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Seismic Collapse Safety of Reinforced ConcreteBuildings.II:Comparative Assessment of Nonductile and Ductile Moment FramesAbbie B.Liel,M.ASCE 1;Curt B.Haselton,M.ASCE 2;and Gregory G.Deierlein,F.ASCE 3Abstract:This study is the second of two companion papers to examine the seismic collapse safety of reinforced concrete frame buildings,and examines nonductile moment frames that are representative of those built before the mid-1970s in California.The probabilistic assessment relies on nonlinear dynamic simulation of structural response to calculate the collapse risk,accounting for uncertainties in ground-motion characteristics and structural modeling.The evaluation considers a set of archetypical nonductile RC frame structures of varying height that are designed according to the seismic provisions of the 1967Uniform Building Code.The results indicate that nonductile RC frame structures have a mean annual frequency of collapse ranging from 5to 14×10À3at a typical high-seismic California site,which is approximately 40times higher than corresponding results for modern code-conforming special RC moment frames.These metrics demonstrate the effectiveness of ductile detailing and capacity design requirements,which have been introduced over the past 30years to improve the safety of RC buildings.Data on comparative safety between nonductile and ductile frames may also inform the development of policies for appraising and mitigating seismic collapse risk of existing RC frame buildings.DOI:10.1061/(ASCE)ST.1943-541X .0000275.©2011American Society of Civil Engineers.CE Database subject headings:Structural failures;Earthquake engineering;Structural reliability;Reinforced concrete;Concrete structures;Seismic effects;Frames.Author keywords:Collapse;Earthquake engineering;Structural reliability;Reinforced concrete structures;Buildings;Commercial;Seismic effects.IntroductionReinforced concrete (RC)frame structures constructed in Califor-nia before the mid-1970s lack important features of good seismic design,such as strong columns and ductile detailing of reinforce-ment,making them potentially vulnerable to earthquake-induced collapse.These nonductile RC frame structures have incurred significant earthquake damage in the 1971San Fernando,1979Imperial Valley,1987Whittier Narrows,and 1994Northridge earthquakes in California,and many other earthquakes worldwide.These factors raise concerns that some of California ’s approxi-mately 40,000nonductile RC structures may present a significant hazard to life and safety in future earthquakes.However,data are lacking to gauge the significance of this risk,in relation to either the building population at large or to specific buildings.The collapse risk of an individual building depends not only on the building code provisions employed in its original design,but also structuralconfiguration,construction quality,building location,and site-spe-cific seismic hazard information.Apart from the challenges of ac-curately evaluating the collapse risk is the question of risk tolerance and the minimum level of safety that is appropriate for buildings.In this regard,comparative assessment of buildings designed accord-ing to old versus modern building codes provides a means of evalu-ating the level of acceptable risk implied by current design practice.Building code requirements for seismic design and detailing of reinforced concrete have changed significantly since the mid-1970s,in response to observed earthquake damage and an in-creased understanding of the importance of ductile detailing of reinforcement.In contrast to older nonductile RC frames,modern code-conforming special moment frames for high-seismic regions employ a variety of capacity design provisions that prevent or delay unfavorable failure modes such as column shear failure,beam-column joint failure,and soft-story mechanisms.Although there is general agreement that these changes to building code require-ments are appropriate,there is little data to quantify the associated improvements in seismic safety.Performance-based earthquake engineering methods are applied in this study to assess the likelihood of earthquake-induced collapse in archetypical nonductile RC frame structures.Performance-based earthquake engineering provides a probabilistic framework for re-lating ground-motion intensity to structural response and building performance through nonlinear time-history simulation (Deierlein 2004).The evaluation of nonductile RC frame structures is based on a set of archetypical structures designed according to the pro-visions of the 1967Uniform Building Code (UBC)(ICBO 1967).These archetype structures are representative of regular well-designed RC frame structures constructed in California between approximately 1950and 1975.Collapse is predicted through1Assistant Professor,Dept.of Civil,Environmental and Architectural Engineering,Univ.of Colorado,Boulder,CO 80309.E-mail:abbie .liel@ 2Assistant Professor,Dept.of Civil Engineering,California State Univ.,Chico,CA 95929(corresponding author).E-mail:chaselton@csuchico .edu 3Professor,Dept.of Civil and Environmental Engineering,Stanford Univ.,Stanford,CA 94305.Note.This manuscript was submitted on July 14,2009;approved on June 30,2010;published online on July 15,2010.Discussion period open until September 1,2011;separate discussions must be submitted for individual papers.This paper is part of the Journal of Structural Engineer-ing ,V ol.137,No.4,April 1,2011.©ASCE,ISSN 0733-9445/2011/4-492–502/$25.00.492/JOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .nonlinear dynamic analysis of the archetype nonductile RC frames,using simulation models capable of capturing the critical aspects of strength and stiffness deterioration as the structure collapses.The outcome of the collapse performance assessment is a set of measures of building safety and relating seismic collapse resistance to seismic hazard.These results are compared with the metrics for ductile RC frames reported in a companion paper (Haselton et al.2011b ).Archetypical Reinforced Concrete Frame StructuresThe archetype nonductile RC frame structures represent the expected range in design and performance in California ’s older RC frame buildings,considering variations in structural height,configuration and design details.The archetype configurations explore key design parameters for RC components and frames,which were identified through previous analytical and experimental studies reviewed by Haselton et al.(2008).The complete set of archetype nonductile RC frame buildings developed for this study includes 26designs (Liel and Deierlein 2008).This paper focuses primarily on 12of these designs,varying in height from two to 12stories,and including both perimeter (P )and space (S )frame lateral resisting systems with alternative design details.All archetype buildings are designed for office occupancies with an 8-in.(20-cm)flat-slab floor system and 25-ft (7.6-m)column spacing.The 2-and 4-story buildings have a footprint of 125ft by 175ft (38.1m by 53.3m),and the 8-and 12-story buildings measure 125ft (38.1m)square in plan.Story heights are 15ft (4.6m)in the first story and 13ft (4.0m)in all other stories.Origi-nal structural drawings for RC frame buildings constructed in California in the 1960s were used to establish typical structural configurations and geometry for archetype structures (Liel and Deierlein 2008).The archetypes are limited to RC moment frames without infill walls,and are regular in elevation and plan,without major strength or stiffness irregularities.The nonductile RC archetype structures are designed for the highest seismic zone in the 1967UBC,Zone 3,which at that time included most of California.Structural designs of two-dimensional frames are governed by the required strength and stiffness to satisfy gravity and seismic loading combinations.The designs also satisfy all relevant building code requirements,including maximum and minimum reinforcement ratios and maximum stirrup spacing.The 1967UBC permitted an optional reduction in the design base shear if ductile detailing requirements were employed,however,this reduction is not applied and only standard levels of detailing are considered in this study.Design details for each structure areTable 1.Design Characteristics of Archetype Nonductile and Ductile RC Frames Stucture Design base shear coefficient a,bColumn size c (in :×in.)Column reinforcementratio,ρColumn hoop spacing d,e (in.)Beam size f (in :×in.)Beam reinforcementratios ρ(ρ0)Beam hoop spacing (in.)Nonductile2S 0.08624×240.0101224×240.006(0.011)112P 0.08630×300.0151530×300.003(0.011)114S 0.06820×200.0281020×260.007(0.014)124P 0.06824×280.0331424×320.007(0.009)158S 0.05428×280.0141424×260.006(0.013)118P 0.05430×360.0331526×360.008(0.010)1712S 0.04732×320.025926×300.006(0.011)1712P 0.04732×400.032930×380.006(0.013)184S g 0.06820×200.028 6.720×260.007(0.014)84S h 0.06820×200.0281020×260.007(0.014)1212S g 0.04732×320.025626×300.006(0.011)1112S h 0.04732×320.025926×300.006(0.011)17Ductile2S 0.12522×220.017518×220.006(0.012) 3.52P 0.12528×300.018528×280.007(0.008)54S 0.09222×220.016522×240.004(0.008)54P 0.09232×380.016 3.524×320.011(0.012)58S 0.05022×220.011422×220.006(0.011) 4.58P 0.05026×340.018 3.526×300.007(0.008)512S 0.04422×220.016522×280.005(0.008)512P0.04428×320.0223.528×380.006(0.007)6aThe design base shear coefficient in the 1967UBC is given by C ¼0:05=T ð1=3Þ≤0:10.For moment resisting frames,T ¼0:1N ,where N is the number of stories (ICBO 1967).bThe design base shear coefficient for modern buildings depends on the response spectrum at the site of interest.The Los Angeles site has a design spectrumdefined by S DS ¼1:0g and S D1¼0:60g.The period used in calculation of the design base shear is derived from the code equation T ¼0:016h 0:9n ,where h n isthe height of the structure in feet,and uses the coefficient for upper limit of calculated period (C u ¼1:4)(ASCE 2002).cColumn properties vary over the height of the structure and are reported here for an interior first-story column.dConfiguration of transverse