ENG1011 Chap.6 Truss Stability, Determinacy and the Method of Joints
Truss Stability, Determinacy and the Method of Joints
Truss Stability, Determinacy and the Method of Joints opens Week 4. A truss is built from straight members pinned at their ends and loaded only at its joints, so every member is a two-force member carrying a single axial force of tension or compression. Before solving, the chapter asks whether a solution exists.
Each joint supplies two equilibrium equations, so a planar truss with j joints has 2j equations for m member forces plus r reactions. If m + r is less than 2j the truss is a mechanism, if it is greater the truss is statically indeterminate, and if they are equal it may be determinate, provided the members are triangulated and the reactions are neither all parallel nor all concurrent.
The method of joints then solves the truss one joint at a time, starting where only two member forces are unknown, drawing every unknown pulling away from the joint as tension so that a negative result means compression.
Symmetry and a final joint check shorten and confirm the work.
Truss items in the Content Test cover determinacy, zero-force members and the method of joints, and the practice test adds choosing the correct free-body diagram for a given joint.
Week 4 is also when the bridge project starts using truss analysis: the Week 7 practical asks each team to run a method of joints analysis on a two-dimensional model of its bridge, which links this chapter directly to the project mark.
What this chapter covers
- 01
Trusses as assemblies of two-force members
- 02
Equations available: two per joint
- 03
Comparing m + r with 2j
- 04
Stability from triangulation and support layout
- 05
Parallel and concurrent reactions as unstable cases
- 06
The method of joints, starting at a support
- 07
Tension positive and compression negative
- 08
Typical chord and diagonal force patterns
Worked example · free
Member forces in a three-member truss
- 1Count: m = 3, r = 3, j = 3, so m + r = 6 = 2j; the triangle is stable, so the truss is determinate.
- 1Reactions by symmetry: Ay = Cy = 5 kN upward.
- 1Joint A, vertical: 5 + FAB times 3/5 = 0, so FAB = minus 8.33 kN, compression.
- 1Joint A, horizontal: FAC + FAB times 4/5 = 0, so FAC = 6.67 kN, tension.
Key terms
- Truss
- A structure of straight members pinned at their ends and loaded only at the joints.
- Two-force member
- A member loaded only at two points, so its force acts along the line joining them.
- Statically indeterminate
- Describes a structure with more unknown forces than independent equilibrium equations.
- Method of joints
- A truss analysis that applies two force equations at each joint in turn to find member forces.
- Mechanism
- An arrangement of members and supports that can move or change shape without any member changing length.
- Triangulation
- Arranging members in triangles so that the framework cannot change shape.
Truss Stability, Determinacy and the Method of Joints FAQ
Is m + r = 2j enough to prove a truss is determinate?
No. Equal counts are necessary but not sufficient. The members must also be triangulated and the supports must restrain movement in both directions and rotation, so three parallel reactions, or three reactions meeting at one point, still leave a truss unstable.
Which joint should I start the method of joints at?
Start at a joint with no more than two unknown member forces, which is usually a support joint once the reactions are known. Then move to neighbouring joints, always choosing one where only two forces remain unknown.
How do I report a compressive member force?
With unknowns drawn as tension, a compressive member comes out negative. In this unit's answer boxes that negative value is entered as it stands; if a question asks for magnitude and type instead, give the positive size and write compression.
What does a pin support add to the count compared with a roller?
A pin supplies two reaction components and a roller one. Replacing the roller of a pin and roller truss with a second pin raises r from 3 to 4, which makes an otherwise determinate truss indeterminate to the first degree.
Exam move
Practise determinacy counts until they are automatic, always followed by a sentence about arrangement. For the method of joints, solve a symmetric truss on one side and confirm the other side by symmetry. Check your final joint, where every force is already known, as the cheapest test of the whole chain.
When choosing between candidate joint diagrams, check that every member is drawn along its own line and pulling away from the joint.
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