Precast Structures Verification Studies
This article summarizes the verification studies and results for the precast reinforced concrete structure features. The reference example is the building in the Turkish Precast Association’s book “Analysis and Design of an Example Precast Reinforced Concrete Industrial Building According to TBDY-2018” (“the book” below). For a step-by-step solution of the same building in StatiCAD with screenshots, see Worked Example: Precast Industrial Building.
1. Verification approach
The verification was carried out in layers; each layer secures the input of the one above it:
- Member core: Unit tests of the nonprismatic member mathematics against closed-form solutions and high-resolution numerical references.
- Section geometry: Comparison of the section properties of the precast templates with SAP2000’s own section calculation.
- Calculation cores: Line-by-line comparison of the Annex 8B, overhead travelling crane, different R–D, connection, façade panel and foundation sliding calculations with the numerical examples in the book; comparison of the short corbel calculation with the example in the Turkish Precast Association handbook and with a hand calculation.
- Building scale: Building and analyzing the book building in StatiCAD; comparing the seismic quantities, internal forces and reinforcement with the book.
- Independent finite element check: Rebuilding the same finite element model in SAP2000 v27 and comparing the periods, reduced stiffness and displacements.
2. Nonprismatic member
The member mathematics was tested with 87-check test programs, all of which passed:
| Test | Reference | Result |
|---|---|---|
| 12×12 stiffness matrix for a constant section | The program’s prismatic Euler and Timoshenko member matrices | Equal to 10⁻⁹ relative precision |
| Cantilever flexibility integrals for a tapered section | 400,000-point numerical integral and analytical averages | Equal to 10⁻⁶ relative precision |
| Rigid body motions and symmetry | K·urigid = 0, K = Kᵀ | Satisfied |
| Fixed-end forces for uniformly distributed load, constant section | qL/2, qL²/12 | Equal to 10⁻⁹ precision |
| Fixed-end forces, tapered and multi-segment member | Force and moment equilibrium | Satisfied |
The calculation of prismatic members is not affected by the addition of the nonprismatic section.
3. Precast section geometry
The properties of sections generated from the parametric templates were compared with the properties calculated by SAP2000 for sections defined in SAP2000 with the same parameters:
| Template | Area and inertia difference | Assessment |
|---|---|---|
| Precast I, Precast Box, Trapezoidal, Box/Tube | ≤ 0.02% | Exact match |
| Precast T | Analytical (sum of rectangular parts) | Exact |
| Precast U | Area −4.1% in the example section | Difference in the flange–wall junction detail |
4. Calculation cores: numerical examples in the book
4.1 TBDY Annex 8B equivalent brace
| Quantity | Book | StatiCAD |
|---|---|---|
| Equivalent axial stiffness (EA)e | 727,960 N | 727,982 N |
| Brace force capacity Fmax | 10,628 N | 10,622 N |
The small differences arise from the rounding of π and cos α in the book.
4.2 Overhead travelling crane loads
| Quantity | Value (book = StatiCAD) |
|---|---|
| Total wheel reaction | 366 kN |
| Bridge weight | 166 kN |
| Mass share per wheel (book: bridge weight / 4) | 41.5 kN |
| Crane girder design moment Md | 692.8 kNm |
| Crane girder design shear Vd | 516 kN |
| Horizontal design moment | 64.3 kNm |
All values are identical to the book. The program divides the bridge mass as a total (bridge weight / g = 16.92 t) equally among the mass columns.
