Ductility Design of Reinforced Concrete Shear Walls

HKIE Transactions

ISSN: 1023-697X (Print) 2326-3733 (Online) Journal homepage: http://www.tandfonline.com/loi/thie20

Ductility design of reinforced concrete shear walls with the consideration of axial compression ratio J S Kuang & Y P Yuen To cite this article: J S Kuang & Y P Yuen (2015) Ductility design of reinforced concrete shear walls with the consideration of axial compression ratio, HKIE Transactions, 22:3, 123-133, DOI: 10.1080/1023697X.2015.1071027 To link to this article: http://dx.doi.org/10.1080/1023697X.2015.1071027

Published online: 25 Sep 2015.

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Date: 14 January 2016, At: 22:56

HKIE Transactions, 2015 Vol. 22, No. 3, 123–133, http://dx.doi.org/10.1080/1023697X.2015.1071027

Ductility design of reinforced concrete shear walls with the consideration of axial compression ratio J S Kuanga∗ and Y P Yuenb a Department of Civil and Environmental Engineering, the Hong Kong University of Science and Technology, Hong Kong, People’s Republic of China; b Department of Civil Engineering, Bursa Orhangazi University, Turkey

Downloaded by [University of Malaya] at 22:56 14 January 2016

(Received 1 November 2013; accepted 9 December 2014 ) To evaluate and quantify the effect of the axial compression ratio on the seismic performance of reinforced concrete walls, a comprehensive statistical analysis with 474 sets of experimental data was conducted. Stipulated limits on the axial compression ratio and their evaluation methods in various design codes were analysed and compared. Based on the results of these analyses, methods for calculating the effective axial compression and the limiting value of the axial compression ratio for reinforced concrete (RC) structural walls stipulated in the Code of Practice for Structural Use of Concrete 2013 may be amended and improved on a more scientific basis. Recommendations are made for possible amendments to the provision of design or detailing for ductility of structural walls in Clause 9.9.3 of the Hong Kong structural concrete code 2013. Keywords: shear wall; axial compression ratio; ductility; reinforced concrete; seismic design

Introduction It has been demonstrated repeatedly by many disastrous earthquakes [1–4] that well-designed structural walls can render excellent lateral stability and drift ductility to medium-to-high-rise reinforced concrete (RC) buildings under seismic actions. Under reversed cyclic loading, well-detailed and confined RC shear walls display very good and stable flexural deformability and energy dissipation capacity, which are attributed to the high curvature ductility and extended plastic hinge length.[5] Meanwhile, as compared with the frame systems, the structural behaviour of shear-wall systems is less influenced by random non-structural component effects such as infill panels, which often trigger soft-storey phenomena in the frame structures.[6] Shear walls are thus recognised as the very important structural members with relatively high ultimate lateral load-carrying capacity in seismic resistant design.[2,7] With credit given to the efforts made in experimental and analytical studies undertaken by researchers in the past decades, the design and analysis methods for typical RC walls have been well-established and standardised. RC shear walls in high-rise buildings are often characterised by high compression forces and aspect ratios, as a consequence of architectural designs which maximise clear floor heights and usable floor areas. Recent studies [8,9] indicated that structural wall elements in tall buildings can sustain axial compression ratios as high *Corresponding author. Email: [email protected] © 2015 The Hong Kong Institution of Engineers

as 0.4 fc Ac or above, which is already beyond the typical range of 0 to 0.2 investigated experimentally.[10–12] A few studies on RC walls under an axial force ratio above 0.3 can be found in the literatures,[12–15] and these experimental studies revealed that high axial force ratios severely deprive drift ductility and stability of RC walls. Shear walls suddenly fail in a brittle manner when subjected to lateral reversed-cyclic loading under a high axial compression ratio, thus losing their vertical load-carrying capacity. The 2010 Chile earthquake is a good example where lessons were learned on the effect of high axial forces on the seismic performance of RC structural walls. It has been indicated from post-earthquake field investigations that thin walls, with thicknesses ranging from 150 mm to 200 mm, in newly built high-rise buildings are normally subjected to a higher axial compression and suffered severer damage than thicker walls in old buildings during the earthquake.[16,17] Out-of-plane insatiability of walls, buckling or fracturing of the boundary reinforcement, and compression failure over the entire wall lengths are typical significant damage modes observed in thin RC walls, as shown in Figure 1. The design of new buildings in Chile mainly follows the American Concrete Institute’s 1995 building code for structural concrete, but the provisions on the detailing of transverse reinforcement at wall boundaries are not included, which can be a major cause of the significant wall damage.

