Earthquake response of tall reinforced concrete chimneys

Engineering Structures 25 (2003) 11–24 www.elsevier.com/locate/engstruct

Earthquake response of tall reinforced concrete chimneys John L. Wilson The University of Melbourne, Melbourne, Australia Received 4 September 2001; received in revised form 7 June 2002; accepted 26 June 2002

Abstract The results from an experimental program have been used to develop a non-linear dynamic analysis procedure for evaluating the inelastic response of tall reinforced concrete chimney structures. The procedure is used to study the inelastic response of ten chimneys, ranging in height from 115 m to 301 m subject to earthquake excitation. Based on the study, a series of code design recommendations have been prepared and incorporated into the 2001 CICIND code to encourage reliance on the development of ductility in reinforced concrete chimneys and to prevent the formation of brittle failure modes. The basis for the selection of a structural response factor of R=2 which halves the seismic design forces is presented. The design recommendations result in both improved performance and cost savings of up to 20% compared with designs undertaken with the 1998 ACI307 and 1998 CICIND codes.  2002 Published by Elsevier Science Ltd. Keywords: Chimneys; Seismic; Ductility; Earthquake forces; Design codes; Inelastic analyses

1. Introduction Codes of practice around the world provide conservative guidelines for the aseismic design of tall reinforced concrete chimneys in the belief that such structures would behave in a brittle manner when subject to severe earthquake excitation. This has resulted in reinforced concrete chimneys being prohibitively expensive in regions of high seismicity. It has recently been established from an experimental program that reinforced concrete chimneys respond in a moderately ductile manner under severe reverse cycle loading through yielding of the reinforcement in tension provided that the sections possess a reasonable curvature capacity [1]. The results from the experimental program have been used to develop a non linear dynamic procedure for evaluating the inelastic response of tall reinforced concrete chimney structures described in this paper. The procedure, which incorporates a cantilever model with discrete plastic hinges is used to study the response of ten chimneys, ranging in height from 115 m to 301 m, to severe earthquake excitation. In particular, the response behaviour and the failure modes of these chimneys asso-

E-mail address: [email protected] (J.L. Wilson). 0141-0296/03/$ - see front matter  2002 Published by Elsevier Science Ltd. PII: S 0 1 4 1 - 0 2 9 6 ( 0 2 ) 0 0 0 9 8 - 6

ciated with an ensemble of earthquake ground motions is described. Based on the non linear dynamic study, a series of code design recommendations have been prepared which encourage the development of ductile behaviour to dissipate the seismic energy and prevent the formation of brittle failure modes. These recommendations have been incorporated into the 2001 CICIND code [2] for the design of reinforced concrete chimneys and result in cheaper chimneys which perform better under earthquake excitation (CICIND is a French acronym for International Committee on Industrial chimneys). The justification for the selection of a structural response factor of R=2 which reduces the seismic design forces and satisfies both the serviceability and structural stability limit states is presented using a deterministic approach. Finally, a comparison of the cost and performance of a 245 m tall chimney designed to the proposed seismic code provisions is made with the 1998 ACI 307, 1998 CICIND, 1996 EC8-3 and 1997 UBC codes of practice [2–5]. The paper focuses on the behaviour of the windshield and does not address the response of the flue liner or the foundation in any detail. However it is noted that a top hung steel flue system has significant structural advantages over other flue systems in seismic regions since a

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Nomenclature ae af aT b c D E EIsec EIeff F⬘c fc fy IF Ig Kzz Kx LF M∗ Mu Md Me My n R t V Vd Ve W fo fu fy rv mφ mφc ⍀m ⍀md ⍀ms ⍀v ⍀vd

‘elastic’ acceleration coefficient ‘failure’ acceleration coefficient ‘acceleration’ coefficient associated with a return period T years acceleration ratio=af/ae acceleration ratio=a2475/a475 windshield mean diameter elastic modulus of concrete=30,000 MPa secant stiffness of windshield effective stiffness of windshield concrete compressive strength axial compressive stress yield stress importance factor gross second moment of area rotational stiffness translational stiffness load factor moment demand ultimate moment capacity base bending moment—with overstrength base bending moment—nominal elastic design yield moment normalised axial force structural response factor windshield thickness shear force shear force—with overstrength shear force—nominal elastic design weight of structure moment overstrength factor ultimate curvature yield curvature longitudinal steel ratio (%) curvature ductility curvature ductility capacity base moment overstrength factor dynamic moment magnification factor large displacement moment magnification factor shear overstrength factor dynamic shear magnification factor

lighter thinner flue in tension can be used. Such tension systems have some inherent ductility and can accommodate the installation of energy dissipation devices at the lateral support locations.

2. Experimental results Four reinforced concrete pipes of length 4565 mm, diameter 1200 mm, thickness 30 mm and possessing 1.0%, 0.25%, 0.25% and 0.85% effective longitudinal

reinforcement ratios (test units 1–4 respectively) were fabricated and arranged as horizontal cantilevers with one end free and the other fixed as shown in Fig. 1. The specimens were subjected to a constant axial stress of 2 MPa (representative of chimney structures) and tested through the application of a cyclic transverse load at the free end. The cyclic load was applied under displacement control with increasing displacements each cycle of m=±0.75, ±1, ±2, ±3 etc until failure. In constructing the models the laws of similitude were followed so that the results were representative of full scale prototypes.

J.L. Wilson / Engineering Structures 25 (2003) 11–24

Fig. 1.

General arrangement of test set-up.

In particular, the following key parameters were representative: (a) diameter/thickness ratio of D/t=40, (b) axial stress level of fc / F⬘c ⫽ 0.05, (c) longitudinal steel ratio rv=0.25–1.0% and (d) shear span ratio M/VD=3.8 (the results from a number of inelastic analyses indicated that the average shear span ratio for full scale chimneys subject to earthquake excitation were in the range M/VD=3–5). Test units 1 and 4 behaved in a ductile and tough manner under cyclic loading as demonstrated from the force deflection hysteresis loops for test unit 1 shown in Fig. 2. A series of circumferential cracks developed along the length of the pipe in units 1 and 4, which opened and closed and widened as the longitudinal strains increased on subsequent cycles. In contrast, the ductility associated with units 2 and 3 was smaller than units 1 and 4 due to the low reinforcement ratio. This low reinforcement ratio resulted in the undesirable feature of the cracking moment exceeding the ultimate section capacity and consequently the development of only a single circumferential crack. The hysteresis shapes associated with units 1–4 were

Fig. 2.