Transfer of the crane load cases to the analysis: Writing the crane load cases to the nodes, the finite element solution, the combinations and the design were verified by hand calculation on a separate test model: two corbel columns (50/50, H = 10 m, spacing 12 m, rigid diaphragm), rails in the X direction, corbel top elevation 7.00 m, e = 40 cm, crane inputs as in the book (γK = 1.6).
| Test | Reference | Result |
|---|---|---|
| Crane loads written to the nodes | Hand calculation: Rkol,max / Rkol,min = 305.7 / 89.1 kN; in the rail direction R/7 = 43.7 / 12.7 kN, in the bridge direction R/10 = 30.6 / 8.9 kN; KG 83 kN per column | Exact match |
| Internal forces with the rigid diaphragm (KV1 / KG) | Hand calculation: tie force between the columns 10.785 / 4.532 kN; column base moment 14.45 kNm (KV1, loaded rail column) / 12.12 kNm (KG) | Exact match |
| Q equivalence | Model with no crane defined, the same node loads written to the Q load case | KV1 results identical at bit level |
| Combinations | 10 crane combinations (65–74) are added to the 64 TBDY combinations; the KG coefficient is 1.0 in Eq. 4.11 and 0.9 in Eq. 4.12 | Satisfied |
| Column axial design force (1.4G + 1.6Q + 1.6KV1 + 1.6KHX1) | Hand calculation Nd = 532.12 kN (TS 500) | Exact match; the axial force check with earthquake (0.40·fck·Ac) takes KG, not the crane combination |
| Rails in the Y direction, min load option at the opposite rail off | MY = +V·ex; the horizontal force from Rkol,max at both rails | Correct |
| Combination coverage check | Full analysis with crane loads on the book building and on a reinforced concrete model with shear walls: stored combination internal forces = factored sum of the load case results | Coincide (relative difference of the order of 10⁻¹⁵ in the shear wall model) |
| Save and transitions | Save–open; remove crane; transition between projects with and without a crane defined | Identical at bit level |
| Invariance in projects without a crane | Seven test projects, before and after the change | 30 of the 31 output files identical; in one only the time stamp differs |
A numerical comparison with the book’s results for the building with crane loads is outside the scope of this study.
4.3 Different R and D for the upper and lower parts
| Case | Quantity (X / Y) | Book | StatiCAD |
|---|---|---|---|
| A (νupper = 0.408 / 0.406) | ν | 0.763 / 0.762 | 0.763 / 0.762 |
| (R̄a)lower | 3.932 / 3.937 | 3.931 / 3.935 | |
| D̄lower | 1.805 / 1.807 | 1.805 / 1.808 | |
| B (νupper = 0.320 / 0.261) | (R̄a)lower | 4.121 / 4.261 | 4.121 / 4.259 |
| D̄lower | 1.929 / 2.02 | 1.929 / 2.018 |
4.4 TBDY Chapter 8 connections
All 43 checks passed; apart from the two deliberate differences noted below, the results are identical to the book.
| Connection | Quantity | Result | Assessment |
|---|---|---|---|
| MFB (roof beam) | Horizontal force, moment, dowel shear strength (2Ø36) | 88.6 kN; 65.77 kNm; 173.3 kN | Exact match |
| MFB | Dowel bar tension force | 358 kN (book 253.5 kN) | The program applies the lever arm in TBDY Figure 8.1; safe side |
| MAB3 (axis E) | Horizontal forces (−/+/with D −/with D +) | 440 / 335 / 1017 / 912 kN | Exact match |
| MAB3 (axis E) | Top/bottom reinforcement, weld area | 1355 / 1032 mm², 5381 mm² | Exact match |
| MAB3 (axis E) | Moment capacities MRd− / MRd+ | 286.5 / 409 kNm | Exact match |
| MAB3 (axis B) | Horizontal shear dowel | 5512 mm² | Exact match |
| MAB3 (axis B) | Top reinforcement | 3339 mm² (book 3630 mm²) | A different quantity was entered into the formula in the book’s axis B calculation; the axis E layout was taken as the basis |
| Purlin | Dowel shear, weld and buckling capacities | 114.6 / 113.4 / 347 kN | Exact match |
4.5 Façade panel and foundation sliding
| Calculation | Result |
|---|---|
| Façade panel (10.1 t, R/I = 3, Tp = 0.787 s) | Equivalent seismic load 102.3 kN, lower limit 41.1 kN — exact match |
| Foundation sliding (axis E) | Rth = 107.5 kN ≥ Vth = 103 kN — exact match |
4.6 Short corbel (TS 500 Clause 8.4)
The book has no corbel calculation (it states that this “will be done separately”). The calculation core was tested with the example on p. 99 of the Turkish Precast Association’s handbook Prefabrike Betonarme Yapılar Tasarım, Üretim ve Montaj Esasları (Principles of Design, Production and Erection of Precast Reinforced Concrete Structures) and with a hand calculation prepared for the DK101 corbel on axis B of the book building (calculation basis: Short Corbel Design).
