VOL. 111, NO. 2 MARCH-APRIL 2014
ACI
STRUCTURAL
J O U R N A L
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ACI Structural Journal
Copyright © 2014 American Concrete Institute. Printed in the United States of America.
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CONTENTS
Board of Direction President Anne M. Ellis Vice Presidents William E. Rushing Jr. Sharon L. Wood Directors Neal S. Anderson Khaled Awad Roger J. Becker Dean A. Browning Jeffrey W. Coleman Robert J. Frosch James R. Harris Cecil L. Jones Cary S. Kopczynski Steven H. Kosmatka Kevin A. MacDonald David M. SuchorskiPast President Board Members
James K. Wight Kenneth C. Hover Florian G. Barth
Executive Vice President
Ron Burg
Technical Activities Committee
Ronald Janowiak, Chair Daniel W. Falconer, Staff Liaison JoAnn P. Browning Chiara F. Ferraris Catherine E. French Fred R. Goodwin Trey Hamilton Kevin A. MacDonald Antonio Nanni Jan Olek Michael M. Sprinkel Pericles C. Stivaros Andrew W. Taylor Eldon G. Tipping Staff
Executive Vice President
Ron Burg Engineering Managing Director Daniel W. Falconer Managing Editor Khaled Nahlawi Staff Engineers Matthew R. Senecal Gregory M. Zeisler Jerzy Z. Zemajtis Publishing Services Manager Barry M. Bergin Editors Carl R. Bischof Kaitlyn Hinman Ashley Poirier Kelli R. Slayden Editorial Assistant Tiesha Elam
ACI S
truCturAlJ
ournAlM
ArCh-A
prIl2014, V. 111, n
o. 2
ajournaloftheamericanconcreteinstitute aninternationaltechnicalsociety
235 Web Crushing Capacity of High-Strength Concrete Structural
Walls: Experimental Study, by Rigoberto Burgueño, Xuejian Liu, and
Eric M. Hines
247 Response of Precast Prestressed Concrete Circular Tanks Retaining
Heated Liquids, by Michael J. Minehane and Brian D. O’Rourke
257 Bond Strength of Spliced Fiber-Reinforced Polymer Reinforcement,
by Ali Cihan Pay, Erdem Canbay, and Robert J. Frosch
267 Flexural Behavior and Strength of Reinforced Concrete Beams with
Multiple Transverse Openings, by Bengi Aykac, Sabahattin Aykac, Ilker
Kalkan, Berk Dundar, and Husnu Can
279 Experimental Assessment of Inadequately Detailed Reinforced
Concrete Wall Components, by Adane Gebreyohaness, Charles Clifton,
John Butterworth, and Jason Ingham
291 Behavior of Epoxy-Injected Diagonally Cracked Full-Scale Reinforced
Concrete Girders, by Matthew T. Smith, Daniel A. Howell, Mary Ann T.
Triska, and Christopher Higgins
303 High-Performance Fiber-Reinforced Concrete Bridge Columns under
Bidirectional Cyclic Loading, by Ady Aviram, Bozidar Stojadinovic, and
Gustavo J. Parra-Montesinos
313 Analysis of Early-Age Thermal and Shrinkage Stresses in Reinforced
Concrete Walls, by Barbara Klemczak and Agnieszka Knoppik-Wróbel
323 Effects of Casting Position and Bar Shape on Bond of Plain Bars, by
Montserrat Sekulovic MacLean and Lisa R. Feldman
331 Performance of Glass Fiber-Reinforced Polymer-Doweled Jointed
Plain Concrete Pavement under Static and Cyclic Loadings, by Brahim
Benmokrane, Ehab A. Ahmed, Mathieu Montaigu, and Denis Thebeau
343 Nonlinear Static Analysis of Flat Slab Floors with Grid Model, by
Dario Coronelli and Guglielmo Corti
353 Effect of Steel Stirrups on Shear Resistance Gain Due to Externally
Bonded Fiber-Reinforced Polymer Strips and Sheets, by Amir Mofidi
and Omar Chaallal
363 Punching of Reinforced Concrete Flat Slabs with Double-Headed
Shear Reinforcement, by Maurício P. Ferreira, Guilherme S. Melo,
Paul E. Regan, and Robert L. Vollum
375 Behavior of Concentrically Loaded Fiber-Reinforced Polymer
Rein-forced Concrete Columns with Varying Reinforcement Types and Ratios, by Hany Tobbi, Ahmed Sabry Farghaly, and Brahim Benmokrane
MEETINGS
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The Institute is not responsible for statements or opinions expressed in its publications. Institute publications are not able to, nor intend to, supplant individual training, responsibility, or judgment of the user, or the supplier, of the information presented.
Papers appearing in the ACI Structural Journal are reviewed according to the Institute’s Publication Policy by individuals expert in the subject area of the papers.
Contributions to
ACI Structural Journal
The ACI Structural Journal is an open forum on concrete technology and papers related to this field are always welcome. All material submitted for possible publi-cation must meet the requirements of the “American Concrete Institute Publi-cation Policy” and “Author Guidelines and Submission Procedures.” Prospective authors should request a copy of the Policy and Guidelines from ACI or visit ACI’s website at www.concrete.org prior to
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Discussion
All technical material appearing in the
ACI Structural Journal may be discussed.
If the deadline indicated on the contents page is observed, discussion can appear in the designated issue. Discussion should be complete and ready for publication, including finished, reproducible illustra-tions. Discussion must be confined to the scope of the paper and meet the ACI Publi-cation Policy.
Follow the style of the current issue. Be brief—1800 words of double spaced, typewritten copy, including illustrations and tables, is maximum. Count illustrations and tables as 300 words each and submit them on individual sheets. As an approxi-mation, 1 page of text is about 300 words. Submit one original typescript on 8-1/2 x 11 plain white paper, use 1 in. margins, and include two good quality copies of the entire discussion. References should be complete. Do not repeat references cited in original paper; cite them by original number. Closures responding to a single discussion should not exceed 1800-word equivalents in length, and to multiple discussions, approximately one half of the combined lengths of all discussions. Closures are published together with the discussions.
Discuss the paper, not some new or outside work on the same subject. Use references wherever possible instead of repeating available information.
Discussion offered for publication should offer some benefit to the general reader. Discussion which does not meet this requirement will be returned or referred to the author for private reply.
Send manuscripts to:
http://mc.manuscriptcentral.com/aci Send discussions to:
2014 MARCH
19-21—ICRI 2014 Spring Convention,
Reno, NV, www.icri.org/Events/2014_ Spring/conv_home.asp
22—ASA Spring 2014 Committee Meetings, Reno, NV, www.shotcrete.org 24-29—ICPI Annual Meeting, New
Orleans, LA, www.icpi.org/node/3996
27—The Changing Future of Cement & Concrete: Threat or Opportunity,
Leicestershire, United Kingdom, http://ict. concrete.org.uk
MARCH/APRIL
30-2—ACPA 2014 Convention,
Indianapolis, IN, http://convention.myacpa. org/indy2014/
UPCOMING ACI CONVENTIONS
The following is a list of scheduled ACI conventions:
2014—March 23-27, Grand Sierra Resort, Reno, NV 2014—October 26-30, Hilton Washington, Washington, DC
2015—April 12-15, Marriott & Kansas City Convention Center, Kansas City, MO For additional information, contact:
Event Services, ACI
38800 Country Club Drive, Farmington Hills, MI 48331 Telephone: 248.848.3795
e-mail: [email protected]
ON COVER: 111-S23, p. 269, Fig. 3—Diagonal reinforcement spiraling around circular openings.
387 Repair of Prestressed Concrete Beams with Damaged Steel Tendons
Using Post-Tensioned Carbon Fiber-Reinforced Polymer Rods, by
Clayton A. Burningham, Chris P. Pantelides, and Lawrence D. Reaveley
397 Study of Composite Behavior of Reinforcement and Concrete in
Tension, by John P. Forth and Andrew W. Beeby
407 Flexural Capacity of Fiber-Reinforced Polymer Strengthened Unbonded
Post-Tensioned Members, by Fatima El Meski and Mohamed Harajli 419 Size Effect on Strand Bond and Concrete Strains at Prestress Transfer,
by José R. Martí-Vargas, Libardo A. Caro, and Pedro Serna-Ros
431 Proposed Minimum Steel Provisions for Prestressed and
Nonpre-stressed Reinforced Sections, by Natassia R. Brenkus and H. R. Hamilton
441 Lateral Strain Model for Concrete under Compression, by Ali Khajeh
Samani and Mario M. Attard
453 Discussion
Cyclic Loading Test for Beam-Column Connection with Prefabricated Reinforcing Bar Details. Paper by Tae-Sung Eom, Jin-Aha Song, Hong-Gun Park, Hyoung-Seop
Kim, and Chang-Nam Lee
Shear Strength of Reinforced Concrete Walls for Seismic Design of Low-Rise Housing. Paper by Julian Carrillo and Sergio M. Alcocer
Performance of AASHTO-Type Bridge Model Prestressed with Carbon Fiber-Reinforced Polymer Reinforcement. Paper by Nabil Grace, Kenichi Ushijima,
Vasant Matsagar, and Chenglin Wu
460 In ACI Materials Journal
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
This paper discusses the relationship between concrete strength and web crushing capacity based on results from large-scale tests of thin-webbed structural walls with confined boundary elements. Eight walls with concrete strengths ranging from 39 to 138 MPa (5.6 to 20 ksi) were tested to web crushing failure under cyclic and monotonic loading. These tests clearly demonstrated differ-ences between elastic and inelastic web crushing behavior and their dependence on concrete strength. Walls with higher concrete strengths reached higher levels of displacement ductility due to an increase in web crushing capacity. Evidence with respect to mono-tonic tests showed that degradation of the diagonal compression struts from cyclic loading increases with concrete strength, thus limiting the inelastic deformation capacity gains. Thus, concrete compressive strength does not linearly increase web crushing strength as implied by rational web crushing models; rather, the relationship is nonlinear, with a decreasing limit as concrete strength increases. The ACI shear stress limit considerably under-estimated the web crushing capacity of the walls. Test results and observations are reported with the intent of providing physical insight into the web crushing failure mechanism and the inherent limits of thin-webbed concrete members in shear.
Keywords: ductility; high strength; shear walls; web crushing.
INTRODUCTION
Over the past 50 years, web crushing capacity of reinforced concrete members has emerged as a primary design concern in three distinct contexts: gravity loading of thin-webbed beams in the 1960s,1-4 seismic loading of structural walls with confined
boundary elements in the 1970s,5-9 and seismic loading of
hollow bridge piers with confined corner elements in the 1990s.10-13 In each context, motivation to design lightweight
members based on physical insight led to large-scale struc-tural testing programs that discovered web crushing capaci-ties significantly in excess of the average shear stress limits recommended by ACI-318.14 Researchers in charge of these
testing programs have repeatedly emphasized the importance of understanding shear behavior in terms of diagonal tension and diagonal compression instead of average shear stresses.
While diagonal compression demands depend on member geometry and reinforcement, diagonal compression capacities depend on the size and strength of the most heavily loaded struts. Previous research programs established consensus regarding the linear dependence of web crushing capacity on concrete compressive strength fc′ and web thickness. Limits on the value of fc′ itself, however, were not evaluated. Could the web crushing capacity of a 30 MPa wall be increased by a factor of four simply by increasing the concrete strength to 120 MPa? Seismic researchers have hesitated to endorse this
possibility because they have observed deformed configura-tions in the inelastic range that could undermine the benefits of increased concrete strength. The work described herein represents an attempt to answer this question experimentally and thereby establish limits for the future analytical prediction of web crushing failures. This experimental program proceeded with the intention of testing the following two hypotheses:
1. Web crushing strength increases in proportion to fc′ as long as the struts are not damaged. Hence, transformation from an elastic web crushing failure to an inelastic web crushing failure can be achieved simply by increasing the concrete strength; and
2. Damage to struts caused by cyclic loading and inelastic deformations can limit web crushing strength independently of fc′. Hence, increases in fc′ may not lead to proportional increases in ductility capacity.
The experimental program designed to test these two hypotheses consisted of two sets of four structural walls with a range of concrete strengths. One set of walls was tested cyclically, and the other set was tested monotonically.
RESEARCH SIGNIFICANCE
Elastic and inelastic web crushing failures were consis-tently achieved in a series of large-scale structural wall tests designed to study the relationship between concrete compressive strength and web crushing strength of thin-webbed members. The results of these tests validate both the dependence of web crushing capacity on fc′ and the signif-icant degradation of web crushing capacity experienced for a range of concrete strengths under cyclic loading in the inelastic range. Physical insight developed from observa-tions and measurements of these tests provides a firm foun-dation for establishing the limits of thin-webbed reinforced concrete member design. Consistency of the test results indi-cates that it may be possible to design thin-webbed elements to experience significant inelastic deformations before failing in shear, opening up new possibilities for acceptable ductile failure modes of reinforced concrete members.
WEB CRUSHING SHEAR CAPACITY
Work in the 1960s on thin-webbed girders established that properly reinforced concrete webs could resist diag-onal compression loads in the elastic range almost equal Title No. 111-S04
Web Crushing Capacity of High-Strength Concrete
Structural Walls: Experimental Study
by Rigoberto Burgueño, Xuejian Liu, and Eric M. Hines
Note: Paper 111-S04 of the January-February 2014 ACI Structural Journal has been reprinted herein with corrected figure art. Please reference the March-April 2014 version of this paper only.
ACI Structural Journal, V. 111, No. 2, March-April 2014.
MS No. 2011-322.R2, doi:10.14359.51686515, was received May 23, 2013, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
to the compressive strength of concrete itself, resulting in average shear stresses an order of magnitude higher than the prevailing provisions.15 It was during this work that the
term “web crushing” was conceived, and a case was made to consider diagonal compression capacity independently of average shear stresses. Work in the 1970s, 1980s, and early 1990s on structural walls with confined boundary elements under seismic loads emphasized the dependence of web crushing capacity on inelastic deformation and the realign-ment of cracks in the web crushing region, but recommended assessment of web crushing capacity in terms of average shear stresses.9,16 Among these works, the effect of concrete
strength on web crushing capacity was witnessed through the tests by the Portland Cement Association (PCA)7,9 in the
mid-1970s on walls with boundary elements. Wall B6 with a concrete compressive strength of 22 MPa (3165 psi) failed in web crushing at significantly lower deformation capacity than Wall B7 with a concrete compressive strength of 49 MPa (7155 psi). No further high-strength concrete (HSC) structural walls were tested, however. Work in the late 1990s and early 2000s on hollow bridge piers with confined corner elements clearly distinguished between elastic web crushing and inelastic web crushing, and tied the assessment of inelastic web crushing to the development of the plastic hinge region,12 emphasizing the interaction of inelastic flexure and
shear behavior in this zone.13 The physically based method
of assessment by Hines and Seible13 recognized the focus
on principal stresses from the 1960s research, accounted for inelastic deformations, and allowed accurate assessment of cross sections with various relations between depth of web and depth of boundary elements. A review of the model is provided as follows; however, for a detailed description of the model, the reader should refer to Reference 13.
