sismos

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DEL 6 AL 9 DE NOVIEMBRE DE 2013, BOCA DEL RO VERACRUZ, HOTEL GALERA PLAZA

SOCIEDAD MEXICANA DE INGENIERA SSMICA A.C.

XIX CONGRESO NACIONAL DE INGENIERA SSMICA

APPLICATION OF A COLLAPSE CAPACITY METHODOLOGY TO MOMENT RESISTING FRAMES WITH HIGH STRENGTH MATERIALS

Luis Francisco Ibarra 1 and Bihanu Bishaw 2

ABSTRACT

This study evaluates the collapse capacity of moment resisting frames that include high strength concrete (HSC), high

strength steel (HSS), and steel fibers. The use of HSC in moment resisting frames located in moderate and high seismic

hazard regions has been limited. Although the increased compressive strength can provide higher gravity load carrying

capacity, the systems ductility decreases, and early spallation is likely to occur. Fiber reinforced concrete (FRC) improves the concretes mechanical properties and reduces early cracking. A collapse capacity methodology developed for modern RC moment-frame buildings is used to predict the improvement on the systems seismic resilience when HSC and high strength fiber reinforced concrete (HSFRC) components are used. Collapse capacity is evaluated in

terms of a relative intensity defined as the ratio of ground motion intensity to a structure strength parameter. The effect

of record-to-record (RTR) variability on the variance of collapse capacity is directly obtained by performing dynamic

analyses of deteriorating hysteretic models for a set of representative ground motions.

The selected frames are evaluated based on nonlinear static procedures (i.e., pushover), and dynamic analyses for a set

of selected far-field ground motions. The collapse capacity is obtained by carrying out incremental dynamic analysis.

The results indicate that the use of HSFRC improves the dynamic performance of the frame and provides a higher

collapse safety margin. However, experimental tests on HSFRC members are necessary to assess their inelastic

behavior and hysteretic performance.

INTRODUCTION

This study evaluates the collapse capacity of moment resisting frames (MRFs) that use high strength concrete (HSC),

high strength steel (HSS), and/or high strength fiber reinforced concrete (HSFRC). The goal is to assess the increase

on seismic resilience of MRFs with respect to that of frames that include normal strength concrete (NSC), or only HSC

structural components. Seismic structural resiliency refers to the buildings ability to withstand expected earthquake levels with minor damage or no damage. In the current seismic design philosophy buildings may be damaged under

rare earthquakes, but they should be designed with ductile characteristics to dissipate energy in nonlinear excursions

and avoid collapse. The acceptable risk of incurring specific levels of damage at specified seismic hazard levels (i.e.,

performance objectives) are based on economical and practical considerations (ATC, 2006).

Traditionally, NSC with a compressive strength () from 3 to 5 ksi [21 35 MPa] is commonly used for design. NSC

frame components can achieve excellent ductile characteristics, but if they were designed to remain damage free under

rare earthquakes, their dimensions would be unreasonably large. An alternative to increase the resilience of reinforced

concrete (RC) MRFs is the use of HSC and HSS. These materials have been available for many years, but their use

has been limited, particularly in high seismic hazard zones, because they are less ductile than conventional materials.

HSC beam-column elements under cyclic loads usually exhibit early spallation (i.e., loss of cover concrete) and brittle

1 Assistant Professor, University of Utah, 110 Central Campus Drive, SLC, UT. 84103. Phone: (801) 585-9307; Fax:

(801)585-5477; [email protected]

2 Graduate Student, University of Utah, 110 Central Campus Drive, SLC, UT. 84103. Fax: (801)585-5477;

[email protected]

XIX Congreso Nacional de Ingeniera Ssmica Boca del Ro, Veracruz, 2013


failure. More importantly, high strength materials have been adopted as a means to reduce costs keeping the same

performance level. However, drift limits start to control the design when smaller high strength component cross

sections are used, offsetting the potential gains in the system capacity. Structural engineers have rarely tried to use

high strength materials to reach a higher performance level without significant cost increases.

In recent years, two trends have separately evolved. First, concrete with compressive strengths more than one order of

magnitude larger than those of NSC has been developed. The yield strength of steel reinforcement has also increased,

although not as dramatically as the strength of HSC. Second, the shape and strength of steel fibers (SFs) have been

optimized to increase the mechanical performance of fiber reinforced concrete, but most studies have used concrete

with relatively low compressive strength. The seismic performance evaluation of structural components that include

these new concretes and fibers has been very limited, particularly under cyclic loading. Studies on HSC components

have shown that these specimens usually do not achieve the expected seismic performance because early spallation

reduces the load carrying capacity, and the inherent brittleness of the concrete mix that reduces the ductility capacity.

The addition of fibers to HSC (i.e., HSFRC) would reduce early cracking and spallation, improving the load carrying

capacity and the inelastic deformation capacity of the system.