Normalised moment versus drift for test unit 1.

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stable with increasing displacements resulting in an increase in the bending moments associated with the strain hardening of the reinforcement. The reduction in stiffness associated with an increase in ductility is characteristic of the closure of wide cracks, softening of the concrete matrix and the softening of the reinforcement due to the ‘Bauschinger’ effect. This ductile behaviour was achieved through yielding of the reinforcement in tension rather than non linear compressive behaviour of the concrete as demonstrated in Fig. 3 for test unit 1. The strains were measured using LVDT transducers mounted on the concrete surface over gauge lengths of 100 mm and 200 mm. The failure of the pipes after some 8–13 cycles was initiated by a combination of the loss of the concrete cover (through progressive deformation in the vicinity of the circumferential cracks as the concrete was cycled back and forth from extreme tension to compression) and the longitudinal steel buckling and fracturing (due to low cycle fatigue and the reduced elastic modulus associated with the ‘Bauschinger’ effect). A more detailed description of the experimental tests is provided in references [1,6,7].

3. Earthquake analysis procedure for inelastic chimneys 3.1. Literature review The earthquake design and analysis of chimneys subjected to earthquake excitation has typically been undertaken using linear dynamic procedures such as the response spectrum or time history modal analysis techniques. Rumman [8–10] published a number of papers describing the calculation of seismic forces for reinforced concrete chimneys using the response spectrum technique some thirty years ago. Rumman [11] also established co-efficients for estimating the modal periods and associated mode shapes of reinforced concrete chimneys that vary linearly in both mean diameter and thickness. Such methods which were very useful for estimating modal shear forces and bending moments have been superseded by finite element analysis software packages

Fig. 3. Normalised moment vs. extreme fibre strain for test unit 1 (tension strain denoted negative strain).

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which can perform dynamic analyses relatively simply and cost effectively. The modal analysis method accurately predicts the response of tall reinforced concrete chimneys in the elastic range as confirmed from a number of experimental studies carried out on real chimneys using ambient wind vibrations [12–16]. However, the response of tall chimneys to severe earthquake ground motions may require the stack to respond beyond the elastic range. A literature review indicated that few studies involving inelastic analyses have been undertaken [17–24]. In most of the studies the inelastic behaviour of the chimney was represented by a stick model using continuous fibre elements to explicitly represent the degrading hysteresis loops of the concrete and the reinforcement. Although these methods provide a useful insight into the inelastic response of chimneys, they assume that all sections are fully cracked and therefore underestimate the stiffness since both the tension stiffening effect and the tensile strength of concrete are ignored. Ignoring both effects results in a unrealistically flexible chimney particularly with the low longitudinal reinforcement ratios typically specified in reinforced concrete chimneys. The studies suggested that considerable ductility was available in reinforced concrete chimneys through the yielding of reinforcement in tension. The conclusions were however qualified in the recognition that the inclusion of tension stiffening effects would have stiffened the chimneys and resulted in the calculation of lower levels of ground shaking needed to cause failure. In contrast, the discrete plastic hinge approach allows the analyst to directly model the effective stiffness of the chimney to account for tension stiffening effects and provides some choice in the shape of the hysteresis loop selected for modelling the non linear and inelastic behaviour. In addition the discrete plastic hinge approach is computationally more efficient, and for these reasons has been selected as the preferred method for studying the aseismic response of reinforced concrete chimneys, using the inelastic analysis program [25]. The procedure developed by the author involves a number of steps which are summarised and discussed in the following sub sections [6,26]. The procedure assumes that the chimney has been designed in accordance with the seismic design guidelines outlined in the 2001 CICIND code [2] so that the inelastic chimney response is dominated by flexural action without the development of brittle modes of failure, such as local failures around openings, shear failures or failures of the foundation system. 3.2. Recommended procedure

Step 1: The chimney is modelled as a stick cantilever with masses lumped at approximately 10 nodes

and connected by elements reflecting the average geometrical sectional properties. Step 2: Plastic hinges are modelled at the base of each element using appropriate yield and ultimate moment capacities calculated for each section. A plastic hinge length equal to 20% of the chimney diameter is recommended based on the experimental results [1]. Step 3: A yield moment equal to 70% of the ultimate moment is considered representative for typical chimney sections based on experimental and theoretical results. (The My/Mu ratio was studied and found to vary over a narrow range between 0.7–0.8 for rv=0.5–2.0% and fc / F⬘c ⫽ 0⫺0.10 considered typical for reinforced concrete chimneys[6].) Step 4: The hysteretic behaviour of the plastic hinges is represented by the modified Takeda hysteresis model which best approximates the actual hysteretic behaviour obtained experimentally [1]. Background damping of 5% is assumed to model the energy losses associated with minor cracking. Step 5: A value of 0.50 EIg is considered a conservative value (from the perspective of predicted earthquake induced forces) for modelling the stiffness properties of a cracked chimney in an inelastic time history analysis and account for the increased stiffness caused by tension stiffening effects [1,6]. This effective stiffness value is consistent with code recommendations for the inelastic analysis of lightly loaded column elements in frames and for wall elements in buildings [27–29]. (It is recognised that this nominal effective stiffness value (EIeff=0.50 EIg) is higher than the secant stiffness value of EIsec=My/fy which is representative of a fully cracked section and hence not directly appropriate for an inelastic time history analysis). Step 6: The failure criteria for the chimney is based on the curvature demand predicted from an inelastic time history analysis reaching the curvature capacity fu at a particular node. The curvature capacity is calculated at each node of the chimney model assuming plane sections remain plane and with limiting compressive and tensile strains of 0.3% and 5% respectively. The curvature capacity fu is plotted in Fig. 4 in terms of the longitudinal reinforcment ratio (rv%) and the axial stress ratio (n ⫽ fc / F⬘c). Step 7: An ensemble of at least three times history ground motions appropriate for the site are applied to the base of the chimney and the maximum curvature demand is calculated at each plastic hinge located at each node. This analysis is repeated with the accelerogram

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reinforcement ratios are summarised in Table 1. The inelastic seismic response of this 245 m tall chimney was then studied using six representative accelerograms. 4.2. Chimney analyses

Fig. 4. Curvature capacity (fu∗D) vs. axial stress ratio and reinforcement ratio.

scaled by the peak ground acceleration until the threshold curvature capacity is reached, at which point the chimney is deemed to have failed.

