Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu

1. Engineering 36 Chp6:Trusses-2 Bruce Mayer, PE Licensed Electrical & Mechanical EngineerBMayer@ChabotCollege.edu

2. Introduction: MultiPiece Structures • For the equilibrium of structures made of several connectedparts, the internal forces as well the external forces are considered. • In the interaction between connected parts, Newton’s 3rd 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

3. Tension Compression Definition of a Truss • A truss consists of straight membersconnected at joints. No member is continuous through a joint. • A truss carries ONLY those loads which act in its plane, allowing the truss to be treated as a two-dimensional structure. • 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 • 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.

4. 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

5. non-rigid rigid Trusses Made of Simple Trusses • Compound trusses are statically determinant, rigid, and completely constrained. • Truss contains a redundant member and is statically indeterminate. • Additional reaction forces may be necessary for a nonrigid truss. • Necessary but INsufficient condition for a compound truss to be statically determinant, rigid, and completely constrained,

6. Method of Sections • When the force in only one member or the forces in a very few members are desired, the method of sections works well. • 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 FBD

7. Example  Method of Sections • Given the Truss with Loading and Geometry Shown • Use the Method of Sections to Determine the Force in Member FD

8. Take Section to Expose FFD Example  Method of Sections • Now Take ΣME = 0

9. 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. • 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. • Determine the force in members just right of Center: • FH • GH • GI

10. 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

11. Pass a section (n-n) through members FH, GH, and GI and take the right-hand section as a free body Example  Method of Sections • Apply the conditions for static equilibrium to determine the desired member forces.

12. Example  Method of Sections

13. Method of Sections - Summary • If needed Determine Support Reactions • Decide on How to CUT the Truss into Sections and draw the Corresponding Free Body Diagrams • 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

14. 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

15. 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 FAB, FFB, FEB, 1000N

16. Pick: Pivot & PoA Example • Pick Pt-C as the Point of Appliction (PoA) for FED • Using Pt-C as the PoA permits using F•d to find the Moment about Pivot-B

17. WhiteBoard Work Let’s WorkSome TrussProblems Find Forces in EL & LM Find Forces in EL & LM

18. Engineering 36 Appendix Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu