three point equilibrium and planar trusses Equilibrium Equilibrium on a Point Equilibrium on a Point

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1 RHITETURL STRUTURES: FORM, EHVIOR, N ESIGN R. NNE NIHOLS SUMMER 2014 lecture three Equilibrium balanced steady resultant of forces on a particle is 0 X point equilibrium and planar trusses nisee.berkeley.edu/godden X = Point Equilibrium 1 rchitectural Structures F2009abn Point Equilibrium 15 Equilibrium on a Point analytically R x Fx R y Fy Equilibrium on a Point collinear force system ex: cables F in line Newton convinces us it will stay at rest Rx Fx R y Fy Point Equilibrium 16 Point Equilibrium 17 1

2 Equilibrium on a Point concurrent force system ex: cables R x Fx R y Fy Free ody iagram F (sketch) tool to see all forces on a body or a point including external forces weights force reactions internal forces Point Equilibrium 18 Point Equilibrium 19 Free ody iagram determine point FREE it from: ground supports & connections draw all external forces acting ON the body reactions (supporting forces) applied forces gravity = m g Free ody iagram sketch F 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 Point Equilibrium 20 Point Equilibrium 21 2

Free ody iagram solve equations most times 1 unknown easily solved plug into

Equilibrium 33 analogous to cables and struts comprised of straight members

3 Free ody iagram solve equations most times 1 unknown easily solved plug into other equation(s) common to have unknowns of force magnitudes force angles ancient (?) wood Romans Renaissance revival 1800 s analysis efficient Point Equilibrium 22 Point Equilibrium 33 analogous to cables and struts comprised of straight members geometry with triangles is stable loads applied only at pin joints Point Equilibrium 34 Point Equilibrium 12 nisee.berkeley.edu/godden F2009abn 3

4 2 force members forces in line, equal and opposite compression tension compression and tension 3 members connected by 3 joints 2 more members need 1 more joint b 2n 3 Point Equilibrium 36 Point Equilibrium 37 statically determinate indeterminate unstable Trusses common designs Point Equilibrium 38 Point Equilibrium 39 4

41 Truss onnections pins Sainsbury enter, Foster 1978 http://

5 Trusses common designs Trusses uses roofs & canopies long spans lateral bracing Point Equilibrium 40 Point Equilibrium 41 Truss onnections pins Sainsbury enter, Foster nisee.berkeley.edu/godden Point Equilibrium 42 Point Equilibrium 43 5

Sainsbury enter, Foster 1978 Truss nalysis visualize

Truss nalysis Method of Joints Method of Joints isolate

rely on equilibrium enforce equilibrium in F x and F y

6 Sainsbury enter, Foster 1978 Truss nalysis visualize compression and tension from deformed shape nisee.berkeley.edu/godden Point Equilibrium 44 Point Equilibrium 45 Truss nalysis Method of Joints Method of Joints isolate each joint P Graphical Methods Method of Sections all rely on equilibrium enforce equilibrium in F x and F y can find all forces F E P of bodies internal equilibrium long easy to mess up Point Equilibrium 46 Point Equilibrium 47 6

Joint ases two bodies connected Joint ases

ases crossed Tools Multiframe in computer

7 Joint ases two bodies connected Joint ases three bodies with two in line or or or even equal equal and 0 x 0 x 0 0 x Point Equilibrium 48 Point Equilibrium 49 Joint ases crossed Tools Multiframe in computer lab P P E E equal Point Equilibrium 50 Point Equilibrium 51 7

8 Tools Multiframe Tools Multiframe frame window to run analysis choose define truss members nalyze menu or pre-defined truss select points, assign supports Linear plot select members, assign section & assign pin ends load window select points, add point load choose options results choose options Point Equilibrium 52 Point Equilibrium 53 8

three Point Equilibrium 1 and planar trusses ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture

three Point Equilibrium 1 and planar trusses ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture three point equilibrium http:// nisee.berkeley.edu/godden and planar trusses Point Equilibrium 1 Equilibrium balanced