4. Seismic response of a 245 m tall chimney 4.1. Chimney properties The elastic and inelastic response of a 245 m tapered reinforced concrete chimney subject to earthquake excitation was studied [6,7]. The diameter of the chimney varied from 16.8m at the top to 26.0 m at the base whilst the thickness ranged from 0.35 m to 0.70 m, respectively. The chimney was founded on piles with foundation compliance represented by a horizontal spring (Kx=3E3 MN/m) and a rotational spring (Kzz=4.8E6 MNm/rad). A fundamental period of 4.2 s was calculated for the uncracked chimney. The earthquake actions were calculated from the 1994 UBC [5] soft soil response spectrum scaled with an acceleration co-efficient of 0.15 g which corresponded to a 1 in 475 year event and represented a region of moderate seismicity. The application of the 1.4 load factor in accordance with the 1998 CICIND [2] recommendations increased the nominal elastic design earthquake to ae=0.21 g. The chimney was detailed for ductility by providing overstrength around the openings to that the base remained essentially elastic thereby encouraging inelastic flexural behaviour to occur at higher levels in the windshield. The wind actions were representative of a temperate wind environment, and were found to be significantly less than the lateral forces resulting from earthquake excitation. Based on the critical bending moments at each of the nodes, the required quantity of longitudinal reinforcement was calculated in accordance with the recommendations for the ultimate limit state strength design of reinforced concrete chimneys using the CICIND and ACI codes[2,3]. The chimney properties including the nodal co-ordinates, diameter, thickness and longitudinal

An elastic time history analysis of the chimney was undertaken in accordance with the 1998 CICIND [2] recommendations assuming 5% damping and gross section properties. The resulting elastic bending moments were evaluated and compared with the ultimate moment capacities at each node, and the accelerogram scaled so that the ratio of the moment demand to moment capacity equaled but did not exceed unity at the critical node. The resulting scaled peak ground acceleration for that accelerogram was deemed the ‘elastic’ acceleration value ae. The chimney was then analysed considering inelastic behaviour in accordance with the method outlined in Section 3.2. Each of the six accelerograms were scaled until the curvature demand exceeded the curvature capacity at one of the plastic hinges, at which the chimney was deemed to have failed. The resulting scaled peak ground acceleration was deemed the ‘failure’ acceleration value af. The acceleration ratio b=af/ae provides a valuable insight for assessing the performance of the chimney in the inelastic range, with a ratio close to unity suggesting a brittle structure whilst a ratio in excess of three to four implying some ductility. The effects of P– ⌬ were studied and found not to be important due to the relatively low axial forces and lateral displacements. The ratio of the maximum curvature demand to corresponding curvature capacity has been plotted as a function of normalised height (height divided by total height of chimney) in Fig. 5 for each of the six ground motions A–F. (Details of the six ground motions are provided in Appendix 1.) The acceleration values ae, af and the acceleration ratio, b have been listed in Table 2. The acceleration ratio ranged from 5 to 8 for the six different accelerograms and indicated that the chimney was not brittle but could respond in the inelastic range with some ductility. The critical section of the chimney was in the region 0.30 to 0.75 of the chimney height and indicated that the inelastic behaviour was widespread with the formation of multiple plastic hinges rather than being confined to one plastic hinge location as shown in Fig. 7b. The response of the chimney to the six accelerograms was quite varied and reflected the different frequency and pulse characteristics of the ground motions. The behaviour of a tall chimney responding to earthquake excitation is quite complex with higher mode effects dominating. The total accelerations are not in phase up the height of the chimney and at any instant of time the accelerations at different sections of the chimney could be acting in opposite directions. This is contrary to the simplistic acceleration distribution assumed in a static pushover analysis where inertial

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Table 1 Geometry and properties of 245m chimney Node

9 8 7 6 5 4 3 2 1

Height (m)

Diameter (m)

245 210 180 150 120 90 60 30 0

16.80 16.80 16.80 16.80 16.80 17.04 18.16 20.00 28.00

Thickness (m)

0.350 0.350 0.350 0.350 0.350 0.365 0.410 0.700 0.700

D/t

48 48 48 48 48 47 44 29 37

n ⫽ fc / F⬘c

0 0.021 0.038 0.056 0.074 0.086 0.089 0.061 0.061

ae=0.21 g rv (%)

fu D

0.50 0.50 0.78 0.85 0.89 0.87 0.97 0.80 0.80

0.053 0.053 0.053 0.052 0.038 0.034 0.030 0.051 0.051

Fig. 5. Ratio of maximum curvature demand to curvature capacity (f∗/fu) over the height of a 245 m chimney for ground motions A–F.

Table 2 Ratio of ‘failure’ to ‘elastic’ acceleration values for 245m Chimney Node

ae (g) af (g) b=af /ae

Ground motions A

B

C

D

E

F

0.13 0.75 6

0.19 1.50 6

0.26 1.86 7

0.37 1.85 5

0.22 1.65 7.5

0.16 0.80 5

forces at all nodes of the structure are assumed to be moving in phase in one direction. The displacements are generally in phase up the height of the chimney with a period of oscillation in the order of 6 s resembling a first mode type response. The maximum displacement at the top of the chimney was approximately 5.0 m and represented a 2% drift (tip displacement/chimney height). The bending moment and normalised curvature ductility demand is generally inphase with the displacement response although the influence of the higher mode effects is evident. The time history plots indicated that multiple plastic hinges develop and co-exist simultaneously up the height of the chimney.

