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Influence of seismic design requirements and building period on the design of low-rise steel buildings
Advances in Steel Structures, Vol. II Z.Y. Shen et. al. (Eds.) © 2005 Elsevier Ltd. All rights reserved.
1359
INFLUENCE OF SEISMIC DESIGN REQUIREMENTS AND BUILDING PERIOD ON THE DESIGN OF LOW-RISE STEEL BUILDINGS R. Tremblay and C.A. Rogers 'Department of Civil Geological and Mining Engineering Ecole Polytechnique of Montreal, Montreal, Canada H3C 3A7 ^Department of Civil Engineering and Applied Mechanics, McGill University Montreal, Canada H3A 2K6
ABSTRACT A Study is performed to examine the impact of capacity design provisions and period limitations prescribed in Canadian design codes and standard on the cost of low-rise steel buildings. Alternative design strategies are also investigated, including: design without a capacity based approach, capacity design with ductile bracing components, and capacity design assuming the steel roof diaphragm forms the main energy dissipation element in the seismic force resisting system. The effects of relaxing period limitations are also examined. The results show that capacity design provisions significantly influence the cost of the structure, especially when tension-compression bracing is used. Substantial savings can be realized with the use of a period obtained from methods of mechanics that account for diaphragm flexibility. Allowing inelastic response in the roof diaphragm can also contribute in reducing the cost of the structure. KEYWORDS Diaphragm, steel, roof deck, bracing members, seismic, earthquakes, period INTRODUCTION Single-storey steel buildings are used for light industrial, commercial and recreational purposes, and represent a vast proportion of the building stock in Canada. As illustrated in Fig. la, the seismic force resisting system (SFRS) of these structures typically includes a steel roof deck diapliragm that transfers horizontal loads to vertical steel bracing bents. The roof diaphragm is made of corrugated steel deck panels that are fastened to each other and to the supporting beams and joists (Fig. lb). These diaphragms are relativelyflexibleand in-plane roof deformations due to lateral loads must be accounted for in design, as illustrated in Fig. Ic. In seismically active regions, structures designed according to modem building codes are expected to experience some degree of inelastic response under strong earthquakes. Current practice requires that the inelastic demand be limited to the vertical bracing system and the roof diaphragms must then be designed to resist lateral loads that correspond to the actual capacity of the vertical elements. Seismic design loads also typically vary with the fundamental period of the structure.
1360
and empirical expressions are prescribed in building codes to estimate the period to be used in design. These formulae have been typically derived for multi-storey structures with rigid floor and roof diaphragms and do not reflect the behaviour of low-rise steel buildings with flexible roof diaphragms. b)
a) Roof Beams (typ.) Steel Deck Units (typ.)
Column (typ.)
c)
Roof Dlaphragm(El, G')
d) . Code Empirical Period
N
^bracing-
TCt t f t t t t f t t t Figure 1: Typical low-rise steel building: a) Main structural components; b) Detail of roof deck panels; c) Plan view of laterally deformed building; d) Period and design spectrum. Past studies have shown that the dynamic response of structures can be affected by the flexibility of the roof diaphragm (e.g., Tremblay and Stiemer 1996). In particular, the fundamental period of vibration is lengthened and, as illustrated in Fig. Id, significant cost savings could be anticipated if longer period values were adopted for design. Recent experimental investigations (Tremblay et al. 2004; Essa et al. 2003) also indicate that deck panels and their connections, when properly detailed, could act as the inelastic fuse in the SFRS, instead of the brace members. Considering that the price of the diaphragm dominates the overall SFRS cost for single-storey buildings, reducing the diaphragm design seismic loads could represent a second promising avenue for reducing construction costs. The objective of this study was to evaluate the impact of recent seismic design provisions on the SFRS costs for singlestorey steel buildings and to assess possible cost savings that would result from applying alternative design options such as relaxing period limits and allowing diaphragm inelastic response. A parametric study was carried out in which a total of seven different design strategies were investigated for different building dimensions, bracing configurations and ductility levels. Further details on this research can be found in Tremblay and Rogers (2005).
