Resistant Design Of Reinforced Concrete Structures
Resistant Design of Reinforced Concrete StructuresBy Dennis M. McCann, Ph.D., P.E. and Steven J. Smith, Ph.D., P.E.Trial 1: 8-Inch WallBlast LoadResistance (trial 1)20Force (kips)The study of blast effects on structures has been an area offormal technical investigation for over 60 years. There arenumerous texts, guides and manuals on the subject, withcontinuing research and technical reporting occurring ata brisk pace. However, there is limited guidance availablein the literature on the direct application of establishedblast effects principals to structural design. Numerousefforts are under way to develop comprehensive guidesand standards to fill this void. This article presents ageneral overview of key design concepts for reinforcedconcrete structures.100-1000.050.10.15Blast Resistance andProgressive Collapse0.20.250.3Time (sec)0.350.40.450.5Trial 2: 10-Inch WallforceForce (kips)Progressive collapse-resistant design mitigates disproBlast Load20portionately large failures following the loss of one orResistance (trial 2)more structural elements. Progressive collapse-resistant10design is system-focused, and is often divided into two approaches, direct and indirect. The direct method designs0the structural system to respond to a specific threat eitherby providing an alternate load path in the event of failure-10of one or more members, or by specific local-resistanceimprovements of key elements. This method is similar to00.050.10.150.20.250.30.350.40.45 0.5blast-resistant design. The indirect method provides genTime (sec)eral systemic improvements to toughness, continuity andredundancy; tension ties are an example of an indirect de- Figure 2: Applied force and internal resistance time histories (using 2% damping).tailing technique.Blast-resistant design is element-focused. It enhances toughness, is v ƒ0td/2m , where ƒ0 and td are shown in Figure 1 and m is theductility, strength and dynamic characteristics of individual structural mass. Thus, in this response regime, the mass of the structural elementelements for resistance to air-blast induced loading. This article is is the only system parameter that controls the magnitude of thedevoted to blast-resistant design, though there is overlap with pro- initial motion of the system – the more massive the structuralelement, the less it will be excited by the impulse from the blastgressive collapse-resistant design.wave. In this regard, the greater mass of concrete structures can beWhat’s Special About Blast Loading?used to great advantage.This load response to a blast is significantly different from the loadThisarticlespecificallyf(t)addresses the affects of response to a seismic event, for which the natural frequency of theshock loading from air- structure, rather than the mass, is the primary factor in the response.blast. This type of load isfoResponse Limits and Member Analysisapplied to the perimeterThe extreme nature of blast loading necessitates the acceptancestructural elements of abuilding due to a high that members will have some degree of inelastic response in mostexplosive blast event ex- cases. This allows for reasonable economy in the structural designternal to the building. and provides an efficient mechanism for energy dissipation. This alsoThe pressure wave ap- requires the designer to understand how much inelastic response ist0plied to the building is appropriate. Greater inelastic response will provide greater dissipationtdtimecharacterized by short of the blast energy and allow for the sizing of smaller structuralFigure 1: Idealized blast pulse with a peakduration and high in- elements, but it will also be accompanied by greater damage and, atintensity, f0 and duration, tdsome point, increased potential for failure of the element.tensity (Figure 1).The U.S. Army Corps of Engineers Protective Design Center (PDC)The blast wave duration, td , is typically in the range of 0.1 – .001seconds. This is often much shorter than, or at most on the order of, the has developed response criteria for many typical structural elementsnatural period, Tn , of typical structural elements. For situations where in terms of maximum allowable support rotation, qmax , or ductilitytd 0.4Tn (some sources advise td 0.1Tn), the blast wave effectively ratio, mmax , as shown in Tables 1 and 2 (see page 24). These limitsimparts an initial velocity to a structural element and the element were developed in conjunction with experts in the field of blastthen continues to respond at its natural frequency. The magnitude of effects and are based on existing criteria and test data. The limitsthat initial velocity, for a single-degree-of-freedom (SDOF) model, can be correlated to qualitative damage expectations ranging fromSTRUCTURE magazine22April 2007
