three equilibrium and planar trusses Equilibrium Equilibrium on a Point Equilibrium on a Point balanced steady resultant of forces on a particle is 0

Transcription

1 ELEMENTS OF RHITETURL STRUTURES: FORM, EHVIOR, N ESIGN R. NNE NIHOLS SPRING 2014 lecture three Equilibrium balanced steady resultant of forces on a particle is 0 X equilibrium and planar trusses X = Equilibrium 1 S2009abn Equilibrium 2 S2006abn 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 Equilibrium 6 Equilibrium 7 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 Equilibrium 8 Equilibrium 10 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 Equilibrium 11 Equilibrium 12 2

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 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 S2006abn Equilibrium 19 Friction resistance to movement contact surfaces determine proportion of normal force ( ) opposite to slide direction static > kinetic able Reactions equilibrium: more reactions (4) than equations but, we have slope relationships X component the same everywhere 4 m 6 m F μ N 2 m 45 kn 45 kn Equilibrium 11 S2009abn Equilibrium 28 3

4 able-stayed Structures diagonal cables support horizontal spans typically symmetrical Patcenter, Rogers 1986 Patcenter, Rogers 1986 column free space roof suspended solid steel ties steel frame supports masts Equilibrium 35 Equilibrium 36 Patcenter, Rogers 1986 dashes cables pulling Truss Structures ancient (?) wood Romans Renaissance revival 1800 s analysis efficient Equilibrium 37 Trusses Intro10 4

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

6 Truss Structures statically determinate indeterminate unstable Trusses common designs Trusses Intro15 Trusses Intro16 Trusses common designs Trusses uses roofs & canopies long spans lateral bracing Trusses Intro17 Trusses Intro18 6

7 Truss onnections pins Sainsbury enter, Foster nisee.berkeley.edu/godden Trusses Intro19 Trusses Intro20 Sainsbury enter, Foster 1978 Truss nalysis visualize compression and tension from deformed shape nisee.berkeley.edu/godden Trusses Intro21 Trusses Intro 22 Lecture 6 7

8 Truss nalysis Method of Joints Method of Joints Graphical Methods Method of Sections all rely on equilibrium isolate each joint enforce equilibrium in F x and F y can find all forces F E P P of bodies internal equilibrium long easy to mess up Trusses Intro22 Trusses Intro23 Joint ases two bodies connected Joint ases three bodies with two in line or or even equal equal and 0 x 0 x 0 0 x Trusses Intro 25 Lecture 6 Trusses Intro 26 Lecture 6 8

9 Joint ases crossed Tools Multiframe in computer lab P P E E equal Trusses Intro 27 Lecture 6 Equilibrium 33 S2008abn Tools Multiframe Tools Multiframe frame window to run analysis choose define truss members nalysis menu or pre-defined truss select points, assign supports select members, assign section & assign pin ends load window Linear plot choose options results choose options Equilibrium 34 select points, add point load S2008abn Equilibrium 35 S2008abn 9