DESIGN AND DESCRIPTION OF THE BUILDINGS STUDIED The seismic provisions in the CSA-S16-01 standard (CSA 2001) and the upcoming 2005 National Building Code of Canada (NBCC) (Heidebrecht 2003) were used as a basis for the study. In NBCC, the design seismic design loads are a function of the building period, for which the design period, Ta,
1361
for braced steel frames is equal to 0.025 //„, where //„ is the building height. Ahematively, the period of the structure obtained from methods of mechanics can be used for Ta, except that such value must not exceed 0.050 /i„. To account for the SFRS ductility and actual capacity, the elastic seismic loads in NBCC are respectively divided by a ductility-related and an overstrength-related force modification factors, Rd and RQ. Inelasticity must be constrained to the bracing members and, hence, the Rd and Ro factors depend solely on the characteristics of the vertical bracing system. Three different braced steel frame categories are specified in NBCC: Moderately Ductile (Type MD, Rd = 3.0), Limited-Ductility (Type LD, Rd = 2.0) and Conventional Construction (Type CC, Rd ~ 1.5). For all categories, Ro is equal to 1.3. Capacity design is prescribed in CSA-S16 for Type LD and MD braced frames. Bracing members must meet slendemess ratio and cross-section width-to-thickness ratio limits to ensure ductile inelastic response. These limits are less stringent for Type LD (Rd = 2.0) compared to Type MD frames (Rd = 3.0). Beams, columns, connections and roof diaphragms must be able to resist forces corresponding to the expected capacity of the bracing members, i.e. the unfactored resistance of the braces obtained with the probable steel yield stress. Seven different design strategies were considered in the parametric study. Design 0 is in accordance with code provisions, i.e. with energy dissipation being concentrated in the bracing members, except that the roof diaphragm is designed for the prescribed seismic loads, not for the forces associated to the actual capacity of the vertical bracing. An iterative design was perfoniied by initially setting the design period equal to 0.025 /;„ and then modifying the design using the period computed from previous design iterations. The process was halted when the seismic loads remained unchanged or the upper limit Ta = 0.050 A„ was attained. All SFRS components were selected to achieve a minimum cost design. If needed, the SFRS was stiffened to meet code drift limitations. Design lA is identical to Design 0 except that strict capacity design rules were applied to prevent inelastic action forming in the roof diaphragm. However, the diapliragm design forces need not exceed elastic level forces, i.e. those corresponding to seismic loads calculated with RoRd = 1.0. For Design IB, the building period at each design cycle was estimated with consideration of the roof diaphragm flexibility, without applying the 0.05 /;„ limit. Designs 2A and 3A are included to study the possibility of reducing building costs by allowing inelasticity in the roof diaphragm. In Design 2A, the procedure used in Design lA was applied except that the design forces for the diapliragm system were limited to those corresponding to RoRd = 1.95, instead of RoRd = 1.0. Design 3 A is a different approach in which the roof diapliragm is the main energy dissipating element of the SFRS. The diaphragm is designed first, using Ro = 1.67 and Rd = 2.0, as proposed by Tremblay et al. (2004) for regular buildings with mechanical deck fasteners, and the perimeter members and bracing bents are then sized to resist the forces associated with the probable shear capacity of the diaphragm. This results in a weak diapliragm-strong brace design. For Designs 2A and 3A the design period was limited to 0.050 //„. That limit was waived in Designs 2B and 3B. The study was performed on rectangular single-storey steel buildings assumed to be located in Vancouver, BC. Seven different building areas from 600 to 4200 m^ and four different aspect ratios (1.0, 1.5, 2.0 and 2.5) were examined. In addition, the building height was varied between 4.8 and 10.8 m, resulting in a total of 227 different building sizes. X-bracing symmetrically distributed along the four perimeter walls were used as the vertical bracing system. Two different bracing systems were considered: tension-compression bracing (T/C) and tension-only bracing (T/0), i.e. frames in which the seismic loads were assumed to be resisted only by the tension-acting braces. For each case, the three braced frame categories (Types MD, LD and CC) were considered, when applicable. The roof deck consisted of 914 mm wide steel panels with a trapezoidal profile 38 mm deep with the flutes spaced at 152 mm apart. The panels were connected to one another with self-tapping screws along the sidelaps and to the underlying frame with powder actuated fasteners. For each structure and design option, the total cost of the SFRS was estimated including the braces, the columns of the bracing bents, the perimeter members, the deck sheets, and the deck fasteners. That cost was then summed and divided by the buildmg area.