reinforcement in each member depends on the required shear strength.There are at least two No.3bars at every location.eConfiguration of transverse reinforcement in ductile RC frames depends on the required shear strength.All hooks have seismic detailing and use No.4bars (ACI 2005).fBeam properties vary over the height of the structure and are reported here are for a second-floor beam.gThese design variants have better-than-average beam and column detailing.hThese design variants have better-than-average joint detailing.JOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011/493D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .summarized in Table 1,and complete documentation of the non-ductile RC archetypes is available in Liel and Deierlein (2008).Four of the 4-and 12-story designs have enhanced detailing,as described subsequently.The collapse performance of archetypical nonductile RC frame structures is compared to the set of ductile RC frame archetypes presented in the companion paper (Haselton et al.2011b ).As sum-marized in Table 2,these ductile frames are designed according to the provisions of the International Building Code (ICC 2003),ASCE 7(ASCE 2002),and ACI 318(ACI 2005);and meet all gov-erning code requirements for strength,stiffness,capacity design,and detailing for special moment frames.The structures benefit from the provisions that have been incorporated into seismic design codes for reinforced concrete since the 1970s,including an assort-ment of capacity design provisions [e.g.,strong column-weak beam (SCWB)ratios,beam-column and joint shear capacity design]and detailing improvements (e.g.,transverse confinement in beam-column hinge regions,increased lap splice requirements,closed hooks).The ductile RC frames are designed for a typical high-seismic Los Angeles site with soil class S d that is located in the transition region of the 2003IBC design maps (Haselton and Deierlein 2007).A comparison of the structures described in Table 1reflects four decades of changes to seismic design provisions for RC moment frames.Despite modifications to the period-based equation for design base shear,the resulting base shear coefficient is relatively similar for nonductile and ductile RC frames of the same height,except in the shortest structures.More significant differencesbetween the two sets of buildings are apparent in member design and detailing,especially in the quantity,distribution,and detailing of transverse reinforcement.Modern RC frames are subject to shear capacity design provisions and more stringent limitations on stirrup spacing,such that transverse reinforcement is spaced two to four times more closely in ductile RC beams and columns.The SCWB ratio enforces minimum column strengths to delay the formation of story mechanisms.As a result,the ratio of column to beam strength at each joint is approximately 30%higher (on average)in the duc-tile RC frames than the nonductile RC frames.Nonductile RC frames also have no special provision for design or reinforcement of the beam-column joint region,whereas columns in ductile RC frames are sized to meet joint shear demands with transverse reinforcement in the joints.Joint shear strength requirements in special moment frames tend to increase the column size,thereby reducing axial load ratios in columns.Nonlinear Simulation ModelsNonlinear analysis models for each archetype nonductile RC frame consist of a two-dimensional three-bay representation of the lateral resisting system,as shown in Fig.1.The analytical model repre-sents material nonlinearities in beams,columns,beam-column joints,and large deformation (P -Δ)effects that are important for simulating collapse of frames.Beam and column ends and the beam-column joint regions are modeled with member end hinges that are kinematically constrained to represent finite joint sizeTable 2.Representative Modeling Parameters in Archetype Nonductile and Ductile RC Frame Structures Structure Axial load a,b (P =A g f 0c )Initial stiffness c Plastic rotation capacity (θcap ;pl ,rad)Postcapping rotation capacity (θpc ,rad)Cyclicdeterioration d (λ)First mode period e (T 1,s)Nonductile2S 0.110:35EI g 0.0180.04041 1.12P 0.030:35EI g 0.0170.05157 1.04S 0.300:57EI g 0.0210.03333 2.04P 0.090:35EI g 0.0310.10043 2.08S 0.310:53EI g 0.0130.02832 2.28P 0.110:35EI g 0.0250.10051 2.412S 0.350:54EI g 0.0290.06353 2.312P 0.140:35EI g 0.0450.10082 2.84S f 0.300:57EI g 0.0320.04748 2.04S g 0.300:57EI g 0.0210.03333 2.012S f 0.350:54EI g 0.0430.09467 2.312S g 0.350:54EI g 0.0290.06353 2.3Ductile2S 0.060:35EI g 0.0650.100870.632P 0.010:35EI g 0.0750.1001110.664S 0.130:38EI g 0.0570.100800.944P 0.020:35EI g 0.0860.100133 1.18S 0.210:51EI g 0.0510.10080 1.88P 0.060:35EI g 0.0870.100122 1.712S 0.380:68EI g 0.0360.05857 2.112P0.070:35EI g0.0700.1001182.1a Properties reported for representative interior column in the first story.(Column model properties data from Haselton et al.2008.)bExpected axial loads include the unfactored dead load and 25%of the design live load.cEffective secant stiffness through 40%of yield strength.dλis defined such that the hysteretic energy dissipation capacity is given by Et ¼λM y θy (Haselton et al.2008).eObtained from eigenvalue analysis of frame model.fThese design variants have better-than-average beam and column detailing.gThese design variants have better-than-average joint detailing.494/JOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .effects and connected to a joint shear spring (Lowes and Altoontash 2003).The structural models do not include any contribution from nonstructural components or from gravity-load resisting structural elements that are not part of the lateral resisting system.The model is implemented in OpenSees with robust convergence algorithms (OpenSees 2009).As in the companion paper,inelastic beams,columns,and joints are modeled with concentrated springs idealized by a trilinear back-bone curve and associated hysteretic rules developed by Ibarra et al.(2005).Properties of the nonlinear springs representing beam and column elements are predicted from a series of empirical relation-ships relating column design characteristics to modeling parame-ters and calibrated to experimental data for RC columns (Haselton et al.2008).Tests used to develop empirical relationships include a large number of RC columns with nonductile detailing,and predicted model parameters reflect the observed differences in moment-rotation behavior between nonductile and ductile RC elements.As in the companion paper,calibration of model param-eters for RC beams is established on columns tested with low axial load levels because of the sparse available beam data.Fig.2(a)shows column monotonic backbone curve properties for a ductile and nonductile column (each from a 4-story building).The plastic rotation capacity θcap ;pl ,which is known to have an important influence on collapse prediction,is a function of the amount of column confinement reinforcement and axial load levels,and is approximately 2.7times greater for the ductile RC column.The ductile RC column also has a larger postcapping rotation capacity (θpc )that affects the rate of postpeak strength degradation.Fig.2(b)illustrates cyclic deterioration of column strength and stiffness under a typical loading protocol.Cyclic degradation of the initial backbone curve is controlled by the deterioration parameter λ,which is a measure of the energy dissipation capacity and is smaller in nonductile columns because of poor confinement and higher axial loads.Model parameters are calibrated to the expected level of axial compression in columns because of gravity loads and do not account for axial-flexure-shear interaction during the analysis,which may be significant in taller buildings.Modeling parameters for typical RC columns in nonductile and ductile archetypes are summarized in Table 2.Properties for RC beams are similar and reported elsewhere (Liel and Deierlein 2008;Haselton and Deierlein 2007).All element model properties are calibrated to median values of test data.Although the hysteretic beam and column spring parameters incorporate bond-slip at the member ends,they do not account for significant degradations that may occur because of anchorage or splice failure in nonductile frames.Unlike ductile RC frames,in which capacity design require-ments limit joint shear deformations,nonductile RC frames may experience significant joint shear damage contributing to collapse (Liel and Deierlein 2008).Joint shear behavior is modeled with an inelastic spring,as illustrated in Fig.1and defined by a monotonic backbone and hysteretic rules (similar to those shown in Fig.2for columns).The properties of the joint shear spring are on the basisofFig.1.Schematic of the RC frame structural analysismodel(a)(b)Fig.2.Properties of inelastic springs used to model ductile and non-ductile RC columns in the first story of a typical 4-story space frame:(a)monotonic behavior;(b)cyclic behaviorJOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011/495D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .selected subassembly data of joints with minimal amounts of trans-verse reinforcement and other nonductile characteristics.Unfortu-nately,available data on nonconforming joints are limited.Joint shear strength is computed using a modified version of the ACI 318equation (ACI 2005),and depends on joint size (b j is joint width,h is height),concrete compressive strength (f 0c ,units:psi),and confinement (γ,which is 12to 20depending on the configu-ration of confining beams)such that V ¼0:7γﬃﬃﬃﬃf 0c p b j h .The 0.7modification factor is on the basis of empirical data from Mitra and Lowes (2007)and reflects differences in shear strength between seismically detailed joints (as assumed in ACI 318Chap.21)and joints without transverse reinforcement,of the type consid-ered in this study.Unlike conforming RC joints,which are assumed to behave linear elastically,nonductile RC joints have limited duc-tility,and shear plastic deformation capacity is assumed to be 0.015and 0.010rad for interior and exterior joints,respectively (Moehle et al.2006).For joints with axial load levels below 0.095,data from Pantelides et al.