AMME1802 Chap.5 Trusses, Frames and Machines
Trusses, Frames and Machines
Trusses turn external loading into axial tension and compression in ideal two-force members. This chapter chooses between methods of joints and sections, identifies zero-force members and then explains why frames and machines require member isolation at internal pins. Every result is closed with a physical load-path statement rather than an unsigned table.
Whole-structure equilibrium finds support reactions before internal members are exposed. A joint offers two planar force equations, so a starting joint with no more than two unknowns is valuable. A section offers force and moment equations and can target remote members without solving the entire truss. Zero-force rules save work only at unloaded, unsupported joints that meet their geometric conditions.
Frames and machines break the pure two-force-member idealisation; internal pin forces appear as equal and opposite interactions after members are separated.
What this chapter covers
- 01
Two-force member idealisation
- 02
Method of joints
- 03
Method of sections
- 04
Zero-force member rules
- 05
Frames and internal pins
- 06
Selecting the simpler side of a section cut
- 07
Whole-structure checks on solved internal member force patterns
- 08
A final load-path account linking member actions to the supports
Worked example · free
Triangular truss load path
- +1Use symmetry to find the two vertical support reactions.
- +1Write the inclined-member direction ratios from geometry.
- +1Use vertical equilibrium at the apex for the inclined member force.
- +1Use horizontal equilibrium at a support joint for the bottom member.
- +1State compression or tension and narrate the load path.
Key terms
- Method of joints
- A truss method applying force equilibrium to one pin at a time.
- Method of sections
- A truss method cutting selected members and applying rigid-body equilibrium to one side.
- Load path
- The physical route by which applied forces travel through members to supports.
- Axial force
- A force directed along the longitudinal axis of a member.
- Member tension
- An axial action that pulls outward on the isolated ends of a member.
- Member compression
- An axial action that pushes inward on the isolated ends of a member.
- Internal pin
- A joint that transmits equal and opposite interaction forces between connected members.
- Section cut
- An imagined division that exposes internal member forces on the retained portion.
Trusses, Frames and Machines FAQ
When should I use the method of joints?
Use joints when adjacent member forces are required or when the load path can be followed from a joint with at most two unknowns. Each planar joint provides only two independent force equations, so the starting joint matters.
When is a section faster?
A section is faster when only a few remote member forces are requested. Cut no more than three unknown planar members and choose a moment centre at the intersection of two force lines to isolate the third.
Are frames analysed like trusses?
Not generally. Frame and machine members may carry more than two interactions, distributed loads or couples, so they require rigid-body equilibrium after separation at internal pins. Use the two-force member shortcut only when its loading conditions are actually satisfied.
What makes a member a two-force member?
Only two external forces act on it, usually at pin connections, with no additional load or couple. Equilibrium then requires those forces to be equal, opposite and collinear. A third interaction invalidates the shortcut and requires rigid-body analysis.
Assessment move
Solve whole-structure reactions first, then select a joint or section based on the requested member. Keep assumed tension arrows and translate negative answers into compression only at the end. After calculations, explain how the applied load reaches each support. Begin revision by identifying two-force members from loading conditions rather than appearance.
For joint drills, circle a joint with at most two unknowns and write direction ratios beside every inclined member. For section drills, draw several candidate cuts and choose the one that crosses no more than three unknown planar members while offering a useful moment intersection. Maintain the tension assumption on every cut arrow until signs are known.
Add zero-force-member questions that include a support or applied load so you learn when the shortcut does not apply. For frames, produce paired diagrams of connected members and mark equal-and-opposite pin forces with consistent subscripts. Check the full structure externally, each separated member internally and the final member labels physically.
A short load-path sentence should explain which pieces push, which pull and where the applied load reaches the supports. Build one truss from a small set of coordinates and solve selected members twice, first by following joints and then by a section. Agreement confirms both the reactions and member signs. Change one applied load and predict which zero-force conclusions survive before recalculating.
For a frame, list the forces acting on each member and classify genuine two-force members before using collinearity. Add a machine problem where the requested output force lies on a different member from the input; trace pin interactions across the assembly rather than combining unrelated forces on one diagram.
End revision by drawing member-force arrows on the original structure so the load path can be inspected without equations.