| Example | Quantity | StatiCAD | Reference | Assessment |
|---|---|---|---|---|
| Handbook p. 99: Vd = 450 kN, Hd = 90 kN, h = 800 mm, d = 770 mm, b = 400 mm, a = 250 mm, C30, B420C | Handbook method As | 656.1 mm² | 656 mm² | Exact match |
| μe (Table 4.16 limit) | 6.87 → 3.4 | 3.4 | Exact match | |
| T2 | 488.0 kN | 488 kN | Exact match | |
| Vr | 1320 kN | 1324 kN | Rounding (fcd = 21.5 MPa in the handbook) | |
| Avh / A’s,min / bottom reinforcement (3Ø18) | 328.0 / 640 / 763 mm² | 328 / 640 / 763 mm² | Exact match | |
| TS 500 Ast | 903.6 mm² (the minimum reinforcement term governs) | — | 38% more than the handbook method | |
| Book building, axis B corbel DK101: Vd = 718 kN, bw = h = 600 mm, d = 550 mm, av = 160 mm, C35 (γmc = 1.4), B420C, μ = 1.4 | Hd = 0.2·Vd | 143.6 kN | Hand calculation 143.6 kN | Exact match |
| Ast ((2/3)·Awf + An governs) / Asv | 1329.4 / 468.1 mm² | 1329.4 / 468.1 mm² | Exact match | |
| Handbook method As | 1000.8 mm² | — | TS 500 / handbook = 1.33 |
The value “1.7 lb = 1200” in the figure on p. 99 of the handbook cannot be reproduced with the handbook’s own definition (1.7 × 576 = 979 mm; an inconsistency within the handbook); the program calculates lb from the definition. The handbook places four rows of 2Ø8 stirrups within d/2; since the TS 500 layout spreads them over 2d/3, the area that remains within the d/2 band is compared for information.
Tests and in-program checks:
- The calculation core was tested with a test program independent of the program and with cases generated by a separately written reference calculation (Python): all 12,835 checks passed (TS 500 equations, scope and section limits, μ and γ options, shear demand with D, reinforcement selection, handbook additions, report texts). The error-detection power of the tests was measured with mutation trials in which errors were deliberately inserted into the calculation.
- The design of the corbels in the model is identical, for five corbels, to a calculation independent of the model with the same inputs; the derivation of the inputs, the shear demand with D, incomplete demand (NOT CHECKED), error cases and report rows are correct in 108 checks.
- Automatic demand: in the two-column overhead travelling crane model (crane inputs of the book, γK = 1.6), Vd = 515.97 kN (1.4·q·L/2 + 1.6·Rkol,max), Hd,ek = 48.92 kN (1.6·Rkol,max/10), Hd = 152.11 kN and av = 150 mm at the end column corbel match the hand calculation exactly; in the model with three columns per rail, Vd = 542.75 kN at the interior column. When a beam and the crane are seated on the same corbel, the two contributions are summed; for a pinned beam, the corbel demand is identical to the beam end force used by the connection design. The demand is counted as incomplete for a wrong face, a 10 cm elevation difference, a model without analysis and a switched-off crane (62 checks; the matching and envelope rules were additionally tested with 316 unit checks).
- Corbel tab: when OK is pressed without changes, the stored data is kept exactly; Cancel changes nothing; an invalid number, a missing h, an elevation that does not fit the column and an ambiguous direction in a rotated column do not close the window; the Calculate result is the same as the saved design; the multiple selection options, Undo, and the Turkish and English texts are correct (117 checks).