(2002)are used as the basis for a linear increase in deformation capacity (to a maximum of 0.025at zero axial load).Limited available data suggest a negative postcapping slope of approximately 10%of the effective initial stiffness is appropriate.Because of insubstantial data,cyclic deterioration properties are assumed to be the same as that for RC beams and columns.The calculated elastic fundamental periods of the RC frame models,reported in Table 2,reflect the effective “cracked ”stiffness of the beams and columns (35%of EI g for RC beams;35%to 80%of EI g for columns),finite joint sizes,and panel zone flexibility.The effective member stiffness properties are determined on the basis of deformations at 40%of the yield strength and include bond-slip at the member ends.The computed periods are signifi-cantly larger than values calculated from simplified formulas in ASCE (2002)and other standards,owing to the structural modeling assumptions (specifically,the assumed effective stiffness and the exclusion of the gravity-resisting system from the analysis model)and intentional conservatism in code-based formulas for building period.Nonlinear static (pushover)analysis of archetype analysis mod-els shows that the modern RC frames are stronger and have greater deformation capacities than their nonductile counterparts,as illus-trated in Fig.3.The ASCE 7-05equivalent seismic load distribu-tion is applied in the teral strength is compared on the basis of overstrength ratio,Ω,defined as the ratio between the ultimate strength and the design base shear.The ductility is com-pared on the basis of ultimate roof drift ratio (RDR ult ),defined as the roof drift ratio at which 20%of the lateral strength of the structure has been lost.As summarized in Table 3,for the archetype designs in this study,the ductile RC frames have approximately 40%more overstrength and ultimate roof drift ratios three times larger than the nonductile RC frames.The larger structural deformation capacity and overstrength in the ductile frames results from (1)greater deformation capacity in ductile versus nonductile RC components (e.g.,compare column θcap ;pl and θpc in Table 2),(2)the SCWB requirements that promote more distributed yielding over multiple stories in the ductile frames,(3)the larger column strengths in ductile frames that result from the SCWB and joint shear strength requirements,and (4)the required ratios of positive and negative bending strength of the beams in the ductile frames.Fig.3(b)illustrates the damage concentration in lower stories,especially in the nonductile archetype structures.Whereas nonlin-ear static methods are not integral to the dynamic collapse analyses,the pushover results help to relate the dynamic collapse analysis results,described subsequently,and codified nonlinear static assessment procedures.Collapse Performance Assessment ProcedureSeismic collapse performance assessment for archetype nonductile RC frame structures follows the same procedure as in the companion study of ductile RC frames (Haselton et al.2011b ).The collapse assessment is organized using incremental dynamic analysis (IDA)of nonlinear simulation models,where each RC frame model is subjected to analysis under multiple ground motions that are scaled to increasing amplitudes.For each ground motion,collapse is defined on the basis of the intensity (spectral acceleration at the first-mode period of the analysis model)of the input ground motion that results in structural collapse,as iden-tified in the analysis by excessive interstory drifts.The IDA is repeated for each record in a suite of 80ground motions,whose properties along with selection and scaling procedures are de-scribed by Haselton et al.(2011b ).The outcome of this assessment is a lognormal distribution (median,standard deviation)relating that structure ’s probability of collapse to the ground-motion inten-sity,representing a structural collapse fragility function.Uncer-tainty in prediction of the intensity at which collapse occurs,termed “record-to-record ”uncertainty (σln ;RTR ),is associated with variation in frequency content and other characteristics of ground-motion records.Although the nonlinear analysis model for RC frames can simulate sidesway collapse associated with strength and stiffness degradation in the flexural hinges of the beams andcolumnsFig.3.Pushover analysis of ductile and nonductile archetype 12-story RC perimeter frames:(a)force-displacement response;and (b)distri-bution of interstory drifts at the end of the analysis496/JOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .and beam-column joint shear deformations,the analysis model does not directly capture column shear failure.The columns in the archetype buildings in this study are expected to yield first in flexure,followed by shear failure (Elwood and Moehle 2005)rather than direct shear failure,as may be experienced by short,squat nonductile RC columns.However,observed earthquake damage and laboratory studies have shown that shear failure and subsequent loss of gravity-load-bearing capacity in one column could lead to progressive collapse in nonductile RC frames.Column shear failure is not incorporated directly because of the difficulties in accurately simulating shear or flexure-shear failure and subsequent loss of axial load-carrying capacity (Elwood 2004).Collapse modes related to column shear failure are therefore detected by postprocessing dynamic analysis results using compo-nent limit state ponent limit state functions are devel-oped from experimental data on nonductile beam-columns and predict the median column drift ratio (CDR)at which shear failure,and the subsequent loss of vertical-load-carrying capacity,will occur.Here,CDR is defined similarly to interstory drift ratio,but excludes the contribution of beam rotation and joint deforma-tion to the total drift because the functions are established on data from column component tests.Component fragility relationships for columns failing in flexure-shear developed by Aslani and Miranda (2005),building on work by Elwood (2004),are employed in this study.For columns with nonductile shear design and detailing in this study and axial load ratios of P =A g f 0c between 0.03and 0.35,Aslani and Miranda (2005)predict that shear failure occurs at a median CDR between 0.017and 0.032rad,depending on the properties of the column,and the deformation capacity decreases with increasing axial load.Sub-sequent loss of vertical-carrying capacity in a column is predicted to occur at a median CDR between 0.032and 0.10rad,again depending on the properties of the column.Since the loss of vertical-load-carrying capacity of a column may precipitate progressive structure collapse,this damage state is defined as collapse in this assessment.In postprocessing dynamic analysis results,the vertical collapse limit state is reached if,during the analysis,the drift in any column exceeds the median value of that column ’s component fragility function.If the vertical collapse mode is predicted to occur at a smaller ground-motion intensity than the sidesway collapse mode (for a particular record),then the collapse statistics are updated.This simplified approach can be shown to give comparable median results to convolving the probability distribution of column drifts experienced as a function of ground-motion intensity (engineering demands)with the com-ponent fragility curve (capacity).The total uncertainty in the col-lapse fragility is assumed to be similar in the sidesway-only case and the sidesway/axial collapse case,as it is driven by modeling and record-to-record uncertainties rather than uncertainty in the component fragilities.Incorporating this vertical collapse limit state has the effect of reducing the predicted collapse capacity of the structure.Fig.4illustrates the collapse fragility curves for the 8-story RC space frame,with and without consideration of shear failure and axial failure following shear.As shown,if one considers collapse to occur with column shear failure,then the collapse fragility can reduce considerably compared to the sidesway collapse mode.However,if one assumes that shear failure of one column does not constitute collapse and that collapse is instead associated with the loss in column axial capacity,then the resulting collapse capac-ity is only slightly less than calculations for sidesway alone.For the nonductile RC frame structures considered in this study,the limit state check for loss of vertical-carrying capacity reduces the median collapse capacity by 2%to 30%as compared to the sidesway collapse statistics that are computed without this check (Liel and Deierlein 2008).Table 3.Results of Collapse Performance Assessment for Archetype Nonductile and Ductile RC Frame Structures Structure ΩRDR ult Median Sa ðT 1Þ(g)Sa 2=50ðT 1Þ(g)Collapse marginλcollapse ×10À4IDR collapse RDR collapseNonductile 2S 1.90.0190.470.800.591090.0310.0172P 1.60.0350.680.790.85470.0400.0284S 1.40.0160.270.490.541070.0540.0284P 1.10.0130.310.470.661000.0370.0178S 1.60.0110.290.420.68640.0420.0118P 1.10.0070.230.310.751350.0340.00912S 1.90.0100.290.350.83500.0340.00612P 1.10.0050.240.420.561190.0310.0064S a 1.40.0160.350.490.72380.0560.0244S b 1.60.0180.290.490.60890.0610.02612S a 1.90.0120.330.350.93350.0390.00912S b 2.20.0120.460.351.32160.0560.012Ductile 2S 3.50.085 3.55 1.16 3.07 1.00.0970.0752P 1.80.0672.48 1.13 2.193.40.0750.0614S 2.70.047 2.220.87 2.56 1.70.0780.0504P 1.60.038 1.560.77 2.04 3.60.0850.0478S 2.30.028 1.230.54 2.29 2.40.0770.0338P 1.60.023 1.000.57 1.77 6.30.0680.02712S 2.10.0220.830.44 1.914.70.0550.01812P1.70.0260.850.471.845.20.0530.016a These design variants have better-than-average beam and column detailing.bThese design variants have better-than-average joint detailing.JOURNAL OF STRUCTURAL ENGINEERING ©ASCE /APRIL 2011/497D o w n l o a d e d f r o m a s c e l i b r a r y .o r g b y S u l t a n Q a b o o s U n i v e r s i t y o n 06/21/14. C o p y r i g h t A S CE .F o r p e r s o n a l u s e o n l y ; a l l r i g h t s r e s e r v e d .。