The approach to web crushing capacity by Hines and Seible13 is based on the assessment of capacity and demand
on individual struts inside the plastic hinge region as it spreads up the height of a wall. As shown in Fig. 1(a), two distinct shear transfer mechanisms were identified for the plastic hinge region and the regions elsewhere. Elastic, or standard shear, struts are formed in the wall web in regions that have not experienced significant tensile strains along both the longitudinal (vertical) and transverse directions, leading to a parallel shear cracking pattern (at an angle θs). In other words, this region is stressed mainly under in-plane shear stress while the effect of elastic flexural strain is not significant. By comparison, plastic flexural strains force the struts inside the plastic hinge region to realign so that they all converge in the flexural compression toe. This can be understood by considering that the flexural crack at the base of the wall prohibits shear force transfer into the footing at any location except for the flexural compression toe, and that the struts should fan upward until they are able to carry the full elastic shear force. These fanning struts are considered as inelastic or flexure-shear struts.
Based on the noted force transfer mechanisms, Hines and Seible13 proposed a web crushing capacity model through
equilibrium analysis of the free body diagrams of isolated elastic (or standard) and inelastic (or flexure-shear) diagonal struts (Fig. 1(b)). Calculating the demand of forces on the elastic struts NDs and the compressive capacity NCs of these struts leads to the standard shear web crushing equation proposed by Oesterle et al.7 and Paulay and Priestley16
N N kf Cs Ds c s s ≤ ′sin cosθ θ (1)
The inelastic struts in the plastic hinge region differ from their elastic counterparts both in demand and capacity. On the demand side, the inelastic struts are required to transfer inelastic shears at angles that are consistent with the spread
Fig. 1—Elastic and inelastic shear web crushing: (a) definition of elastic and inelastic web crushing failure modes and critical regions in wall; (b) free body diagrams used for assessing flexure-shear web crushing capacity of structural wall with confined
of plasticity Lpr. On the capacity side, these struts become narrower toward the compression toe from which they fan.
Following Hines and Seible,13 the critical flexure shear
crack angle θfs is calculated as
θfs v yv w yav jd A f s f t T T j = + −
(
)
= − − tan 1 tan 1 1 2 dd Lpr (2)Web crushing is then estimated to occur when the capacity
NCfs of the critical strut (Eq. (3)) is equal to the demand NDfs on this strut (Eq. (4))
NCfs= ′kf t Rdc w θ (3) NDfs T f st fs w fs = ∆ − cosθ 1 sinθ (4)
The related variables are determined from a moment-cur-vature analysis of the cross section and the strut geometry, as shown in Fig. 1(b). The concrete compressive strength softening factor k is calculated according to the modified compression field theory17 with a simplified approach for
determining the principal tensile strain ε1. It should be noted
that while the model has no explicit limit on fc′, its predic-tion quality for HSC is uncertain because the available test data for calibration of the model was from tests of normal-strength concrete (NSC) walls.
ACI 318-1114 does not reflect the direct dependence of web
crushing capacity on fc′, but rather defines the expression in Eq. (1) as 0.83√fc′ (MPa) (10√fc′ [psi]), although √fc′ is a quantity commonly related to concrete tensile strength and diagonal tension failures. A maximum value of 0.69 MPa (100 psi) is adopted by the code because of the lack of test data and practical experience with concrete strengths more than 69 MPa (10,000 psi).
The proportional increase of web crushing capacity with
fc′ implied by Eq. (3) indicates the potential of achieving a ductile force-displacement response in structural walls even if ultimately limited by web crushing. Figure 2 shows simulated force-displacement responses for structural walls with heavily reinforced boundary elements12 along with
web crushing predictions. Curves for walls with concrete compressive strengths varying from 34 to 138 MPa (5 to 20 ksi) are shown. The web-crushing capacity envelopes after Hines and Seible13 and the ACI Code14 limits are also
plotted. It can be seen that force-deformation response of the walls is only slightly affected by the increased concrete compressive strength. The Hines and Seible model, however, predict the web crushing capacity to increase dramatically with an increase of concrete strength. The ACI limit is clearly conservative and independent of the inelastic defor-mations in the wall. The Hines and Seible model implies that a 34 MPa (5 ksi) wall would fail by web crushing at the onset
of yielding, while a 138 MPa (20 ksi) wall would fail in flexure. The model, however, assumes integrity of the struts, which are known to degrade with increase ductility demand and cyclic loading as schematically shown by the cracking pattern in Fig. 1(c). Nonetheless, the suggestion that web crushing strength can be directly and consistently related to concrete compressive strength is indicative of new possibili-ties for increasing shear capacipossibili-ties of thinned-webbed struc-tural members with increased concrete strength.
EXPERIMENTAL PROGRAM Test unit identification, geometry, and reinforcement details
To verify the aforementioned hypotheses and establish rational performance levels on the inelastic web crushing limits for HSC structural walls, eight 1/5-scale cantilever structural walls with design concrete compressive strengths of 34, 69, 103, and 138 MPa (5, 10, 15, and 20 ksi) were tested under cyclic and monotonic loading.18 The walls
had a barbell-type cross section with thin webs and heavily confined boundary elements, and were designed to induce a web crushing failure and not to represent a component from a prototype structure. The test unit cross sections with rein-forcement details are shown in Fig. 3. The identification name for the walls starts with M, followed by two digits denoting the design concrete compressive strength in kip/in.2
(1 kip/in.2 [ksi] = 6.895 MPa) and then by a letter describing
the loading protocol: C for cyclic and M for monotonic loading. For example, test unit M10C refers to the wall with a design concrete strength of 69 MPa (10 ksi) and subjected to cyclic loading. All walls had an effective length of 2540 mm (100 in.) for an aspect ratio (M/V) of 2.5. In all cases, the wall web was 508 mm (20 in.) deep and 76 mm (3 in.) thick. The boundary elements had a depth of 254 mm (10 in.). As shown in Fig. 3 and Table 1, the steel reinforcement was essentially the same for all walls, with a small variation in the longitudinal reinforcement of the boundary elements in Wall M15C and in the transverse reinforcement spacing for Walls M20C and M20M. The reinforcement ratios for the web and boundary elements of the test units are given in Table 2.
Fig. 2—Analytical force-displacement response with web crushing capacity predictions.
Material properties
The HSC for this research was attained with traditional mixture constituents following examples from commer-cially available mixtures.18 Compressive, tensile, and
flex-ural strengths were assessed through standard testing, and the values at the day of testing for all walls are provided in Table 3. Table 1 lists the properties for the steel reinforce-ment with reference to the nomenclature noted in Fig. 3. The properties given in Table 1 are average values from three tensile tests on 457 mm (18 in.) long segments for each of the reinforcement bars.