A typical hysteresis plot of the moment versus curvature at the critical plastic hinge located at approx. 120 m above the base is shown in Fig. 6. The hysteresis behaviour modelled using the modified Takeda hysteresis rule provides a good representation of the behaviour observed in the experimental program. The maximum curvature developed at the critical plastic hinge was 0.0018 m⫺1 (0.034/D) which corresponded to a very small plastic hinge rotation of 0.0061 radian or 0.35 degrees, assuming a plastic hinge length of 3.4 m (0.2D). The number of complete inelastic cycles is very low and in the order of 2, which reflects the response of a long period structure to a relatively short duration earthquake. Increasing the duration threefold to say 36 s would increase the number of inelastic cycles to around 6, but significantly most of these inelastic excursions would be small and less than 50% of the ultimate curvature capacity. The number of inelastic cycles is important particularly for the performance of lapped splices since it represents the number of occurrences the reinforced concrete section could be subjected to severe tensile strains followed by moderate compressive strains. Consequently the effects of strength degradation and low cycle fatigue should not be critical for tall reinforced concrete chimneys subject to earthquake excitation.

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Fig. 7. (a) Chimney acceleration and displacement response at 6.2 and 6.9 s. (b) Chimney bending moment and normalised curvature response (f∗/fu) at 6.2 and 6.9 s.

Fig. 6. Moment curvature hysteretic behaviour at plastic hinge 120 m above base.

4.3. Chimney mode of failure The chimney is deemed to fail when the normalised moment curvature exceeds unity, which occurs at approx. 6.9 s at a height of around 120 m. An explanation for the failure can be reasoned from Fig. 7(a) and (b) which presents a plot of a series of instantaneous acceleration, displacement, bending moment and normalised curvature values versus chimney height at 6.2 s and 6.9 s. At 6.2 s the accelerations above the base are all in phase and induce inertia forces that push the chimney in one direction, with a resulting bending moment diagram that decreases with height, as would be expected for a cantilever that has been effectively loaded in one direction. This force pattern results in a maximum

displacement in the chimney at around 6.5 s. Between 6.2 s and 6.9 s the acceleration pattern changes dramatically, resulting in amplified inertia forces which change direction over the lower 180 m of the chimney. This results in the development of maximum bending moments at a height of between 90 and 120 m and causes the ultimate curvature to be exceeded at a height of approx 120 m, which is defined as nominal failure. Interestingly at this instance of nominal failure, the bending moment at the base is quite small and has reversed direction whilst the chimney deflections have decreased. This study has highlighted the complex dynamic response of a typical reinforced concrete chimney under earthquake excitation. The structure can be thought of as a highly tuned profiled cantilever which is “whippy” in nature and dominated by higher mode effects. The behaviour of such a structure cannot be readily predicted using a simple static push over analysis nor by a simple single degree of freedom substitute structure. Overall dynamic stability of the chimney is maintained as a result of the chimney sections possessing adequate curvature ductility through the yielding of reinforcement combined with the nature of earthquake ground motions that are characterised by a number of short duration high frequency pulses that continually change direction.

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5. Summary of case study chimneys 5.1. Ratio of failure to elastic peak ground acceleration values The detailed analyses carried out for the 245 m tall chimney were repeated for a further nine chimneys ranging in height from 115 m to 301 m and similar results were obtained [6,7]. The results of the analyses suggest that a correlation exists between the global ductility of the chimney (as assessed from the acceleration ratio b=af/ae) and the local curvature capacity of the plastic hinges at the critical sections within the chimneys as summarised in Table 3. It is recommended that chimneys be designed and detailed for moderate ductility so that the minimum ‘failure’ to ‘elastic’ peak ground acceleration ratio exceeds four (af/aeⱖ4). This design objective will enable the seismic design forces to be reduced by the introduction of a structural response factor (ductility or R factor) which will be discussed further in Section 6. Based on the analyses a chimney could be defined as moderately ductile provided that a minimum curvature capacity of fu=0.03/D is provided over the height of the chimney where inelastic action may be expected (i.e. above the openings to around 80% of the chimney height). The minimum ultimate curvature of fu=0.03/D corresponds to a concrete compressive strain of 0.3% and a steel tensile strain of 2.7%. This can be achieved by limiting the longitudinal reinforcement percentage to approx. rv(%)=2.40⫺14n (where n is the ratio of the axial stress to ultimate concrete compressive strength) and indicates that for n=0, 0.05, 0.10 and 0.15, the reinforcement ratio should not exceed r=2.4%, 1.7%, 1.0% and 0.3%, respectively. 5.2. Inelastic displacements A study was also undertaken to compare the chimney inelastic displacements corresponding to an acceleration af=4ae with the elastic displacements associated with an ‘elastic’ acceleration, ae. The inelastic displacements of the windshield are an important parameter when checking the likely performance of the chimney liners under an extreme earthquake event. The ratio of the inelastic to elastic displacements at the top of the chimney were calculated for each of the fifty analyses carried out on the case study chimneys. The results suggest that the Table 3 Correlation between curvature capacity and overall chimney ductility Minimum curvature capacity

Acceleration ratio

Chimney ductility

fu⬍0.03/D φu⬎0.03/D

af/ae=2–3 af/aeⱖ4

Limited ductility Moderate ductility

inelastic displacements were in the order of 25% greater than the displacements calculated from an elastic analysis assuming the same input ground motion. The inelastic tip displacement at the failure acceleration (af=4ae) was typically in the order of 1% of the chimney height, with a maximum drift value of 1.8% calculated. Such drift values are less than the 2–3% limits typically specified for building structures under extreme earthquake excitation [29,30]. 5.3. Shear overstrength factors An estimate needs to be made of the maximum shear force that may develop in a chimney during an extreme earthquake event to ensure that flexural inelastic action develops and shear failure is prevented. The shear force distribution that develops during an elastic dynamic response is different from that resulting from a response spectrum analysis. Further, a time history analysis carried out in the inelastic range will produce different results from an elastic analysis performed using the same earthquake ground motion. The maximum shear force Vd that develops under inelastic action can be evaluated from the product of the shear overstrength factor ⍀v and the nominal design shear force Ve as follows: Vd ⫽ ⍀v·Ve

(1a)

and ⍀v ⫽ fo·⍀vd

(1b)