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J.S. Kuang and Y.P. Yuen Definitions and effects of axial compression ratios Effect on ductility of RC walls Axial force has a crucial role in governing the drift ductility of RC walls. An apparent and instant effect with a higher axial compression is the reduction of the curvature ductility μφ of walls,[5,21] which is directly and inversely proportional to the natural axis depth c and in turn is a monotonic increasing function of axial compression, given as follows:


μφ =

φu εcu lw = , φy 2.00εy c

(1)

where lw is the wall length. Hence, the curvature ductility, as well as the drift ductility μ , decreases with an increase in axial compression. On the other hand, when the strain penetration effect is deemed negligible and the plastic hinge length is assumed to be lp ≈ 0.08lw , the drift ductility of flexural-controlled wall segments can be estimated as follows: φy H 2 /3 + (φu − φy )lp H u ≈ y φy H 2 /3 1 0.12εcu − 0.24 , =1+ αV εy cαV

μ =

Figure 1. Compression failure of a shear wall during the 2010 Chile earthquake. (Courtesy of M Francisco; acquired from NISEE e-Library, EERC, University of California, Berkeley, the USA).

To prevent undesirable brittle failures of RC walls, many design codes of practice for RC structures, including the Hong Kong structural concrete code 2013 (HKConcrete2013),[18] Chinese seismic code GB 50011–2010,[19] and Eurocode 8,[20] stipulated upper limits for axial compression ratios and boundary-element detailing requirements for various ranges of axial compression ratios. Nonetheless, later it can be seen that the provisions in different codes of practice have dissimilarities, including the definitions and limiting values. In view of this issue, this paper presented a comprehensive survey and study on the suitability of various code provisions on axial compression ratios. The detailed effect of axial compression ratios on the seismic performance of RC walls was firstly studied, followed by a comprehensive comparison and discussion on the corresponding code provisions. Based on an analysis of the results, methods for calculating the effective axial compression and the limiting value of axial compression ratio for RC structural walls stipulated in the Code of Practice for Structural Use of Concrete 2013 [18] may be amended and improved on a more scientific basis. Recommendations were made for possible amendments to the provision of design or detailing for ductility of structural walls in Clause 9.9.3 of the HKConcrete2013.

(2)

where αV is the vertical aspect ratio (H /lw ) and H is the wall height. Equation (2) further indicates that the aspect ratio αV , concrete crushing strain εcu and steel yielding strain εy are also effective parameters of the drift ductility of a wall segment, as well as the natural axis depth c as an influential parameter. This explains why confining boundary elements for wall segments subjected to high axial forces are required by various design codes to compensate for the reduced ductility due to axial compression. The confined concrete in the confining boundary elements can attain a much higher ultimate crushing strain, εcu , than the unconfined concrete; hence, the higher curvature ductility can be achieved in RC walls with confining boundary elements. In addition, strength and stiffness degradation of RC members under cyclic loading is much more pronounced under high axial compression, which is attributed to the low cyclic fatigue effect.[22] High axial compression can prompt pre-emptive buckling of thin RC walls, thus leading to a sudden and complete loss of axial force carrying capacity in a brittle manner. Although on some occasions, axial compression may be beneficial to the shear strength of squat RC walls with potential shear failure modes such as diagonal tension and sliding shear,[23] this benefit generally cannot compensate for the overall adverse effect. It is thus widely recognised that RC walls subjected to the high axial compression are more vulnerable to seismic effects.