This study utilizes a collapse capacity methodology developed to predict the seismic collapse safety of modern RC

MRFs. The seismic evaluation is based on a concentrated plasticity model developed in OpenSees (2010). The plastic

models can account for strength and stiffness deterioration, cyclic deterioration, and geometric nonlinearities. A set of

far-field ground motions was selected to perform a study based on Incremental Dynamic Analysis (IDAs). The

methodology is modified to include high strength materials. Prior to the analysis, limited experimental tests are

performed on concrete mixtures to ensure that it is possible to develop HSFRC components without significant aging

deteriorating problems. The results indicate that the use of HSFRC improves the dynamic performance of the frame

and provides higher collapse safety margin. However, further experimental tests on HSFRC members are necessary to

assess their inelastic behavior and hysteretic performance.

GLOBAL COLLAPSE

Global collapse under seismic excitations refers to the inability of a structural system to support gravity loads in the

presence of lateral forces. To evaluate the variance of collapse capacity, structural analyses require hysteretic models

that include strength and stiffness deterioration parameters. In recent years, deterioration models and experiments have

been used to evaluate structural collapse (Haselton and Deierlein, 2006; Villaverde, 2007; Lignos and Krawinkler,

2009) considering record-to-record (RTR) variability as the only source of uncertainty affecting the variance of the

structural response. A limited number of studies have evaluated the effect of uncertainty in the modeling parameters

on collapse capacity for SDOF systems (Ibarra and Krawinkler, 2005, 2011; Liel et al., 2009). The level of uncertainty

of modeling parameters can be large because of their intrinsic aleatory variability and especially the inability to

accurately evaluate them (i.e., epistemic uncertainty).

Evaluation of collapse capacity should be based on structural analyses that incorporate modeling of deterioration

characteristics of structural components subjected to cyclic loading and the inclusion of geometric nonlinearities (P-

effects). Collapse of SDOF systems was first studied by including only P- effects in seismic response, which may

cause a negative inelastic tangent stiffness that eventually will cause system collapse. For SDOF systems, P- effects are usually included by rotating the backbone curve based on a parameter known as the elastic stability coefficient, (Jennings and Husid, 1968; Sun, et al. 1973; Bernal, 1987; MacRae, 1994; Vian and Bruneau, 2001; Adam, et al. 2004)

(Figure 1). The development of hysteretic models that include strength and stiffness deterioration (Sivaselvan and

Reinhorn, 2000; Song and Pincheira, 2000; Ibarra and Krawinkler, 2005) improved the assessment of collapse capacity.

Vamvatsikos and Cornell (2002) carried out incremental dynamic analyses (IDAs) for pinched hysteretic SDOF

systems that included a negative post-capping stiffness and residual strength, but no cyclic deterioration. The study

concluded that the displacement at the peak (cap) strength and the slope of the post-capping stiffness are the two

parameters that most affect the performance of medium period systems (Figure 1).

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Figure 1 Backbone Curves for Hysteretic Models with and without P-

The collapse capacity methodology has been incorporated to generic frames (Ibarra and Krawinkler, 2005), and for

NSC frames with a compressive strength, , up to 6 ksi [41 MPa] (Haselton and Deierlein, 2007). The potential

benefits of increasing the compressive strength of the concrete and/or the steel yield strength, however, has not been

evaluated from the perspective of collapse capacity. This study investigates the effect of HSC and HSFRC on the

collapse capacity of mid-high rise frame buildings. It is expected that HSC and HSS materials will significantly

increase the linear elastic capacity of the beam-column elements, whereas steel fibers and transverse reinforcement

will provide enough ductility to avoid brittle failure.

METHODOLOGY TO EVALUATE THE VARIANCE OF COLLAPSE CAPACITY

Deterioration Models To evaluate collapse capacity, the peak-oriented deterioration model developed by Ibarra, et al. (2005) is used in the

study. Figure 1 shows the backbone curve of this model, which consists of an elastic stiffness Ke, a strain hardening

interval capped at a maximum strength Fc, and a negative tangent stiffness cKe (post-capping stiffness). The displacement associated with the peak strength is normalized as c/y, and may be viewed as a monotonic ductility

capacity. The effect of P- is to rotate the backbone curve in accordance with the elastic stability coefficient, .

hF

W

y

y (1)

where W is the seismic weight of the system, and h is the height of the system. The hysteretic model includes four modes of cyclic deterioration based on energy dissipation. As observed in Figure 2, basic strength and post-capping

strength deterioration effects translate the strain hardening and post-capping branch toward the origin, unloading

stiffness deterioration decreases the unloading stiffness, and reloading (accelerated) stiffness deterioration increases

the target maximum displacement. The amount of deterioration depends on the parameter i, which may be different for each cyclic deterioration mode. For instance, the unloading stiffness in the ith excursion (Ku,i) is deteriorated as:

1,,, )1( iuikiu KK (2)

F



Figure 2 Cyclic Deterioration in a Peak Oriented Model

where k,i, is the deterioration parameter for unloading stiffness in the ith excursion. In its general form, i is expressed as:

c

i

j

jt

ii

EE

E

1

(3)

Ei = hysteretic energy dissipated in excursion i

Ej = hysteretic energy dissipated in previous positive and negative excursions

Et = yyF = reference hysteretic energy dissipation capacity of component

c = 1 for this study, which implies an almost constant rate of deterioration.

