Anemodia

Lab · Structural Mechanics

Truss Analysis Lab

Analyze one planar pin-jointed truss globally, joint by joint, or across a section. Both local methods apply to the triangle; Method of Joints is usually the clearest teaching path for a truss that small.

Truss

Loads

CFx = ≈ 0 kNFy = -10.0 kNF = +10.0 kNθ = -90°
F = 10 kNFyABC
3 joints, 3 members, 2 supports, 1 nodal loads. Drawn to scale with equal x and y scaling. Values are rounded for the diagram; tables retain the detailed results.

Examples

Joints

A
B
C

Coordinates are authoritative: +x to the right, +y upwards. Up to 24 joints in this version. Removing a joint also removes the members, support and loads attached to it.

Members

AB
AC
BC

Area is optional: leave it at 0 and the member force is still solved, only its stress is withheld. Up to 48 members in this version.

Supports

s1
s2

A truss support carries translational reactions only — an ideal pin joint transmits no moment. One support per joint; a planar truss needs at least three restrained directions.

Nodal loads

l1
F = 10\u00a0kNθ = -90°

Loads act at joints only. Angles are measured counter-clockwise from +x; magnitude cannot be negative. Several loads at one joint add, and a load at a support joint is valid.

Classification

Determinate

m + r = 3 + 3 = 2j = 6, with full matrix rank 6.

Largest member force |N|

6.009 kN

Magnitude only; signed tension/compression values are shown below.

Largest joint residual

≈ 0 kN

Numerical round-off relative to the force scale.

What this Lab models

A planar, pin-jointed, statically determinate truss. The global solution supplies reactions and final member forces; Method of Joints and Method of Sections (Ritter method) independently derive selected forces for explanation and cross-checking.

Model scope

  • · Axes: +x to the right, +y upwards; an external moment is positive counter-clockwise.
  • · A load angle θ is measured counter-clockwise from +x. Magnitude-angle entry is converted once to the canonical Fx and Fy used by every equilibrium equation.
  • · Member force N > 0 is tension and N < 0 is compression; a positive tensile force pulls each joint towards the other end of its member.
  • · Loads act at joints only. Members are straight two-force members carrying axial force only, with no bending and no self-weight.
  • · Reactions are translational only: an ideal truss support transmits no moment.
  • · Stability is decided by the rank of the actual joint-equilibrium matrix, not by the count m + r = 2j alone.
  • · Statically indeterminate trusses are refused in this version rather than given one arbitrary solution.
  • · Method of Joints applies ΣFx = 0 and ΣFy = 0 at one joint at a time; unknown member forces are assumed tensile and act away from the joint.
  • · Method of Sections applies ΣFx = 0, ΣFy = 0 and ΣMz = 0 to one retained part of the truss. Ritter moments can isolate a target when the other two cut-member lines meet at a usable point.
  • · These educational methods apply to the current stable, statically determinate V1 model; neither solves a statically indeterminate truss.
  • · No stiffness, displacement, elongation or deflected shape is computed; no member sizing, code check or connection design is performed.

Related calculations