ENGR-36_Lec-15_Trusses-2.pptx 1 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Licensed Electrical & Mechanical Engineer Engineering 36 Chp 6: Trusses-2

ENGR-36_Lec-15_Trusses-2.pptx 2 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Introduction: MultiPiece Structures  For the equilibrium of structures made of several connected parts, the internal forces as well the external forces are considered.  In the interaction between connected parts, Newton’s 3 rd Law states that the forces of action and reaction between bodies in contact have the same magnitude, same line of action, and opposite sense.  The Major Categories of Engineering Structures Frames: contain at least one multi-force member, i.e., a member acted upon by 3 or more forces Trusses: formed from two-force members, i.e., straight members with end point connections Machines: structures containing moving parts designed to transmit and modify forces

ENGR-36_Lec-15_Trusses-2.pptx 3 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Definition of a Truss  A truss consists of straight members connected at joints. No member is continuous through a joint.  Bolted or welded connections are assumed to be pinned together. Forces acting at the member ends reduce to a single force and NO couple. Only two-force members are considered  LoA CoIncident with Geometry  A truss carries ONLY those loads which act in its plane, allowing the truss to be treated as a two-dimensional structure.  When forces tend to pull the member apart, it is in tension. When the forces tend to push together the member, it is in compression. Tension Compression

ENGR-36_Lec-15_Trusses-2.pptx 4 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Truss Defined  Members of a truss are SLENDER and NOT capable of supporting large LATERAL loads i.e.; IN-Plane, or 2D, loading only Members are of NEGLIBLE Weight  Loads MUST be applied at the JOINTS to Ensure AXIAL-ONLY Loads on Members. Mid-Member Loads Produce BENDING-Loads which Truss Members are NOT Designed to Support Beams Apply RoadBed Load at JOINTS Only

ENGR-36_Lec-15_Trusses-2.pptx 5 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Trusses Made of Simple Trusses Compound trusses are statically determinant, rigid, and completely constrained. Truss contains a redundant member and is statically indeterminate. Necessary but INsufficient condition for a compound truss to be statically determinant, rigid, and completely constrained, non-rigid Additional reaction forces may be necessary for a nonrigid truss. rigid

ENGR-36_Lec-15_Trusses-2.pptx 6 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Method of Sections  To determine the force in member BD, pass a section through the truss as shown and create a free body diagram for the left side.  With only three members cut by the section, the equations for static equilibrium may be applied to determine the unknown member forces, including F BD  When the force in only one member or the forces in a very few members are desired, the method of sections works well.

ENGR-36_Lec-15_Trusses-2.pptx 7 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example  Method of Sections  Given the Truss with Loading and Geometry Shown  Use the Method of Sections to Determine the Force in Member FD

ENGR-36_Lec-15_Trusses-2.pptx 8 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example  Method of Sections  Take Section to Expose F FD  Now Take ΣM E = 0

ENGR-36_Lec-15_Trusses-2.pptx 9 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example  Method of Sections  Determine the force in members just right of Center: FH GH GI  SOLUTION PLAN Take the entire truss as a free body. Apply the conditions for static equilibrium to solve for the reactions at A and L. Pass a section through members FH, GH, and GI and take the right-hand section as a free body. Apply the conditions for static equilibrium to determine the desired member forces.

ENGR-36_Lec-15_Trusses-2.pptx 10 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example Method of Sections  SOLUTION PLAN Take the entire truss as a free body. Apply the conditions for static equilibrium to solve for the reactions at A and L

ENGR-36_Lec-15_Trusses-2.pptx 11 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example  Method of Sections  Pass a section (n-n) through members FH, GH, and GI and take the right-hand section as a free body  Apply the conditions for static equilibrium to determine the desired member forces.

ENGR-36_Lec-15_Trusses-2.pptx 12 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Example  Method of Sections

ENGR-36_Lec-15_Trusses-2.pptx 13 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Method of Sections - Summary 1.If needed Determine Support Reactions 2.Decide on How to CUT the Truss into Sections and draw the Corresponding Free Body Diagrams 3.Try to Apply the Eqns of Equilibrium to avoid generation of simultaneous Eqns Moments should be Summed about points that lie at the intersection of the LoA’s of 2+Forces, making simpler the solution for the remaining forces

ENGR-36_Lec-15_Trusses-2.pptx 14 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Pick: Pivot & PoA  When doing Sections Recall that the LoA for Truss Members are defined by the Member Geometry  Use Force Transmissibility → Forces are SLIDING Vectors Pick a Pivot Point, on or Off the Body, where the LoA’s of many Force LoA’s Cross Apply the Force of interest so that ONE of its X-Y Components passes Thru the Pivot

ENGR-36_Lec-15_Trusses-2.pptx 15 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Pick: Pivot & PoA Example  After Finding support RCNs find force in Member ED → Use Section a-a  Pick Pt-B as Pivot to Eliminate from Moment Calc F AB, F FB, F EB, 1000N

ENGR-36_Lec-15_Trusses-2.pptx 16 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Pick: Pivot & PoA Example  Pick Pt-C as the Point of Appliction (PoA) for F ED  Using Pt-C as the PoA permits using Fd to find the Moment about Pivot-B

ENGR-36_Lec-15_Trusses-2.pptx 17 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics WhiteBoard Work Let’s Work Some Truss Problems Find Forces in EL & LM

ENGR-36_Lec-15_Trusses-2.pptx 18 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics Bruce Mayer, PE Registered Electrical & Mechanical Engineer Engineering 36 Appendix

ENGR-36_Lec-15_Trusses-2.pptx 19 Bruce Mayer, PE Engineering-36: Engineering Mechanics - Statics