The parameter for each deterioration mode is calibrated from experimental results. Reasonable results are obtained

if all cyclic deterioration modes are represented by a single parameter kacs ,,, , where the subscripts kacs ,,,

correspond to basic strength, post-capping strength, accelerated stiffness, and unloading stiffness deterioration,

respectively. The term deteriorating models is used here for hysteretic models that possess a post-capping stiffness branch in the backbone curve and/or experience cyclic deterioration.

Collapse Capacity

Collapse of SDOF systems is assumed to occur when the loading path is on the backbone curve and the restoring force

approaches zero (Figure 1). Thus, collapse requires the presence of a backbone curve branch with negative slope, a

condition caused by P- effects and/or a negative tangent stiffness branch of the hysteresis model. In this study, the

relative intensity (Sa/g)/ is used to estimate collapse capacity, where Sa is the 5% damped spectral acceleration at the elastic period of the SDOF system (without P- effects), and = Fy/W is the base shear yield strength of the system,

HYSTERETIC BEHAVIOR W/CYCLIC DET.Peak Oriented Model, NR94hol Record , =5%,

P-=0, s=0.03, c=-0.10, c/y=4, s,c,k,a=25

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

-4 -2 0 2 4 6

Normalized Displacement

No

rma

lize

d F

orc

e

Initial

Backbone

Unloading

Stiffnes Det.

Post- Capping

Strength

Basic

Strength

Accelerated

Stiffness

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Fy, normalized by weight, W. The relative intensity is equivalent to the ductility dependent strength reduction factor,

R, if the ground motion intensity is kept constant; or it can be viewed as the intensity of the ground motion, if is assumed to be constant.

Nonlinear history analyses are conducted for increasing (Sa/g)/values until the system response becomes unstable. Collapse can be visualized by plotting the relative intensity against an engineering demand parameter (EDP) of interest.

For instance, Figure 3 presents individual and statistical relative intensity normalized displacement curves, (Sa/g)/ max/Sd. The deterioration characteristics of the system cause the individual curves to eventually approach a zero slope as (Sa/g)/ increases. The last point of each individual curve represents the system collapse capacity, (Sa,c/g)/.

Figure 3 (Sa/g)/ EDP Curves for Baseline SDOF Systems

The SDOF system used in Figure 3 is referred to as the baseline system. This peak-oriented model includes

intermediate parameter values of this study, such as small P-(see definition in the parameter study section); c/y = 4; c = -0.1; and s,c,a = 50, k = 100. The strain hardening stiffness is s = 0.03, the percentage of critical damping

is = 5%, and there is no residual strength, yr FF (i.e., 0 ). The system is subjected to the ground motion

set LMSR-N described by Medina and Krawinkler (2003).

Modified Hysteretic Model

A modified version of the hysteretic models was developed in OpenSees (Lignos and Krawinkler, 2009; Haselton

and Deierlein, 2007) that emphasizes the rotational capacity, as one of the main parameters in nonlinear seismic

evaluation (Figure 4). This modified hysteretic model will be used for the nonlinear static and dynamic models.

(Sa/g)/ vs NORMALIZED DISP., T=0.5 sec.

Peak Oriented Model, LMSR-N, =5%, P-='0.1N',

s=0.03, cap=-0.10, c/y=4, s,c,k,a=100

0

2

4

6

8

10

0 1 2 3 4 5

Normalized Displacement, max/Sd

(Sa/g

)/

Median

84th

Individual

50th

Vertical

Statistics

(computed)



Figure 4 (a) Parameters of Backbone Curve for Modified Ibarra-Krawinkler Model, and (b) cyclic behavior

of the hysteretic model used in the study (Haselton and Deierlein, 2007)

HIGH RESISTANCE MATERIALS

HSC ductile behavior

HSC is not commonly used in high seismic hazard zones because it exhibits a steeper descending stressstrain curve in compression than NSC (Figure 5), which may lead to brittle failure mode (Palmquist and Jansen, 2001). The

performance of HSC largely improves when steel reinforcement is added, but crushing concrete failure is still very

abrupt (Kaminska, 2002). Experimental tests have shown early spallation (i.e., loss of cover concrete) in HSC columns

before reaching the axial capacity calculated by ACI equations (ACI, 1996; Paultre and Mitchell, 2003; Saatcioglu and

Razvi, 1992). Early spallation is caused by low permeability of HSC that leads to drying shrinkage strain in the cover

concrete, and a closely spaced reinforcement cage.