::no damage with elements responding elastically to severe damage3) Elastic rebound after reaching the maximum displacement:with elements responding far into the inelastic regime. Table 3 (see R(x,t) Rm – ke[xm - x(t)], where xm is the maximum displacement.page 25), provides a sampling of damage expectations for specificWhile closed form solutions exist for some simple load profiles, it isstructural components, and Table 4 (see page 26) provides guidance often necessary to solve the SDOF equations of motion numerically.on overall structural damage that the Department of Defense (DoD) Such methods and a more complete treatment of equivalent SDOFequates with varying levels of protection.systems can be found in texts on structural dynamics.These limits are calibrated to an equivalent single degree of systemDesign(SDOF) model of the structural member with lumped mass andThe design procedure includes:stiffness, and should only be compared to responses determined1) Blast load definitionin that manner. The SDOF method assumes the response of the2) Response limit selectionmember can be appropriately modeled as a single mode, neglecting3) Trial member sizing and reinforcingcontributions from all other modes. The calibration process used for4) Nonlinear dynamic SDOF analysis of the memberthe PDC limits incorporates mapping the idealized SDOF to actual5) Comparing the calculated SDOF response with the responsestructural response.limit and adjusting the trial member as necessaryThe undamped SDOF equation of motion is written:As noted above, some amount of inelastic response is generallyme x(t) R(x,t) f (t) where f (t) is the blast load, x(t) is the accelerationresponse, me is the equivalent or activated mass of the structural anticipated when designing members for blast response. Economy ofelement, and R(x,t) is the internal resistance as a function of time and design is achieved by selecting smaller members and allowing greaterdisplacement. Assuming elasto-plastic material behavior, the resistance inelasticity. Where greater protection is warranted, larger members areselected, potentially even such that the response to the design blastis divided into three phases:threat remains elastic. While member sizes can be scaled to match the1) Elastic response until yield: R(x,t) ke x(t), where ke is thedesired level of protection, proper detailing of joints, connections andequivalent stiffness and x(t) is the displacement response.reinforcing should always be provided so that the members can achieve2) Plastic deformation after yield when deformation continueslarge, inelastic deformations even if the intent is for elastic responsewithout increase in resistance: R(x,t) Rm , where Rm is the(thus providing greater margins against an actual blast that is largermaximum resistance.Table 1: Maximum Response Limits for SDOR Analysis of Flexural ElementsaExpected Element DamageSuperficialElement TypeReinforced ConcreteSingle-Reinforced Slab or BeamDouble-Reinforced Slab or Beam without Shear ReinforcementbDouble-Reinforced Slab or Beam with Shear ReinforcementbSlab or Beam with Tension Membranec (Normal Proportionsd)Slab or Beam with Tension Membranec (Deep Elementsd)Prestressed ConcreteeSlab or Beam with wp 0.30Slab or Beam with 0.15 wp 0.30Slab or Beam with wp 0.15 and Shear ReinforcementbSlab or Beam with wp 0.15 and Shear ReinforcementbSlab or Beam with Tension Membranec,f (Normal ral Steel (Hot-Rolled)Beam with Compact SectionhBeam with Noncompact SectionhPlate Bent about Weak maxμmaxqmax11111––––––––––2 2 4 6 6 –––––5 5 6 12 7 ––––10 10 10 20 12 0.70.80.811–––––0.80.25/ wp0.25/ wp–––1 1 1 1 0.90.29/ wp0.29/ wp–––1.5 1.5 2 6 10.33/ wp0.33/ wp–––2 2 3 10 11––––1.5 2 ––4 8 ––8 15 10.74––1 30.8583 3 2 1212010 10 6 251.24020 20 12 Where a dash (–) is shown, the corresponding parameter is not applicable as a flexural response limitStirrups or ties that satisfy the minimum requirements of Section 11.5.6 of ACI 318 and enclose both layers of flexural reinforcement throughout the span lengthTension membrane forces shall be restrained by a member capable of resisting the corresponding loads and typically cannot be developed along a slab free edgedElements with normal proportions have a span-to-depth ratio greater than or equal