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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 three equilibrium and planar trusses Equilibrium 1 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  1. 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 three equilibrium and planar trusses Equilibrium 1 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  2. Equilibrium • balanced • steady • resultant of forces on a particle is 0 X = X Equilibrium 2 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  3. Equilibrium on a Point • analytically    R F 0 x x    R F 0 y y http://www.physics.umd.edu • Newton convinces us it will stay at rest Equilibrium 3 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  4. Equilibrium on a Point • collinear force system – ex: cables   F 0  line in       R F 0 R F 0 x x y y Equilibrium 4 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  5. Equilibrium on a Point • concurrent force system – ex: cables    0 R F x x    0 R F y y Equilibrium 5 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  6. Free Body Diagram • FBD (sketch) • tool to see all forces on a body or a point including – external forces – weights – force reactions – internal forces Equilibrium 6 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  7. Free Body Diagram • determine point • FREE it from: – ground – supports & connections • draw all external forces acting ON the body – reactions (supporting forces) = m· g – applied forces – gravity Equilibrium 7 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  8. Free Body Diagram • sketch FBD with relevant geometry • resolve each force into components – known & unknown angles – name them – known & unknown forces – name them • are any forces related to other forces? • for the unknowns • write only as many equilibrium equations as needed • solve up to 2 equations Equilibrium 8 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  9. Free Body Diagram • solve equations – most times 1 unknown easily solved – plug into other equation(s) • common to have unknowns of – force magnitudes – force angles Equilibrium 9 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  10. Force Reactions • result of applying force • unknown size • connection or support type – known direction – related to motion prevented no vertical motion no translation Equilibrium 10 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  11. Friction • resistance to movement • contact surfaces determine  • proportion of normal force (  ) – opposite to slide direction – static > kinetic F  μ N Equilibrium 11 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  12. Cable Reactions • equilibrium: – more reactions (4) than equations – but, we have slope relationships – x component the same everywhere B 4 m 6 m A 2 m C 45 kN 45 kN Equilibrium 12 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  13. Cable-Stayed Structures • diagonal cables support horizontal spans • typically symmetrical • Patcenter, Rogers 1986 Equilibrium 13 Elements of Architectural Structures www.columbia.edu S2019abn Lecture 3 ARCH 614

  14. Patcenter, Rogers 1986 • column free space • roof suspended • solid steel ties • steel frame supports masts Equilibrium 14 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  15. Patcenter, Rogers 1986 • dashes – cables pulling Equilibrium 15 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  16. Truss Structures • ancient (?) wood – Romans 500 B.C. • Renaissance revival • 1800’s analysis • efficient Equilibrium 16 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  17. Truss Structures – analogous to cables and struts Equilibrium 17 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  18. Truss Structures • comprised of straight members • geometry with triangles is stable • loads applied only at pin joints http:// nisee.berkeley.edu/godden Equilibrium 18 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  19. Truss Structures • 2 force members – 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 Equilibrium 19 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  20. Truss Structures • compression and tension Equilibrium 20 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  21. Truss Structures • statically determinate • indeterminate • unstable Equilibrium 21 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  22. Trusses • common designs Equilibrium 22 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  23. Trusses • common designs Equilibrium 23 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  24. Trusses • uses – roofs & canopies – long spans – lateral bracing Equilibrium 24 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  25. Truss Connections • “pins” http:// nisee.berkeley.edu/godden Equilibrium 25 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  26. Sainsbury Center, Foster 1978 Equilibrium 26 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  27. Sainsbury Center, Foster 1978 Equilibrium 27 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  28. Truss Analysis • visualize compression and tension from deformed shape http:// nisee.berkeley.edu/godden Equilibrium 28 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  29. Truss Analysis • Method of Joints • Graphical Methods • Method of Sections • all rely on equilibrium – of bodies – internal equilibrium Equilibrium 29 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  30. Method of Joints • isolate each joint P • enforce C D F equilibrium in A E B F x and F y • can find all forces P • long • easy to mess up Equilibrium 30 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  31. Joint Cases • two bodies connected equal equal and 0 Equilibrium 31 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  32. Joint Cases • three bodies with two in line C A C B D B A C B or or even D D A 0 x x x 0 0 Equilibrium 32 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  33. Joint Cases • crossed D D P A C D B B A C B C B C A A D E E P equal Equilibrium 33 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  34. Tools – Visual Analysis (Educational) • in open access labs and VOAL and https://www.iesweb.com/edu/index.htm Equilibrium 34 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  35. Tools – Visual Analysis (Educational) • model view / structure tab – grid and units – define truss members • or pre-defined truss (Create) – select points, assign supports – select members, assign member shapes & assign releases Equilibrium 35 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

  36. Tools – Visual Analysis (Educational) • loading tab – select points, add point load – edit load case with no self weight • results view – status bar – results filter – Fx, axis force • member graph – choose options • report view - choose and drag options Equilibrium 36 Elements of Architectural Structures S2019abn Lecture 3 ARCH 614

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