Figure 5 Stress-strain curves for concrete mixes of different compressive strength

(Palmquist and Jansen, 2001)

High Strength Concrete with Steel Fibers (HSFRC)

The ductile properties of HSC components can be enhanced by using adequate transverse reinforcement, but early

spallation and abrupt concrete crushing failure are difficult to prevent. Addition of fibers to the concrete mix increases

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the energy absorbing capability, ductility, and toughness of plane concrete (Naaman, 1985; Cucciara, et al., 2004; ACI,

2002). Also, the randomly oriented fibers arrest both microcracking and its propagation, which reduces the

permeability of the concrete. Even more important for HSC performance, the arresting of microcracks significantly

reduces spalling. Finally, fibers increase concretes durability because aging concrete degradation is usually associated with corrosion of reinforcing steel (Braverman, et al., 2001; Mehta and Monteiro, 2006; Ibarra and Dasgupta, 2011).

The smaller crack widths of HSFRC impede chloride ions to contact the steel rebars (Sahmaran et al., 2008), hinder

the development of expansive corrosion products (Grubb et al., 2007), and corrosion of steel fibers near the concrete

surface consume the oxygen required for steel rebars cathode reaction (Kosa, 2003).

Steel fibers (SFs) have a slight influence on the ascending portion of the concrete stress-strain curve but cause a

significant increase in ductility. Polypropylene fibers do not have a noticeable effect on the energy absorption capacity

of the concrete (Poon et al., 2004) (Figure 6). SFs with high aspect ratio (i.e., length-to-thickness ratio) are more

effective in improving the post-peak performance because of their high resistance to pullout from the matrix. The

pullout resistance can be increased by enlarging or hooking the ends of SFs, roughening their surface texture, or

crimping the fiber to produce a wavy profile (Chao et al., 2009, Hamad, et al. 2011; Sarsam and Kani, 2010, Fantilli

and Vallini, 2007). SFs also improve the bond between the concrete and the deformed bars (Ezeldin and Balaguru,

1989; Rodriguez et al., 1992). The addition of 1.0-1.5% by volume of SFs on concrete can increase the compressive

strength up to about 15%, the rupture modulus 70-80%, and the splitting tensile strength more than 160% (Wafa and

Ashour, 1992; Sarsam and Kani, 2010; Song and Hwang, 2004; Hamad et al., 2011). The tensile strain-hardening

characteristics of fiber reinforced concrete (FRC) also help reduce congestion of reinforcement.

Figure 6 Stress-strain curves for plane concrete (PC-0), concrete with SFs (OPC-1), concrete with PPF (OPC-2), concrete with SFs and PPFs (OPC-3) (Poon et al., 2004)

In reinforced HSC components, SFs reduce the brittleness of the mechanism involving crushing of compressed regions.

For instance, Campione et al, (2007) evaluated the monotonic response of corbels with ranging from 7.2 to 11.6 ksi

[50 to 80 MPa], concluding that the inclusion of fibers can activate flexural failure mechanisms. SFs also increased

the ultimate load of RC corbels and columns by more than 50% (Campione et al., 2007; Kimura, 2007), whereas the

concrete cracking load increased more than 100% because of the crack arresting mechanism provided by the fibers

(Saeed, 2008; Muhammad, 1998). Similar benefits were reported for beam-column subassemblages made of HSC (

of 11.6 ksi [80 MPa]) with SFs, in which the use of fibers decreased the rate of stiffness degradation, and increased

the load carrying capacity of the joints (Ganesan et al., 2007).

High Strength Steel (HSS)

Steel with yield strength, larger than 60 ksi [415 MPa] is usually considered HSS. The use of longitudinal HSS rebars increases the shear and flexural strength capacity of beam-columns members, and reduces residual

displacements (Hassam et al., 2008; Qazi et al., 2006). HSS is more efficient when used along with HSC, instead of

NSC. For instance, Sumpter et al. (2009) concluded that the full strength of HSS steel stirrups usually cannot be reached



in NSC components because failure is controlled by crushing of the concrete. HSS with yield strength up to 99 ksi

[685 MPa] is already being used for construction, whereas steel grades with up to 142 ksi (980 MPa) are being evaluated at experimental facilities (Nishiyama, 2009). The use of HSFRC is more necessary when using HSS because

the elongation of this steel is usually 30-40% lower than that of conventional steel (Grade 60). The benefits of using

steel rebars with very high yield strengths have not been clearly demonstrated for components subjected to seismic

loading (e.g., Ousalem et al., 2009).