to 4; deep elements have a span-to-depth ratio less than 4eReinforcement index wp (A ps /bd)(f ps /f c )fValues assume bonded tendons, draped strands and continuous slabs or beamsgValues assume wall resistance controlled by brittle flexural response or axial load arching with no plastic deformation; for load-bearing walls, use Superficial or Moderatedamage limits to preclude collapsehLimiting width-to-thickness ratios for compact and noncompact sections are defined in ANSI/AISC 360abcDeveloped from PDC-TR-06-08, Single Degree of Freedom Response Limits for Antiterrorism Design,Protective Design Center, U.S. Army Corps of Engineers, October 2006.STRUCTURE magazine23 April 2007
than the design blast). Without proper detailing, it is uncertainwhether a structure intended for blast resistance will achievethe design intent. The January, 2007 STRUCTURE articleConcrete Detailing for Blast provides effective recommendationsfor concrete detailing. In addition to that article, general designand detailing considerations include:Resistance (trial 1)Resistance (trial 2)Blast Load1)2)3)10Force (kip)15Balanced design often leads to a strong column – weak beamapproach, with the intent that beam failure is preferable tocolumn failure.Provide sufficient shear transfer to floor slabs so that directlyapplied blast loads can be resisted by the diaphragms ratherthan weak-axis beam bending.Transfer girders should be avoided in regions identified ashaving a high blast threat.(3)(3)50-5-10-150.60.500.511.51.4 in0.322.5Displacement (in)ColumnsDesign critical columns to be able to span two stories, in theevent that lateral bracing is lost, particularly when using a weakbeam approach.Detailing and Connections1) Use special seismic momentframe details.2) Avoid splices at plastichinge locations.3) Provide continuousreinforcing through joints.4) Used hooked bars wherecontinuous reinforcing is notpossible (particularly at corners).Example(2)(1)20Beams(2)(1)2533.1 in3.500.10.20.4Time (sec)Figure 3: Three dimensional SDOF response histories for each trial section(using 2% damping). Two dimensional resistance-displacement anddisplacement-time projections are also shown. Regions of (1) initial elasticdeformation, (2) plastic deformation, and (3) elastic rebound are indicated onthe resistance-displacement projections.Table 2: Maximum Response Limits for Sdof Analysis of Compression ElementsaExpected Element maxqmaxμmaxqmaxμmaxqmaxSingle-Reinforced Slab orBeam-Column1––2 –2 –2 Double-Reinforced Slabor Beam-Column withoutShear Reinforcementb1––2 –2 –2 Element TypeReinforced ConcreteConsider an exterior panel wall meaDouble-Reinforced Slabsuring 12 feet tall by 30 feet long,or Beam-Column with1––4 –4 –4 attached to the primary structural fraShear Reinforcementbming system at its top and bottom.Walls and SeismicThe wall is to be designed to resist0.9–1–2–3–Columnsc,dthe effects of a high explosive blastNon-seismic Columnsc,d0.7–0.8–0.9–1–resulting in a 12 pounds per squareinch (psi) peak reflected pressure Masonryand a positive phase pulse duration,Unreinforcedc1––1.5 –1.5 –1.5 td 50 milliseconds.Reinforced1––2 –2 –2 Since the wall is attached at its topand bottom, the vertical reinforce- Structural Steel (Hot-Rolled)ment will provide the primary loadBeam-Column withpath and blast resistance; as such this1–33 33 33 Compact Sectionf,gexample will be limited to design ofBeam-Column withthe vertical reinforcement. As an ini0.7–0.853 0.853 0.853 Noncompact Sectionf,gtial trial, an 8-inch thick wall with #4reinforcing bars spaced every 6 inchesColumn (Axial Failure)d0.9–1.3–2–3–at each face will be considered. For aWhere a dash (–) is shown, the corresponding parameter is not applicable as a flexural response limiteach trial section, the bending and bStirrups or ties that satisfy the minimum requirements of Section 11.5.6 of ACI 318 and enclose both layers of flexuralthroughout the span lengthshear (yield) strength of a unit strip are reinforcementcSeismic columns have ties or spirals that satisfy, at a minimum, the requirements of Section 21.12.5 of ACI 318; seecomputed, applying strength increase Chapter 9 for complete detailing requirementsfactors (SIF) to account for the actual de Ductility ratio is based on axial deformation, rather than flexural deformationValues assume wall resistance controlled by brittle flexural response or axial load arching with no plastic deformation; for(rather than code minimum) strength load-bearingwalls, use Superficial or Moderate damage limits to preclude collapsefof materials and dynamic increase fac- Limiting width-to-thickness ratios for compact and noncompact sections are defined in ANSI/AISC 360gUse connection shear capacity, rather than element flexural capacity, to calculate ultimate resistance for analysistors (DIF) to account for the increasedstrength of materials exhibited under Developed from PDC-TR-06-08, Single Degree of Freedom Response Limits for Antiterrorism Design,Protective Design Center, U.S. Army Corps of Engineers, October 2006.STRUCTURE magazine24April 2007