Loading protocol
The test setup (Fig. 4) was designed to load the walls in-plane as cantilevers. The walls were loaded monotoni-cally and cyclimonotoni-cally with constant axial load. The axial load for all test units was 579 kN (130 kip), corresponding to 0.10fc′Ag for a reference concrete strength of 34 MPa (5 ksi). Axial load was applied using hydraulic jacks and high-strength rods reacting against the top load stub through a spandrel beam. The horizontal load was applied with a servo-controlled actuator connected to a load stub at the top of the wall. Lateral stability was provided by a pair of parallel inclined tensioned chains on both sides of the wall. Cyclic and monotonic loading, respectively, were applied on two test units with the same design concrete strength to assess shear strength/stiffness degradation and inelastic web crushing limits under different loading histories. Cyclic tests were done according to an incrementally increasing fully reversed cyclic pattern. Four cycles (in quarter incre-ments) were first applied in force control until the theoret-ical first yield force, Fy′, defined as the force at the onset of yield of the extreme longitudinal reinforcing bar in tension as obtained from a moment-curvature analysis. The top displacement at the theoretical first yield force, Δy′, deter-mined by the average of the measured values from the posi-tive and negaposi-tive loading excursions, was used to define the experimental elastic bending stiffness, KE = Fy′/Δy′. The ideal yield displacement,19 Δy, corresponding to
displace-ment ductility one (μΔ = 1), was determined using the
exper-imental stiffness at first yield and the ideal yield force, Fy, by Δy = Fy/KE. The ideal yield force Fy was computed by means of a moment-curvature analysis and corresponded to the moment at the critical section at which either the extreme confined concrete fibers reached εc = 0.004 or the extreme steel fiber in tension reached εs = 0.015, whichever occurred first.19 The remainder of the test was conducted in
ment control with two cycles each at the system
displace-Fig. 3—Test unit cross sections with reinforcement details (refer also to Table 3).
Table 1—Test unit steel reinforcement material properties and layout
Test
unit Bar Size
Spacing, mm fy, MPa fu, MPa εsh Esh, MPa M05C M05M M1 M25 4 bars 524 —* — 11,034 M2 M22 4 bars 448 672 0.0026 11,262 m M10 127 445 692 0.0083 7759 T M10 102 445 692 0.0083 7759 S M10 76 459 703 0.0075 7759 M10C M10M M1 M25 4 bars 464 697 0.0096 8966 M2 M22 4 bars 448 672 0.0094 8966 m M10 127 476 746 0.0060 8966 T M10 102 476 746 0.0060 8966 S M10 76 545 730 0.0050 7586 M15C M M19 12 bars 439 705 0.0078 8966 m M10 127 481 759 0.0054 9655 T M10 102 481 759 0.0054 9655 S M10 102 503 756 0.0030 7931 M15M M1 M25 4 bars 586 — — 2759 M2 M22 4 bars 421 630 0.0093 8621 m M10 127 478 748 0.0060 10,690 T M10 102 478 748 0.0060 10,690 S M10 76 510 656 0.0072 5517 M20C* M20M M1 M25 4 bars 451 703 0.0054 9310 M2 M22 4 bars 446 699 0.0060 8966 m M10 127 438 703 0.0043 8793 T M10 76*, 102 438 703 0.0043 8793 S M10 76 443 717 0.0037 8621
*— is not displayed in response. Note: 1 MPa = 0.145 ksi.
Table 2—Test unit steel reinforcement ratios
Test unit ρl ρn ρs ρh
M15C 0.0528 0.0147 0.0357 0.0183 M20C and M20M 0.0556 0.0147 0.0237 0.0244 All others 0.0556 0.0147 0.0237 0.0244
ment ductility levels μΔ = 1, 1.5, 2, 3, 4, and 6, or until
failure of the test unit. The monotonic tests were conducted by applying the lateral load in force control until Fy′, and then in displacement control until failure. The values of Fy′ and Δy that defined the loading protocol are listed in Table 4.
Instrumentation
The walls were instrumented to measure segmental flex-ural curvatures, shear deformations, and steel reinforcement strains. The layout of the external instrumentation is shown in Fig. 5. Flexural section curvatures were calculated using displacement transducers placed along the height of the column on both sides of the boundary elements. Average
shear deformations were measured on two wall segments (one from the wall base to 1016 mm [40 in.] high, and the second one from the noted level to the wall top) with a pair of displacement transducers arranged in opposing diagonal directions on one wall face. Global displacement at the effective height of the wall (2540 mm [100 in.]) was measured with a string potentiometer. Further details of the instrumentation are reported elsewhere.18
OBSERVATIONS Common behavior
Common behavior observed on all test units is described herein. No cracking was observed up to 0.25Fy′. At 0.5Fy′, flexural cracking in the boundary elements and diagonal shear cracking in the webs appeared. At 0.75Fy′, elastic shear cracking developed throughout the entire web. The HSC walls developed a denser pattern of flexural and shear cracks than the NSC walls. With increasing displacement ductility crack density increased and the active cracks became wider. Overall, shear crack spacing in the HSC walls was much smaller than for the NSC walls. Even though diagonal shear cracking under tension does not control the capacity of the walls, it defines the height and width of the struts, and thus affects the strut capacities. Strut capacity is also affected by crack width, which dictates shear slip behavior at the crack interface. Finally, relatively larger cover concrete spalling on the compression boundary element was observed on the HSC walls. Nonetheless, the heavily confined boundary elements had no problem resisting the compression force.
Table 3—Test unit concrete material properties
Test unit
Design
fc′, MPa
fc′, MPa ft′, MPa fr′, MPa
x σ x σ x σ M05C 34 46.0 1.37 3.25 0.207 5.49 0.0897 M05M 34 38.9 1.23 3.55 0.0966 5.37 0.0551 M10C 69 56.4 1.86 4.50 0.331 6.57 0.221 M10M 69 84.0 1.37 5.54 0.490 7.33 0.669 M15C 103 102 1.01 5.70 0.441 9.01 0.559 M15M 103 111 4.99 6.17 0.910 0.935 1.08 M20C 138 131 3.01 6.19 0.400 11.5 0.359 M20M 138 115 2.55 5.96 0.172 10.2 0.593
Note: 1 MPa = 0.145 ksi.
Fig. 4—Test setup overview.
Table 4—Force and displacement values at theoretical and ideal yield
Test M05C M05M M10C M10M M15C M15M M20C M20M Fy′, kN 578 576 583 618 586 644 576 572 Δy′, mm 17.6 18.5 18.4 15.8 15.7 16.2 13.5 15.2 Fy, kN 842 836 723 745 731 816 809 803 Δy, mm 25.7 26.9 22.9 19.1 19.6 20.6 19.1 21.3
Damage patterns and failure mechanisms
Peculiarities on damage pattern, web crushing failure, and ductility capacity are described herein individually. All walls failed in web crushing according to the experimental aim. Walls M05C and M10C failed on the first excursion to μΔ = 2, and web crushing occurred at μΔ = 1.8. In both walls,
there was a sudden loss of strength upon failure of approxi-mately 40%. Wall M15C performed in a ductile manner up to μΔ = 4, and failed in web crushing on the second excursion
to ductility 4. This HSC wall had a gradual loss of strength upon failure, losing only approximately 8% of its strength compared with the load reached during the first cycle at ductility 4. Wall M20C performed in a ductile manner up to its failure by web crushing on the first excursion to μΔ =
6. Web crushing started to develop at a top displacement of 66 mm (2.6 in.), and the wall strength degraded by roughly 40% when the displacement reached the target displacement for ductility six. Wall M05M failed by elastic web crushing at μΔ = 2.3. Walls M10M, M15M, and M20M performed in
a ductile manner up to web crushing failure at μΔ = 7, 6.5,
and 9.2, respectively.
