A worked example — a two-column spread footing

Two columns, two load cases: column 1 brings 8,500 kN with 120 kN and 5,500 kN·m, column 2 brings 8,000 kN with 130 kN and 6,000 kN·m, and the combination adds them. The ground answers through springs, so the pressure under the footing is not uniform. The Technical Book example opens in AStrutTie with its dimensions, loads, materials and bars already entered in the two-column spread-footing template.

The template puts the top chord 100 mm below the top and the bottom chord 100 mm above the bottom, with two nodes under each column and a vertical at every node: 20 nodes and 37 members. As in the Technical Book, the columns are the supports and the ground pressure comes in as loads along the bottom chord. With the springs the truss is statically indeterminate to the second degree, so the app solves it by stiffness analysis. The book's final model, refined by its optimized analysis, has 24 nodes and 45 elements, so the member forces differ: the largest bottom-chord tension is 2,549.6 kN here against the book's 2,535.4 kN (+0.6%), and the largest compression is 4,498.6 kN in diagonal m31 against 4,844.4 kN in the book's top chord (−7.1%).

49 of 49 strength checks pass. The minimum safety factor is 1.25, on the vertical tie m22 near column 1, which the #6 shear bars carry. Anchorage is reported separately from the strength verdict, and the two ends of the bottom tie fail it; step ⑦ explains why.

Under and beyond the columns the bottom chord is in tension, up to 2,549.6 kN in m3, which needs 8,499 mm²; 33-#8 give 16,721 mm² (1.97). Between the columns the footing bends the other way and the top chord takes the tension, up to 2,236 kN in m14 and m15. The vertical ties are the shear reinforcement: m22 carries 1,853.6 kN against 27 legs of #6 within its effective width, 7,696 mm² (1.25). The tie checks the book prints, such as T45 at 2,535.40 kN needing 8,451.34 mm², come out the same in the app's comparison.

The footing's shear bars, #6 at 300 mm both ways, give ρ ≈ 0.0013 vertically and 0.0011 horizontally, below the 0.0025 per direction that §23.5 asks for β_s = 0.75. Every strut is therefore taken as β_s = 0.40, as in the Technical Book: f_ce = 8.16 MPa. The template's default would be 0.75, which assumes reinforcement this footing does not have. The most loaded strut is the diagonal m31 from column 1, 4,498.6 kN, needing 147 mm of the 282.5 mm available (1.92).

The tightest node is t3, the inner support under column 1: its bearing face needs 97.1 of 200 mm (2.06). Where ties meet along the chords the nodes are CTT; b4, where the diagonal m31 lands, is the lowest at 3.04. The book's check of node N3, face C-3 with 4,050.0 kN needing 52.9 mm, is reproduced exactly in the app's comparison.

The bottom-chord bars end at nodes b1 and b10, 350 mm from the ends of the footing. Straight, a #8 bar needs ℓd = 1,220 mm; the extended nodal zone leaves 514 mm, a safety factor of 0.42. A hook would bring the requirement down to 753 mm, still more than 514 mm, because the node sits so close to the edge. The Technical Book's check tables for this example do not cover anchorage; the NG is shown as the app reports it.

Same footing, same loads, same bars. The strength equations and φ are the same in both editions, so every value the book's check tables print comes out the same. What differs is the model — the template's truss against the book's optimized one — and two checks: the struts keep the book's β_s = 0.40 because the footing lacks §23.5 reinforcement, and the app checks the anchorage of every tie end.