HKIE Transactions To parametricise the axial compression effect on the structural performances of RC walls, the axial compression ratio is usually used, defined as follows:


η=

N . fc A

(3)

Indeed, in addition to the confinement detailing, aspect ratios, lap and splices etc., the axial compression ratio is a very important indicator for evaluating the expected ductility and fragility of RC walls during earthquakes. However, it should not be confused with the load and resistance design or limit state design concepts, since the axial compression ratio alone cannot represent or be used to assess the actual seismic performance of RC walls. Furthermore, this axial compression ratio is particularly effective for RC structures with high ductility demands such as under seismic or other exceptional loading cases. Therefore, the axial force in the numerator is often evaluated based on the realistic situation, when the rare loading cases take place and no critical load combination procedure is generally required by design codes.

(a)

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Effect on displacement and load capacity A comprehensive statistical analysis was conducted for evaluating and quantifying the effect of the axial force ratio on the seismic performance of RC structural walls. A total of 474 sets of data, composed of experimental results of small to full-scale RC walls of various shapes and detailing methods, were collected from the literatures.[10–15,22,24–54] The gathered loaddisplacement data were analysed, wherein the definitions of yield displacement, ultimate displacement and displacement ductility of the loading curves are based on Park.[55] In the collected database, more than 60% of the tests were conducted with a relatively low axial force ratio of below 0.05; in contrast, only about 15% and 7% were tested with an axial force ratio of above 0.15 and 0.30, respectively. Nonetheless, these high axial force tests demonstrated that RC walls fail in very different manners such as out-of-plane buckling, resembling the observed damage modes of walls in the 2010 Chile earthquake (Figure 1). RC walls that fail in out-of-plane buckling are generally the very brittle members, which exhibit

(b)

(c)

Figure 2. Relationship between displacement ductility and axial compression ratio for different types of RC (a) all walls; (b) slender walls; and (c) squat walls.


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J.S. Kuang and Y.P. Yuen

relatively low ductility, and hence the classical ductility evaluation methods that assumed in-plane flexural failure are no longer applicable to these walls. Figure 2(a) shows the relationship between drift ductility and axial force ratio of different kinds of RC shear walls. It is shown that RC walls can easily achieve high ductility (μ ≥ 6) at a low axial force ratio (η ≤ 10%) as long as the boundary elements are well detailed and designed. However, when the axial compression ratio increases to above 20%, RC walls can only barely maintain moderate ductility (4 < μ ≤ 6) and special detailing methods like composite-reinforced boundary elements are necessary in order to acquire high ductility. When the axial compression ratio is above 35%, preemptive out-of-plane buckling can be the dominating failure mode as reported in the literatures,[13–15] thus RC walls are not suitable for providing lateral and vertical resistances in seismic design. (a)

It is recognised that squat shear walls with an aspect ratio (H /L) lower than 1.5 are prone to shear failure, in particular sliding shear failure rather than flexural failure, and the displacement ductility is not necessarily reduced by an increase in axial compression. In contrast to the ductility of slender shear walls (Figure 2(b)), the ductility of squat walls (Figure 2(c)) is less influenced by the axial compression ratio such that the inherent ductility generally remains in the range of 2 < μ ≤ 5. The relationship between the ultimate displacement capacity and axial compression ratio of various types of RC shear walls is also plotted in Figure 3(a). Again, as shown in Figure 3(b), there is a trend of diminishing the ultimate displacement capacity of slender walls with an increase in axial compression ratio, owing to the reduction in neutral axial depth, low cycle fatigue effect and potential out-of-plane buckling. In contrast, the ultimate displacement capacity of squat walls tends to increase (b)

(c)

Figure 3. Relationship between ultimate displacement ratio and axial compression ratio for different types of RC (a) all walls; (b) slender walls; and (c) squat walls.

HKIE Transactions with the axial compression ratio, as shown in Figure 3(c). This reversed trend is actually due to the fact that the shear strength and sliding resistance of cracks in squat walls are enhanced by axial compression, which increases the interfacial friction between crack faces. Another important structural property of RC walls related to axial compression is the shear strength. For comparison purposes, the peak base shears reported by the tests in the database are further normalised by the following equation:


vn =

Vp , fc 0.5 Aw

(4)

where Aw is the web area of the wall. Figure 4 shows the relationship between the normalised shear strength and the axial compression ratio. It shows that a higher axial compression tends to increase the shear strength of all types of RC walls, in particular the squat RC walls, as shown in Figure 4(c). This is because axial compression not only can enhance the shear strength of walls, but also the moment resistance in some

(a)

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cases.[9,23] Nevertheless, the enhanced shear strength attributed to axial compression cannot generally compensate for the adverse effect of reduced drift capacity, and after all, the system ductility is far more important than the strength in seismic design.