Durability of HSC and HSFRC

The seismic performance of RC structures is affected by aging of concrete, which is affected by the concretes strength, permeability, and cracking resistance. In the case of HSC, its large compressive strength minimizes surface wear

problems, such as abrasion and erosion. The permeability of HSC is lower because the concrete is denser and the

mineral admixtures (e.g., silica fume) significantly reduce chloride penetration. However, HSC exposed to aggressive

environmental conditions tends to crack easily due to low creep and high shrinkage characteristics controlled by the

high cementitious content. Once the water-tightness is lost, the concrete starts to deteriorate due to different causes.

Therefore, cracking is the main source of concrete deterioration in HSC, which leads to corrosion of steel reinforcing

bars. Fibers should increase concretes durability because they arrest cracking. Moreover, smaller crack widths in FRC impede chloride ions from contacting the steel rebars (Sahmaran et al., 2008), hindering the development of expansive

corrosion products.

OPTIMIZATION OF CONCRETE COMPRESSIVE STRENGTH BASED ON DURABILITY

CHARACTERISTICS

HSC is characterized by a high amount of cement and pozzolanic materials (e.g., silica fume), lower water-to-

cementitious materials (w/cm) ratio, and smaller sized coarse aggregates. These characteristics increase the strength

and impermeability of the concrete matrix, but also its brittleness and shrinkage strain. The structural performance of

HSC components has been evaluated in the past, but the optimization of high performance concrete mixtures to achieve

adequate seismic performance and durability characteristics has not been given enough emphasis. To identify whether

a concrete mixture with = 12 is more susceptible of aging degradation that a NSC specimen, six concrete

mixtures were prepared to evaluate the factors affecting strength and durability characteristics of HSC.

The first mixture included NSC with a design of 4 ksi. For the second mixture, steel fibers were added to the NSC

mixture to create FRC. The amount of steel fibers was 1%. Low carbon hooked steel fibers of aspect ratio 60, diameter

0.022 in. and length 1.3 in. were used. The third mixture was the baseline case, a HSC mixture with a design of 12

ksi. The fourth case included fibers in the HSC mixture to create HSFRC. The last two cases corresponded to HSC and

HSFRC mixtures that included shrinkage reducing admixture (SRA) to reduce early cracking associated with

shrinkage. Trial tests were conducted to evaluate the plastic behavior of some of the typical mixtures and measure their

compressive strength development. Compressive and tensile strength, drying shrinkage, and permeability tests were

performed on these specimens. Drying shrinkage tests were carried out to investigate the effect of steel fibers and SRA

on shrinkage strains. Rapid chloride permeability test (RCPT) was also performed to evaluate the concretes ability to perform under aggressive environmental conditions (Bishaw and Ibarra, 2012).

Table 1 shows the mix proportions for the six different types of concrete mixtures prepared for testing. For the first

four concrete mixtures, nine 4 8 in. cylindrical specimens were prepared, whereas three 4 8 in. cylindrical

specimens were prepared for the last two mixtures that include SRA. In addition, three 3 in. square and 10 in. long

prismatic specimens for measuring drying shrinkage were prepared for the HSC mixtures.

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Table 1. Concrete mix proportions

Mixture properties Concrete Mixture Cases

NSC FRC HSC HSFRC HSC + SRA HSFRC + SRA

Target f'c at 28 days (ksi) 4 4 12 12 12 12

w/cm ratio 0.45 0.45 0.30 0.30 0.28 0.28

Type II Portland cement (lb/yd3) 500 500 790.5 790.5 790.5 790.5

Silica fume (7% of cm) (lb/yd3) - - 59.5 59.5 59.5 59.5

Sand (lb/yd3) 1200 1200 1200 1200 1200 1200

in. coarse aggregate (lb/yd3) 1700 1655 1800 1755 1800 1755

Steel fibers (1% by vol.) (lb/yd3) - 132.5 - 132.5 - 132.5

Water (lb/yd3) 225 225 255.0 255.0 238.0 238.0

SRA (gal/yd3) - - - - 1 1

HRWRA (gal/yd3) 4 5 3.7 4.1 3.5 2.9

Cementitious material content and w/cm ratio

The HSC specimens were designed to achieve the target compressive strength (i.e., = 12 ksi at 28 days) with the

minimum amount of cementitious material. Silica fume was added to the mixtures to increase the strength and reduce

permeability, as well as decrease the risk of thermal cracking by reducing the total cementitious material content. Very

low w/cm ratios were avoided to control autogenous shrinkage, which is a result of self-desiccation in low w/cm

mixtures where sufficient water is not provided to complete the reaction with the cement. To address these constraints,

the total cementitious material was lower than 1000 lb/yd3 and the percentage of silica fume was 7%. The w/cm ratio

was about 0.30, which also prevents large autogenous shrinkage, and at the same time, is sufficiently low to allow the

development of the required = 12 ksi.