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RESULTS OF THE PARAMETRIC STUDY Table 1 gives the average SFRS costs per unit floor for each bracing system and design strategy (weighted average of the 227 building cases). Figure 2a presents the SFRS unit cost of all Design 0 T/C and T/0 buildings. In each graph, three sets of values are given for each building area, depending on the system category, and the results for Types MD and CC have been slightly shifted to the left and the right of Type LD results to help distinguish between the tliree cases. This representation has also been used in subsequent similar figures. The results show that using a higher Rd factor generally leads to a reduced SFRS cost, regardless of the building area and the bracing configuration (T/C v.v T/0 systems), indicating that the benefits of reducing the seismic loads overcome the negative impact of brace ductility detailing requirements for Rd = 2.0 and 3.0 structures. TABLE 1 WEIGHTED AVERAGE OF ESTIMATED COSTS OF THE SFRS ( $ / M ^ )
System 0 53.10 62.60 69.10 52.90 61.80 69.40
T/C Type MD T/C Type LD T/C Type CC T/O Type MD T/0 Type LD T/0 Type CC a)
lA 84.00 93.90 93.80 61.90 75.10 75.10
Design No. 2A 71.40 74.80 69.80 61.70 69.30 68.70
IB 80.70 91.00 90.00 49.10 49.80 55.50
2B 59.40 62.80 57.80 45.80 46.00 47.10
3A
3B
58.90
45.30
60.30
43.90
100.0 ^
80.0
C/3
60.0
s-
40.0
o V> 8 20.0
e
iii,!i||l||l|l'|l'|l 1+
T/C Bracing o o Type MD * o Type LD <• + Type CCJ
w a:
60 0
u.
^ o to
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8
200
III
,|i||l|P|P|l'l o « +
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4000
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^
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2000 3000 Building Area (m^)
4000
< p 16
(+
T/0 Bracing o o TypeMD * o Type LD + t Type CCj
Jul I U'. 1000
2000 3000 Building Area (m^)
4000
Figure 2: Unit SFRS costs: a) Cost of Design 0 structures; b) Cost ratios between Design 1A and Design 0 structures. Figure 2b shows the cost increase when applying strict capacity protection to the roof diaphragm. Overall, the increase in unit cost is 30%. The impact is significantly more pronounced for T/C bracing (34, 49 and 56% greater for the CC, LD and MD frames, respectively) because braces designed for
1363
compression can possess substantial extra resistance in tension, resulting in a higher shear demand on the roof diaphragm with the capacity based design requirement. Given Design lA for single-storey buildings, the most cost effective design solution is the Type MD T/0 bracing. Figure 3a compares the period Ta and the computed period for all Design lA structures, illustrating the period lengthening from roof flexibility. Figure 3b compares the design periods and design base shear ratios V/W when Designs lA and IB are applied to Type LD T/0 bracing. The reduction in design seismic loads due to design period relaxation is evident. In Fig. 3c, the net impact on SFRS costs is given for all structures. For the T/C bracing, only the large buildings with longer periods benefited from the relaxation on design period whereas smaller buildings were still governed by the upper plateau of the design spectrum. Savings for the T/0 systems are more significant because tension-only braces typically resuk in more flexible structures. Although period lengthening was more pronounced when higher Rd values were used for T/0 bracing, capacity design forces levelled out the cost reductions between all braced frame categories. For all T/0 systems, period relaxation was however sufficient to counteract the cost increase induced by applying capacity design requirements, with a cheaper SFRS than Design 0 obtained in approximately 80% of cases.
b) 1.6
^ ^ — Design Spectrum O O O Design 1A O O Design IB
2 12 •o
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— I — ' — I — • — 1 — ' 1000
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2000
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I 4000
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8
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4000
4000
Mi " ° o O CO 04
ii
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2000 3000 Building Area (m^)
4000
Figure 3: a) Design and computed periods for Design lA structures; b) Normalised design earthquake loads, V/W, for T/0 Types LD structures designed according to Designs 1A and IB; c) Cost ratios between Design IB and Design lA structures; d) Cost ratios between Design 3A-3B and Design 1A structures.