外文翻译--结构分析的矩阵方法

南京理工大学毕业设计(论文)外文资料翻译学院（系）：机械工程学院专姓学业：名：号：机械工程及自动化徐峰010*******外文出处：(用外文写)Theory of structuresPublisher:McGraw Hill 附件： 1.外文资料翻译译文；2.外文原文。

指导教师评语：翻译内容符合毕业设计内容的要求，翻译工作量较大，翻译基本正确、符合科技外语的翻译习惯和用法，较好的完成了翻译工作。

签名：年月日附件1：外文资料翻译译文结构分析的矩阵方法1. 力法和应变方法在前述的章节已经介绍解决静不定系统的各种各样的方法。

它们可分为两大类。

例如，在分析拱门和框架结构时，分析步骤如下。

首先，所有的冗余的约束被对应的冗余的力（或力矩）取代，这些力的大小可通过基于应变能的最小势能原理解得。

类似的过程也被用于解静不定桁架的分析，这些方法统称为力法。

在连续梁和框架分析中，另一种不同的方法曾被使用。

在这个情况下，我们首先计算了结点的旋转的角度(变形)而冗余力是后来才求的。

在连续梁的分析中使用了的3角度方程代表另一种方法。

这样的方法称为应变方法。

我们用一个例子来说明这两种方法之间的区别，如图10.1的平面静不定桁架，一力P 分解为Px和PY，作用在的5根悬于刚性基础的等截面杆交点A处。

因为杆数量大于A 点平衡方程的数目，很明显这是一个静不定问题。

一般来说，如果绞点A由n根杆铰接而成，那么冗余的杆将是(n-2)。

因此，为了根据力法解出对应的冗余的力X1，X2,X3，……Xn-2，我们根据这些力的作用，通过最小势能原理获得应变能表达式，进而获得所需的方程：эU/эX1=0эU/эX2=0 ……(a)其中每个方程都包含所有冗余力，因此随着杆数目的增加，方程（a）的求解将变得越来越麻烦。