The damage and failure patterns in the wall bottom third region (850 mm [33 in.]) for all test units are shown in Fig. 6. Test units with lower concrete compressive strength (M05C, M05M, and M10C) failed after only minor levels of inelastic response (Fig. 6(a) to (c)). Tensile cracking was minimal, and cracks fully closed upon load reversal. No crack realignment was observed and thus these walls were limited by standard, or elastic, web crushing. The failures were sudden and the crushing of the concrete struts occurred along the interface of the wall web and the compression boundary element, and instantly propagated along the wall height. The rest of the test units exhibited moderate to high ductile behavior before web crushing failure. Cracking was more extensive, and
crack spacing was much smaller. The fanning flexure-shear cracking pattern was formed within the plastic hinge region, with fairly flat cracks close to the bottom and much steeper cracks at the top. An example of this inelastic flexure-shear failure mode is shown in Fig. 6(d) for Wall M10M.
Loading protocol had a large influence on damage and failure patterns. This can be seen by comparing the failure modes between the cyclic and monotonic tests for Walls M15 and M20 (Fig. 6(e) to (h)). The monotonically loaded units developed a denser crack pattern, with multiple branching and wedge-shaped struts. Conversely, the cyclic tested walls had wider spaced cracks and struts with a more uniform width. The uniform damage pattern from denser cracking in the monotonic tests allowed for more diagonal compres-sion load paths in the wall web. The consistent loading also permitted the struts to remain integral, thus allowing these walls to sustain larger inelastic deformations. In constrast, the wider cracking pattern from cyclic loading led to larger crack misalignment and damage to the diagonal struts, which reduced deformation capacity.
The cracking pattern due to cyclic loading is illustrated in Fig. 1(c) and shown in Fig. 7, which illustrates the degra-dation of inelastic struts for wall M20C upon reaching the second negative displacement target (second cycle) for μΔ = 4. Figure 7(a) is a view of the bottom region of the
wall from which the fanning crack pattern inside the plastic zone can be discerned. The close-up view of the wall web in Fig. 7(b) shows the crisscross cracking pattern from the reversed loading cycles. Upon reloading, crack misalignment results from shear deformations due to yielding and bond-slip effects in the longitudinal and transverse web reinforcement. As cracks close for the compression load path to reestablish in the previously formed struts, the crack misalignment induces large local stresses due to shear friction and distortion of the struts. This causes the web cover concrete to lose its bond to the reinforcement and spall off, as seen in the lower left region of the wall web (Fig. 7(b)). The test units gradually lost their load-carrying capacity as a result of the diminished load transfer efficiency of the concrete struts. Web crushing in the cyclically loaded walls was observed to expand over a large area within the plastic hinge region, and crushing of the flexure-shear struts initiated in the center of the web and then extended to the edge of the compression boundary element (Fig. 6(e) and (g)). The noted differences between the cyclic and monotonic responses became more significant for higher values of concrete compressive strength.
RESULTS Force-deformation response
The hysteretic force-displacement response of the four walls under cyclic loading is shown in Fig. 8. Again, failure in all cases was due to web crushing. Recalling that the rein-forcement details were essentially the same for all walls, the test results demonstrate that increased concrete compressive strength allowed the walls to considerably increase their inelastic deformation capacity by delaying shear failure. Web crushing was thus shifted from an essentially elastic level for Wall M05C, failing after completion of two cycles at μΔ = 1.5,
to a highly stable ductile response for Wall M20C, failing after
Fig. 5—External instrumentation layout (units in mm). (Note: 1 mm = 0.0394 in.)
sustaining two full cycles at μΔ = 4. Comparison of inelastic
deformation capacity in terms of displacement ductility is adequate because the ideal yield displacement for all walls did not vary greatly, as shown in Table 4. The ductile behavior displayed by Walls M15C and M20C shows that these units preserved the high stiffness and lateral load-carrying capacity characteristic of structural walls, mostly provided by the web, while benefiting from the inelastic deformation capacity of column flexural hinges at the boundary elements. Finally, the energy dissipation capacity, as judged by the area of the hysteresis loops, is also notably increased solely due to the increase of the concrete compressive strength.
Inelastic behavior characteristics
According to Eq. (2) the length of the plastic hinge region
Lpr is directly proportional to the angle of the flexural-shear cracking, and hence the force demand on the critical inelastic strut. The spread of plasticity can be taken as the length over which plastic curvatures exceed the yield curvature from an
idealized bilinear moment-curvature response.19 The
curva-ture profiles of the M10 and M20 walls are shown in Fig. 9. For cyclic loaded test units that failed at low to medium ductility levels, the curvature distribution along the height was almost linear until failure. For monotonic loaded test units that failed at a high ductility level, the plastic rotation was mainly concentrated within 300 mm (12 in.) from the bottom of the wall. It can be seen, however, that the spread of plasticity is very similar at equal displacement ductility levels for both monotonic and cyclic loaded walls. The curva-ture distributions provide local-level evidence of the signif-icant inelastic flexural deformations sustained by the walls. Furthermore, the observed fanning crack pattern (Fig. 6) and the essentially linear distribution of plastic curvatures along the plastic hinge region (with the linearity only disturbed by boundary effects at the footing) suggests that Eq. (4) can be used to assess the demand on the critical inelastic strut.
Table 5 shows the separate contribution of flexure and shear effects to the displacement at the wall top for the
cally tested units at the first positive peak of each ductility level. The flexure-induced displacement Δf at the top of the wall was calculated by adding the contribution of indi-vidual sectional rotations. The top wall displacement due to shear Δs was calculated by summing the shear deformations measured on the two wall segments (Fig. 5). From the data in Table 5 it can be confirmed that the shear displacements are linearly related to the flexural displacements.12 For the
eight tested walls,18 the average ratio of shear to flexural
displacements was 0.23, with a standard deviation of 0.04. Figure 10 shows the average shear stress versus shear strain hysteretic response of Wall M20C in the bottom and top wall segments. The shear deformations were mainly concentrated in the bottom wall segment (1016 mm [40 in.] from the base), which is where the plastic hinge region develops. It can be seen that the average shear stresses considerably exceeded the ACI limits. This observation applies to all walls because they had similar levels of lateral load resistance.
To provide further insight and quantitative information on the performance of the tested walls, Fig. 11 provides a brief overview of average strain demands at mid-depth on the wall
web. Shown in Fig. 11(c) are longitudinal strain profiles for the M20 walls, which have a linear variation along the height (with disturbance near the footing). The strains were calculated using the displacement transducers along both sides of the boundary elements (Fig. 5). The profiles are consistent with the moment gradient on the wall. It can be further observed that the strain profiles for both M20 walls are essentially the same at equal displacement ductility demands. This was consistent for the other three wall sets, supporting the evidence of equal flexural demands on monotonic and cyclic tests.
Principal strains in the wall web were estimated from consid-eration of a whole wall segment (web and boundary elements) through Mohr’s circle with the measured longitudinal strains, the measured average shear strains (Fig. 5), and neglecting the transverse strains (due to the presence of the heavily reinforced boundary elements). Principal strain values calculated this way at the web mid-depth are shown in Fig. 11(b) against displace-ment ductility for all walls. Except for some deviations for the M05 walls, the average principal strains were equal for all walls at the same displacement ductility level.
Fig. 7—Degradation of inelastic struts for M20C wall during ductility 4 cycling: (a) view of wall bottom third region (850 mm [33.5 in.]); and (b) close-up view of wall web.
