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.
- 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 | 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.
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 |
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 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.