Code provisions on axial compression ratio In view of the adverse effect of axial compression on the seismic performance of RC structural walls, most of the modern design codes of practice for RC structures stipulate upper limits for the axial compression ratio. RC walls with an axial compression ratio beyond the limits are generally deemed to be ineffective in resisting seismic action, even with confinement detailing in the critical regions of the members (such as expected plastic hinges). These provisions, in addition to confinement detailing, intend to ensure that sufficient drift ductility and axial force carrying capacity can be retained in RC structures during earthquakes or other exceptional load cases.

(b)

(c)

Figure 4. Relationship between the normalised shear strength and axial compression ratio for different types of RC (a) all walls; (b) slender walls; and (c) squat walls.

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The HKConcrete2013 In Clause 9.9.3.3 of the HKConcrete2013,[18] the upper limit of axial compression ratios of RC structural walls is specified as follows:


NW,HK ≤ 0.75, 0.45fcu Ac

(5)

where NW,HK is the design axial force, which is 1.4Gk + 1.6Qk (wherein Gk is the total permanent or dead load and Qk is the total live load for the wall due to gravity load); fcu is the characteristic cube strength of concrete under uniaxial compression at 28 days; and Ac is the gross area of the concrete section. It was noted that the safety factor for concrete compressive strength used in the Hong Kong code is 1.5, which is divided by the characteristic concrete strength giving the design strength. The constant 0.45 = 0.67/1.5 in the denominator converts the characteristic concrete strength into the equivalent design compressive strength for the sections subjected to the dominant flexural bending action, wherefore another multiplying factor 0.67 is used. Meanwhile, the axial force in the numerator takes the ultimate load value due to the sole gravity action, without considering possible non-permanent imposedload reductions or representative gravity action during rare events with exceptional loading actions, such as earthquakes and explosions. Chinese seismic design code (GB50011–2010) In the Chinese seismic design code GB50011–2010,[19] the upper limits of the axial compression ratio for RC shear walls (sectional aspect ratio L/t > 8) take different values under different seismic fortification intensities and structural grades. There are four classes of structural grades: Grade I structures have high drift ductility, Grade II and III structures have moderate-to-high drift ductility, and Grade IV structures have relatively low drift ductility. The upper limits for structures with different grades are given as follows: ⎧ 0.4 Grade I, Intensity 9 ⎪ ⎪ ⎪ ⎨ NW,C 0.5 Grade I, Intensity 7 or 8 ≤ , (6) ⎪ fc Ac 0.6 Grade II or III ⎪ ⎪ ⎩ − Grade IV where NW,C isthe factored axial force for the wall, which is 1.2(Gk + i rdi Qki ) (wherein rdi is the combination coefficient (≤ 1) for variable action i [19] due to representative gravity load); and fc is the design axial compressive strength of concrete under uniaxial compression at 28 days, which is equal to the characteristic axial strength of concrete fck divided by the safety factor 1.4. The characteristic axial strength fck is determined by 150 mm × 150 mm × 300 mm prism compression tests.

