1. Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu
Engineering 36
Chp 6: Trusses-1
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. 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 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. Definition of a Truss
A truss consists of straight members connected 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
Tension
Compression
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. Beams Apply RoadBed Load at JOINTS Only
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. Types of Trusses

6. Yet More Trusses http://www.caltruss.com/products.htm

7. Simple Trusses
A rigid truss will not collapse under the application of a load.
A simple truss is constructed by successively adding two members and one connection to the basic TRIANGULAR truss
In a simple truss, m = 2n − 3 where m is the total number of members and n is the number of joints
m = no. of members * n = no. of Joints/pins

8. Method of Joints for Trusses
Dismember the truss and create a freebody diagram for each member and pin.
The two forces exerted on each member are equal, have the same line of action, and opposite sense as the load on the associated Pin
Forces exerted by a member on the pins or joints at its ends are directed along the member and are equal & opposite.
Conditions of equilibrium on the pins provide 2n equations for 2n unknowns. For a simple truss, 2n = m May solve for m member forces and 3 reaction forces at the supports.
Conditions for equilibrium for the entire truss provide 3 additional equations which are not independent of the pin equations.

9. Zero-Force Members
Forces in opposite members intersecting in two straight lines at a joint are equal (to maintain pin equilibrium).
The forces in two opposite members are equal when a load is aligned with a third member. The third member force is equal to the load (including zero load). If P=0, Then AC Applies NO Force to the pin; AC is then a ZERO-FORCE MEMBER
The forces in two members connected at a joint are equal if the members are aligned and zero otherwise.
Recognition of joints under special loading conditions (ZFMs) simplifies truss analysis.

10. Zero Force Members (ZFMs)
TWO-Member Version
When only TWO members form a NON-CoLinear truss joint and NO external load or support reaction is applied to the joint then the members MUST be ZERO-FORCE members.
THREE-Member Version
When THREE members form a truss joint for which two of the members are CoLinear and the third is forms an angle with the first two, then the NON-CoLinear member is a ZERO-FORCE member provided NO external force or support reaction is applied to the joint
NOTE that The CoLinear members carry EQUAL loads.

11. Zero Force Members (ZFMs)
Truss members that canNOT carry load are called Zero Force Members.
Examples of Zero Force Members (ZFMs) are the colored members (AB, BC, and DG) in the truss shown at Right

12. Zero Force Members (ZFMs)
Again Consider
Summing the forces in the y-direction in the AB FBD shows that FAB must be ZERO since it is NOT balanced by another y-force.
With FAB =0 Summing forces in the x-direction shows that FBC must also be zero
FBD for AB & BC

13. Zero Force Members (ZFMs)
Again Consider
Summing forces in the y-direction in the DG free-body-diagram, reveals that FDG must be zero since it is not balanced by another y-force
The FBD for DG

14. Space Trusses
An elementary space truss consists of 6 members connected at 4 joints to form a tetrahedron.
A simple space truss is formed and can be extended when 3 new members and 1 joint are added at the same time.
In a simple space truss, m = 3n − 6 where m is the number of members and n is the number of joints.
Conditions of equilibrium for the Ball-and-Socket joints provide 3n equations (no moments). For a simple truss, 3n = m + 6 and the equations can be solved for m member forces and 6 support reactions.
Equilibrium for the entire truss provides 6 additional equations which are not independent of the joint equations.

15. Example  2D Truss Solution Plan
Based on a free-body diagram of the entire truss, solve the 3 equilibrium eqns for the reactions at A and D
Joint D is subjected to only two unknown member forces. Determine the member forces from the joint (or pin) equilibrium requirements.
In succession, determine unknown member forces at joints C, B, and A from pin equilibrium requirements.
Use Pin-E equilibrium requirement to check the results
Using the method of joints, determine the force in each member of the truss

16. Black/White Board Work
Solve by Method of Joints
Weight of Members & Truss is Negligible Relative to Applied Load(s)

18. Example  2D Truss SOLUTION PLAN
Based on a free-body diagram of the entire truss, solve the 3 equilibrium equations for the reactions at E and C.
Joint A is subjected to only two unknown member forces. Determine these from the joint (or pin) equilibrium requirements.
In succession, determine unknown member forces at joints D, B, and E from pin equilibrium requirements.
All member forces and support reactions are known at joint C. However, the joint equilibrium requirements may be applied to check the results
Using the method of joints, determine the force in each member of the truss.

19. Example  2D Truss SOLUTION So-Far, So-Good
Based on a free-body diagram of the entire truss, solve the 3 equilibrium equations for the reactions at E and C.
So-Far, So-Good

20. Example  2D Truss
Joint A is subjected to only two unknown member forces. Determine these from the pin (or joint) equilibrium requirements.
There are now only two unknown member forces at joint D.

21. Example  2D Truss
There are now only two unknown member forces at joint B. Assume both are in tension.
There is one unknown member force at joint E. Assume the member is in tension.

22.  Example  2D Truss CHECK
All member forces and support reactions are known at joint C. However, the joint equilibrium requirements may be applied to check the results. 

23. A Real Truss Joint Idealized
2 in Tension, 3 in Compression

24. Let’s Work These Nice Problems
WhiteBoard Work
Let’s Work These Nice Problems
ENGR-36_Lab-20_Fa07_Lec-Notes.ppt

25. ENGR-36_Lab-20_Fa07_Lec-Notes.ppt

26. APPENDIX Truss Analysis
Engineering 36
APPENDIX Truss Analysis
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer –

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34. Truss-Member Load Analysis
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