Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach
Abstract
:1. Introduction
2. Theory
2.1. Transverse Shear Stress Distribution Within a Cross-Section—Analytical Formulation
2.2. Transverse Shear Stress Distribution Within a Cross-Section—Numerical Formulation
2.3. Constant Transverse Shear Stress Distribution
3. Results
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Area | |
Area of Discrete Element | |
Area Used to Calculate | |
Numerical Index Where Stress Is Calculated | |
Constant Relating and | |
Centroid of Discrete Element | |
Flare-out Point | |
Height of Discrete Element | |
Cross-section Height | |
Area Moment of Inertia | |
Area Moment of Inertia of Discrete Element | |
Element Index | |
Neutral Axis of Cross-section | |
Total Number of Discrete Elements for Top Half of Cross-section | |
First Moment of Area | |
First Moment of Area Where Transverse Shear Stress is Calculated | |
Sectional Width of Cross-section Where Transverse Shear Stress is Calculated | |
Thickness of Discrete Element | |
Shear Force Carried by the Section, Found from the Shear Force Diagram | |
Vertical Component of Cross-section | |
Centroid of Area Used to Calculate | |
Centroid of Component Area Used to Calculate | |
Horizontal Component of Cross-section | |
Half Width of Discrete Element Where Transverse Shear Stress is Calculated | |
Half Width of Discrete Element | |
Half Width of Top Discrete Element | |
Ratio of Widest to Thinnest Discrete Element | |
Transverse Shear Stress | |
Average Transverse Shear Stress | |
Transverse Shear Stress at Discrete Element a | |
Efficiency of Cross-section | |
Maximum Transverse Shear Stress |
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100 | 41.81 | 43.21 | 0.1717 | 99.00% |
200 | 85.09 | 86.43 | 0.1206 | 99.50% |
300 | 128.43 | 129.64 | 0.0987 | 99.67% |
400 | 171.80 | 172.85 | 0.0865 | 99.75% |
500 | 215.18 | 216.07 | 0.0772 | 99.80% |
600 | 258.57 | 259.28 | 0.0710 | 99.83% |
700 | 301.97 | 302.49 | 0.0658 | 99.86% |
800 | 345.37 | 345.71 | 0.0613 | 99.88% |
900 | 388.77 | 388.92 | 0.0578 | 99.89% |
1000 | 432.18 | 432.13 | 0.0551 | 99.90% |
1100 | 475.59 | 475.35 | 0.0523 | 99.91% |
1200 | 519.00 | 518.56 | 0.0505 | 99.92% |
1300 | 562.41 | 561.77 | 0.0485 | 99.92% |
1400 | 605.82 | 604.99 | 0.0465 | 99.93% |
n | log(n) | Ratio Name | |||
---|---|---|---|---|---|
7 | 0.84 | 1.0 | 1 | Ten | 85.51706% |
9 | 0.96 | 100 | 2 | Hundred | 89.13779% |
12 | 1.06 | 1000 | 3 | Thousand | 91.31023% |
18 | 1.27 | 1.0 × 106 | 6 | Million | 94.56880% |
25 | 1.40 | 1.0 × 109 | 9 | Billion | 96.05011% |
32 | 1.51 | 1.0 × 1012 | 12 | Trillion | 96.89651% |
235 | 2.37 | 1.0 × 10100 | 100 | Googol | 99.57403% |
702 | 2.85 | 1.0 × 10303 | 303 | Centillion | 99.85754% |
1400 | 3.15 | 1.0 × 10606 | 606 | 99.92857% | |
2319 | 3.37 | 1.0 × 101000 | 1000 | 99.95687% | |
2,314,103 | 6.36 | 1.0 × 101,000,000 | 1.0 × 106 | 99.99995% | |
2.31 × 109 | 9.36 | 1.0× 101,000,000,000 | 1.0× 109 | 99.99999% |
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Share and Cite
Bednarz, E.T.; Mulligan, R.R. Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach. Appl. Syst. Innov. 2020, 3, 3. https://doi.org/10.3390/asi3010003
Bednarz ET, Mulligan RR. Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach. Applied System Innovation. 2020; 3(1):3. https://doi.org/10.3390/asi3010003
Chicago/Turabian StyleBednarz, Edward T., and Ryan R. Mulligan. 2020. "Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach" Applied System Innovation 3, no. 1: 3. https://doi.org/10.3390/asi3010003
APA StyleBednarz, E. T., & Mulligan, R. R. (2020). Investigation of a Cross-Section with a Constant Transverse Shear Stress Distribution Using a Numerical Approach. Applied System Innovation, 3(1), 3. https://doi.org/10.3390/asi3010003