In the Chinese code, it can conservatively be taken as 0.67 of the characteristic cube strength fcu,k , which resembles the value of fcu adopted in the Hong Kong code. The average value of the ratio fck /fcu,k or so-called effectiveness factor is about 0.76 based on the experimental studies.[56,57] More stringent provisions are set for short pier RC shear walls (4 < L/t ≤ 8) such that the axial compression ratios for Grades I, II and III short pier walls should not exceed 0.45, 0.50 and 0.55, respectively in the critical regions (JGJ3-2010).[58] The axial force in Equation (6) is first calculated from the representative gravity action (Gk + i rdi Qki ), instead of the ultimate gravity action, and expected to be taken by structures during earthquakes; then a multiplying factor of 1.2 is used to account for the additional axial force incurred by unforeseen and excluded actions on the walls. In the calculation of the representative gravity action, the combination coefficient rdi is used to consider the reduced likelihood that full variable actions are considered during earthquakes and, for instance, the combination coefficient for residential floor live load is 0.5. The reduction factors for floor live loads (GB50009-2012) [59] in multi-storey buildings are already absorbed in the combination coefficients; in other words, variable actions Qki should not be reduced before multiplying by combination coefficients. Furthermore, it was noted that the design axial compressive strength fc used in Equation (6) can be rewritten in the form of characteristic compressive cube strength as fc = 0.67fcu /γc = 0.67fcu /1.4 = 0.48fcu , which is close to the value (0.45fcu ) used in the Hong Kong code calculation, which is presented in Equation (5). Eurocode 8 (EC8) (EN 1998-1:2004) EC8 [20] stipulates the upper limits for axial compression ratio (calculated from the normalised axial force) for ductile walls and columns designed for moderate (DCM) and high (DCH) ductility classes, but there is no restriction for low (DCL) ductility classes as follows: ⎧ ⎪0.35 DCH NED,EC ⎨ ≤ 0.4 (7) DCM , ⎪ fcd Ac ⎩ − DCL where NED,EC is the design axial force from the analysis for the seismic design situation (i.e. Gk + i ψE,i Qki + E, wherein E is seismic action and ψE,i is the combination coefficient (≤ 1) for variable action Qki ); and fcd is the design (with a safety factor of 1.5) cylinder strength of concrete under uniaxial compression at 28 days, which approximately equals 0.8 times the corresponding cube strength. The definitions of axial compression ratio for RC walls and columns are identical in EC8. The denominator

HKIE Transactions in Equation (7) has a similar form to that of Equation (6), but the cylinder strength is used in RC designs with EC8. If the design cylinder strength fcd in EC8 is converted to the characteristic cube strength fcu , it can be shown below:


fcd = 0.8fcu /γc = 0.8fcu /1.5 = 0.53fcu . The design axial force in Equation (7) consists of two major components: (i) axial force induced by representative gravity action and (ii) axial force induced by seismic action. Similar to the Chinese seismic code, the limits for columns are less restrictive than walls and the representative gravity load is used by EC8 in calculation of the axial force, in which the effect of seismic action for RC walls is also included. Although axial forces incurred in cantilever walls by seismic loads are relatively minor as compared with permanent gravity action in general, coupled shear walls have to bear significantly extra axial forces incurred by seismic action due to the coupling action aggregated from the shear forces of coupling beams, which obviously has a non-negligible effect on the seismic performance of the walls. Therefore, amongst the three aforementioned design codes, the definition of the axial compression ratio used in EC8 can be considered as the most appropriate description of realistic stress states experienced by RC structures during earthquakes. Actually, limits of the axial compression ratio stipulated in EC8 can readily be compared with experimental studies to see whether the provisions can ensure sufficient ductility of the RC members. New Zealand concrete code (NZS 3101:2006) and other design codes New Zealand concrete code NZS 3101:2006 [60] does not have similar provisions on the axial force ratios as those in the Hong Kong, GB and EC codes, but does specify

129

limiting sectional curvatures or strains in potential plastic hinge regions for different RC members (Clause 2.6.1.3.4, Part 1:2006). Limiting material strains is apparently the most direct method to control curvature ductility of RC members; however, whether it is sufficient to prevent the low cyclic fatigue phenomenon or rapid strength and stiffness degradation of RC members under cyclic loading is uncertain. It is also worth mentioning that the United States (US) ACI 318-11 [61] also does not introduce similar limits on the axial compression ratio for RC columns and walls. Nevertheless, a standard for the seismic rehabilitation of buildings ASCE/SEI 41-06 [62] stated that RC walls with axial loads greater than 35% of nominal axial load strength P0 shall not be considered effective in resisting seismic forces. The Canadian concrete code CSA A23.3-04 (R2010) [63] also stated that flexural members with factored axial loads in excess of 0.35P0 shall have a nominal resistance greater than the induced member force, i.e. not be designed to form potential plastic hinges and dissipate energy in any circumstances under seismic effects. Comparisons of code provisions Although the definitions of axial force ratio in the Hong Kong, GB and EC codes are not the same, particularly the axial forces in the numerators, the compressive strength term in the denominators can conveniently be converted to the characteristic equivalent axial strength with fck = 0.67fcu for comparison. Table 1 summarises the key comparisons of the provisions on the axial compression ratios defined in the three codes. At first sight, looking at the last row in Table 1, the Hong Kong code has the least stringent limit on the axial compression ratio for RC walls as compared with the other two codes. In addition, it was noticed that the axial

Table 1. Comparisons of code provisions on axial compression ratios for RC walls.