Aggregate content in HSC is the most important factor affecting the concretes drying shrinkage and creep. To keep the drying shrinkage and creep low, the cement paste-aggregate volume ratio was maintained close to 35:65

and the fine-coarse aggregate volume ratio was kept close to 2:3 (Mehta and Monteiro, 2006). Also, limestone coarse

aggregate with a maximum size of in. was used to prevent drying shrinkage.

Figure 7 Effect of aggregate content on shrinkage ratio (ACI, 1971)



Results of concrete mixture tests

Standard compressive strength tests were conducted on three samples from each set after 28 days, according to ASTM

C39 procedure. The FRC samples (NSC with steel fibers) rendered a lower due to a significant reduction in the

workability of the concrete mixture that resulted in larger compaction voids. The average for the HSC mixture was

13.5 ksi after 28 days. The addition of steel fibers to the mixture (i.e., HSFRC) slightly reduced the average , and

increased the variability of measured strengths. This indicates that the level of dispersion and directional orientation

of the fibers affect of concrete containing fibers. However, the addition of steel fibers led to an increase of the strain

at peak strength of about 25 % (Figure 8). Also, the average tensile strength increased approximately 45 % for the

HSFRC samples with respect to the tensile strength of HSC. The compressive strength of specimens containing SRA

was reduced. The decrease was significant in the mixture with fibers (HSFRC+SRA) because of the combined effect

of the SRA and a reduction in workability due to the lower w/cm ratio and the presence of steel fibers.

Stress-strain curves for the NSC, HSC, HSFRC and HSC + SRA concrete samples were obtained by using three

equidistant strain gages attached at the mid height of each specimen (Figure 8). For this particular set of tests, the

HSFRC sample provided the highest strength and ultimate strain. It was observed that some of the steel fibers in the

HSFRC sample had already yielded at the ultimate load, an indication of adequate bond formation between the fibers

and the concrete. The other important result from this test is that the modulus of elasticity of the HSFRC specimen is

lower than that of the HSC, although the HSFRC specimen has higher ultimate strength.

Figure 8 Stress-strain curves for selected specimens

Free drying shrinkage test

HSC mixtures usually exhibit large drying shrinkage. Free drying shrinkage tests were conducted to evaluate the effect

of fibers and SRA on drying shrinkage. The tests were conducted as per ASTM C490 standard. As observed in Figure

9, the HSFRC specimens exhibited lower drying shrinkage values compared to the HSC samples, indicating that steel

fibers mitigate drying shrinkage. Samples that included SRA showed superior performance in terms of reducing long

term drying shrinkage. In general, the relatively low drying shrinkage values validate the concrete mixture designs.

In addition, rapid chloride permeability tests (RCPT) were performed on the specimens. The results indicated that HSC

has a chloride permeability rate three times lower than that of NSC. Conclusive results were not obtained for HSFRC

because fibers conductivity affected the chloride permeability rate in these specimens. It is expected that the permeability of FRC and HSFRC will be even lower than that of equivalent cases with no steel fibers. Fiber

reinforcement reduces the permeability of cracked concrete because it imparts crack growth resistance, and increases

surface roughness of individual cracks.

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Figure 9 Drying shrinkage curves

STRUCTURAL NUMERICAL SIMULATION

Several studies on the seismic performance of RC buildings with high strength materials have been performed in the

past. These studies, however, have used a narrow range of parameter values (e.g., Kimura et al., 2007), or not

incorporate some important components such as steel fibers (Konstantinidis, 2005).

The experimental tests on concrete mixes showed that specimens with compressive strengths of up to 12 ksi can achieve

adequate ductility and durability characteristics can be achieved using conventional methods. Thus, it was decided to

evaluate a MRF with a concrete compressive strength = 12 for columns, and

= 10 for beams. The selected 12-story frame has three bays with 30 ft. spacing, a first story height of 15 ft., and 13 ft. high stories after that

(Figure 10). The frame was initially designed for a site in California (Haselton and Deierlein, 2007) using NSC with

= 6 for columns, and

= 5 for beams. The original design included 30 30 in. columns. for all stories, and beams which were 30 34 in. for lower floors and 30 28 in. for upper floors. The fundamental period of the

original design was 1 = 2.16 . For the modified building with HSC and HSS, the column sections remained the same whereas the beams were changed to 30 28 in. The vibrational period of the modified design was 1 = 2.21 . The cross section was not reduced with the use of HSC because of joint shear requirements and strong column weak beam

considerations. In terms of the seismic performance comparison, the similarity of the first period of vibration is

beneficial because there will not be modifications in the systems collapse capacity due to different seismic hazard during the scaling process.



Figure 10 12-story Frame Used for Nonlinear Static and Dynamic Evaluations

This frame was selected for several reasons. First, the building was independently designed by two consulting firms in

California based on current codes and standards. Second, the original design includes relatively large axial loads in

some of the base columns, which justifies the use of HSC components. For instance, the exterior and interior base

columns in the original design support axial loads equivalent to 0.32 and 0.56

respectively ( is the columns cross section). Third, a three-bay model is preferred over typical generic frames with 1-bay because the variation of axial load at the exterior columns will lead to different performance for interior and exterior columns.