Monotonic versus cyclic loading
A comparison of the force-displacement envelopes of the cyclic and monotonic tests is shown in Fig. 12. It is clear that higher fc′ resulted in higher inelastic deformation capacity. The force-deformation response of the walls, up to their respective deformation limit, is considered to have been essentially the same, with minor differences due to: a) variations in fc′; b) longitudinal reinforcement differences for Wall M15C (Fig. 3); c) earlier spalling in the compres-sion toe for Wall M20C; and d) reduction of the effective concrete compressive strength due to more severe cracking for the cyclically loaded walls.
The increase in deformation capacity, however, was not directly proportional to fc′, particularly for the cyclic loaded walls. The monotonic and cyclic deformation capacities of the M05 walls were essentially the same (Fig. 12(a)). The response was similar because both walls failed close to the elastic range, and only minimal cycling was done on Wall M05C. The responses of the other walls show that while increased concrete strength leads to larger deforma-tion capacity, cyclic loading curtails this improvement.
The deformation capacity reduction of the cyclically tested walls is attributed to the damage of the flexure-shear struts from cyclic loading, which reduces their capacity to transfer load from the tension to the compression boundary element. This effect is best seen by observing the responses for the M15 walls in Fig. 12(c). The effect was not as clearly captured for the M10 walls (Fig. 12(b)) because fc′ for M10C was lower than that for M10M. Nonetheless, given the response of Wall M15C, it can be expected that if fc′ for Wall M10C had been closer to the design target, its deformation capacity would have been increased, and the cyclic and monotonic envelopes would have been similar to those obtained for the M15 walls. Comparison of the M20 wall response envelopes indicates a
significant effect of cyclic loading on the deformation limit of Wall M20C despite the larger concrete strength in M20C compared with that in M20M. It is thus hypothesized that the reduced deformation capacity in the cyclically tested HSC walls is due to the negative convergence of an increased stress intensity field at crack misalignment and a reduced cracking bridge zone from the higher strength concrete. This can be understood upon considering that HSC experiences dramatic strength degradation in the postpeak response, and the effect of further strength increase is not appreciable. For structural walls, the later effect would indicate a curtailing effect on the increased inelastic deformation gains on web crushing capacity for increasing values of fc′.
The reduced gain in deformation capacity of Wall M20C compared with that of Wall M15C would seem to indicate
Fig. 9—Average curvature strain profiles for: (a) M10 walls; and (b) M20 walls.
Table 5—Flexure and shear components of wall top displacement at first positive peak of each ductility level Ductility Displacement M05C M10C M15C M20C μΔ = 1.0 Δf, mm 18.5 18.0 14.5 14.5 Δs, mm 5.08 6.10 3.53 3.30 μΔ = 1.5 Δf, mm 28.4 27.7 22.6 23.1 Δs, mm 7.62 7.87 4.83 4.57 μΔ = 2.0 Δf, mm — — 30.5 30.7 Δs, mm — — 6.60 6.60 μΔ = 3.0 Δf, mm — — 47.0 47.0 Δs, mm — — 9.40 9.91 μΔ = 4 Δf, mm — — 62.5 62.0 Δs, mm — — 13.2 15.5 Note: 1 mm = 0.0394 in.
that increased concrete strength does not lead to additional deformation capacity beyond a certain point. Wall M20C, however, failed after completion of two cycles at μΔ = 4, while
M15C failed during the first loading branch of the second cycle at μΔ = 4. Evaluation of the dissipated hysteretic energy
(area inside the hysteresis loop) shows that all walls provided essentially the same level of specific energy dissipation for a given displacement ductility level.18 This can be qualitatively
seen by observing the hysteretic responses in Fig. 8. Because the walls had the same reinforcement details, this is to be expected. Thus, the increased shear capacity of the HSC walls improved their hysteretic energy dissipation capability. Based on this evaluation, Wall M20C had 27% higher energy dissi-pation capacity than Wall M15C.18 The sum of the dissipated
energy for all ductility levels shows that increased concrete strength increased the inelastic energy dissipation capacity of the walls by delaying web crushing failure.
Considering the strut resistance mechanism proposed by Hines and Seible13 (Fig. 1(b)), the similitude in principal strain values
(Fig. 11(b)) indicates that the force demand in the walls at equal displacement ductility levels was the same. It is clear, however, that the walls had different deformation and web crushing capac-ities. The difference is then attributed to the concrete strength (as reflected in Eq. (3)) and the loading pattern. This was explored by estimating the concrete softening factor k using experimen-tally derived values for Lpr and the shear force at web crushing failure. Equation (1) was used for Walls M05C, M05M, and M10C because they are considered to have failed by elastic web
crushing, while the rest of the walls, which failed by inelastic web crushing, followed Eq. (3). Figure 13(a) plots the calculated values of k versus normalized shear distortions in the plastic hinge region. The maximum (condition before web crushing) average shear distortion within the plastic hinge region, γm, was normalized by the strain at peak stress in compression εco′, which was estimated from the model by Tasemir et al.20 The figure also
shows the concrete strength reduction factor relation proposed by Collins21 in terms of shear strains, which is essentially the
constitutive model for cracked concrete in compression in the modified compression field theory (MCFT). This relation has been shown to relate well to test data in which the compression stresses act along uniform parallel struts across the section,9 or
elastic shear. Results from this program, however, deviate from the noted model in interesting ways. The data in Fig. 13(a) shows how the monotonic and cyclic tests follow different degradation trends for the softening factor k, with lower values and a faster decay with increasing shear distortion for the cyclic walls.
The experimental k values are plotted against concrete strength in Fig. 13(b), where again the data is clearly segre-gated in terms of the loading protocol. The cyclic and mono-tonic wall data was fitted with exponential functions only for the purpose of illustrating the data trends. It can be seen that the M05 data points are close to each other because both failed in elastic web crushing. For increasing concrete strengths, the softening factor decays faster for the cyclic walls. It is of interest to note that the softening factor (and thus, the inelastic web crushing capacity) is affected both by the cyclic loading and the increase in concrete strength, or, stated differently, cyclic loading had an increased detri-mental effect on the effective capacity of the shear resisting struts with increasing concrete compressive strength.
Web crushing capacity models
Table 6 compares the web crushing capacities with different predictive models. It can be noted that ACI shear provisions considerably underestimate the web crushing strength. At the same time, the prediction quality of the model by Hines and Seible13 on the cyclic tests deteriorates with increasing concrete
strength. Thus, the experimental program revealed that rational web crushing models like the one by Hines and Seible need further considerations to be applicable to HSC structural walls. A modified version of the Hines and Seible model, as well as the finite element implementation of the MCFT in modeling the behavior of the HSC walls was proposed by Liu,22 and will
be reported in a future paper by the authors.
CONCLUSIONS
Eight cantilever walls were tested with design concrete compressive strengths of 34, 69, 103, and 138 MPa (5, 10, 15, and 20 ksi) under cyclic and monotonic loading to study the effects of HSC and damage accumulation on the inelastic web-crushing capacity of structural walls. The following conclusions are offered specifically referring to structural walls with well-confined boundary elements:
1. The experiments clearly demonstrated the differences between elastic and inelastic web crushing behavior and their dependence on concrete compressive strength;
Fig. 11—Overview of average strain demands on wall webs: (a) longitudinal strain profiles in M20 walls; and (b) prin-cipal strains versus ductility.
2. Increase in concrete compressive strength enhances the ductility and hysteretic energy capacity of structural walls by preventing web crushing shear failures;
3. Web crushing strength increases in proportion to fc′ as long as struts remain undamaged. Hence, transformation from an elastic web crushing failure to an inelastic web crushing failure can be achieved simply by increasing the concrete strength;
4. Damage to struts caused by cyclic loading and inelastic deformations limits web crushing strength independently of fc′.