1364
As shown in Table 1, relaxing the upper limit on capacity design forces in Design 2A reduced the cost of the T/C systems, but the effect was negligible for T/0 systems as the upper limit did not govern the diaphragm design for this bracing configuration. When combined to period relaxation (Design 2B), substantial savings could be achieved both for T/C and T/0 systems. Nearly all T/0 structures of this group have SFRS that are less costly than in Design 0. Overall, the weak-diaphragm Design 3A resulted in the cheapest option among all buildings designed widi a period limit of 0.050 h„. Likewise, for the buildings for which period relaxation was permitted (Series B designs). Design 3B is again the most cost effective option in all cases. SFRS costs from Design 3 A and 3B are compared to the costs of Type LD {R(i = 2,0) Design 0 buildings in Fig. 3d. Design 3 A allows on average a 37 and 18% cost reduction for the T/C and T/0 systems, respectively. Corresponding savings using Design 3B are respectively 50% and 40%. All Design 3B structures are less expensive than the corresponding Design 0 frames. CONCLUSIONS Following strict requirements of capacity design similar to those prescribed in recent Canadian design codes resulted in a significant cost increase compared with past practice in which roof diaphragms were not adequately protected against inelastic deformations. The cost increase is more pronounced for T/C bracing. Relaxing current code limits on periods would reduce construction costs to some extent, but not to the level associated with past practice. Partially relaxing diaphragm capacity protection decreased the cost of T/C bracing systems from the full capacity design approach. When combined with period relaxation, such a method resulted in less expensive T/0 structures compared to the corresponding unprotected diaphragm designs. More substantial savings can be achieved if a weak-diaphragm design with Rd - 2.0 is applied, particularly when no limit is placed on the design periods. Weak-diaphragm structures generally were more cost effective than buildings designed according to past practice, even when period limits were applied. The designer must however be warned that very limited field data is available to support analytically computed period values taking advantage of diaphragm deformations. Similarly, prior to allowing for weak-diaphragm design, sufficient information on the inelastic seismic performance of metal deck systems must be made available. Until such validation is made, it is recommended not to use full period relaxation in the design and allow limited inelastic demand in diaphragms.
ACKNOWLEDGEMENTS Tliis research was supported by the Natural Sciences and Engineering Research Council of Canada. The assistance of the Canam Manac Group for providing unit cost estimates is appreciated.
REFERENCES CSA. 2001. CSA-S16-01, Limit States Design of Steel Structures. Canadian Standards Association. Toronto, ON. Essa, H.S., Tremblay, R., and Rogers, C. 2003. Behavior of roof deck diaphragms under quasi-static cyclic loading. J. of Struct. Eng., ASCE 129:12, 1658-1666. Heidebrecht, A.C. 2003. Overview of NBCC 2005 seismic provisions. Can. J. of Civ. Eng. 30:2, 241254. Tremblay, R. and Rogers, C. 2005. Impact of capacity design provisions and period limitations on the seismic design of low-rise steel buildings. Int. J. of Steel Struct, (in press) Tremblay, R., Rogers, C.A., Martin, E., Yang, W. 2004. Analysis, testing and design of steel roof deck diaphragms for ductile earthquake resistance. J. of Earthquake Eng. 8:5, 775-816. Tremblay, R., Stiemer, S.F. 1996. Seismic behavior of single-storey steel structures with flexible diaphragm. Can. J. of Civ. Eng. 23, 49-62.