The moment overstrength factor fo allows for overstrength in a section due to capacity reduction factors and strain hardening of the reinforcement with values typically in the range fo=1.2–1.5 depending on the material overstrength factor, axial stress ratio, and longitudinal reinforcement ratio. The dynamic shear magnification factor ⍀vd allows for the increased shear developed in a windshield responding inelastically due to higher mode effects and the development of multiple plastic hinges causing a change in the shear force distribution. Similar effects have been observed by Goyal and Maiti [20] who reported shear enhancement factors ranging from 1.8 to 2.4 for their case study chimneys. A number of studies have been undertaken to evaluate the dynamic shear effects associated with structural walls [31–33]. In all these studies, a single plastic hinge was assumed to form at the base of the uniform wall, and the dynamic shear effects were evaluated both analytically [32] and experimentally [31,33]. Whilst such wall configurations are not typical of tall profiled chimneys, the conclusions are consistent, demonstrating the importance of the higher mode effects in modifying the shear force distribution. Paulay [28] recommends a dynamic shear magnification factor between 1.0 and 1.8 for short

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and tall structural walls responding inelastically respectively. A study was undertaken to evaluate the dynamic shear magnification factor, ⍀vd, associated with the case study chimneys resulting from the application of an acceleration af=4ae. The shear force demand was evaluated from the inelastic seismic analysis (af=4ae) for each ground motion and compared with the nominal shear forces, Ve, resulting from an elastic modal analysis using the design response spectrum. The ⍀vd factor, defined as the ratio of the inelastic to the nominal elastic design shear forces, was then calculated. The shear forces were magnified in different regions of the chimney depending on the chimney geometry and characteristics of the earthquake ground motion [6] A statistical study was undertaken and the following mean values were evaluated: ⍀vd=1.75 at the base of the chimney (lower 10% of height), ⍀vd=1.0 at the top of the chimney (upper 20% of height) and ⍀vd=1.55 in the remaining intermediate region. The overall shear overstrength factors were then evaluated from the product of fo=1.4 and ⍀vd resulting in ⍀v=2.5 at the base and ⍀v=2.2 in the intermediate region. A shear overstrength value of 1.0 is recommended near the top where inelastic effects are minimal. This additional shear demand is typically not critical as the circumferential reinforcement required for ovalling wind moments usually provides sufficient shear capacity for seismic design. 5.4. Base moment overstrength factor The principles of capacity design dictate that the foundation and base of the chimney in the vicinity of the openings be designed for overstrength to prevent the development of brittle failure modes and encourage ductile flexural action in the windshield. The maximum base moment Md that develops under inelastic action can be evaluated from the product of the base moment overstrength factor ⍀m and the nominal elastic design bending moment Me as follows: Md ⫽ ⍀m·Me

(2a)

and ⍀m ⫽ fo·⍀md·⍀ms

(2b)

An overall base moment overstrength factor of ⍀m=1.5 is recommended based on dynamic (⍀md) and large displacement (⍀ms) moment magnification mean values of ⍀md=1.05 and ⍀ms=1.05, respectively (obtained from analyses) combined with a reasonable moment overstrength value of fo=1.4. The low values of ⍀ms and ⍀md indicates that in tall chimneys the amplification effects due to P–⌬ effects are minimal and that the dynamic amplification of the base bending moment

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is small due to the moments in the upper sections being limited through the formation of multiple plastic hinges. 6. 2001 CICIND Code Recommendations 6.1. Design Philosophy The seismic design approach described in this section which has been incorporated into the 2001 CICIND code [2] is based on dual performance criteria: 1. designing the chimney elastically to resist earthquake induced forces considered reasonable for a serviceability limit state earthquake event (SLS), and 2. designing the chimney with sufficient ductility so that the chimney will not collapse when subject to an extreme earthquake event at the structural stability limit state (SSLS). In regions of moderate to high seismicity it is recommended that chimneys be designed for ductility (R=2). This design strategy will result in chimneys that are both economical and sufficiently ductile to survive an extreme earthquake event [26]. 6.2. Seismic actions 6.2.1. Return period The design basis earthquake is a representative earthquake associated with a return period of 475 years (i.e. 10% chance of exceedance in 50 years). 6.2.2. Elastic response The elastic response of the chimney shall be calculated assuming gross section properties and using an appropriate response spectrum for the site with 5% critical damping and 50% shape bound probability. Sufficient number of modes shall be included so that at least 90% of the mass of the chimney is accounted for in the modal analysis 6.2.3. Seismic design actions The seismic design actions shall be obtained from the elastic response by multiplying the actions by an importance factor (IF) and dividing by a structural response factor (R) to account for ductility. 6.2.3.1. Importance factor The importance factor is dependent on the importance class of the chimney: Class 1: IF=1.0 Class 2: IF=1.4. 6.2.3.2. Structural response factor The structural response factor is dependent on the level of seismic detailing:

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R=1.0 No specific seismic detailing R=2.0 Specific design requirements (as outlined in Section 6.3). 6.3. General seismic design and detailing requirements associated with R=2 6.3.1. General capacity design principles The design of the chimney should be consistent with the principles of capacity design. The flexural and shear capacities of the foundation system and the shell in the vicinity of openings should be designed for overstrength so that inelastic flexural behaviour will develop in the ductile regions of the windshield away from significant openings. In particular the following specific detailing requirements should be satisfied to ensure ductile behaviour. 6.3.2. Specific detailing and design requirements 1. Base moment overstrength to prevent flexural failure developing at the chimney base (in the vicinity of openings) and in the foundation. The recommended moment overstrength factor is ⍀m=1.5. 2. Shear overstrength factors to discourage shear failure in the windshield and foundations. The recommended shear overstrength factors to be applied to the nominal design shear forces are: ⍀v=2.5 (0–10% chimney height), ⍀v=2.2 (10–80% chimney height), ⍀v=1.0 (80–100% chimney height). 3. Curvature capacity in the windshield over the range 10%–80% of chimney height to exceed 0.03/D (i.e. fuD ⬎ 0.03). This will ensure that the compression strains and compression zone are small (with a neutral axis depth less than four times the wall thickness for a typical windshield) and will alleviate the need for confinement steel. The limiting curvature capacity of 0.03/D can be achieved by limiting the maximum longitudinal steel reinforcement percentage to rv=2.40⫺14n, where n is the axial stress ratio (n ⫽ fc / F⬘c) and fy=400 MPa. 4. Ultimate moment capacity of the chimney between the base and 80% of the chimney height exceeds the cracking moment capacity so that plastic hinges of reasonable length can develop. 5. Longitudinal steel reinforcement is ductile with an ultimate tensile strain in excess of 10–15%, consistent with the recommendations for the ductile response of any reinforced concrete structure. 6. Staggered longitudinal splices are specified so that at any cross section not greater than 50% of the reinforcement bars are spliced to prevent a plane of weakness from developing. It is recommended that the standard development length be increased by 30% to provide additional protection from bond failure under cyclic loading.