While this conclusion may be generally well recognized for walls limited by both elastic and inelastic web crushing, exper-imental evidence from this research, based on corresponding monotonic and cyclic tests, showed that degradation from cyclic loading increases with increasing concrete strength;
5. Concrete compressive strength does not linearly increase web crushing strength as implied by rational web crushing models; rather, the relationship is nonlinear, with a decreasing limit as concrete strength increases. This
obser-Fig. 13—Average compression softening factor k versus: (a) normalized maximum shear distortion in plastic region; and
(b) concrete compressive strength.
Table 6—Comparison of web crushing capacities with models
Test unit
Experiment ACI 31814 Hines and Seible13
Δu, mm Fu, kN Δu, mm Fu, kN Difference, % Δu, mm Fu, kN Difference, % M05C 45.0 803 8.64 342 –81 48.5 821 8 M05M 45.0 855 8.13 322 –82 26.9 725 –40 M10C 42.7 751 8.38 387 –80 64.3 751 51 M10M 130 900 9.91 478 –92 101 853 –22 M15C 78.7 819 10.2 497 –87 128 889 62 M15M 133 934 11.7 542 –91 160 966 20 M20C 76.5 815 14.0 589 –82 Flexure M20M 189 923 13.2 553 –93 196 992 3
Notes: 1 kN = 0.225 kip; 1 mm = 0.0394 in.
Fig. 12—Comparison of force-displacement envelopes for cyclic and monotonic tests: (a) M05; (b) M10; (c) M15; and (d) M20. (Note: 1 kN = 0.225 kip; 1 mm = 0.0394 in.; 1 ksi = 6.895 MPa.)
vation is not well-described by current web crushing models. Therefore, it is advised that these models consider the limits demonstrated by the reported tests when considering HSC to improve the web crushing performance of walls;
6. The web crushing capacity of structural walls with well-confined boundary elements was found to be well in excess of levels acceptable in current practice for a wide range of concrete compressive strengths; and
7. Rational assessment of web crushing limits can open up new possibilities for acceptable ductile failure modes on reinforced concrete structural walls.
AUTHOR BIOS
ACI member Rigoberto Burgueño is an Associate Professor of structural
engineering and Director of the Civil Infrastructure Laboratory at Michigan State University, East Lansing, MI. He received his BS, MS, and PhD from the University of California, San Diego, La Jolla, CA. He is a member of ACI Committees 341, Earthquake-Resistant Concrete Bridges, and 440, Fiber-Re-inforced Polymer Reinforcement. His research interests include nano-engi-neered structural materials, composite materials and structures, multi-scale modeling, and seismic performance of reinforced concrete structures. ACI member Xuejian Liu is a former Graduate Research Assistant at
Michigan State University, where he received his PhD in civil engineering. He is a member of Joint ACI-ASCE Committee 445, Shear and Torsion. His research interests include the seismic behavior of reinforced concrete structures and fiber-reinforced concrete.
ACI member Eric M. Hines is a Principal at LeMessurier Consultants,
Inc., Cambridge, MA, and is a Professor of Practice at Tufts University, Medford, MA. He received his PhD in structural engineering from the University of California, San Diego. He is a member of ACI Committee 341, Earthquake-Resistant Concrete Bridges. His research interests include the seismic performance of low-ductility structural systems in moderate seismic regions and inelastic behavior of reinforced concrete structures.
NOTATION
Av = area of transverse steel at given level
dθ = incremental angle for calculating critical strut area
Esh = elastic modulus at onset of strain hardening
Fu = shear force at ultimate
Fy = ideal yield shear force
Fy′ = first yield shear force
f1 = principal tensile stress
fc′ = unconfined concrete compressive cylinder strength
fu = ultimate steel stress
fy = steel yield stress
fyv = transverse steel yield stress
jd = distance between flexural tension and compression force resultants
k = concrete compression strength softening factor
Lpr = plastic hinge region length
NCfs = flexure-shear strut compression capacity
NCs = standard shear strut compression capacity
NDfs = flexure-shear strut compression demand
NDs = standard shear strut compression demand
R = radius for critical compression strut fan
S = transverse reinforcement vertical spacing
T = flexural tensile force resultant
Tyav = effective average flexural tensile yield force resultant
tw = structural wall thickness
Δu = test unit flexural top displacement
Δy = ideal yield lateral displacement
ΔT = incremental tensile flexural force ε1 = principal tensile strain
εsh = steel strain at onset of strain hardening
φy = ideal yield curvature
μΔ = displacement ductility
θfs = flexure-shear crack angle measured from longitudinal axis
θs = shear crack angle measured from longitudinal axis
ρh = structural wall transverse reinforcement ratio
ρl = boundary element longitudinal reinforcement ratio
ρn = structural wall longitudinal reinforcement ratio
ρs = boundary element transverse reinforcement ratio
ACKNOWLEDGMENTS
The research described in this paper was carried out under funding from the National Science Foundation under Grant No. CMS-0530634. The authors thank the staff and students of MSU’s Civil Infrastructure Labora-tory, where the reported work was conducted.
REFERENCES
1. Leonhardt, F., and Walther, R., “The Stuttgart Shear Tests 1961,”
Transaction No. 111, Cement and Concrete Association, London, UK, 1961, 134 pp.
2. Mattock, A. H., and Kaar, P., “Precast-Prestressed Concrete Bridges, 4, Shear Tests of Continuous Girders,” Journal, Portland Cement
Associ-ation Research and Development Labs, V. 3, No. 1, Jan. 1961, pp. 19-46. 3. Robinson, J. R., “Essais a l’effort trenchant de pouters a ame mince en béton armé,” Annales des Ponts et Chaussées, Mar.-Apr. 1961, pp. 226-255.
4. Placas, A., and Reagan, P. E., “Shear Failure of Reinforced Concrete Beams,” ACI Journal, V. 68, No. 10, Oct. 1971, pp. 763-773.
5. Wang, T. Y.; Bertero, V. V.; and Popov, E. P., “Hysteretic Behavior of Reinforced Concrete Framed Walls,” Earthquake Engineering Research
Center Report 75/23, University of California, Berkeley, Berkeley, CA, Dec. 1975, 367 pp.
6. Oesterle, R. G.; Fiorato, A. E.; Johal, L. S.; Carpenter, J. E.; Russell, H. G.; and Corley, W. G., “Earthquake Resistant Structural Walls—Tests of Isolated Walls,” NSF Report GI-43880, Portland Cement Association, Skokie, IL, 1976, 315 pp.
7. Oesterle, R. G.; Ariztizabal-Ochoa, J. D.; Fiorato, A. E.; Russell, H. G.; and Corley, W. G., “Earthquake Resistant Structural Walls—Tests of Isolated Walls, Phase II,” NSF Report ENV77-15333, Portland Cement Association, Skokie, IL, 1979, 331 pp.
8. Vallenas, J. M.; Bertero, V. V.; and Popov, E. P., “Hysteretic Behavior of Reinforced Concrete Structural Walls,” Earthquake
Engi-neering Research Center Report 79/20, University of California, Berkeley, Berkeley, CA, 1979, 234 pp.
9. Oesterle, R. G.; Fiorato, A. E.; and Corley, W. G., “Web Crushing of Reinforced Concrete Structural Walls,” ACI Journal, V. 81, No. 3, May-June 1984, pp. 231-241.
