412
(a) (b) 413
414
(c) (d) 415
Fig. 12. Effective stress ratio (ESR) of T-sections at column DR of (a) 1%; (b) 2%; (c) 3% and 416
(d) 4%.
417 418
7. Comparison with Current AISC Seismic Provisions 419
All specimens with b/2tf and (h/tw)eq smaller than λr have a buckling strength larger than Py under 420
all loading schemes. Even when b/2tf exceeds λr, e.g. F5W1 specimens, a peak strength of at least 421
Py is still achieved. While not shown in this paper, the computational study also supports this 422
finding. As a result, the current λr limit is considered adequate for flanges in beams and columns 423
under the monotonic and cyclic loading schemes considered in this work.
424 425
From the experimental results, it is also clear that λhd is reasonable under monotonic loading. This 426
assessment is based on the observed good post-buckling responses exhibited by monotonically 427
loaded specimens with F1 and F2 flanges. The same can be said for specimens subjected to cyclic 428
axial loading for demands under the CB protocol. The degradation in tensile strength is much 429
milder than the post-buckling degradation seen under compression, which combined, will likely 430
allow most available cross-sections to carry at least 80% of their plastic moment capacity up to 431
4% rotation. Therefore, current limits on λhd for flanges appear to provide appropriate highly 432
ductile behavior for beams under cyclic loading.
433 434
Specimen F2W1-CC, which has a b/2tf smaller than the current λhd limit, exhibits an ESR of 0.78Py
435
at a NAD corresponding to 4% column drift. Equation (1) indicates that ESR reaches 0.65 at the 436
highly ductile slenderness limit. The evidence in this paper suggests that, barring other failure 437
modes such as global instability, a W24 column with slenderness characteristics similar to those 438
considered would be able “to withstand significant plastic rotation of 0.04 rad or more” per current 439
design philosophy and still support a substantial axial load. However, the key question of whether 440
the moment or axial capacities have been degraded too much by cyclic FLB is not addressed in 441
current seismic provisions. Unlike beams, where current seismic design provisions require that the 442
moment capacity be at least 80% of the plastic capacity at 4% drift, columns have no such 443
requirement. The research in this paper points out the need for more precise performance 444
requirements for columns.
445 446
8. Conclusions 447
The effect of cyclic FLB on the capacity of structural members in special moment frames was 448
experimentally and computationally investigated in this study. Nineteen half-scale T-section 449
specimens were axially loaded to represent the flange/web subassembly in the plastic hinge region 450
of a wide flange section under combined axial and flexural loading. The specimens were selected 451
to cover a wide range of slenderness ratios and subjected to three different loading schemes. The 452
loading schemes included monotonic compression, meant to obtain the flange capacity without 453
cyclic degradation, and two cyclic axial loading histories, one that reflected the axial demands on 454
beam flanges and another for column flanges under cyclic drift loading. To further study the cyclic 455
behavior of column flanges and justify the observation from the test results, a parametric 456
computational study with different slenderness ratios was performed. The effect of slenderness 457
ratios on column compression capacity due to flange strength degradation was then evaluated.
458 459
The test results showed that most T-section specimens could reach a peak strength of Py regardless 460
of the value of b/2tf, but b/2tf substantially influenced post-buckling behavior. Under monotonic 461
loading, the current value for λhd for a flange was shown to be a boundary between large buckling 462
capacity and rapid degradation after reaching peak strength. The effect of (h/tw)eq, on the other 463
hand, was shown to be secondary and became significant only when both b/2tf and (h/tw)eq were 464
large and negatively interacted with each other.
465 466
Specimens under the CB loading protocol exhibited much more severe compressive strength 467
degradation than the monotonic protocol. Depending on a specimen’s b/2tf, the compressive 468
strength dropped to as low as 0.53 Py at deformation levels that corresponded to 4% beam rotation.
469
The tensile strength had a much milder degradation rate than the compressive strength. However, 470
the required tensile strain for recovery of tensile strength after unloading from compression 471
depended on the slenderness ratio due to the effort of stretching out the buckled shape.
472 473
The backbone curves of specimens under CC loading were much higher than those for specimens 474
under CB loading and were quite close to the responses under M loading. This result was attributed 475
to the smaller tensile plastic strain demands and led to a milder cyclic degradation rate under 476
compression. Nevertheless, the degradation at higher drift levels could be substantial and could 477
compromise the axial and flexural capacities of the columns.
478 479
The experimental and computational data was used to evaluate the current AISC seismic 480
provisions. It was shown that the current λr limit is adequate for flanges in beams and columns 481
under the monotonic and cyclic loading schemes considered in this work. It was also shown that 482
λhd is reasonable for members under monotonic loading and CB loading, which is representative 483
of the demands seen in beams. The conclusion for λhd and λmd under CC loading, representative of 484
the demands seen in columns, was not definitive because the performance expectations of the 485
AISC seismic provisions are not as explicit as they are for beams. The research outlined in this 486
paper provides useful input to refine current specifications to address this issue.