解决相同的问题，Navier 建议使用的移置方法。

在图10.1的系统中，如果知道在力P 作用下A点的各自的水平位移u、垂直位移v，那么系统变形将完全确定下来。

框架结构的抗震设计思路外文文献翻译

文献信息：文献标题：Frame Structure Anti-earthquake Design Way of Thinking （框架结构的抗震设计思路）国外作者：Theodore V.Galambos文献出处：《Journal of Constructional Concrete Research》,2000, 55:289-303 字数统计：英文4451单词，22990字符；中文5601汉字外文文献：Frame Structure Anti-earthquake Design Way of ThinkingAbstract Currently, the anti-earthquake norms all round the world almost adopt to a kind of way of thinking: The adoption presses the earthquake strong or weak of possible situation to divide the line earthquake cent area; According to everyplace the history occurrence of the area earthquake of covariance result or to geology structure of the history investigate to have to explicit statistics the meaning establish the sport peak in waterproof and quasi-ground value acceleration; Make use of again the reaction acceleration that the acceleration reaction composes different period; Get a design to use acceleration level through earthquake dint adjust met coefficient R. In the meantime, most nations all approve such point，establishing to defend the earthquake intensity level can take to use a different value, choosing to use to establish to defend the earthquake intensity level more and highly, the ductility request of the structure also more low, choose to use to establish to defend earthquake intensity level more and lowly, structure of ductility request more high. The structure ductility guarantee of precondition is the ductility of the member, pass again an effectively reasonable conjunction in adopting a series of measure guarantee member the foundation of the ductility, the structure system choice is reasonable in the meantime, the degree just distributes reasonable of under condition ability basic assurance structure of ductility.Keywords: frame structure; anti-earthquake design; design way of thinking1.Simple Review of Anti-earthquake Design Way of ThinkingThe development that constructs the structure anti- earthquake is along with people all the earthquake move with the structure characteristic of the understanding is continuously thorough but develop gradually, however, from is born up to now the history of a hundred years, have mostly several to develop a stage as follows:(1) Quiet dint stage: It first from a Japanese professor passed to harm to prognosticate the anti- earthquake design theories that put forward with the theories understanding at that time to the limited earthquake, being applicable to only just rigid body structure. It didn't think characteristic and the place difference to consider structure to the influence that constructs structure.(2) Respond the table stage: Along with vibrate to record of obtain and the development of the structure dynamics theories, the Biota professor of the United States put forward flexibility to respond the concept of the table in 1940, respond the table is list the freely flexible system, it was obtain of numerous earthquakes record of encourage, the structure period or respond of the relation, include the acceleration reaction table, the speed responded a table, moved to respond a table. It consider the motive characteristic of the structure, it still is the foundation that all countries norm design earthquake dint takes a value up to now. The calculation of the earthquake function dint usually use shears with the bottom and flaps a decomposition to respond a table a method, flapping a decomposition to respond a table a method of basic define: Suppose the building structure is the line flexibility more freedom degree system, making use principle of flap a decomposition and flap a type, it will solve a freedom degree the earthquake of the flexible system to respond to resolve for solve an independence of etc. the effect single freedom degree flexible system most the heavy earthquake respond. Then begging should in each function affect that flaps a type. At this time, according to consider the way dissimilarity of the earthquake function, adopt a different array, group method, order flexible system to many qualities of the flat surface vibration, it can use a SRSS method, it is according tosuppose the importation earthquake as steady random process, each of a flap reaction is independent mutually but deduce to get; For consider even-twists many qualities that the lotus connect to order flexible system, the adoption CQC method, it lies in with the main differentiation of the SRSS method: Suppose when flat surface vibrate each flap a type independent mutually, and each contribution that flap a type increased along with the frequency high but lower；But even-twist lotus connect hour each flap a frequency span very small, close together and higher flap the frequency of the type and may near to this relativity that will consider a dissimilarity to flap a very much, also have influence of turn round the weight and not necessarily increase along with the frequency high but lower, sometimes higher flap the influence possibility of the type big in lower flap the influence of the type, it will consider more influences that flap a type while comparing SRSS. The bottom shears the dint method in consideration of the special of the structure system to the simplification that flaps a decomposition to respond to compose a method, be the building height not big, took shearing to slice to transform as the lord and the quality to follow height to distribute more even structure with degree just, the structure vibration moved to respond usually with the first flapped a type for lord, and when the first flapped a type to near to in the straight line, can flap a decomposition method simplification to shear the dint method calculation formula for the basic bottom. The level earthquake function that each quality that this basic formula calculation get order can better reflection just degree bigger structure, but when structure the basic period was long, the place characteristic period to compare with hour, the calculation income coping earthquake function be partial to small. of course , the Anti-earthquake Norm provision, be the structure basic period more than 1.4 place characteristic period, at coping additional level earthquake function.(3)the motive theories stage: Along with move understanding and comprehend to the earthquake of deepen continuously, know to some shortage of the reaction table, such as to the earthquake move hold of influence consideration not week, and the exaltation of the calculator function, make the motive method develop gradually, its essence solves a square distance of motive directly, but because of earthquake theground sport acceleration is very irregular, it can't beg for differential calculus square distance, it shuts to match a solution, so adopt number integral calculus method more. Usual way of doing is carry on a continuous cent a segment a processing towards having already record of the earthquake wave, each data all see do the constant, then the function get to structure up, pass an equilibrium and square distance of motive to beg at the moment of the acceleration, speed, move reaction, moving with ex- the acceleration, speed, the segment to carry on folding to add immediately after folding the result for add as the beginning that descends at that time a segment to start a data, pushing according to this kind, end beg structure at the give for low week again and again the earthquake wave under of the acceleration, speed and move the dint reaction variety process.(4) At American Northridge earthquake in 1994 and Japanese Kobe earthquake in 1995 after, the beautiful day scholar put forward again according to the anti- earthquake design method of behavior, it was during the period of usage to make the building structure satisfy various requests that used function according to the basic thought of behavior. Tradition according to the design method dissimilarity of the dint, adjudicate to the structure function mainly is according to move standard, move index sign to come with the different to the structure function to carry on a different control. But descend structure because of the big earthquake of not- flexible transform hard and accurate estimate of, make to can stay around according to the design method of behavior theoretically. But put forward its aggressive meaning to have 2:00 at least:a. Emphasize the system and the society of the earthquake engineering;b. The part that knows an original anti- earthquake to design norm is unsuited to reasonableness.Conduct and actions according to the foundation of the function anti- earthquake design, should to the particular level earthquake function of a certain covariance meaning under of the structure move, the speed and acceleration carry on accurate valuation, should also have a reasonable of valuation method with available valuation tool. It is exactly because of this purpose, put forward and developed the Pushover method and ability to compose a method. The basic way of thinking of the Pushovermethod is an adoption the quiet dint add to carry, supposing the side of the some penny cloth form toward lotus to carry a function on