1359
INFLUENCE OF SEISMIC DESIGN REQUIREMENTS AND BUILDING PERIOD ON THE DESIGN OF LOW-RISE STEEL BUILDINGS R. Tremblay and C.A. Rogers 'Department of Civil Geological and Mining Engineering Ecole Polytechnique of Montreal, Montreal, Canada H3C 3A7 ^Department of Civil Engineering and Applied Mechanics, McGill University Montreal, Canada H3A 2K6
ABSTRACT A Study is performed to examine the impact of capacity design provisions and period limitations prescribed in Canadian design codes and standard on the cost of low-rise steel buildings. Alternative design strategies are also investigated, including: design without a capacity based approach, capacity design with ductile bracing components, and capacity design assuming the steel roof diaphragm forms the main energy dissipation element in the seismic force resisting system. The effects of relaxing period limitations are also examined. The results show that capacity design provisions significantly influence the cost of the structure, especially when tension-compression bracing is used. Substantial savings can be realized with the use of a period obtained from methods of mechanics that account for diaphragm flexibility. Allowing inelastic response in the roof diaphragm can also contribute in reducing the cost of the structure. KEYWORDS Diaphragm, steel, roof deck, bracing members, seismic, earthquakes, period INTRODUCTION Single-storey steel buildings are used for light industrial, commercial and recreational purposes, and represent a vast proportion of the building stock in Canada. As illustrated in Fig. la, the seismic force resisting system (SFRS) of these structures typically includes a steel roof deck diapliragm that transfers horizontal loads to vertical steel bracing bents. The roof diaphragm is made of corrugated steel deck panels that are fastened to each other and to the supporting beams and joists (Fig. lb). These diaphragms are relativelyflexibleand in-plane roof deformations due to lateral loads must be accounted for in design, as illustrated in Fig. Ic. In seismically active regions, structures designed according to modem building codes are expected to experience some degree of inelastic response under strong earthquakes. Current practice requires that the inelastic demand be limited to the vertical bracing system and the roof diaphragms must then be designed to resist lateral loads that correspond to the actual capacity of the vertical elements. Seismic design loads also typically vary with the fundamental period of the structure.
1360
and empirical expressions are prescribed in building codes to estimate the period to be used in design. These formulae have been typically derived for multi-storey structures with rigid floor and roof diaphragms and do not reflect the behaviour of low-rise steel buildings with flexible roof diaphragms. b)
a) Roof Beams (typ.) Steel Deck Units (typ.)
Column (typ.)
c)
Roof Dlaphragm(El, G')
d) . Code Empirical Period
N
^bracing-
TCt t f t t t t f t t t Figure 1: Typical low-rise steel building: a) Main structural components; b) Detail of roof deck panels; c) Plan view of laterally deformed building; d) Period and design spectrum. Past studies have shown that the dynamic response of structures can be affected by the flexibility of the roof diaphragm (e.g., Tremblay and Stiemer 1996). In particular, the fundamental period of vibration is lengthened and, as illustrated in Fig. Id, significant cost savings could be anticipated if longer period values were adopted for design. Recent experimental investigations (Tremblay et al. 2004; Essa et al. 2003) also indicate that deck panels and their connections, when properly detailed, could act as the inelastic fuse in the SFRS, instead of the brace members. Considering that the price of the diaphragm dominates the overall SFRS cost for single-storey buildings, reducing the diaphragm design seismic loads could represent a second promising avenue for reducing construction costs. The objective of this study was to evaluate the impact of recent seismic design provisions on the SFRS costs for singlestorey steel buildings and to assess possible cost savings that would result from applying alternative design options such as relaxing period limits and allowing diaphragm inelastic response. A parametric study was carried out in which a total of seven different design strategies were investigated for different building dimensions, bracing configurations and ductility levels. Further details on this research can be found in Tremblay and Rogers (2005).
