University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l What is a truss a truss is an assembly of linear members connected together to form a triangle or triangles that convert all external forces into axial compression or tension in its members l Single or number of triangles a triangle is the simplest stable shape l Joints assumed frictionless hinges 1/27 loads placed at joints

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Primitive dwelling heavy timber trusses Rafter pair - Joist simple roof construction loading along rafters - bending Simple Truss 2/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Depth or Rise Panel Span l l Flat Truss or Parallel Chord Truss VerticalDiagonal Web Members (verticals & diagonals) Top Chord Bottom Chord Joint, Panel point or Node 3/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 BowstringFlat PrattTriangular Howe Flat HoweInverted BowstringSimple Fink WarrenFink CamelbackTriangular PrattCambered Fink ScissorsShed Lenticular 4/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l A truss provides depth with less material than a beam l It can use small pieces l Light open appearance (if seen) l Many shapes possible 5/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Multipanel Trusses Sainsbury Centre Norwich, England Foster & Partners Anthony Hunt Associates Warren Trusses Centre Georges Pompidou Paris Piano & Rogers Ove Arup & Partners Shaping Structures: Statics, W. Zalewski and E. Allen (1998) 6/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Shaping Structures: Statics, W. Zalewski and E. Allen (1998) 3-Hinged Truss Arches Waterloo Terminal for Chunnel Trains Nicholas Grimshaw & Partners Anthony Hunt Associates 7/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Stadium Australia Homebush, Sydney, 1999 Bligh Lobb Sports Architects Sinclair Knight Merz (SKM) Modus Consulting Engineers 8/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Much more labour in the joints l More fussy appearance, beams have cleaner lines l Less suitable for heavy loads l Needs more lateral support Triangular-section steel truss (for lateral stability) 9/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Domestic roofing, where the space is available anyway l Longspan flooring, lighter and stiffer than a beam l Bracing systems are usually big trusses Longspan floor trusses 10/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Span-to-depth ratios are commonly between 5 and 10 l This is at least twice as deep as a similar beam l Depth of roof trusses to suit roof pitch Beam, depth = span/20 Truss, depth = span/4 Truss, depth = span/10 Typical proportions 11/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Gangnail joints in light timber l Gusset plates (steel or timber) Nailplate joint Riveted steel gusset plates 12/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Welded joints in steel l Various special concealed joints in timber Steel gussets concealed in slots in timber members 13/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l The members should form triangles l Each member is in tension or compression l Loads should be applied at panel points l Loads between panel points cause bending l Supports must be at panel points Load causes bending Extra member 14/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 C C C C C C C C C T TT T T TT T Only tension & compression forces are developed in pin-connected truss members if loads applied at panel points 15/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 Basic truss assemblies Imagine diagonals removed Look at deformation that would occur Look at role of diagonal in preventing deformation Final force distribution in members Analogy to ‘cable’ or ‘arch’ action T cc T 0 c 0 c cc TT c 16/27 Truss ATruss B B DF c AC E cc

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l The top and bottom chord resist the bending moment l The web members resist the shear forces l In a triangular truss, the top chord also resists shear Top chord Bottom chord Web members 17/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l For detailed design, forces in each member l For feasibility design, maximum values only are needed Maximum bottom chord Maximum top chord Maximum web members 18/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Find all the loads and reactions (like a beam) l Then use ‘freebody’ concept to isolate one piece at a time l Isolate a joint, or part of the truss This joint in equilibrium 19/27 This piece of truss in equilibrium

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Three methods 1. Method of Joints 2. Method of Sections 3. Graphical Method 20/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Have to start at a reaction l Move from joint to joint l Time-consuming for a large truss Start at reaction (joint F) Then go to joint A Then to joint E Then to joint B... generally there is only one unknown at a time 21/27 ABC DEF

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Resolve each force into horizontal and vertical components A AF AB AE Angle  Vertically: AF + AE sin  = 0 If you don’t know otherwise, assume all forces are tensile (away from the joint) Horizontally: AB + AE cos  = 0 22/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Quick for just a few members d1 d2 W1 W2 W3 R1 A T1 T3 T2 H 23/27 taking moments about A W1 * d1 + W2 * d2 + T1 x H = R1 * d1

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l useful to find maximum chord forces in long trusses 24/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l Uses drafting skills l Quick for a complete truss g,h,o a b c d e f i j,m k l n Scale for forces Maxwell diagram Bow’s Notation 4 3m m a bcde f g h i j kl m n o 25/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l The chords form a couple to resist bending moment l This is a good approximation for long trusses C T d First find the Bending Moment as if it was a beam A shallower truss produces larger forces Resistance Moment = Cd = Td therefore C = T = M / d 26/27

University of Sydney –Building Principles Trusses Peter Smith 1998/Mike Rosenman 2000 l The maximum forces occur at the support First find the reactions A shallower truss produces larger forces R C T  Then the chord forces are: C = R / sin  T = R / tan  27/27