the structure, adding to carry gradually until attain the structure control point target to move or the structure break, getting the level side of the control point to move to shear the dint relation curve with substrate thus, evaluating in order to the anti-vibration ability of the structure. The Pushover method depends on to distribute a form and play the plasticity reaction table target to move to really settle in the side force.2.Basic Way of Thinking of Frame Structure Anti-earthquake Design—ductility StandardAfter the flexibility respond table put forward, the people's detection computes to gain from here of the structure respond with the actual earthquake the breakage phenomenon of the structure contain certain antinomy, mainly is press the flexibility reaction table to calculate of the structure responded the acceleration as habitual to design the earthquake dint to take to be worth big quite a few at that time doubly, and took to settle according to the habitual of the function of the design earthquake dint descends the house structure of design, the harm of the structure system wasn't serious in the earthquake.60's last century, the New mark passed to start to the beginning of different period just degree homology of the single freedom degree the system carried on analysis under the situation that many waves input, put forward etc. moved the principle and etc. energy principle, and put forward the concept of the structure ductility. Studied single and free system to accept defeat the level and flexibility thoroughly again from the relation of flapped the biggest not- flexible motive in the period and structure to respond afterward, this be customarily say of the theories of the R-μ -T effect. Passing these researches, announcing to public the ductility ability and plasticity to consume an ability is a structure Be taking to use to accept defeat level under not high circumstance, at big earthquake under the structure doesn't take place severity to break and doesn't don't tumble down of assurance. Arrive here, concerning the design earthquake dint's taking the basic problem of the value size have to arrive understanding definitely, be the anti- earthquake the earthquake dinttake a value of the size isn't a number of assurance, but with the structure ductility function and consume the ability mechanism related quantity value. Here what to need to be explain BE, designed the earthquake dint to take a value to resolve a problem only, but to the structure ductility function guarantee of the measure have to can also promise, this will at underneath a section discuss.Currently, the anti- earthquake norms all round the world almost adopts so a kind of way of thinking: The adoption presses the earthquake strong or weak of possible situation to divide the line earthquake cent area; According to everyplace the history occurrence of the area earthquake of covariance result or to geology structure of the history investigate to have to explicit statistics the meaning establish the sport peak value in waterproof and quasi- ground value acceleration; Make use of again the reaction acceleration that the acceleration reaction composes different period to descend structure to; get a design to use acceleration level through the earthquake dint adjustment coefficient R. In the meantime, most nations all approve such standpoint, establishing to defend the earthquake intensity level can take to use a different value, choosing to use to establish to defend the earthquake intensity level more and highly, the ductility request of the structure also more low, choose to use to establish to defend the earthquake intensity level more and lowly, structure of ductility request more high. The structure ductility guarantee of precondition is the ductility of the member, pass again an effectively reasonable conjunction in adopting a series of measure guarantee member the foundation of the ductility, the structure system choice is reasonable in the meantime, the degree just distributes reasonable of under condition ability basic assurance structure of ductility.Underneath this kind of discusses the our country anti- earthquake norm mostly way of thinking, the current Chinese norm didn't adopt a variety to establish to defend the earthquake intensity level to take to use, but don’ Ted add a distinction of unify an adoption of the earthquake dint adjustment coefficient R=1/0.35;In the meantime, mostly according to establish a dissimilarity of defend the earthquake intensity, divide the line the different anti- earthquake grade, fix attention on in establish to defend earthquake intensity differently, adopt the anti- earthquake measure of the differentassurance ductility. Very obvious here exist a misunderstanding of concept, also be according to the theories of the R-μ-T effect, the little more than earthquake dint adjustment coefficient R=1/0.35, should give the same ductility guarantee measure to the structure, but the Chinese norm adopt the different ductility guarantee measure, along with anti- earthquake the exaltation of the grade, ductility guarantee the ability correspond to strengthen. This kind of usefulness of the way of doing under way and not the line motive respond of verification, can describe so as a result mostly: For the district of 8 degrees 0.3 g and 9 degrees 0.4 g, because of correspond of the anti- earthquake grade is higher, the measure of the guarantee ductility is also stronger, so generally and more safe; And for the district of 6 degrees 0.05 g and 7 degrees 0.1 g, gain from here to of the level earthquake effect be partial to small, the general lotus carries an array, group is carried the control function by the gravity lotus, although to should of the measure of the guarantee ductility isn't very strong, can also guarantee structure generally under the big earthquake of not- flexible transform of function; But to the district of 7 degrees 0.15 g and 8 degrees 0.2 g, circumstance another the person worry, because of at the lotus carry an array, group, the earthquake function can have generally control function, but correspond measure of guarantee the ductility and be partial to weak, so difficult don't need to exist certain potential safety hazard to suffer from. See again other national earthquake dint adjustment coefficient R to choose to use, in order to have kept concrete understanding of view:The earthquake dint adjustment coefficient of all countries norm provision3．Ability Design MethodTop a part emphasized to discuss the design earthquake dint to take the problem of the value, but wanted to promise structure under the big earthquake of function, also need to establish the valid anti- earthquake measure, make the structure really have need of keep vertical loading under the dint condition not- flexible transform an ability, this be the so-called ability design method.Ability design method from New Zealand the reinforced concrete anti- earthquake expert scholars such as the T. Parlay and the R. Park etc. development with initiate, main way of thinking is to the member occasionally member dissimilarity inside the piece is subjected to the dint form of the loading ability differ of control, promise the reinforced concrete structure formation the beam swing joint organization and ductility bigger is cut noodles to be subjected to the dint breakage appearance, make the structure have to play plasticity to transform function enough, promise big earthquake hour have an enough ability to consume to spread function, avoid creation brittleness to break and appear disadvantageous of organization form. The key of the ability design method is the anti- earthquake design that leads the control concept into structure, there is the leading formation of the purpose to the beneficial breakage mechanism is to the structure and break mode, avoid not reasonable of the structure break appearance, and try assurance to anticipate to break part to play plasticity to transform an ability.The ability design method mainly passes the following three kinds of measure to give assurance:1. Enlarge pillar opposite in the anti- of the beam-curved ability, artificial of leading of the structure swing joint part.2. Raise opposite in is cut the noodles loading dint of the anti- shear ability, avoiding appearing non- ductility to shear to slice breakage.3. To the part that appears the plasticity swing probably, the adoption corresponds of structure measure, assurance necessity of not- flexible transform function.First, the reasonable part of the swing joint carry on a discussion, all countriesmostly of the way of thinking inclines toward to make the project that the beam carries first to carry to appear in the pillar about and all. This kind of swing joint project has a following advantage: The ductility of the beam is easy to a control, and under general circumstance compare pillar of the ductility is big; The whole plasticity of the beam swing joint ratio pillar swing joint formation transform small; The plasticity of the beam swing joint organization formation transform more stable. There are also two kinds of different