7. Comparison of proposed code provisions with other codes of practice This section compares the cost and performance of a 245 metre tall chimney (see Section 4) designed using the limited ductility design provisions of the 2001 CICIND code [2] with designs undertaken using the following codes of practice: 1998 CICIND, 1998 ACI 307, 1997 UBC and 1996 EC8-3 [2–5]. The earthquake forces were described by the normalised soft soil elastic response spectrum (ERS) specified in the 1994 edition of the UBC [5]. An acceleration co-efficient corresponding to the 475 year return period event of a475=0.30 g was selected to reflect a region of moderately high seismicity. The wind forces reflected a temperate wind regime and were found to be significantly less than the earthquake forces. The costs have been calculated on the basis of standard supply and construction rates for concrete US$280/m3 and for reinforcement (longitudinal and circumferential) US$1400/tonne. Further details of the study are provided in [6,7,34]. The limited ductility design (LDD) approach recommended in the 2001 CICIND code (and outlined in the previous section) is the most cost effective aseismic design strategy and allows the earthquake forces to be reduced for ductility by encouraging the simultaneous formation of multiple plastic hinges in the windshield away from the openings and foundation system. The development of multiple plastic hinges has the advantage that the inelastic behaviour and curvature demand will be spread over a wider region of the chimney to dissipate the seismic energy, and will limit the seismic forces that are transmitted to the foundation system. The associated nominal ‘elastic’ earthquake acceleration value is ae=0.21 g (LF=1.0, IF=1.4 and R=2) with a ‘failure’ acceleration value in excess of af=0.80 g (including the effects of overstrength will further increase af), and a windshield cost in the order of US$2.5 million. (Further justification for the recommendation of a structural response factor R=2 is provided in Appendix 2). The elastic seismic design approach recommended in the 1998 CICIND and 1998 ACI307 encourages elastic behaviour with no requirements for ductility. The nominal ‘elastic’ design earthquake (used to scale the normalised response spectrum and to calculate the ultimate bending moments in the windshield) is effectively ae=0.42 g (LF=1.4, IF=1.0 and R=1.0) for the CICIND code, with an associated windshield cost in the order of US$3.25 million. In contrast, the ACI code specifies factors of LF=1.43 (reduced from LF=1.87 in the 1995 edition), IF=1.0 and R=1.33, resulting in ae=0.32 g and a windshield cost in the order of US$2.8 million. In addition, the load factors specified for the design of the foundations in ACI307 are lower than those specified for the design of the windshield, which is contrary to normal capacity design principles for structures. Significantly,

J.L. Wilson / Engineering Structures 25 (2003) 11–24

both codes encourage chimneys to be designed elastically without consideration to the likely mode of failure, and consequently under extreme ground shaking the chimneys may fail in a brittle and catastrophic manner around the openings or in the foundation system. Further, with the reduced earthquake forces specified in ACI307, the chimneys could be more vulnerable than equivalent designs undertaken using the 1998 CICIND code. A further study of six chimneys ranging in height from 115m to 300m suggest that the LDD approach recommended in the 2001 CICIND code results in windshield cost savings in the order of 20% and 10% compared with the 1998 CICIND and 1998 ACI307 methods, respectively. Additional cost savings would be associated with the design of the foundation system. UBC-97 allows the earthquake design forces to be reduced for ductility through the introduction of a ductility factor, without specifying any special design and detailing requirements. Further, the R factor recommended is both site and natural period dependent and consequently does not appear to have a totally rational basis. The nominal elastic design earthquake associated with the UBC design for this chimney configuration is ae=0.21 g (LF=1.0, IF=1.0 and R=1.5) with an associated windshield cost of US$2.5 million. EC8-3 recommends the chimney be designed to encourage ductility through the formation of one plastic hinge using capacity design principles. The overstrength factors recommended are considered by the author to be non-conservative due to higher mode effects significantly magnifying the chimney response. The nominal ‘elastic’ design earthquake acceleration is effectively ae=0.14 g (IF=1.4, R=3) at the hinge and ae=0.21 g (LF=1.0, IF=1.4 and R=2) away from the hinge resulting in a windshield costing in the order of US$2.3 million. However, if the overstrength factors are increased in the chimney to account for the higher mode effects then the cost increases to US$3.2 million. In addition the concentration of the damage and inelastic behaviour at one location has further design, detailing, construction and cost implications. 8. Conclusions 1. A discretised inelastic frame model was developed based on the results from an experimental study. The cantilever model using discrete plastic hinges was more accurate and computationally more efficient than other models using continuous finite element model techniques, and produced reasonable estimates of the inelastic response of a chimney to earthquake excitation. The inelastic and elastic response of 10 case study chimneys (which had been designed for moderate ductility) to six different earthquake ground motions were studied from which the following conclusions could be drawn:

21

(a) Tall reinforced concrete chimneys respond in a complex manner under earthquake excitation. The structure can be thought of as a highly tuned profiled cantilever which is ‘whippy’ in nature and dominated by higher mode effects. (b) The inelastic response of a chimney cannot be readily predicted using linear static or non linear static procedures such as a simple static push over analysis or by a single degree of freedom substitute structure. (c) The chimney responds inelastically with the development of multiple plastic hinges in the windshield. Higher mode effects dominate the response with significant inelastic deformations typically concentrated over the region between 30–80% of the chimney height. (d) A moderately ductile chimney, which responds inelastically through the formation of multiple plastic hinges, can sustain earthquake ground shaking at a level at least four times greater than the motion needed to cause the elastic moment demand to exceed the ultimate moment capacity, assuming uncracked section properties. This result is significant as it implies that a chimney designed elastically using uncracked section properties can survive an earthquake scaled by at least a factor of four (i.e. afⱖ4ae). 2. A number of general design and detailing recommendations have been presented in Section 6.3 to ensure a chimney possesses moderate ductility. Some of the design issues include the specification of; overstrength, minimum strength, minimum ultimate curvature values and staggered splice requirements. 3. Recommendations have been developed for the elastic design (ED, R=1) and limited ductile design (LDD, R=2) of both ordinary (IF=1.0) and special (IF=1.4) chimney structures to satisfy the serviceability limit state (SLS) and structural stability limit state (SSLS). The probability of exceedance over a 50 year life for ordinary and special chimneys are in the order of 50% and 25% for the SLS and 2% and 1% for the SSLS. 4. The LDD approach specified in the 2001 CICIND code is strongly recommended for the design of tall chimney structures. This method allows a 50% reduction in earthquake forces (R=2) to account for ductility effects, provided some basic design guidelines are followed. In contrast, the ED approach which assumes R=1 (1998 CICIND) and R=1.3 (1998 ACI 307), results in a chimney that may fail in a brittle manner. 5. The limited ductile design approach recommended in the 2001 CICIND code,which encourages the formation of multiple plastic hinges in the windshield away from openings to dissipate the seismic energy, results in a chimney with a significantly improved performance at the SSLS, and significantly reduced design forces for both the windshield and foundations.

22

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6. A detailed study of six case study chimneys indicated that special chimneys designed using the 2001 CICIND code LDD method (R=2) resulted in cost savings for the windshield of 20% compared with the 1998 CICIND design method. Further cost savings would be associated with the design of the foundations. 7. The seismic design approach specified in the 1998 ACI 307 and 1998 CICIND encourages elastic behaviour with no specific requirements specified for ductility. Consequently, a chimney designed following the guidelines will be significantly more expensive and may behave in a brittle manner under an extreme earthquake event. 8. The seismic design recommendations of EC8-3, which encourages ductile behaviour through the formation of one plastic hinge using capacity design principles, are considered non conservative due to higher mode effects magnifying the chimney response. Significantly larger moment amplification factors are needed in the upper section of the chimney with resulting design and cost implications. The concentration of the damage and inelastic behaviour at one location has further design, construction and cost implications. 9. The seismic design approach recommended in the 1997 UBC code allows a reduction in the elastic forces for ductility without specifying any special design and detailing requirements. Consequently a ductile response of the chimney under extreme earthquake excitiation cannot be guaranteed. Further, the ‘R’ factor recommended in the UBC being both site and natural period dependent does not appear to have a rational basis. Acknowledgements Acknowledgements and appreciation are extended to the CICIND organisation, University of Melbourne and Ove Arup and Partners and the very helpful comments from the reviewers. CICIND and the University provided financial assistance and infrastructure support for the testing program whilst Arups provided valuable chimney design experience for the author whilst working in their London office. Appendix 1. Details of Earthquake Accelerograms See Table 4. Appendix 2. Justification of Structural Response Factors The selection of the seismic load factors recommended in the 2001 CICIND code [2] are justified in this section

using the ATC-3-06 provisions [35] and also checked using the NEHRP provisions [36] (further information is available in [37]). The ATC provisions have the significant advantage that acceleration levels can be predicted approximately using the Weibull distribution for different return periods ranging from 50 to 10,000 years [24]. Such a relationship does not exist for the NEHRP provisions, however an indirect check can be undertaken using the range of acceleration ratios that exist between the 2475 and 475 year hazard curves. (a) ATC-3-06 hazard The return periods associated with the serviceability limit state (SLS) and structural stability limit state (SSLS) are evaluated in this section assuming a seismic hazard consistent with the ATC-3-06 provisions. The SLS is associated with the seismic demand equalling the ultimate strength of the chimney and is equivalent to the ‘elastic’ acceleration, ae. The SSLS is associated with inelastic failure of the chimney at an acceleration level of af. The ratio of the ‘failure’ acceleration to the ‘elastic’ acceleration has been assumed equal to a minimum value of b=af/ae=4×1.4=5.6 for chimneys designed for limited ductility (R=2). The factor 4 is based on the analytical studies of Section 5, whilst the factor 1.4 represents the likely flexural overstrength. Similarly the acceleration ratio for chimneys designed elastically with no consideration given to ductility (R=1) has been estimated to be in the order of b=af/ae=1.4 based on the available overstrength. The ‘elastic’ acceleration value (ae) associated with the SLS can be calculated from the various importance factors (IF) and structural response factors (R) assuming a design basis earthquake associated with a return period of 475 years (a475): ae ⫽ (IF / R)·a475

(A1)

or ae / a475 ⫽ IF / R

(A2)

Similarly the failure acceleration af associated with the SSLS can be calculated: af ⫽ b·(IF / R)·a475

(A3)

or af / a475 ⫽ b·(IF / R)

(A4)

The effective return periods associated with the SLS (ae) and SSLS (af ) can be estimated from the ATC hazard curves as listed in Table 5 for each of the different chimney classes, types of detailing and levels of seismicity. In addition the acceleration ratios ae/a475 and af/a475 have been listed. It should be emphasised that the prediction of return periods for a given level of seis-

J.L. Wilson / Engineering Structures 25 (2003) 11–24

23

Table 4 Details and characteristics associated with the six earthquake accelerograms A–F Parameter

Units

Earthquake Date Magnitude Re Soil type PGA PGV PGD PGV/PGA PGA/PGV PGD/PGA (PGD×PGA)/PGV2 td td (accel 5–95%) td (velocity 5–95%)