DESIGN AND DESCRIPTION OF THE BUILDINGS STUDIED The seismic provisions in the CSA-S16-01 standard (CSA 2001) and the upcoming 2005 National Building Code of Canada (NBCC) (Heidebrecht 2003) were used as a basis for the study. In NBCC, the design seismic design loads are a function of the building period, for which the design period, Ta,
1361
for braced steel frames is equal to 0.025 //„, where //„ is the building height. Ahematively, the period of the structure obtained from methods of mechanics can be used for Ta, except that such value must not exceed 0.050 /i„. To account for the SFRS ductility and actual capacity, the elastic seismic loads in NBCC are respectively divided by a ductility-related and an overstrength-related force modification factors, Rd and RQ. Inelasticity must be constrained to the bracing members and, hence, the Rd and Ro factors depend solely on the characteristics of the vertical bracing system. Three different braced steel frame categories are specified in NBCC: Moderately Ductile (Type MD, Rd = 3.0), Limited-Ductility (Type LD, Rd = 2.0) and Conventional Construction (Type CC, Rd ~ 1.5). For all categories, Ro is equal to 1.3. Capacity design is prescribed in CSA-S16 for Type LD and MD braced frames. Bracing members must meet slendemess ratio and cross-section width-to-thickness ratio limits to ensure ductile inelastic response. These limits are less stringent for Type LD (Rd = 2.0) compared to Type MD frames (Rd = 3.0). Beams, columns, connections and roof diaphragms must be able to resist forces corresponding to the expected capacity of the bracing members, i.e. the unfactored resistance of the braces obtained with the probable steel yield stress. Seven different design strategies were considered in the parametric study. Design 0 is in accordance with code provisions, i.e. with energy dissipation being concentrated in the bracing members, except that the roof diaphragm is designed for the prescribed seismic loads, not for the forces associated to the actual capacity of the vertical bracing. An iterative design was perfoniied by initially setting the design period equal to 0.025 /;„ and then modifying the design using the period computed from previous design iterations. The process was halted when the seismic loads remained unchanged or the upper limit Ta = 0.050 A„ was attained. All SFRS components were selected to achieve a minimum cost design. If needed, the SFRS was stiffened to meet code drift limitations. Design lA is identical to Design 0 except that strict capacity design rules were applied to prevent inelastic action forming in the roof diaphragm. However, the diapliragm design forces need not exceed elastic level forces, i.e. those corresponding to seismic loads calculated with RoRd = 1.0. For Design IB, the building period at each design cycle was estimated with consideration of the roof diaphragm flexibility, without applying the 0.05 /;„ limit. Designs 2A and 3A are included to study the possibility of reducing building costs by allowing inelasticity in the roof diaphragm. In Design 2A, the procedure used in Design lA was applied except that the design forces for the diapliragm system were limited to those corresponding to RoRd = 1.95, instead of RoRd = 1.0. Design 3 A is a different approach in which the roof diapliragm is the main energy dissipating element of the SFRS. The diaphragm is designed first, using Ro = 1.67 and Rd = 2.0, as proposed by Tremblay et al. (2004) for regular buildings with mechanical deck fasteners, and the perimeter members and bracing bents are then sized to resist the forces associated with the probable shear capacity of the diaphragm. This results in a weak diapliragm-strong brace design. For Designs 2A and 3A the design period was limited to 0.050 //„. That limit was waived in Designs 2B and 3B. The study was performed on rectangular single-storey steel buildings assumed to be located in Vancouver, BC. Seven different building areas from 600 to 4200 m^ and four different aspect ratios (1.0, 1.5, 2.0 and 2.5) were examined. In addition, the building height was varied between 4.8 and 10.8 m, resulting in a total of 227 different building sizes. X-bracing symmetrically distributed along the four perimeter walls were used as the vertical bracing system. Two different bracing systems were considered: tension-compression bracing (T/C) and tension-only bracing (T/0), i.e. frames in which the seismic loads were assumed to be resisted only by the tension-acting braces. For each case, the three braced frame categories (Types MD, LD and CC) were considered, when applicable. The roof deck consisted of 914 mm wide steel panels with a trapezoidal profile 38 mm deep with the flutes spaced at 152 mm apart. The panels were connected to one another with self-tapping screws along the sidelaps and to the underlying frame with powder actuated fasteners. For each structure and design option, the total cost of the SFRS was estimated including the braces, the columns of the bracing bents, the perimeter members, the deck sheets, and the deck fasteners. That cost was then summed and divided by the buildmg area.