design methods while admit the premise of have the initiative the formation beam swing joint, a kind of from is a representative New Zealand of, incline toward the formation ideal beam swing joint organization, be promise the beam carries to appear the plasticity swing, but in addition to first floor, the post all doesn't appear the plasticity swing, at this time to in addition to the first floor pillar give post opposite compare bigger and super and strong coefficient(probably 2.0) in the beam, the advantage is a post(in addition to first floor) and doesn't need to be carry on to go together with hoop complicatedly at this time, because of adopt such coefficient can promise a swing joint very explicit. But is exactly because this kind of design method pursues the ideal beam swing joint organization to cause the first floor post compare weaker, the possibility for throng will be a swing joint, the plasticity that correspond and then have to adopt the structure measure to promise this part transforms function. In the meantime, such as if the first floor the influence of the swing joint upon the structure will compare greatly, once pressing and mating because structural whole tumble down, this has to be given guarantee up from the structure, increasing a structure of difficulty. Another project includes total body, Chinese etc. in the United States, Europe, this kind of project leading structure pillar swing joint the night appears in the beam swing joint, unlimited make the emergence of the swing joint in the meantime, but request structure and do not become the layer side to move structure, at this time to post of super go together with coefficient to compare with to request New Zealand of want to be small, goes together with the project that the stirrup takes in to control to the post adoption in the meantime. BE super to go together with coefficient to really settle problem comparison complications to the post adoption in fact: The beam carries thesuper influence for go together with for construct; The beam carries the plasticity swing to appear inside the dint is heavy to distribute of influence; Before accept defeat of the not- flexible characteristic may make the post bending moment physically big get in the flexibility analysis of bending moment ;The indetermination factor that the material difference bring; Growth of the structure not- flexible characteristic cause the influence etc. that the structure motive characteristic variety bring. According to the request of the ability design, the plastic hinge that shears the dint wall appears generally in the bottom of the wall limb. The joining beam shear the loading dint and ductility that the loading dint and ductility and entrance to cave of the dint wall connect beam contain very great relation, designing generally and possibly weak connect beam, the leading that has intention to know connects beam at earthquake accept defeat first, then is the bottom wall to accept defeat, also be anticipate the area of plastic hinge to accept defeat.Avoided appearing to shear reason of slice the breakage early easy, be because of shearing to slice to break to belong to the brittleness breakage, disadvantage in promise the ductility of the structure, promise of way be according to the dissimilarity of the anti- earthquake grade to all beams, pillars, wall etc. the adoption is opposite to bend in the anti- of different super go together with coefficient.The basic request that the anti- earthquake anti- shear is before the beam carry plastic hinge that big epicenter need turn to move and don't take place to shear to slice breakage, this sheared concept difference with the non- anti- earthquake anti-.For various different processing methods that the structure anti- of the member shears mechanism and the our country norm, there is the necessity elucidation here once. Beam: When anti- shake because of low week again and again the function made the beam appear to cross an inclined fracture, fissure, the inclined fracture, fissure distributed an anti- of come to a decision the anti- earthquake to shear the ability ratio not an anti- earthquake to have to descend, reason: The anti- shake of shear to slice to break occurrence after the end long tendon accept defeat, the fracture, fissure compare at this time greatly; The harm that crosses the emergence of the fracture, fissure to the concrete is more serious; The enlargement beam carried the number of the negativebending moment when anti- shake, cause bigger sheared the dint value to appear under the beam to carry, sprinkle plank now because of descending to carry to have no, break more easily. But at this time the function and function for non- anti- to shake of the stirrup differ only a few, in the norm to the consideration of this disadvantageous function is to adopt to resist to shear formula in to the concrete item 0.6 of fold to reduce, in the meantime, in order not to non- ductility of inclined break bad, while adopting to shake than the non- anti- more scathing restriction measure, cut noodles to shear the dint design value ratio non- anti- earthquake multiply 0.8 of fold and reduce coefficient. Pillar: It resist earthquake in the norm the anti- of the pillar shear the processing principle of the formula similar, also is adopt to the concrete item 0.6 of fold and reduce coefficient, adopt more scathing measure to prevent from equally inclined break bad, cut noodles to shear the dint design value ratio non- anti- earthquake multiply 0.8 of fold and reduce coefficient. But because of under general circumstance, the stalk pressure comparison of the pillar is big, this kind of pressure shears function to be partial to the anti- of the member after appearing the plastic hinge to the pillar emollient, according to this kind of way of thinking, pillar the adoption fold to reduce with beam similarly to seem to be not greatly reasonable. Wall: When the anti- shake, there is almost no related on trial data in domestic, is an adoption only the earthquake is to the non- anti- of the anti- sheared formula to adopt to the concrete item and the reinforcing bar items 0.8 of fold and reduce coefficient, in the meantime, in bar of and inclined break bad, adoption the restriction shear a way of press the ratio, cut noodles to shear the dint design value ratio non- anti- earthquake multiply 0.8 of fold and reduce coefficient. What to need to be explaining BE, under general circumstance, the part that shears the dint wall anti- to shear a problem probably is a lower part are a few floors. Node: The main acceptance shears the dint member, the node shears dint mainly is depend on the truss organization, inclined press pole organization, the stirrup of the stipulation effect three organizations or path to bear. The truss organization mainly is resist the reinforcing bar lord to pull should dint, inclined press the pole organization mainly is the lord that resists the concrete and the reinforcing bar creation to press should dint, the stipulation effect of thestirrup then strengthens the anti- of the concrete to shear ability. Along with the node concrete inside the area not- line development, the truss the function of the structure lets up continuously, and then both of function but be strengthening continuously. Therefore, the main target of the node anti- earthquake is under the situation that be subjected to dint again and again, pass to strengthen inclined press the pole organization and the stirrup to control an effect to avoid the core area concrete inclined to press thus a diplomatic corps to order at attain to anticipate of the big earthquake respond before do not take place to shear to slice breakage.After shearing the discussion of mechanism to the above anti-earthquake, can be do with the function of the beam stirrup to tally up as follows: The first obvious function is to used for an anti- to shear; The second function controls concrete, this to guarantee the structure ductility contain count for much function, can also say literally here the obstacle that once high and strong concrete meet when used for anti- earthquake, this is related with the material of the high and strong concrete first, strength more high concrete more frailty, its should attain in the dint contingency relation biggest press should the contingency of the dint is smaller, this makes the design become the ductility member a difficulty with very great formation, is more high because of the strength of the concrete in the meantime, the stirrup rises the effect of the stipulation more bad, also can't the extreme limit of the enough valid exaltation concrete press a contingency, so cause to adopt the ductility of the structure member of the high and strong concrete hard get a guarantee; The third function is the stipulation function that carries to the beam lengthways reinforcing bar, prevent forming lengthways reinforcing bar lose steady, this has something to do with the special material of the reinforcing bar.中文译文：框架结构的抗震设计思路摘要目前，世界各国的抗震规范都采用这种思路：按可遇地震的强弱划分地震分区；根据各地区的历史发生地震的统计或对地质构造的考察得出设防水准地面的运动峰值加速度；再利用加速度反应谱给出不同周期下结构的反应加速度；通过地震力调整系数R得到设计加速度水准。

