A RCHITECTURAL S TRUCTURES : Equilibrium F ORM, B EHAVIOR, AND D ESIGN ARCH 331 • balanced D R. A NNE N ICHOLS • steady S PRING 2019 • resultant of forces on a particle is 0 lecture four X http:// nisee.berkeley.edu/godden point equilibrium = and planar trusses X Point Equilibrium 1 Architectural Structures F2009abn Lecture 4 ARCH 331 Point Equilibrium 15 Foundations Structures F2008abn Lecture 4 ARCH 331 Equilibrium on a Point Equilibrium on a Point • analytically • collinear force system – ex: cables R F 0 x x F 0 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 Point Equilibrium 17 Foundations Structures F2008abn Point Equilibrium 16 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 1
Equilibrium on a Point Free Body Diagram • concurrent force system • FBD (sketch) – ex: cables • tool to see all forces on a body or a point including R F 0 x x – external forces – weights R F 0 y y – force reactions – internal forces Point Equilibrium 18 Foundations Structures F2008abn Point Equilibrium 19 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 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 • solve up to 2 equations – gravity Point Equilibrium 20 Foundations Structures F2008abn Point Equilibrium 21 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 2
Free Body Diagram Truss Structures • solve equations • ancient (?) wood – most times 1 unknown easily solved – Romans 500 B.C. – plug into other equation(s) • Renaissance revival • 1800 ’ s analysis • common to have unknowns of • efficient – force magnitudes – force angles Point Equilibrium 22 Foundations Structures F2008abn Point Equilibrium 33 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 Truss Structures Truss Structures – analogous to cables and struts • comprised of straight members • geometry with triangles is stable • loads applied only at pin joints http:// nisee.berkeley.edu/godden Point Equilibrium 12 Foundations Structures F2009abn Point Equilibrium 34 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 3
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 Point Equilibrium 36 Foundations Structures F2008abn Point Equilibrium 37 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 Truss Structures Trusses • statically determinate • common designs • indeterminate • unstable Point Equilibrium 38 Foundations Structures F2008abn Point Equilibrium 39 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 4
Trusses Trusses • common designs • uses – roofs & canopies – long spans – lateral bracing Point Equilibrium 40 Foundations Structures F2008abn Point Equilibrium 41 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 Truss Connections Sainsbury Center, Foster 1978 • “pins” http:// nisee.berkeley.edu/godden Point Equilibrium 42 Foundations Structures F2008abn Point Equilibrium 43 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 5
Sainsbury Center, Foster 1978 Truss Analysis • visualize compression and tension from deformed shape http:// nisee.berkeley.edu/godden Point Equilibrium 45 Foundations Structures F2008abn Point Equilibrium 44 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 Truss Analysis Method of Joints • Method of Joints • isolate each joint P • Graphical Methods • enforce C F D equilibrium in • Method of Sections A E B F x and F y • can find all forces P • all rely on equilibrium – of bodies • long – internal equilibrium • easy to mess up Point Equilibrium 46 Foundations Structures F2008abn Point Equilibrium 47 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 6
Joint Cases Joint Cases • two bodies connected • three bodies with two in line C C A D B B A C C A C B B B or or or even A D D A 0 x equal equal and 0 x x 0 0 Point Equilibrium 49 Foundations Structures F2008abn Point Equilibrium 48 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 Tools – Visual Analysis (VA Edu) Joint Cases • in open access labs and VOAL and • crossed https://www.iesweb.com/edu/index.htm D D P A C D B B A C C B B A C A D E E P equal Point Equilibrium 28 Architectural Structures F2018abn Point Equilibrium 50 Foundations Structures F2008abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 7
Tools – Visual Analysis (VA Edu) Tools – Visual Analysis (VA Edu) • 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 Point Equilibrium 30 Architectural Structures F2018abn Point Equilibrium 29 Architectural Structures F2018abn Lecture 4 ARCH 331 Lecture 4 ARCH 331 8
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