1362
RESULTS OF THE PARAMETRIC STUDY Table 1 gives the average SFRS costs per unit floor for each bracing system and design strategy (weighted average of the 227 building cases). Figure 2a presents the SFRS unit cost of all Design 0 T/C and T/0 buildings. In each graph, three sets of values are given for each building area, depending on the system category, and the results for Types MD and CC have been slightly shifted to the left and the right of Type LD results to help distinguish between the tliree cases. This representation has also been used in subsequent similar figures. The results show that using a higher Rd factor generally leads to a reduced SFRS cost, regardless of the building area and the bracing configuration (T/C v.v T/0 systems), indicating that the benefits of reducing the seismic loads overcome the negative impact of brace ductility detailing requirements for Rd = 2.0 and 3.0 structures. TABLE 1 WEIGHTED AVERAGE OF ESTIMATED COSTS OF THE SFRS ( $ / M ^ )
System 0 53.10 62.60 69.10 52.90 61.80 69.40
T/C Type MD T/C Type LD T/C Type CC T/O Type MD T/0 Type LD T/0 Type CC a)
lA 84.00 93.90 93.80 61.90 75.10 75.10
Design No. 2A 71.40 74.80 69.80 61.70 69.30 68.70
IB 80.70 91.00 90.00 49.10 49.80 55.50
2B 59.40 62.80 57.80 45.80 46.00 47.10
3A
3B
58.90
45.30
60.30
43.90
100.0 ^
80.0
C/3
60.0
s-
40.0
o V> 8 20.0
e
iii,!i||l||l|l'|l'|l 1+
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w a:
60 0
u.
^ o to
40.0
8
200
III
,|i||l|P|P|l'l o « +
0.0 3000 Building Area (m2)
TAD o o 4-
2000 3000 Building Area (m2)
4000
Bracing o Type MD o Type LD + TypeCC, "T4000
b) < g
1.6
^
1.2
'II hri'iijui: < I •, rn o o + 1000
T/C Bracing o o Type MD « « Type LD + + Type CCJ
2000 3000 Building Area (m^)
4000
< p 16
(+
T/0 Bracing o o TypeMD * o Type LD + t Type CCj
Jul I U'. 1000
2000 3000 Building Area (m^)
4000
Figure 2: Unit SFRS costs: a) Cost of Design 0 structures; b) Cost ratios between Design 1A and Design 0 structures. Figure 2b shows the cost increase when applying strict capacity protection to the roof diaphragm. Overall, the increase in unit cost is 30%. The impact is significantly more pronounced for T/C bracing (34, 49 and 56% greater for the CC, LD and MD frames, respectively) because braces designed for
1363
compression can possess substantial extra resistance in tension, resulting in a higher shear demand on the roof diaphragm with the capacity based design requirement. Given Design lA for single-storey buildings, the most cost effective design solution is the Type MD T/0 bracing. Figure 3a compares the period Ta and the computed period for all Design lA structures, illustrating the period lengthening from roof flexibility. Figure 3b compares the design periods and design base shear ratios V/W when Designs lA and IB are applied to Type LD T/0 bracing. The reduction in design seismic loads due to design period relaxation is evident. In Fig. 3c, the net impact on SFRS costs is given for all structures. For the T/C bracing, only the large buildings with longer periods benefited from the relaxation on design period whereas smaller buildings were still governed by the upper plateau of the design spectrum. Savings for the T/0 systems are more significant because tension-only braces typically resuk in more flexible structures. Although period lengthening was more pronounced when higher Rd values were used for T/0 bracing, capacity design forces levelled out the cost reductions between all braced frame categories. For all T/0 systems, period relaxation was however sufficient to counteract the cost increase induced by applying capacity design requirements, with a cheaper SFRS than Design 0 obtained in approximately 80% of cases.