Table 3: Qualitative Damage Expectations for Reinforced Concrete ElementsElement - IssueSuperficialModerateHeavyHazardousBeam and Column ReinforcementNo damageNo damageLocal bucklingof longitudinalreinforcementFracture of longitudinal andtransverse reinforcementBeam and Column Core ConcreteNo visible, permanentstructural damageMinor cracking (repairableby injection grouting)Substantial damageRubbleBeam and Column CoverNo visible, permanentstructural damageSubstantial spallingLostLostBeam and Column StabilityNoneNoneLocal bucklingof longitudinalreinforcementGlobal bucklingFracture and loss ofanchorage at jointRubble at coreConnection ReinforcementNoneNoneLimited fracture andcompromised anchorageat joint (load transfermaintained)Connection ConcreteNo visible, permanentstructural damageMinor spalling and cracking(repairable)Substantial damageSlab Diaphragm ActionHair line crackingin the vicinity of theblast; concrete andreinforcement essentiallyundamaged; diaphragmaction uncompromisedfor the lateral force andgravity force resistanceSpalling of concrete coverlimited to the immediatevicinity of blast; connectionto supporting beam intactexcept in the immediatevicinity of blast wherelocalized separation islikely; diaphragm actionuncompromised for lateralforce and gravity resistance.fast load application rates. SIF and DIF values for reinforced concrete design are suggested in Design of Blast Resistant Buildings in Petrochemical Facilities (ASCE 1997) and TM5-1300, Structures to Resistthe Effects of Accidental Explosions (USACE 1990). The lesser of thecomputed bending or shear strengths is used as the maximum resistance, Rm, in the elasto-plastic resistance function. Rm 10 kips forthe 8-inch thick unit strip trial section.The equivalent SDOF is then computed. The effective stiffnessin this case would be computed based on the center deflection ofa simply supported beam. Since both elastic and plastic response isanticipated, the moment of inertia used for the stiffness calculationis taken as the average of the gross and cracked moments of inertia.Load (stiffness) and mass transformation factors may be applied tocompute the effective mass of the trial section. The effective masscan be thought of as the portion of the total mass of the sectionthat participates in the SDOF response. A more complete treatmentof mass participation and load-mass factors used to compute theeffective mass can be found in Introduction to Structural Dynamics(Biggs 1964). The 8-inch thick unit strip trial section has anequivalent stiffness, ke 27.7 kip/in, and an equivalent mass,me 2.24 pounds-seconds2/inch, giving a natural period of vibrationof the equivalent SDOF ofTn 2p me / ke 0.057 seconds (sec.).Since the pulse duration and natural period are sim-ilar (i.e. td / Tn 0.05sec/0.057 sec 1) in this case, the assessment of the response requiressolution of the SDOF equation of motion. Numerical solution ofthe SDOF equation of motion gives a peak displacement responseof xm 3.1 inches with a permanent deformation after rebound ofxp 2.7 inches and a ductility ratio of m xm / (xm – xp) 7.75. TheMinor damage concreteSignificant damage toand reinforcement;concrete and reinforcement;connection to supportingdiaphragm actionbeam yields but fracturecompromised for lateralis likely in vicinity offorce resistance but providesblast resulting in localizedstability for gravity forceseparationresistancepeak displacement corresponds to rotations at the top and bottom ofthe wall section of q tan-1 (xm / 0.5hwall) 2.5 degrees, which exceedsthe response limit for flexural members of qmax 2.0 degrees. Hence,the analysis must be conducted again with a new trial section.Using the same reinforcing steel spacing, but increasing the wallthickness to 10 inches, increases the maximum resistance to 13.4 kips,the equivalent stiffness to 53.5 kip/inch, and the effective mass to2.8 pounds-seconds2/inch. This results in a natural period of 0.045seconds for the new trial section. Numerical solution of the equivalentSDOF