Original definition of axial compression ratio Limit Seismic/lateral force effects Variable load reduction Re-normalised axial compression ratio limit vs fck

HKConcrete2013

GB50011-2010

EC8

NW,HK 0.45fcu Ac

NW,C fc A c

NED,EC fcd Ac

≤ 0.75 × × NW,HK ≤ 0.50 fck Ac

⎧ ⎪ 0.4 ⎪ ⎪ ⎨0.5 ≤ ⎪0.6 ⎪ ⎪ ⎩−

Grade I, Intensity 9 Grade I, Intensity 7 or 8∗ Grade II or III Grade IV × ⎧ ⎪ 0.29 Grade I, Intensity 9 ⎪ ⎪ NW,C ⎨0.36 Grade I, Intensity 7 or 8 ≤ ⎪0.43 Grade II or III fck Ac ⎪ ⎪ ⎩− Grade IV

⎧ ⎪ ⎨0.35 DCH ≤ 0.4 DCM ⎪ ⎩− DCL

NED,EC fck Ac

*Limits for Grades I, II and III short pier RC shear walls (4 < H /B ≤ 8) are 0.45, 0.50 and 0.55, respectively.

⎧ ⎪ ⎨0.28 DCH ≤ 0.32 DCM ⎪ ⎩− DCL

130



out-of-plane buckling. It can be shown, however, that the limit of the HKConcrete2013 is somehow unjustifiable in the sense of targeting to control the ductility and is far beyond the other limits stipulated in GB and EC8, if it is accepted that the ultimate design gravity 1.4Gk + 1.6Qk is effective in evaluating the axial compression ratio during exceptional loading cases. Therefore, the provision in the HKConcrete2013 on the axial compression ratio for RC walls has some improvable aspects, including the definition, load combination method and specified limit.

Figure 5. Code-specified axial compression ratio limits and expected achievable ductility.

force in the numerator is generally much larger than those of the GB and EC codes, where the full ultimate gravity action is considered instead of the representative gravity action. For instance, if both sides of the inequality are divided by 1.4 (a safety factor for dead loads in the HKConcrete2013), the limit is immediately toughened to 0.36 and the possible reduction in variable or live loads is not even considered yet. The limits of axial compression ratio stipulated in the Chinese code resemble those in EC8, but again, the combinations of actions for calculating the axial forces are different in the two codes as mentioned before. For cantilever walls, the Chinese code is virtually more stringent because the safety factor 1.2 is used to amplify the action. But for coupled shear walls, it is not conclusive in which one of the two codes is more conservative, since the factor of 1.2 may not be sufficient to cover the exceeding axial forces induced by the coupling action. Nevertheless, EC8 provides a more realistic assessment for these cases by taking into the consideration of seismic action or generally lateral force effects. If the relationship between the displacement ductility and the axial compression ratio shown in Figure 2 is introduced again and plotted together with the code-specified limits of the axial compression ratio, the expected achievable ductility of RC walls can clearly be evaluated as shown in Figure 5. In general, the required displacement ductility for fully ductile structures under moderate-to-high seismic effect should not be less than 3.5 [5] and EC8 provisions undoubtedly satisfy this target level of ductility. The Grade I structures designed according to the Chinese code can also satisfy this target, but the Grade II and III structures may only have restricted inherent ductility and are susceptible to

Recommendations for possible amendments to Clause 9.9.3, the HKConcrete2013 Based on the results of a comprehensive statistical analysis using 474 sets of experimental data and comparisons with other design codes, the methods for calculating the effective axial compression and the limiting value of the axial compression ratio for RC structural walls stipulated in the HKConcrete2013 may be amended and improved on a more scientific basis. Recommendations are made for possible amendments to Clause 9.9.3, the HKConcrete2013 as follows: (1) In Clause 9.9.3.3, the value of axial compression should be calculated based on the realistic representative or the effective gravity action rather than the ultimate gravity action; hence it should be determined as follows:

