Design of the structures

The structure design was performed in accordance with the provisions of NBCC 2010 (NRCC 2010) and the CSA S16-09 (CSA 2009) design standard for steel structures. The braced frames were first designed for earthquake resistance and then verified for wind loading conditions. In CSA S16, link beams in EBFs can be regular links that are part of roof and floor beams or replaceable links that are bolt connected to the beams. In this study, replaceable link beams with bolted end plate connections as proposed by Mansour et al. (2011) and depicted Figure 4-6a were used for all frames studied. The links were made of ASTM A992 W shapes with Fy = 345 MPa. The length of the links (e) was adjusted to yield in shear (short link behaviour) while maintaining link plastic rotations within the code prescribed limit of 0.08 radians. Following capacity design principles, the

b)

c)

EBF TBF M-TBF EBF TBF M-TBF-1 M-TBF-2

8 @ 3800 = 30 400 16 3860 800 @00 =

10 @ 7600 = 76 000

5 @ 7600 = 38 000

a) _{250 (typ.)}

N

Frame Studied

link beams were sized first to resist the code specified seismic forces as obtained from response spectrum analysis. All other members were designed to remain essentially elastic under the forces induced by the links reaching their probable resistances including strain-hardening effects combined with concomitant gravity loads effects. Braces and vertical ties were square tubing conforming to ASTM A500, grade C (Fy = 345 MPa) whereas beams and columns were ASTM A992 W shapes. For the columns, the same section was kept for two consecutive floors, as commonly done in practice.

In the NBCC, the seismic design base shear V is determined from:

(1) ^{a V E}

d o

S(T )M I W V  R R

where S is the design spectrum based on uniform hazard spectrum (UHS) ordinates established for a probability of exceedance of 2% in 50 years, Ta is the structure fundamental period, MV accounts for higher mode effects on base shear, IE is the importance factor, W is the seismic weight, and Rd

and Ro are the ductility- and overstrength-related force modification factors, respectively. For the site studied, S is equal to 1.20 for Ta < 0.2 s and 0.09 for Ta > 4 s. The other values are: S(0.5 s) = 0.82, S(1.0 s) = 0.38, and S(2.0 s) = 0.18. For intermediate periods, S is linearly interpolated. For the structures investigated, MV = 1.0 and the buildings were assumed to be of the normal importance category with IE = 1.0. For all three framing configurations, the values Rd = 4.0 and Ro

= 1.5 were used, as specified in NBCC for steel eccentrically braced frames. For design, the period Ta can be taken equal to the computed structure fundamental period except that it cannot exceed 0.05 hn for braced frames, where hn is the building height (in meters). The upper limits on Ta for the calculation of V were, therefore, equal to 1.52, 3.04, and 4.56 s, respectively, for the 8-storey, 16-storey and 24-storey buildings.

The final periods from the modal analysis for the first three lateral modes, T1, T2, and T3, are given in Table 4-1. As shown, T1 exceeded the code upper limit on Ta for all frames. The upper limit, therefore, governed the value of V. In addition, as per NBCC, V should not be less than the value determined for Ta = 2.0 s, which applies to the studied 16-storey and 24-storey buildings. For all frames, the response spectrum analysis (RSA) was used to determine the seismic induced storey

shears from which link shears were calculated. When using the RSA method, NBCC requires that the analysis results be scaled up by the ratio 0.8V/Vd when Vd is less than 0.8V. Herein, Vd is the dynamic base shear resulted from the RSA. The aforementioned correction applies to all studied structures. Values of 0.8V were equal to 3.68% W for the 8-storey frames and 2.4% W for the 16-storey and 24-16-storey frames. In NBCC and CSA S16, seismic 16-storey shears used to design the links must be further increased to account for P-delta effects and notional load effects.

For all EBFs, the links were designed individually to resist the shear forces obtained from the analysis. For the TBF system, identical links designed for the average link shear force computed over the entire building height were used at all levels (CL = constant link), as proposed by Rossi et al. (2007). For the 16-storey TBFs, a second design was performed where links were designed individually to resist the link shear forces from the analysis (VL = variable links). Constant link (CL) design was also adopted for the M-TBFs in anticipation of uniform inelastic response within each module. Hence, the same section was used for all links in a module; that section is determined to resist the average shear force demand over the height of the module. Values of the design factored link shears Vf including stability effects that were used in all frames are plotted in Figure 4-3. The resulting link factored shear capacity-to-demand ratios, Vr/Vf, are also presented in the figure. As shown, the ratios are close to 1.0 for all frames except at the roof level of the EBF structures due to minimum detailing requirement governing the design of lightly loaded links.

The design of the truss members for frames with elastic vertical trusses is described in the next section. After completion of the design for seismic resistance, seismic storey drifts including inelastic effects were verified against the NBCC limit of 2.5%hs, where hs is the storey height. No change was needed for the 8-storey and 16-storey structures. For the three 24-storey frames, the code limit was exceeded in the EBF top levels. Thus, to reduce the overall bending, the column sizes at the bottom ten storeys were increased and to satisfy the 2.5% hs limit, larger brace sections were required at levels 7 to 10.

Table 4-1 Building periods, steel tonnage and maximum seismic base shears (/frame).

Figure 4-3 Factored link shear forces Vf and factored link shear resistance to shear force Vr/Vf ratios for: a) 8-storey building; and b) 16-storey building.

The reference wind pressure at the site is 0.57 kPa for a return period of 50 years. Because the structure periods are longer than 1.0 s, wind loading was determined using the dynamic analysis procedure of NBCC in which the gust factor depends on the building dynamic properties. In the calculations, urban exposure conditions and a critical damping ratio of 1% were considered. For all structures, forces from factored wind loads were less than seismic induced forces, and maximum wind deflections were lower than the limit of 1/400 hs prescribed for these structures. Hence, wind loading did not influence the braced frame designs.