487 488
The evaluation in this paper is only valid for the specific wide flange section sizes, loading 489
protocols and range of parameters studied. Although this research points out specific drawbacks 490
in the current AISC seismic provisions, additional research is needed to broaden the results and 491
draw comprehensive conclusions that warrant specification changes.
492 493
Acknowledgements 494
This work was supported by the University of Michigan and US NSF grant number ACI-1638186.
495
Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the 496
authors and do not necessarily reflect the views of the sponsor.
497 498
References 499
[1] ANSI/AISC 360-16 Specification for Structural Steel Buildings. Chicago, IL: American 500
Institute for Steel Construction; 2016.
501
[2] ANSI/AISC 341-16 Seismic Provisions for Structural Steel Buildings. Chicago, IL: American 502
Institute for Steel Construction; 2016.
503
[3] Sawyer HA. Post-Elastic Behavior of Wide-Flange Steel Beams. Journal of the Structural 504
Division ASCE 1961; 87 (ST8): 43–71.
505
[4] Lay MG. Some Studies of Flange Local Buckling in Wide-Flange Shapes. Journal of the 506
Structural Division ASCE 1965; 91(6): 94-116.
507
[5] Bansal JP. The Lateral Instability of Continuous Steel Beams. CESRL Dissertation No. 71-1.
508
Austin, TX: University of Texas; 1971.
509
[6] Kemp AR. Factors Affecting the Rotation Capacity of Plastically Designed Members. Struct 510
Eng 1986; 64B(2): 28-35.
511
[7] Richards PW, Uang C-M. Effect of flange width-thickness ratio on eccentrically braced frames 512
link cyclic rotation capacity. J Struct Eng ASCE 2005; 131(10): 1546–1552.
513
[8] Newell JD, Uang C-M. Cyclic behavior of steel wide-flange columns subjected to large drift.” J 514
Struct Eng ASCE 2008; 134(8):1334-1342.
515
[9] Cheng X, Chen Y, Nethercot DA. Experimental study on H-shaped steel beam-columns with 516
large width-thickness ratios under cyclic bending about weak-axis. Eng Struct 2013; 49: 264-517
274.
518
[10] Elkady A, Lignos DG. Analytical investigation of the cyclic behavior and plastic hinge 519
formation in deep wide-flange steel beam-columns. Bull Earthquake Eng. 2015; 13: 1097-520
1118.
521
[11] Fogarty J, El-Tawil S. Collapse resistance of steel columns under combined axial and lateral 522
loading. J Struct Eng ASCE 2015; 142(1): 04015091.
523
[12] Fogarty J, Wu T.-Y., El-Tawil S. Collapse Response and Design of Deep Steel Columns 524
Subjected to Lateral Displacement. J Struct Eng ASCE 2017; 143(9): 04017130 525
[13] Wu T-Y, El-Tawil S, McCormick J. Highly ductile limits for deep steel columns. J Struct Eng 526
ASCE 2018; 144(4): 04018016.
527
[14] Altair Computing. Hypermesh Version 12.0. Troy, MI: Altair Engineering Inc.; 2013.
528
[15] Hallquist J. LS-DYNA. Livermore, CA: Livermore Software Technology Corp; 2013.
529
[16] Engelmann BE, Whirley RG, Goudreau GL. A simple shell element formulation for large-530
scale elastoplastic analysis. In: Noor AK, Belytschko T, and Simo JC, editors. Analytical and 531
computational models of shells. New York: ASME, New York; 1989.
532
[17] Huang Y, Mahin SA. Simulating the inelastic seismic behavior of steel braced frames 533
including the effects of low-cycle fatigue. Rep. No. PEER 2010/104. Berkeley, CA: Pacific 534
Earthquake Engineering Research Center, Univ. of California at Berkeley; 2010.
535
[18] Arasaratnam P, Sivakumaran KS, Tait MJ. True stress-true strain models for structural steel 536
elements. ISRN Civ Eng 2011. http://dx.doi.org/10.5402/2011/656401 537
[19] Wu T-Y, El-Tawil S, McCormick J. Seismic collapse response of steel moment frames with 538
deep columns. J Struct Eng ASCE 2018; 144(9): 04018145.
539
[20] MacRae GA, Carr AJ, Walpole WR. The seismic response of steel frames. Research Rep. No.
540
90-6. New Zealand: Dept. of Civil Engineering, Univ. of Canterbury; 1990.
541
[21] ASTM E8/E8M-15a Standard test methods for tension testing of metallic materials. West 542
Conshohocken, PA: ASTM; 2015.
543
[22] Ozkula G, Harris J, Uang C-M. Observations from cyclic tests on deep, wide- beam-column 544
columns. AISC Eng. J. 2017; 54(1): 45–61.
545
[23] Elkady A, Lignos DG. Full-Scale Testing of Deep Wide-Flange Steel Columns under 546
Multiaxis Cyclic Loading: Loading Sequence, Boundary Effects, and Lateral Stability Bracing 547
Force Demands. J Struct Eng ASCE 2017; 144(2): 04017189.
548
[24] Ozkula G, Harris J, Uang C-M. Classifying Cyclic Buckling Modes of Steel Wide-Flange 549
Columns under Cyclic Loading. Structures Congress 2017: 155-167.
550