cases Joint Cases • two bodies connected • three bodies with two in line C A C D B B A C B or or even D D A 0 x equal equal and 0 x x 0 0 Trusses Intro 25 Elements of Architectural Structures S2005abn Trusses Intro 26 Elements of Architectural Structures S2005abn Lecture 6 ARCH 614 Lecture 6 ARCH 614 8

Tools – Visual Analysis (Educational) Joint Cases • crossed • in open access labs and VOAL and https://www.iesweb.com/edu/index.htm D P D A C D B B A C C B B A C A D E E P equal Trusses Intro 27 Elements of Architectural Structures S2005abn Equilibrium 34 Elements of Architectural Structures F2018abn Lecture 6 ARCH 614 Lecture 3 ARCH 614 Tools – Visual Analysis (Educational) Tools – Visual Analysis (Educational) • loading tab • model view / structure tab – select points, add point load – grid and units – edit load case with no self weight – define truss members • results view • or pre-defined truss (Create) – select points, assign supports – status bar – select members, – results filter – Fx, axis force assign member shapes & • member graph assign releases – choose options • report view - choose and drag options Equilibrium 6 Elements of Architectural Structures F2018abn Equilibrium 35 Elements of Architectural Structures F2018abn Lecture 3 ARCH 614 Lecture 3 ARCH 614 9