The potential beneficial effects of HSC and HSS are not the same for different combinations of axial and bending

loads. Figure 11 presents column interaction diagrams developed for 22 22 in. columns with the same longitudinal

reinforcement area. The only difference in these curves is the concrete and steel strength. In the legend, C6fy60 refers

to a column with = 6 , and = 60 . As observed, the effect of high strength materials is significant when

the axial load is higher. Comparing cases C6fy60 and C12fy60 is clear that HSC does not provide a noticeable

improvement for columns subjected to low axial loads, but the performance is significantly better for axial loads close

to the balanced load or higher. In the case of the column C12fy100 (i.e., = 12 , and = 100 ), the

improvement is significant for low axial loads, but the capacity is very similar to that of column C12fy100 for high

axial loads. That is, the use of high strength steel for longitudinal reinforcement only provides significant benefits for

columns with low axial loads.

Figure 11 P-M interaction diagram for three cases of a column

Pushover curves

For the static and dynamic nonlinear analyses, the Open System for Earthquake Engineering Simulation (OpenSees,

2010) was used. To represent nonlinear behavior, the beam-column elements contain concentrated plasticity

parameters where plastic hinges and ductile behavior are expected to occur at the members ends. These elements also consider stiffness and strength deterioration, as well as cyclic deterioration (Ibarra et al., 2005).

To evaluate the effect of high strength materials under nonlinear static behavior, pushover analyses were performed

for four versions of the 12-story frame with different material properties: i) the original frame, NSC, ii) a frame with

HSC and conventional steel, iii) a frame with HSC and HSS, and iv) a frame with HSRFC and HSS. The resulting

pushover curves are shown in Figure 12.

-800

-400

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

0 200 400 600 800 1000

P (

kip

s)

Mx (kips-ft)

P-M Interaction Diagrams

C6fy60

C12fy60

C12fy100

DE




The curve NSC with fy = 60 ksi in Figure 12, corresponds to the original design where the columns have = 6 ksi,

beams have a strength = 5 ksi, and conventional steel rebars are used with = 60 ksi. The nonlinear characteristics

are provided by Haselton and Deierlein (2007). For a typical bending hinge, / 1.2, 0.07 for columns

and 0.04 for beams, whereas 0.1 (see Figure 4). The curve HSC with fy = 60 ksi considers = 12 ksi

for columns, = 10 ksi for beams, and HSS rebars with = 100 ksi. For HSC, the backbone curve properties were

obtained from a literature search (see Appendix A). During this task, the lack of experimental tests of specimens under

monotonic loads was made obvious. The hysteretic models with cyclic loading include cyclic degradation and in most

cases axial loads. Both factors modify the backbone curve. Although the information was incomplete, a clear reduction

in ductile characteristics was observed. For a typical bending hinge, the ratio / was reduced to 1.1. Also, was reduced to 0.036 for columns, whereas approximately the same value of 0.04 was used for beams. The parameter

controlling the negative post-capping stiffness was significantly reduced to typical values 0.025. Thus, the

behavior after the peak strength is several times more brittle than for NSC. As observed in the figure, although was

doubled, the building strength did not significantly change. The small increase in the buildings capacity was influenced by the relatively low axial loads in the columns (see interaction diagrams), and the more brittle behavior of

HSC components in the nonlinear interval.

Figure 12 Pushover curves for the different analysis cases

One of the advantages of increasing from 6 to 12 ksi is that the rebar yield strength, , can be increased to 100 ksi,

as in the curve HSC with fy = 100 ksi. The use of HSS almost doubles the buildings shear capacity, although the ductility is reduced with respect to NSC. Finally, the curve HSFRC with fy = 100 ksi has the same strength characteristics than the curve HSC, but steel fibers are included in the hysteretic model that increase the systems ductility. Experimental tests for HSFRC are even scarcer than for HSC. Based on a couple of references (Wafa and

Ashour, 1992) that tested FRC components under monotonic failure, a backbone curve with ratios similar to that of

NSC was used. That is, / 1.2, 0.07, and 0.1. The pushover curve HSFRC shows that the addition of fibers has a significant increase on the buildings ductility.

