ENG1011 Chap.7 Zero-Force Members and the Method of Sections
Zero-Force Members and the Method of Sections
Zero-Force Members and the Method of Sections finishes Week 4 with two shortcuts. Zero-force members carry nothing under a particular loading and can be found without equations. At an unloaded joint where only two non-collinear members meet, both are zero-force members; at an unloaded joint where three members meet and two are collinear, the third is zero.
Neither rule applies at a joint with a load or a support reaction. The method of sections finds one member force directly by cutting the truss through no more than three unknown members and treating one side as a rigid body.
Moments about the point where two of the cut members meet isolate the third, so the top and bottom chords come from moment equations whose lever arm is the truss depth, and the diagonal comes from a vertical force balance. The Content Test in Week 6 does not require the method of sections, but it remains part of the Week 4 outcomes and the wider unit.
The two methods are complementary rather than competing.
Inspection removes zero-force members before any equation is written, and a well-chosen section reaches an interior member in one moment equation. Used together they turn a long joint-by-joint calculation into a few lines, which matters under time pressure in the Final Assessment.
What this chapter covers
- 01
Why some members carry no force
- 02
Rule one: two non-collinear members at an unloaded joint
- 03
Rule two: one member joining two collinear members
- 04
Loaded and supported joints as exceptions
- 05
Choosing a section through three unknown members
- 06
Moment points where two cut members meet
- 07
Chord forces from the moment at a joint and the depth
Worked example · free
Bottom chord force by the method of sections
- 1The left part carries the 10 kN reaction at 3 m from the moment point, giving a clockwise moment of 10 times 3 = 30 kN m.
- 1The bottom chord force acts 1.5 m below the moment point; drawn as tension it gives an anticlockwise moment of 1.5 F.
- 1Balance: 1.5 F minus 30 = 0, so F = 20 kN, tension.
Key terms
- Zero-force member
- A truss member carrying no axial force under the given loads, found by inspecting an unloaded joint.
- Method of sections
- A truss analysis that cuts through members and applies rigid-body equilibrium to one part.
- Collinear members
- Two members lying along the same straight line through a joint.
- Chord
- A top or bottom member running along the length of a truss.
- Truss depth
- The vertical distance between the top and bottom chords, which is the lever arm for chord forces.
Zero-Force Members and the Method of Sections FAQ
Can a zero-force member be removed from the truss?
Not safely. It carries nothing under the present loading, but it braces other members against buckling and may carry force when the loads change, so it remains part of the structure even though its force is zero now.
When is the method of sections better than the method of joints?
When a question asks for one or two members in the middle of a truss. Walking joint by joint from a support could take several joints to reach them, while a single section and one moment equation gives the force directly.
Is the method of sections tested in the Content Test?
The Content Test information excludes the method of sections, although the test covers the rest of Weeks 1 to 4. The method is still part of the Week 4 outcomes for the unit as a whole.
Why do the inspection rules fail at a loaded joint?
The rules rely on the members being the only forces at the joint. A load or reaction adds another force that can balance a member's force, so the reasoning that forces the member to zero no longer holds and equations are needed.
Exam move
Before every truss question, scan the unloaded joints for zero-force members and mark them; it removes unknowns for free. For sections, sketch the cut, list the three unknowns, and mark the two moment points before writing anything. Cross-check one section result against the method of joints to confirm both methods agree.
Practise one truss three ways: by joints, by a section, and by inspection for zero-force members, and confirm that the answers agree.
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