b) 1.6
^ ^ — Design Spectrum O O O Design 1A O O Design IB
2 12 •o
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c)
< ^
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I 4000
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4000
4000
Mi " ° o O CO 04
ii
'I i| ' ' "
T/0 Bracing + + Design 3A o o Design 3B^ 1000
2000 3000 Building Area (m^)
4000
Figure 3: a) Design and computed periods for Design lA structures; b) Normalised design earthquake loads, V/W, for T/0 Types LD structures designed according to Designs 1A and IB; c) Cost ratios between Design IB and Design lA structures; d) Cost ratios between Design 3A-3B and Design 1A structures.
1364
As shown in Table 1, relaxing the upper limit on capacity design forces in Design 2A reduced the cost of the T/C systems, but the effect was negligible for T/0 systems as the upper limit did not govern the diaphragm design for this bracing configuration. When combined to period relaxation (Design 2B), substantial savings could be achieved both for T/C and T/0 systems. Nearly all T/0 structures of this group have SFRS that are less costly than in Design 0. Overall, the weak-diaphragm Design 3A resulted in the cheapest option among all buildings designed widi a period limit of 0.050 h„. Likewise, for the buildings for which period relaxation was permitted (Series B designs). Design 3B is again the most cost effective option in all cases. SFRS costs from Design 3 A and 3B are compared to the costs of Type LD {R(i = 2,0) Design 0 buildings in Fig. 3d. Design 3 A allows on average a 37 and 18% cost reduction for the T/C and T/0 systems, respectively. Corresponding savings using Design 3B are respectively 50% and 40%. All Design 3B structures are less expensive than the corresponding Design 0 frames. CONCLUSIONS Following strict requirements of capacity design similar to those prescribed in recent Canadian design codes resulted in a significant cost increase compared with past practice in which roof diaphragms were not adequately protected against inelastic deformations. The cost increase is more pronounced for T/C bracing. Relaxing current code limits on periods would reduce construction costs to some extent, but not to the level associated with past practice. Partially relaxing diaphragm capacity protection decreased the cost of T/C bracing systems from the full capacity design approach. When combined with period relaxation, such a method resulted in less expensive T/0 structures compared to the corresponding unprotected diaphragm designs. More substantial savings can be achieved if a weak-diaphragm design with Rd - 2.0 is applied, particularly when no limit is placed on the design periods. Weak-diaphragm structures generally were more cost effective than buildings designed according to past practice, even when period limits were applied. The designer must however be warned that very limited field data is available to support analytically computed period values taking advantage of diaphragm deformations. Similarly, prior to allowing for weak-diaphragm design, sufficient information on the inelastic seismic performance of metal deck systems must be made available. Until such validation is made, it is recommended not to use full period relaxation in the design and allow limited inelastic demand in diaphragms.
ACKNOWLEDGEMENTS Tliis research was supported by the Natural Sciences and Engineering Research Council of Canada. The assistance of the Canam Manac Group for providing unit cost estimates is appreciated.
REFERENCES CSA. 2001. CSA-S16-01, Limit States Design of Steel Structures. Canadian Standards Association. Toronto, ON. Essa, H.S., Tremblay, R., and Rogers, C. 2003. Behavior of roof deck diaphragms under quasi-static cyclic loading. J. of Struct. Eng., ASCE 129:12, 1658-1666. Heidebrecht, A.C. 2003. Overview of NBCC 2005 seismic provisions. Can. J. of Civ. Eng. 30:2, 241254. Tremblay, R. and Rogers, C. 2005. Impact of capacity design provisions and period limitations on the seismic design of low-rise steel buildings. Int. J. of Steel Struct, (in press) Tremblay, R., Rogers, C.A., Martin, E., Yang, W. 2004. Analysis, testing and design of steel roof deck diaphragms for ductile earthquake resistance. J. of Earthquake Eng. 8:5, 775-816. Tremblay, R., Stiemer, S.F. 1996. Seismic behavior of single-storey steel structures with flexible diaphragm. Can. J. of Civ. Eng. 23, 49-62.