1 Introduction
2 Research Significance
3 Previous Research for Flexural Behavior of Arch Deck
4 Punching Shear Test Investigation
4.1 Design of the Specimen
Material | Member | Strength | Type |
---|---|---|---|
Concrete | Arch deck | 49.5 | OPC |
CIP | 38.5 | ||
Reinforcing bar | – | 400 | SD400 |
4.2 Performance Evaluation of the Grip Couplers
Index | Area (mm2) | Yield strength (N/mm2) | Ultimate strength (N/mm2) | Breaking point | Decision |
---|---|---|---|---|---|
H16 | 198.6 | 448.1 | 680.8 | Rebar | OK |
H19 | 286.5 | 420.0 | 617.7 | Rebar | OK |
H22 | 387.1 | 516.7 | 658.1 | Rebar | OK |
H25 | 506.7 | 462.4 | 613.6 | Rebar | OK |
H29 | 642.4 | 446.0 | 584.2 | Rebar | OK |
H32 | 794.2 | 425.0 | 575.9 | Rebar | OK |
Criterion | – | – | 560 | Rebar | OK |
4.3 Punching Shear Test Setup and Procedure
Loading sequence (kN) | Loading rate (mm/min) | Crack checking cycle (kN) |
---|---|---|
0–300 | 0.3 | – |
300–650 | 0.2 | 50 |
650–\({P}_{u}\) | 0.5 |
5 Punching Shear Test Results
Load | PCAD 1–1 | PCAD 1–2 | PCAD 1aver | PCAD 2 | |
---|---|---|---|---|---|
Test | Cracking load (\({P}_{\mathrm{cr},\mathrm{p},\mathrm{ test}})\) | 300.0 | 350.0 | 325.0 | 350.0 |
Yield load (\({P}_{y,p,\mathrm{ test}}\)) | 625.3 | 675.2 | 650.3 | 675.2 | |
Ultimate load (\({P}_{u,p,\mathrm{test}}\)) | 759.8 | 825.0 | 792.4 | 819.5 | |
KHBD | Design punching shear service load (\({V}_{\mathrm{ser},\mathrm{khbd}}\)) | 303.8 | |||
Design punching shear strength (\({V}_{u,\mathrm{khbd}}\)) | 746.1 | ||||
ACI 318 | Design punching shear strength (\({V}_{u,\mathrm{aci}}\)) | 750.4 | |||
Eurocode 2 | Design punching shear strength (\({V}_{u,\mathrm{ec}2}\)) | 724.5 | |||
Failure mode | Punching shear failure |
5.1 Punching Shear Capacity
5.2 Crack Patterns
5.3 Load–displacement Behavior
5.4 Load–Strain Behavior
5.5 Joint Behavior
6 Analytical Validation
6.1 Numerical Modeling
Material | Models/criteria | Young’s modulus (MPa) | Weight density (kN/m3) | Poisson’s ratio | Strength (MPa) |
---|---|---|---|---|---|
Concrete | Hordijk (Tension model) Thorenfeldt (Compression model) | 30,000 | 24.5 | 0.167 | AD: 49.5 CIP: 38.5 |
Rebar | von Mises (Yield criterion) | 200,000 | 78.6 | 0.3 | 400 |
6.2 Validation of the FEA Results for Deflection
6.3 Validation of the FEA Results for Strain
6.4 Validation of the FEA Results for Failure Mode
7 Prediction for Punching Shear Behavior Using Analytical Approach
7.1 Arching Action Verification of the SSAD and SSFD
7.2 Arching Action Verification of the PCAD and PCFD
Specimens | \({P}_{u}\) (kN) | \({V}_{u,\mathrm{khbd}}\) (kN) | \({V}_{u,\mathrm{aci}}\) (kN) | \({V}_{u,\mathrm{ec}2}\) (kN) | \({P}_{\mathrm{cr}}\) (kN) | \({V}_{\mathrm{ser},\mathrm{khbd}}\) (kN) | \({\Delta P}_{u}\) (mm) | \({\Delta V}_{\mathrm{ser}}\) (mm) | \({\Delta V}_{u}\) (mm) | \({\Delta V}_{u,\mathrm{test}}\)/\({\Delta V}_{u,\mathrm{FEA}}\) |
---|---|---|---|---|---|---|---|---|---|---|
PCAD 1–1 | 759.8 | 746.1 | 750.4 | 724.5 | 300 | 303.8 | 15.5 | 2.2 | 6.4 | 1.14 |
PCAD 1–2 | 825.0 | 350 | 14.8 | 1.5 | 4.7 | 0.84 | ||||
PCAD 1aver | 792.4 | 325 | 15.2 | 1.9 | 5.6 | 1.00 | ||||
PCAD 2 | 819.5 | 350 | 13.0 | 2.2 | 4.8 | 0.86 | ||||
PCAD FEA | 850 | – | 374 | – | 18.8 | 2.3 | 5.6 | – |
7.3 Prediction Formula for Punching Shear Resistance of AD
7.3.1 Modification for the Perimeter of Critical Section
7.4 Parametric Analysis of the PCAD
Parameters | Rebar ratio (%) | Concrete strength (MPa) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Design factor | 60 | 80 | AD (100) | 120 | 140 | 30 | 40 | AD (50) | 60 | 70 |
Punching shear strength (\({V}_{u,\mathrm{pro}}\), kN) | 720.5 | 768.4 | 808.8 | 844.2 | 875.8 | 720.5 | 768.4 | 808.8 | 844.2 | 875.8 |
7.5 Punching Shear Capacity Comparison for Predicted Code and Calibrated FEA
Model | Predicted strength (kN) | Strength ratio, \({V}_{u,\mathrm{fea}}/{V}_{u, \mathrm{pred}}\) | |||||||
---|---|---|---|---|---|---|---|---|---|
\({V}_{u,\mathrm{fea}}\) | \({V}_{u,\mathrm{pro}}\) | \({V}_{u,\mathrm{khbd}}\) | \({V}_{u,\mathrm{aci}}\) | \({V}_{u,\mathrm{ec}2}\) | \({V}_{u,\mathrm{fea}}/{V}_{u,\mathrm{ pro}}\) | \({V}_{u,\mathrm{fea}}/{V}_{u,\mathrm{ khbd}}\) | \({V}_{u,\mathrm{fea}}/{V}_{u,\mathrm{ aci}}\) | \({V}_{u,\mathrm{fea}}/{V}_{u, ec2}\) | |
60% | 782.0 | 720.5 | 629.3 | 581.3 | 649.3 | 1.09 | 1.24 | 1.35 | 1.20 |
80% | 816.0 | 768.4 | 692.7 | 671.2 | 690.1 | 1.06 | 1.18 | 1.22 | 1.18 |
Standard AD (100%) | 850.0 | 808.8 | 746.1 | 750.5 | 724.5 | 1.05 | 1.14 | 1.13 | 1.17 |
120% | 884.0 | 84.2 | 792.9 | 822.1 | 754.6 | 1.05 | 1.11 | 1.08 | 1.17 |
140% | 910.0 | 875.8 | 834.7 | 888.0 | 781.5 | 1.04 | 1.09 | 1.02 | 1.16 |
Mean | 1.06 | 1.15 | 1.16 | 1.18 | |||||
Standard deviation | 0.02 | 0.05 | 0.11 | 0.01 |