BRACED FRAMES
5.6 RESPONSE OF BRACED FRAMES TO CYCLIC LATERAL LOADS When the externally applied loading becomes complex, for example, time
dependent, resulting in stress reversals, recent research work1–4indicates that the rules of simple geometry no longer work and are replaced by more pow-erful laws such as compatibility of deformations and other factors.
The braced frame of this project is a split-braced frame; in a graphical sense, the diagonal brace elements run between the first and third floors and then from the third to the fifth level (roof). In other words, the brace system connects the odd-numbered floors and crisscrosses at every even-numbered floor (in our building, second and fourth floors). If we were to not connect
136 SEISMIC STEEL DESIGN: BRACED FRAMES
the crisscrossing joint to the even-numbered floors, these floors would be free to displace laterally and cause the frame columns to bend considerably be-tween the brace points of first and third and the third and fifth levels. It would be a hybrid structure, partly braced frame, partly MRF, and the values of a braced frame that provide economy and stiffness against displacement would be lost.
What makes this a split-braced frame is that the crisscrossing points of the diagonal braces are also tied into the second and fourth floors, which provides sufficient stiffness to the system and lateral support to the columns at each floor level. If the frame were subjected only to lateral static loads, the vertical and horizontal force components of the braces would balance out between each other and the externally applied load at each nodal point, including the crisscrossing point.
If asked whether the brace reactions cause bending of the second-floor beam connected to the diagonal bracings, a reader with structural background would answer, without hesitation, that there will be no bending if the CGs of the members intersect at the work point—our basic assumption for this proj-ect. However, the issue is complex in an earthquake because we are not dealing with statically applied lateral loads. The earthquake causes serious reversals of structural deformations, inertial loads, and internal forces.
As the ground movement at the base reverses rapidly, as much as two to four cycles per second, the structure sways left and right with high-frequency response. A picture of, say, the second floor taken with a sufficiently sensitive high-speed camera would demonstrate that the floor has displaced to the right while the base of the structure has moved to the left and the structure is leaning heavily on the right diagonal brace of the inverted V, putting the brace in compression. Due to the tendency of a compressed member to buckle, the brace will bow out under compression (Figure 5.5).
Tests on structures subject to similar cyclic loading showed a marked drop in element stiffness in the compression brace as compared to the stiffness of the corresponding diagonal tension brace of the inverted-V system. Because of the marked difference in element stiffness, the diagonal tension brace picks up a considerably larger share of the lateral inertial loads acting on the struc-ture as compared to the compression brace.
Research has also proved that, because of the imbalance of axial loads in the diagonal braces, a considerable unbalanced vertical-load component exists at the floor-beam / diagonal brace connection. The unbalanced vertical reaction causes bending of the connecting floor beam, a phenomenon that was not envisaged under the purely theoretical concepts of braced frames subjected to static loading. The bending of the beam intensifies as the stiffness of the compression brace deteriorates under cyclic loading.
If the floor beam is not properly engineered it might undergo local or torsional buckling. Therefore it is imperative that
5.6 RESPONSE OF BRACED FRAMES TO CYCLIC LATERAL LOADS 137
Figure 5.5 Deformation of a one-story brace frame module subjected to lateral load.
(a) the brace-to-beam joint be laterally supported against buckling and (b) the choice of beam be such that the section is compact and the laterally
unsupported length is equal to or smaller than Lp to allow a fully plasticized moment response.
The special provisions of the 1997 UBC in CHAP. 22, DIV. IV, reflect re-search results when calling for compact sections and a minimum strength for lateral bracing to beam flanges equal to 1.5% of the nominal yield strength times the beam flange area to resist lateral buckling of the beam.
The above-described phenomena, demonstrated on one story of the struc-ture, apply to all floor beams and diagonal braces. The bowing out of the diagonal brace has other serious consequences such as stress reversals; these are generated mostly in the diagonal bracings when the structure undergoes repetitive cyclic loading. When the cross-bracing bows out under compres-sion, the structure, subjected to reversals, displaces in the opposite direction, inducing high tensile force into the diagonal member that was, an instant before, in compression. Because of its relatively sluggish response to stress reversals, the bowed-out member will not straighten out fast enough to re-spond to the high-tension demand of the force reversal. The result is a whip-lash of dynamic impact prone to cause joint damage. This phenomenon was observed in experimental tests on steel specimens as well as in structures damaged by the Northridge earthquake.
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The slenderer the diagonal brace element, the stronger the dynamic impact and potential damage to the joint. Recent research work has verified this fact.
Consequently, the 1997 UBC, CHAP. 22, DIV. IV, special detailing provision 9.2.a, limits the slenderness ratio of the brace member to
L 720 r ⱕ 兹Fy
In addition, test results and observation of earthquake-damaged buildings have shown that slender components of brace members could undergo local buck-ling, resulting in brace damage. Thus the 1997 UBC does not allow slender components that do not fall into the category of compact or noncompact sections.
To avoid local buckling and subsequent brittle fracture, 1997 UBC, CHAP.
22, DIV. IV, 9.2.d, restricts the diameter-to-wall thickness and flat-width-to-wall thickness ratios of structural pipes and tubing. In addition, the code encourages the designer to increase the ‘‘design strength of the brace member . . . at least 1.5 times the required strength using Load Combinations 3-5 and 3-6 . . . [for] V and Inverted V type bracing’’ (CHAP. 22, DIV. IV, 9.4.a.4).
These load combinations are similar in nature to formulas (12-5) and (12-6) of CHAP. 16, 1612.2.1. When increasing the brace member design strength by 50%, UBC 1997 clearly asks the designer to compensate for the dynamic impact on deflected shape and for the stress reversals normally not taken into account in structural calculations.