- Save and transitions: the corbel definitions and the KONSOL rows are restored exactly in both file formats (.sy4, .sbd); Undo / Redo restores the corbels; in copying, storey copying, mirroring and rotation the corbel directions are transformed correctly. In the Turkish and English reports, the KONSOL rows are printed correctly after the connection rows.
- No change in projects without corbels: in 12 test projects, the analysis and design outputs, the saved files and the report text are identical to the previous version (only the version number differs).
5. Building-scale comparison
The book building (40×75 m plan, 10 m height, mezzanine floor at elevation +5.00 between A–C, 200 kN overhead travelling crane between C–E; roof beams pinned to the columns, floor beams moment-resisting; different R–D in the lower part) was built in StatiCAD.
| Quantity | Book | StatiCAD | Assessment |
|---|---|---|---|
| SDS / SD1 | 1.384 / 0.477 | 1.3836 / 0.477 | Exact match |
| Tp in the equivalent method | 0.787 s | 0.787 s | Exact match |
| Total mass | 3243 t | 3165 t | −2.4% (model detail) |
| Storey force shares | 0.576 / 0.424 | 0.576 / 0.424 | Exact match |
| ν, (R̄a)lower, D̄lower | Section 4.3 | Section 4.3 | Exact match |
| Floor 1 relative drift (Y) | 0.011 | 0.0109 | Exact match |
| Floor beam support moment (axis B) | −988 kNm | −1021 kNm | +3% |
| Dominant period Tx / Ty (modal) | 1.107 / 1.042 s | 0.806 / 0.830 s (rigid roof) | See below |
Period difference: The book gives the dominant periods in a single mode; in the book’s model the roof is semi-rigid with Annex 8B equivalent braces. In StatiCAD, with the rigid roof assumption, the mezzanine frames and the cantilever column array vibrate like separate subsystems. When the same model was built independently in SAP2000 v27, the StatiCAD periods were reproduced within 1% (Section 6). Therefore the difference does not come from the finite element solution but from the roof diaphragm and frame idealization.
6. Independent finite element comparison with SAP2000 v27
The finite element model built by the program (joints, members, effective section modifiers, hinges, rigid end zones, floor masses) was rebuilt in SAP2000 with the same assumptions; in addition to the modal analysis, the reduced stiffness matrix was compared term by term by applying unit loads to the floor master joints.
| Model | Quantity | StatiCAD | SAP2000 | Difference |
|---|---|---|---|---|
| Square 3×3 axes, 2 floors | Tx / Ty | 0.6192 / 0.6192 s | 0.6240 / 0.6240 s | 0.8% |
| Rectangular 5×2 axes, 2 floors | Tx / Ty | 0.5677 / 0.6362 s | 0.5677 / 0.6316 s | 0.0% / 0.7% |
| Book building, without braces | Tx / Ty | 0.8135 / 0.8965 s | 0.8194 / 0.9005 s | 0.7% / 0.4% |
| Book building, with Annex 8B braces and purlins | Tx / Ty | 0.8314 / 0.9166 s | 0.8383 / 0.9209 s | 0.8% / 0.5% |
The diagonal terms of the reduced stiffness matrix agreed within 2.5%, and the mass matrices were found to be identical. In derivatives of the book building with the roof beams, crane girders or gutter beams removed, the two programs also agreed within 1%.
7. Overall assessment
- The nonprismatic member and the precast sections have been verified with closed-form solutions and SAP2000.
- The Annex 8B, overhead travelling crane, different R–D, connection, façade panel and foundation sliding calculations match the numerical examples in the book exactly, except for the points where the program applies the code on the safe side.
- The transfer of the crane load cases to the analysis model, the combinations and the design has been verified by hand calculation on a two-column test model and by the combination coverage check on two building models.
- The short corbel (TS 500 Clause 8.4) calculation reproduces the handbook example and the hand calculation of the book building’s corbel; the automatic demand matches the hand calculation exactly in the overhead travelling crane test models.
- The finite element solution agrees within 1% in periods with the independent model built in SAP2000 v27.
It is essential that all results produced by the software are checked by the responsible engineer.