2-D truss analysis
A plane pin-jointed truss of any shape analysed by the direct stiffness method for each ASCE 7-22 load combination: member axial forces (tension positive), support reactions and joint displacements. It is an analysis tool: its status reads "Calculated", and the members and joints are designed in their own calculations.
Inputs of the truss analysis #
- Sections: up to three AISC shapes (Shapes Database v16.0, including double angles); a member takes its area A and radius of gyration r from its section. A member can instead use an A (and optionally an r) entered in its row.
- Joints: numbered 1, 2, ... in table order, at (x, y) with x to the right and y up, up to 300 joints. A support is free, a pin, a roller holding Y (level surface), a roller holding X (vertical surface) or a roller on a surface at an angle from the horizontal (it holds the direction normal to the surface). A joint no member reaches is ignored.
- Members: from joint i to joint j, up to 600 members, the section and E (29,000 ksi for steel, AISC 360-22 B4, prefilled; enter the modulus of your material). Every member is pinned at both ends.
- Joint loads: Fx (right positive) and Fy (up positive) by load type, at the joints only.
- Self-weight of the members: optional, lumped half to each end joint as dead load, from the shape's weight or, for an entered A, from the unit weight you enter.
- Effective length factor K: used only in the slenderness note; 1.0 is prefilled. Choosing it is your judgment.
- Load combinations: the ASCE 7-22 2.3.1 (LRFD) or 2.4.1 (ASD) combinations of the load types present, chosen by the method switch (W and E in both directions), or one load set: the unfactored sum of the loads.
There is nothing to size, so this type has no auto-design.
Results and checks of the truss analysis #
| Item | Basis |
|---|---|
| Determinacy | The count of members and reactions against twice the joints: determinate, indeterminate to a stated degree, or too few (NOT FEASIBLE) |
| Stability | The free stiffness matrix: a mechanism is NOT FEASIBLE, and its smallest eigenvalue names the joint and the direction that move |
| Equilibrium of the truss | The applied loads and the reactions, for every combination |
| Member forces and reactions | The largest tension and compression of each member, and the extremes of each reaction component, over the combinations |
| Largest joint displacement | The resultant displacement and its combination |
| Slenderness of compression members | Advisory: KL/r preferably not over 200 (AISC 360-22 E2 user note). Single angles use rz; other shapes the smaller of rx and ry |
| Slenderness of tension members | Advisory: L/r preferably not over 300 (AISC 360-22 D1 user note; not for rods or hangers) |
The drawings (on screen, in the report and as a PDF / DXF drawing sheet) show the truss elevation with joint numbers, member marks, supports, joint loads and chain dimensions, and the member forces of the governing combination on the truss (for example "12.3 T", "8.1 C"). A large truss is drawn in parts across several views.
Limitations #
- First-order linear elastic analysis. A truss that is part of a lateral system needs a stability analysis (AISC 360-22 C1, C2).
- Loads act at the joints only. Bending of a chord loaded between joints, joint eccentricity and the secondary moments of real gusseted joints are not included.
- No member design or connection design: use the forces in the member's own calculation.
- No support settlement, temperature, fabrication error or spring supports, although the source textbook treats some.
- Pattern live load is not generated: enter the arrangements as separate calculations if they govern.
Verification examples #
Verification status: 67 values compared in 12 examples (12 published, 0 hand calculations from the cited equations): 67 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
Compared with published worked examples, one unfactored load set. The test file holds every value and its page.
| Source | Example | Compared |
|---|---|---|
| McGuire, Gallagher, Ziemian, Matrix Structural Analysis, 2nd Ed. | 2.1, 3.2, 3.3 (indeterminate), 3.5, 3.6 (indeterminate) | Displacements, reactions and member forces |
| Udoeyo, Structural Analysis (open textbook, 2020) | 5.2, 5.3, 8.6, 8.7, 8.11 | Member forces and reactions (determinate) |
| Udoeyo | 10.8, 10.9 (force method, indeterminate) | Member forces |
For Example 2.1 the book prints the horizontal components of the bar forces at joint a, not the bar forces, so those components are compared.
Udoeyo's book has printing errors, which are left out of the comparison and explained in each example's note: Example 5.2's force BC (5.42 kN printed, 9.17 kN by statics), Example 8.6's force DE (60 kips printed, 45 kips by statics) and its displacement, and the displacements of Examples 8.7 and 8.11. The behaviour tests compare the corrected displacements as hand calculations. Inclined rollers, self-weight lumping, the load combinations and the slenderness notes have no published example; they are checked by hand calculation.