1 Introduction
2 Experimental Plan
2.1 Testing Specimens
MEM-1:5 | MEM-1:1 | MEM-1:0 | |||
---|---|---|---|---|---|
Material properties | Longitudinal bars | Yield strength (MPa) | 353.33 | 353.33 | 353.33 |
Ultimate strength (MPa) | 573.33 | 573.33 | 573.33 | ||
Elastic modules (GPa) | 200 | 200 | 200 | ||
Diameter (mm) | 8 | 8 | 8 | ||
Stirrups | Yield strength (MPa) | 276.7 | 276.7 | 276.7 | |
Ultimate strength (MPa) | 446.7 | 446.7 | 446.7 | ||
Elastic modules (GPa) | 200 | 200 | 200 | ||
Diameter (mm) | 6 | 6 | 6 | ||
Spacing (mm) | 70 | 70 | 70 | ||
Concrete | Compressive strength of prism specimen (MPa) | 39.62 | 35.40 | 40.92 | |
Elastic modules (GPa) | 36.7 | 34.5 | 34.4 | ||
Loading conditions | Eccentricity (mm) | 166.25 (L/40) | 831.25 (L/8) | Pure torsion | |
T-BM ratio | 1:5 | 1:1 | 1:0 |
2.2 Experimental Setup
2.3 Location of Potential Critical Sections
2.4 Arrangement of Measurement Points and Testing Procedure
3 Test Results and Discussion
3.1 Failure Procedure
MEM-1:5 | MEM-1:1 | MEM-1:0 | ||
---|---|---|---|---|
Flexural cracking | Load percentage | 13% | 11% | 12% |
Load detail | P = 27.0, e = 0.166, T = 4.5, M = 22.5 | P = 11.5, e = 0.831, T = 9.6, M = 9.6 | P = 13.0, e = 1.33, T = 17.3, M = 0 | |
Location | Top of loaded web at support | Top of loaded web at support | Top of loaded web at support and top of unloaded web at mid-span | |
Diagonal cracking | Load percentage | 49% | 33% | 24% |
Load detail | P = 103.0, e = 0.166, T = 17.1, M = 85.5 | P = 36.6, e = 0.831, T = 30.4, M = 30.4 | P = 26.8, e = 1.33, T = 35.7, M = 0 | |
Location | External surface of loaded web at 3L/8-section | External surface of loaded web at 5L/16-section | External surfaces of both webs at L/4-section | |
Steel bar yielding | Load percentage | 57% | 58% | 60% |
Load detail | P = 119.3, e = 0.166, T = 19.8, M = 99.0 | P = 64.3, e = 0.831, T = 53.4, M = 53.4 | P = 66.3, e = 1.33, T = 88.2, M = 0 | |
Location | Top of loaded web at support | Top of loaded web at support | Top of loaded web at support and top of unloaded web at mid-span | |
Stirrup yielding | Load percentage | Not yield | Not yield | 86% |
Load detail | Not yield | Not yield | P = 95.1, e = 1.33, T = 126.4, M = 0 | |
Location | Not yield | Not yield | External legs of both webs at L/4-section | |
Ultimate state | Load detail | P = 209.6, e = 0.166, T = 34.8, M = 174.0 | P = 110.7, e = 0.831, T = 92.0, M = 92.0 | P = 110.5, e = 1.33, T = 147.0, M = 0 |
Location | Ductile flexural failure at both support and mid-span sections of loaded web | Ductile flexural failure at both support and mid-span sections of loaded web | Ductile flexural failure at both support and mid-span sections of two webs |
3.2 Rotations, Deflections and Ductility
Rotational ductility coefficient | Deflection ductility coefficient | |
---|---|---|
MEM-1:5 | 9.2 | 10.3 |
MEM-1:1 | 9.3 | 9.5 |
MEM-1:0 | 8.4 | No deflection |
3.3 Crack Patterns
3.4 Failure Modes
4 Method to Calculate the First Cracking Load and the Ultimate Load
4.1 Calculation of the Flexural Cracking Load
Beams | Cracking torque (kNm) | Test/calculation | |
---|---|---|---|
Test | Calculation | ||
MEM-1:5 | 4.5 | 4.7 | 0.96 |
MEM-1:1 | 9.6 | 10.2 | 0.94 |
MEM-1:0 | 17.3 | 16.9 | 1.02 |
MEM-Collins-1:0 | 23 | 18.5 | 1.24 |
Average value | 1.04 | ||
SD | 0.12 | ||
Coefficient of variation | 11.5% |
4.2 Calculation of the Ultimate Load
4.2.1 Equivalent Action Acting on the Loaded Half U-Section at Mid-Span
4.2.2 Ultimate Equilibrium Equation on the Loaded Half U-Section at Mid-Span
4.2.3 Comparison of Calculating Results and Testing Results
Beams | Ultimate torque (kNm) | Test/calculation | |||||
---|---|---|---|---|---|---|---|
Test | Proposed method | Elfgren et al. (1974) | Luccioni et al. (1991) | Proposed method | Elfgren et al. (1974) | Luccioni et al. (1991) | |
MEM-1:5 | 34.8 | 35.5 | 28.9 | 38.3 | 0.98 | 1.20 | 0.91 |
MEM-1:1 | 92.0 | 88.5 | 71.8 | 111.5 | 1.04 | 1.28 | 0.83 |
MEM-1:0 | 147.0 | 139.0 | 107.3 | 198.2 | 1.06 | 1.37 | 0.74 |
MEM-Collins-1:0 | 266.0 | 248.9 | 198.7 | 369.8 | 1.07 | 1.34 | 0.72 |
Average value | 1.04 | 1.29 | 0.80 | ||||
SD | 0.04 | 0.07 | 0.07 | ||||
Coefficient of variation | 3.8% | 5.4% | 8.8% |