Mo km g m/s m mm/s/g g/m/s m/g s s s

A

B

C

D

E

F

Synthetic ∗ ∗ ∗ Soft (S=2) 0.10 0.32 0.39 3200 0.31 3.90 0.38 26 16 16

Kobe 17/01/95 7.2 20 Stiff 0.84 0.91 0.24 1083 0.92 0.29 0.24 30 8 9

El-Centro 18/05/40 6.6 8 Stiff 0.32 0.36 0.19 1125 0.89 0.59 0.47 30 24 24

Pacoima Dam 9/02/71 6.6 8 Stiff 1.19 1.15 0.40 966 1.03 0.34 0.36 40 7 6

Honshu 16/05/68 7.9 290 Stiff 0.22 0.33 0.12 1500 0.67 0.55 0.24 90 33 34

Synthetic ∗ ∗ ∗ Soft (S=2) 0.10 0.26 0.21 2600 0.38 2.10 0.31 12 7 6

Re=Epicentral distance; td=duration; PGA=peak ground acceleration; PGV=peak ground velocity; PGD=peak ground displacement. Table 5 Return periods associated with SLS and SSLS Class

Detailing

1

Elastic

1

Seismic

2

Elastic

2

Seismic

Seismicity

Low High Low High Low High Low High

IF

1.2 1.2 1.0 1.0 1.4 1.4 1.4 1.4

R

1 1 2 2 1 1 2 2

af/ae

1.4 1.4 5.6 5.6 1.4 1.4 5.6 5.6

micity is an inexact science and the values should be taken as indicative only. The results indicate that chimneys designed for limited ductility with R=2 are not likely to fail since the return period associated with the SSLS are typically well in excess of 2475 years. Importantly, the SLS appears satisfactory with return periods in the order of 50–100 years for ordinary chimneys and 100–200 years for special chimneys. Special chimneys designed elastically with R=1 and IF=1.4 possess a reasonable return period at the SSLS and appear totally over designed at the SLS. (b) NEHRP hazard An alternative approach for the selection of a structural response factor, R, is on the basis that an ordinary chimney (IF=1.0) should survive the 2475 year SSLS event without collapse (2% exceedance in 50 years). The ‘elastic’ acceleration value ae has been previously defined as the acceleration level at which the seismic demand equals the ultimate strength of the chimney. The

ae/a475

1.2 1.2 0.5 0.5 1.4 1.4 0.7 0.7

af/a475

1.7 1.7 2.8 2.8 2.0 2.0 3.9 3.9

Return period DB

SLS

SSLS

475 475 475 475 475 475 475 475

475 475 120 40 1075 2600 220 120

1075 2600 8300 10000+ 2700 10000+ 10000+ 10000+

elastic acceleration can be expressed in the form ae=a475 (IF/R). This can be re-arranged in terms of the structural response factor, R: R ⫽ IF·a475 / ae ⫽ IF·(a475 / a2475)·(a2475 / ae)

(A5)

⫽ IF·b / c where b=a2475/ae and for af=a2475, b=af/ae and c=a2475/a475. The factor b is dependent on the chimney design whilst the factor c is dependent on the seismicity of the site. The ratio of the failure to elastic acceleration for a chimney designed for limited ductility and allowing for overstrength is at least b=af/ae=4×1.4=5.6. The ATC-3-06 provisions suggest that c varies from 1.5 to 2.0 for high and low seismic regions respectively. The seismic hazard maps published in the NEHRP provisions suggest similar values for the high seismicity regions and c=2–3 for the low seimicity regions. However, in some moderate seismic regions, near large

24

J.L. Wilson / Engineering Structures 25 (2003) 11–24

Table 6 ‘R’ values asociated with a range of c values (c=a2475/a475) and IF factors R

c=2

c=3

c=5

IF=1.0 IF=1.4

2.8 3.9

1.9 2.7

1.1 1.5

intraplate faults which rupture infrequently (e.g. New Madrid fault) the c value may increase to c=4–6. The structural response factors R which results from the combination of b=5.6 and a range of c factors are summarised in Table 6. A structural response factor of R=2 appears reasonable for the seismic hazard specified in the ATC-3-06 and NEHRP provisions. An exception is the moderate seismicity region where according to the NEHRP provisions c may approach a value in the range 4–6 and result in an R factor less than 2. For such regions the design basis earthquake (a475) could be artificially increased for design purposes to a475=a2475/c where c=2–3. Alternatively, the design basis earthquake could be associated with the 2475 year event a2475 and the structural response factor increased from R=2 to R=3.

References [1] Wilson JL. The aseismic design of tall reinforced concrete chimneys. ACI Structural Journal (in press). [2] CICIND. Model code for concrete chimneys, Part A: the shell. International Committee on Industrial Chimneys, Switzerland, 1998/2000. [3] ACI 307. Standard practice for the design and construction of cast in place reinforced concrete chimneys. American Concrete Institute, MI, 1995/98. [4] Eurocode 8-1. Design provisions for earthquake resistance of structures, Part 1: general rules. DD Env 1998-1-1, Brussels, 1996. [5] International Conference of Building Officials. Uniform Building Code, Chapter 23: Earthquake Design. ICBO, CA, 1994/97. [6] Wilson JL. Earthquake design and analysis of tall reinforced concrete chimneys. PhD thesis, Department of Civil and Environmental Engineering, University of Melbourne, Australia, 2000. [7] Wilson JL. Earthquake design and analysis of tall reinforced concrete chimneys. CICIND Report 1999;15(2):16–26. [8] Rumman WS. Earthquake forces in reinforced concrete chimneys. ASCE Journal of Structural Division 1967;93((ST6)):55– 70. [9] Rumman WS. Basic structural design of concrete chimneys. ASCE Journal of Power Division 1970;96((P03)):309–18. [10] Maugh LC, Rumman WS. Dynamic design of reinforced concrete chimneys. ACI Journal Paper 1967;64-47:558–67. [11] Rumman WS. Modal characteristics of linearly tapered reinforced concrete chimneys. Journal of ACI 1985;82:531–6. [12] Omote Y. Vibration test of existing chimney. Report of the Technical Research Institute, Ohbayashi-Gumi Ltd., Japan, 1975. p. 13–5. [13] Adachi N, Koshida H. Vibration characteristics of a 200 m high reinforced concrete chimney. Kajima Corporation, Kajima Institute of Construction Technology 1982;30:107–14.

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