with these parameters gives a peak displacement response of1.4 inches with a permanent deformation of 1.1 inches, or a ductilitydemand just over 4.5 times the elastic limit. Rotations at the top andbottom of the wall are reduced to 1.1 degrees, which is now withinthe response limit. Figure 2 (see page 22) shows the applied force andinternal resistance time histories for each of the trial sections. Figure 3(page 24) shows the SDOF response for each trial in three dimensions,with two-dimensional projections of the resistance-displacementcurves and the displacement time history.SummaryReinforced concrete can provide substantial protection from evenextreme blast loading. The relatively large mass of concrete elementsprovides an inherent resistance to impulsive loads. Structural designconsiderations include sizing members to provide an expected degreeof deformation and associated damage and optimizing the structureto resist and transfer blast loads in a reliable manner. Proper detailingis the final critical component of the design process to ensure that thestructural elements have sufficient toughness to achieve the desiredinelastic deformations. Table 4 and References on next pageSTRUCTURE magazine25 April 2007
Table 4: Department Of Defense Damage DescriptionsLevel of ProtectionComponent Damage2Potential Overall Structural Damage1Below ATStandards3(Blowout)Severely damaged; frame collapse/massive destruction;little left standing.Very Low(VLLOP)Heavily damaged - onset of structural collapse: majordeformation or primary and secondary structuralmembers, but progressive collapse is unlikely; collapse ofnon-structural elements.A
Protective Design Center, U.S. Army Corps of Engineers, October 2006. no damage with elements responding elastically to severe damage with elements responding far into the inelastic regime. Table 3 (see page 25), provides a sampling of damage expectations for specific structural components, and Table 4 (see page 26) provides guidance
vary the overall capacity of the reinforced concrete and as well as the type of interaction it experiences whether for it to be either over reinforced or under reinforced. 2.2.2.1 Under Reinforced Fig. 3. Under Reinforced Case Figure 3.2 shows the process in determining if the concrete beam is under reinforced. The
reinforced concrete for pavement applications. However, Merta et al., (2011) studied wheat straw reinforced concrete for building material applications. They concluded that there is an increase (i.e. 2%) in fracture energy of wheat straw reinforced concrete. Thus, wheat straw reinforced concrete needs to be investigated for rigid pavements.
Recommended Practice for Glass Fiber Reinforced Concrete Panels - Fourth Edition, 2001. Manual for Quality Control for Plants and Production of Glass Fiber Reinforced Concrete Products, 1991. ACI 549.2R-04 Thin Reinforced Cementitious Products. Report by ACI Committee 549 ACI 549.XR. Glass Fiber Reinforced Concrete premix. Report by ACI .
experimental flexural behavior of concrete beams reinforced with glass fiber reinforced polymers bars" is done. D.Modeling . ANSYS Workbench 16.1 is used to model the concrete beams and 28 different models are considered. Concrete beams reinforced with reinforced with steel bars of circular cross
Concrete Beams 9 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete - stress/strain Concrete Beams 10 Lecture 21 Elements of Architectural Structures ARCH 614 S2007abn Reinforced Concrete Analysis for stress calculations steel is transformed to concrete concrete is in compression above n.a. and
10. Seismic Design of Reinforced Concrete Structures 465 10.1 INTRODUCTION 10.1.1 The Basic Problem The problem of designing earthquake-resistant reinforced concrete buildings, like the design of structures (whether of concrete, steel, or other material) for other loading
lateral systems. The report focuses on 'Special Reinforced Concrete Moment Resisting Frames' and 'Special Reinforced Concrete Shear Walls'. The parent project aims to relate design and assessment for a broad spectrum of building layouts and heights, for both reinforced concrete and structural steel lateral resisting systems.
reinforced concrete, Ultra-high performance concrete, Reactive powder concrete. The most common and well researched material is fibre reinforced concrete using different fibers. The concept of using fibers is to enhance the tensile behaviour of the concrete by bridging the cracks and improving the load carrying capacity of the structural members.
