three Equilibrium 1 and planar trusses ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture ARCH 614
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1 ELEMENTS OF ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SPRING 2015 lecture three equilibrium and planar trusses Equilibrium 1
2 Equilibrium balanced steady resultant of forces on a particle is 0 X X = Equilibrium 2
3 Equilibrium on a Point analytically R = F x x = 0 R = F y y = 0 Newton convinces us it will stay at rest Equilibrium 3
4 Equilibrium on a Point collinear force system ex: cables F in line = 0 = x R F = 0 R F = 0 y x = y Equilibrium 4
5 Equilibrium on a Point concurrent force system ex: cables R = F x x = 0 = R F y y = 0 Equilibrium 5
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
7 Free Body Diagram determine point FREE it from: ground supports & connections draw all external forces acting ON the body reactions (supporting forces) applied forces gravity = m g Equilibrium 7
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
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
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
11 Friction resistance to movement contact surfaces determine µ proportion of normal force ( ) opposite to slide direction static > kinetic F = µ N Equilibrium 11
12 Cable Reactions equilibrium: more reactions (4) than equations but, we have slope relationships x component the same everywhere A 4 m 6 m B 2 m C 45 kn 45 kn Equilibrium 12
13 Cable-Stayed Structures diagonal cables support horizontal spans typically symmetrical Patcenter, Rogers 1986 Equilibrium 13
14 Patcenter, Rogers 1986 column free space roof suspended solid steel ties steel frame supports masts Equilibrium 14
15 Patcenter, Rogers 1986 dashes cables pulling Equilibrium 15
16 Truss Structures ancient (?) wood Romans 500 B.C. Renaissance revival 1800 s analysis efficient Equilibrium 16
17 Truss Structures analogous to cables and struts Equilibrium 17
18 Truss Structures comprised of straight members geometry with triangles is stable loads applied only at pin joints Equilibrium 18 nisee.berkeley.edu/godden
19 Truss Structures 2 force members forces in line, equal and opposite compression tension 3 members connected by 3 joints 2 more members need 1 more joint b = 2n 3 Equilibrium 19
20 Truss Structures compression and tension Equilibrium 20
21 Truss Structures statically determinate indeterminate unstable Equilibrium 21
22 Trusses common designs Equilibrium 22
23 Trusses common designs Equilibrium 23
24 Trusses uses roofs & canopies long spans lateral bracing Equilibrium 24
25 Truss Connections pins nisee.berkeley.edu/godden Equilibrium 25
26 Sainsbury Center, Foster 1978 Equilibrium 26
27 Sainsbury Center, Foster 1978 Equilibrium 27
28 Truss Analysis visualize compression and tension from deformed shape nisee.berkeley.edu/godden Equilibrium 28
29 Truss Analysis Method of Joints Graphical Methods Method of Sections all rely on equilibrium of bodies internal equilibrium Equilibrium 29
30 Method of Joints isolate each joint P enforce equilibrium in A F E C D B F x and F y can find all forces P long easy to mess up Equilibrium 30
31 Joint Cases two bodies connected A B C or A B C equal equal and 0 Equilibrium 31
32 Joint Cases three bodies with two in line C B A D or A B C D or even A D B C x 0 x 0 0 x Equilibrium 32
33 Joint Cases crossed A B D P C A D B P C A D B E C A D B E C equal Equilibrium 33
34 Tools Multiframe in computer lab Equilibrium 34
35 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 Equilibrium 35
36 Tools Multiframe to run analysis choose Analyze menu plot Linear choose options results choose options Equilibrium 36
three Point Equilibrium 1 and planar trusses ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
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