ψri Qki , (8) NW,HK = 1.2 Gk + i

where ψri is the combination coefficient (≤ 1) reducing the imposed action Qki to the corresponding effective gravity action during rare loading cases. Values of ψri for various actions in different usage can be taken from Table 2. The factor of 1.2 is used to account for incurred axial force due to excluded actions. (2) As Hong Kong is a region of moderate seismicity,[19] for the design of building structures, it would be appropriate to design for displacement ductility values μ corresponding to the structures of limited ductility [64] and the ductility factor may be taken as 2 < μ ≤ 4. Referring to the results of the comprehensive statistical analysis presented in Figure 5, a reasonable limit on the axial compression ratio of RC structural walls is found and given as follows: ncr =

N W,HK ≤ 0.4. fck Ac

(9)

HKIE Transactions Table 2.

Values of ψri for various imposed actions.

Specific use

Storey

Areas for domestic and residential activities, offices and places where people may congregate.

Examples

Roof Storeys with correlated occupancies. Independently occupied storeys.

Areas in retail shops, department stores, storage, industrial use and accumulation of goods may occur.

By rewriting Equation (9) and taking fck = 0.67fcu , then the axial compression ratio of RC structural walls is given as follows:


131

ncr =

N W,HK ≤ 0.27. fcu Ac

(10)

To preserve the clear physical meaning of the axial compression ratio, it is not necessary for the factor of 0.45 to be included in the denominator (Equation (5)). Conclusions Excellent lateral stability and drift ductility of reinforced concrete shear walls are important in the design of medium-to-high-rise buildings to resist seismic actions and other exceptional loads. However, shear walls in modern buildings are often subjected to very high axial compression, which has been pushing the limits of the conventional design and analysis theories. A comprehensive statistical analysis using 474 sets of experimental data was conducted to investigate the effect of the axial compression ratio on the structural performance of various types of RC structural wall. It was shown that the ductility of shear walls generally diminished with an increase in axial compression ratio, and this trend was particularly noticeable for slender walls with an aspect ratio greater than 1.5. Provisions on the limits of the axial compression ratio stipulated in various design codes of practice were then compared. The expected attainable ductility of RC walls designed to different codes was evaluated and compared with the statistical analysis results. Based on the analysis results, recommendations were made for possible amendments to Clause 9.9.3 detailing for ductility of walls in the HKConcrete2013 [18] for calculation of the effective axial compression and determination of the limiting value of the axial compression ratio. The suggested amendments include: (1) the calculation of the effective axial compression in RC structural walls should be based on a realistic, representative gravity action; and (2) the limiting value for the axial compression ratio should guarantee that well-detailed RC structural walls can attain moderate or at least restricted ductility.

ψri

School, theatre, etc.

1.0 0.8

Dwelling area, restaurant, etc.

0.5

Warehouse, library, mechanical room, etc.

1.0

Funding This work was supported by the Hong Kong Research Grants Council [grant number 614011].

Notes on contributors Ir Prof J S Kuang is a Professor of Civil and Environmental Engineering, the Hong Kong University of Science and Technology. His areas of expertise span seismic engineering, with an emphasis on seismic design and the behaviour of concrete structures, seismic vulnerability assessment of tall buildings, large-scale testing of structural concrete, and computational mechanics and simulation in structural engineering. Ir Prof Kuang’s awards include the Telford Premium and the TK Hsieh Award from the Institution of Civil Engineers UK in 2014 and 2006, respectively, and the HKIE Transactions Prize from the Hong Kong Institution of Engineers in 2007.

Dr Y P Yuen is currently an Assistant Professor of the Department of Civil Engineering at the Bursa Orhangazi University, Turkey. His research interests include seismic analysis and engineering of building and bridge structures, theoretical and computational mechanics of materials, reinforced concrete and masonry structures, and tall building structures. Dr Yuen is the recipient of the 2014 Telford Premium from the Institution of Civil Engineers in the UK, presented for the best paper on engineering and computational mechanics.

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Ductility Design of Reinforced Concrete Shear Walls

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