A worked example — a two-column pile cap on 21 piles

Two columns, two load cases: column 1 brings 5,700 kN with 900 kN and 5,300 kN·m, column 2 brings 5,300 kN with 1,000 kN and 5,200 kN·m, and the combination adds them. In the two-dimensional model the three piles of each row act together. The Technical Book example opens in AStrutTie with its dimensions, piles, loads, materials and bars already entered in the pile-footing template.

The template puts the top chord 100 mm below the top and the bottom chord 200 mm above the bottom, the book's setting, with three nodes under each column and a vertical at every node: 22 nodes and 41 members, the same counts as the book's final model. As in the book, the columns are the supports and the pile reactions come in as loads along the bottom chord, from 810 kN at one end to 2,395 kN at the other. Solved as built, three of the template's diagonals — m33, m39 and m40 — are in tension, and the book has no bars in that direction, so with no steel to carry the tension they fail. The book met the same thing: after its first optimized analysis one diagonal (E28) went into tension, and it changed that member's direction and re-ran a normal analysis. The three diagonals were turned the same way, to the other diagonal of their panels; on the re-run m34 went into tension and was turned too, and no diagonal is in tension after that. The built-in example opens with these four already turned. The truss is statically indeterminate to the fourth degree, so the app solves it by stiffness analysis. The largest bottom-chord tension is 1,612.5 kN, the book's E40 exactly; the largest compression is 3,225.8 kN in diagonal m38 against 3,671.8 kN in the book's top chord (−12.1%).

47 of 47 strength checks pass. The minimum safety factor is 2.20, on the top-chord ties m15 and m16 between the columns. Every tie end is anchored too: 6 of 6 development length checks pass.

Between the columns the top chord is in tension: m15 and m16 carry 873.2 kN and need 3,881 mm²; the 22-#7 top bars give 8,535 mm² (2.20). Under and beyond the columns the bottom chord takes the tension, up to 1,612.5 kN in m9 and m10, needing 7,167 mm² of the 21,788 mm² of 43-#8 (3.04) — the book's T40 at 1,612.49 kN needing 7,166.64 mm². The vertical ties are the shear reinforcement; the most loaded, m25 on the inner side of column 1, carries 883.1 kN against 31 legs of #6, 8,836 mm² (2.25).

The shear bars, #6 at 400 mm both ways, give ρ ≈ 0.0016 vertically and 0.0009 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 (which used 1.00 for one strut, E28): f_ce = 8.16 MPa. The most loaded strut is the diagonal m38 down from column 2, 3,225.8 kN, needing 117 mm of the 281 mm available (2.40). Two diagonals carry the book's forces exactly: m32 at 973.4 kN (E12) and m41 at 3,035.1 kN (E30).

The tightest node is t8, the inner support under column 2: its bearing face needs 55.4 of 200 mm (3.61). The book's check of node N3, face C-3 with 3,671.8 kN needing 53.3 mm, is reproduced exactly in the app's comparison.

The bottom bars end over the first pile row, 650 mm from the ends of the cap. Straight, a #8 bar needs ℓd = 915 mm, and the extended nodal zone leaves 1,022 mm (1.12). The top-chord tie between the columns has 4,018 mm available against 801 mm (5.02). All six tie ends pass. The Technical Book's check tables for this example do not cover anchorage.

Same cap, 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. The model is the template's, with the book's own fix applied where diagonals went into tension. The struts keep the book's β_s = 0.40 because the cap lacks §23.5 reinforcement, and the app checks the anchorage of every tie end; all pass here.