10. Hines, E. M.; Seible, F.; and Priestley, M. J. N., “Seismic Perfor-mance of Hollow Rectangular Reinforced Concrete Piers with Highly-Con-fined Corner Elements—Phase I: Flexural Tests, and Phase II: Shear Tests,”
Structural Systems Research Project Report 1999/15, University of Cali-fornia, San Diego, La Jolla, CA, 1999, 266 pp.
11. Hines, E. M.; Dazio, A.; and Seible, F., “Seismic Performance of Hollow Rectangular Reinforced Concrete Piers with Highly-Confined Corner Elements—Phase III: Web Crushing Tests,” Structural Systems Research Project
Report 2001/27, University of California, San Diego, La Jolla, CA, 2001, 239 pp. 12. Hines, E. M.; Restrepo, J. I.; and Seible, F., “Force-Displacement Characterization of Well Confined Bridge Piers,” ACI Structural Journal, V. 101, No. 4, July-Aug. 2004, pp. 537-548.
13. Hines, E. M., and Seible, F., “Web Crushing of Hollow Rectangular Bridge Piers,” ACI Structural Journal, V. 101, No. 4, July-Aug. 2004, pp. 569-579.
14. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp.
15. ACI Committee 318, “Building Code Requirements for Reinforced Concrete (ACI 318-63),” American Concrete Institute, Farmington Hills, MI, 1963, 144 pp.
16. Paulay, T., and Priestley, M. J. N., Seismic Design of Reinforced
Concrete and Masonry Buildings, Wiley Interscience, New York, 1992, 768 pp. 17. Vecchio, F. J., and Collins, M. P., “The Modified Compression-Field Theory for Reinforced Concrete Elements Subjected to Shear,” ACI
Journal, V. 83, No. 2, Mar.-Apr. 1986, pp. 219-231.
18. Liu, X.; Burgueño, R.; Egleston, E.; and Hines, E. M., “Inelastic Web Crushing Performance Limits of High-Strength-Concrete Structural Wall— Single wall Test Program,” Report No. CEE-RR–2009/03, Michigan State University, East Lansing, MI, 2009, 281 pp.
19. Priestley, M. J. N.; Seible, F.; and Calvi, G. M., Seismic Design and
Retrofit of Bridges, John Wiley & Sons, Inc., New York, 1996, 686 pp. 20. Liu, X., “Inelastic Web Crushing Performance Limits of High-Strength-Concrete Structural Walls,” PhD dissertation, Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, 2010, 215 pp.
21. Tasdemir, M. A.; Tasdemir, C.; Akyuz, S.; Jefferson, A. D.; Lydon, F. D.; and Barr, B. I. G., “Evaluation of Strains at Peak Stresses in Concrete: A Three-Phase Composite Model Approach,” Cement and Concrete
Composites, V. 20, 1998, pp. 301-318.
22. Collins, M. P., “Toward a Rational Theory for RC Members in Shear,” Proceedings, ASCE, V. 104, No. ST4, Apr. 1978, pp. 649-666.
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
The present study investigated the influence of heated water storage, upward to 95°C (171°F), on precast prestressed concrete circular tanks. Modern design standards for concrete liquid- retaining structures require that thermal effects be considered for the serviceability limit state and the ultimate limit state when deemed significant. Most recognized standards, however, do not provide guidance for the analysis of such effects. Research in this area is also limited and almost exclusively concerned with ambient thermal conditions, with a maximum temperature change of 30°C (54°F) in any instance.
A finite element study incorporating thermomechanical coupling investigated the magnitude of stresses associated with thermal storage. A linear eigenvalue analysis examined the ultimate limit state of buckling for restrained tank walls due to the thermally- induced combined axial compression and bending. Consequent design implications were established and recommendations made for accommodating thermal loading.
Keywords: buckling; elevated temperature; finite element analysis;
mate-rial properties; prestressed concrete; reservoirs; thermal loading; thermal storage.
INTRODUCTION
The significance of thermal effects on concrete reservoir walls for ambient conditions is long established. An early study by Priestley1 determined that temperature gradients of
30°C (54°F) through the wall thickness can exist in warm climates when the effects of solar radiation are considered. Priestley1 demonstrated that the resulting tensile stresses
were large enough to overcome the residual compression, and cracking would inevitably occur. Ghali and Elliott2
developed closed-form solutions for the thermal analysis of elastic tank walls with varying base restraint and that are free at the top. Through numerical examples, it was shown that a gradient of 30°C (54°F) through the wall thickness was sufficient to cause cracking. This supported Priestley’s1 proposal that the design should be based on a
serviceability criterion of limiting crack widths rather than a limiting tensile stress. Although modern design standards require that thermal effects are considered for the service-ability limit state, few provide guidance for the analysis of such effects. Pioneering design codes with regard to this are NZS 31063 and AS 3735,4 which provide design tables,
originally derived by Priestley,1 to calculate hoop forces and
vertical moments for tank walls free at the top and either free-sliding, pinned, or fixed at the base.
The studies reviewed were exclusively applicable to tank walls free at the top. As thermal storage tanks require a roof, the associated radial restraint at the top of the wall alters the internal force distribution. Moreover, the magnitude of the internal forces resulting from the thermal expansion of
the tank walls will be shown to be prohibitive from a design perspective, unless provisions are made for radial displace-ment during service.
RESEARCH SIGNIFICANCE
This paper investigates the feasibility and implications of thermal storage using cylindrical concrete reservoirs, for which there is currently a paucity of information. The research has practical applications in the oil, gas, and nuclear containment industries, in addition to thermal storage for district heating and related schemes. Although particular reference is made throughout to precast prestressed concrete storage tanks, the research is also applicable to partially prestressed and reinforced concrete reservoirs.
INFLUENCE OF ELEVATED TEMPERATURES ON MATERIAL PROPERTIES
Mechanical properties
EN 1992-1-2,5 EN 1992-3,6 and FIB Bulletin 55: Model
Code 20107 each define the reductions in the mechanical
properties of both the concrete and steel reinforcement for elevated temperatures. For the temperature range under consideration for the current study, the associated strength reductions are insignificant. It is reasonable to suggest that any minor reduction in the strength and stiffness of concrete may be discounted when the effect of long-term thermal exposure is considered. Mears8 tested concrete specimens
subjected to a constant temperature of 65°C (149°F) for 5000 days and observed that the long-term exposure had, in fact, the effect of increasing the compressive strength and the modulus of elasticity of concrete. The same trend was also recorded by Komendant et al.,9 who tested concrete at
71°C (160°F) for 270 days, and Nasser and Lohtia,10 who
tested concrete at 121°C (250°F) for 200 days.
It would appear, however, that this trend is only valid for temperatures below 150°C (302°F), as long-term exposure to temperatures in excess of this resulted in a reduction in the mechanical properties of concrete.10,11
Creep
Creep of concrete increases at higher temperatures. Exten-sive research has been carried out on the influence of temperature on concrete creep for structures used in nuclear Title No. 111-S21
Response of Precast Prestressed Concrete Circular Tanks
Retaining Heated Liquids
by Michael J. Minehane and Brian D. O’Rourke
ACI Structural Journal, V. 111, No. 2, March-April 2014.
MS No. S-2012-065, doi:10.14359.51686441, was received February 23, 2012, and reviewed under Institute publication policies. Copyright © 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including author’s closure, if any, will be published ten months from this journal’s date if the discussion is received within four months of the paper’s print publication.