Note that HSS is not commonly used with NSC because of the possibility of concrete crushing failure and reduced

confinement due to the smaller amounts of required HSS. Thus, the main benefit of using HSC is the optimal utilization

of HSS. Efficient use of HSS can be obtained for mixtures with of 10-12 ksi. Pilot studies with concrete strength in

columns = 18 ksi, showed that a larger concrete strength only leads to less ductile characteristics and durability

problems.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.0450

200

400

600

800

1000

1200

Base S

hear

(kip

s)

Roof Drift Ratio

HSC with fy = 100 ksi

HSC with fy = 60 ksi

NSC with fy = 60 ksi

HSFRC with fy = 100 ksi



DYNAMIC ANALYSIS

Nonlinear dynamic analysis were conducted in OpenSees to simulate the seismic performance of the above models,

using IDA curves. A set of 22 far-field ground motions was selected from FEMA-695 database (Haselton and

Deierlein, 2008). The scaling of the ground motions was carried out according to ASCE-41 recommendations. Figure

13 shows the scaled response spectra.

Figure 13 Response spectra for scaled ground motions

Figure 14 shows the / relationships (i.e., intensity measure vs. maximum interstory drift) for the original 12-story frame (Figure 14a), the frame with HSC and HSS (Figure 14b), and for the frame with HSFRC and HSS

(Figure 14c). The plots include the median, 16 and 84 percentiles. The use of HSC and HSS does not provide a

significant benefit on the collapse capacity, unlike the results obtained from the pushover curve. The main reason is

the very steep post-capping stiffness that leads to abrupt failure of a large number of records under dynamic

solicitations.

(a)

10-1

100

101

10-2

10-1

100

Period [s]

Sa [g]

Individual records

Median

16th percentile

84th percentile

0 0.03 0.06 0.09 0.12 0.150

0.5

1

1.5

2

2.5

Maximum Interstory Drift Ratio

Sa (

T1 =

2.0

0s)

[g]

Individual records

Median

16th percentile

84th percentile

DE




(b)

(c)

Figure 14 / relationships for MRF with (a) NSC, (b) HSC and HSS, and (c) HSFRC and HSS

The use of HSFRC (Figure 14c), on the other hand, resulted in an increase of more than 50% on the collapse capacity

of the system. The uncertainty in the response due to RTR variability increases for HSFRC systems, which is in

agreement with the collapse capacity of more ductile systems (Ibarra and Krawinkler 2011). Note that the uncertainty

in the nonlinear system parameters is not included in the response, and may be relevant for high strength materials

where the epistemic uncertainty is large due to the lack of confidence in the data.

Conclusions

This paper presents an overview of a collapse capacity methodology based on concentrated plasticity models. The

methodology incorporates deteriorating hysteretic models that account for strength and stiffness deterioration, as well

0 0.03 0.06 0.09 0.12 0.150

0.5

1

1.5

2

2.5


Sa (

T1 =

2.1

0s)

[g]

Individual records

Median

16th percentile

84th percentile

0 0.03 0.06 0.09 0.12 0.150

0.5

1

1.5

2

2.5


Sa (

T1 =

2.1

0s)

[g]

Individual records

Median

16th percentile

84th percentile



as cyclic deterioration. In addition, material nonlinearities (i.e., P- effects) are directly included in the models developed in OpenSees. The study provides a quantitative evaluation of the effect of high strength materials on the

seismic performance of MRFs. In particular, the possibility of using HSC or HSFRC in high seismic hazard regions is

investigated. The objective of the research is to determine whether HSFRC is a viable alternative to NSC in achieving

structural resilience and a higher seismic collapse safety margin.

The numerical simulation showed that HSFRC can increase the buildings collapse capacity by more than 50 percent. The use of HSC with HSS provided mixed results, in terms of the computed collapse capacity, depending on the type

of analyses used for the simulation (i.e., static versus dynamic nonlinear analysis). The IDA curves indicated that the

benefits of HSC with HSS are very limited because of the low ductile characteristics of the non-linear parameters. One

of the main benefits of using HSC is the possibility of using HSS, whereas steel fibers can enhance the internal

confinement and ductile component characteristics. The use of pushover analysis may overestimate the collapse

capacity in systems with low-ductile characteristics, such as a steep negative post-capping stiffness.

Experimental tests of concrete cylinders showed that concrete mixtures with of 10-12 ksi can be used to create

HSFRC mixtures. Concrete mixtures with larger compressive strengths will only lead to less ductile characteristics

and durability problems without a significant improvement on the systems seismic performance. It is noted that concrete is almost always specified based solely on its compressive strength, but usually failures of concrete structures

are due to durability issues. This issue is especially important for HSC in which early cracking reduces durability of

concrete.

Acknowledgements

The authors are grateful to the University of Utah for the funding provided for this research. They also thank Catherine

Tucker for helping reviewing the manuscript.

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DE




APPENDIX A

The elastic element and plastic hinge properties of RC components were calibrated based on available experimental

studies. A database was created with values from the experimental tests, as well as normalized values that simulate the

structural components considered for the investigation. Experimental tests of HSFRC structural components under

cyclic loads are limited. Therefore, an effort was made to collect data from tests with closely related behavior. A

summary of the calibration values for HSC and HSFRC is shown in Table A1.

Table A1. HSC elements calibration

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