外文翻译基本框架设计模式

基本框架设计模式Essential Framework DesignPatternsWolfgang PreeUniversity of ConstanceD-78434 Constance, GermanyVoice: +49.7531.88.44.33; Fax: +49.7531.88.35.77E-mail: pree@informatik.uni-konstanz.de摘要大多数优秀的面向对象的框架仍然或多或少的处于混乱发展过程中，通常进行的类似设置的研究。

这种贡献首先涉及几点框架建设的基本原则。

框架代表的是特定域的通用解决方案，使面向对象软件配置的全部潜力得以开发:不仅源代码和单个组件，体系结构设计也被重复使用。

预定义细化发生的适应点我们称之为扩展点。

如果发现这些扩展点有明确的需求阶段，它们能以基本的形式组合成特定域的设计模式。

这种扩展点驱动的框架设计可以为一个更系统的发展过程做出贡献。

关键词：设计模式，框架，面向对象设计，面向对象软件发展，软件可重用性1.框架类型框架非常适合大量类似的应用程序的重写。

框架结构定义了一种通过创建特定领域的应用程序的高级语言专业化（=适应）。

特定领域的一种扩展槽我们称之为扩展点。

如果一个框架提供了足够的可以改编的扩展点，我们就认为这是一个具备合格属性的框架。

例如，Lewis et al. (1995 年) 提供大量高质量框架。

白盒框架中的扩展点白盒框架由几个不完整的类组成，也就是类包含没有实际实现的办法。

A类的抽象方法必须在子类中重写。

这种类型的框架中的抽象方法形成扩展点。

图1 的示例框架中描述的A 类层次结构说明了一个白盒框架的这一特性。

A类的抽象方法必须在子类中重写。

这种类型的框架中的抽象方法形成扩展点。

图1 示例框架类层次结构程序员通过衍生子类或重写父类的成员方法来修改白盒框架的方法。

必须重写的方法意味着程序员必须在一定程度上了解框架的设计和实施的细节信息。

结构设计--中英文翻译

外文翻译结构设计结构设计Augustine J.Fredrich摘要：结构设计是选择材料和构件类型，大小和形状以安全有用的样式承担荷载。

一般说来，结构设计暗指结构物如建筑物和桥或是可移动但有刚性外壳如船体和飞机框架的工厂稳定性。

设计的移动时彼此相连的设备（连接件），一般被安排在机械设计领域。

关键词：结构设计；结构分析；结构方案；工程要求Abstract: Structure design is the selection of materials and member type ,size, and configuration to carry loads in a safe and serviceable fashion .In general ,structural design implies the engineering of stationary objects such as buildings and bridges ,or objects that maybe mobile but have a rigid shape such as ship hulls and aircraft frames. Devices with parts planned to move with relation to each other(linkages) are generally assigned to the area of mechanical .Key words: Structure Design ；Structural analysis ；structural scheme ；Project requirementsStructure DesignStructural design involved at least five distinct phases of work: project requirements, materials, structural scheme, analysis, and design. For unusualstructures or materials a six phase, testing, should be included. These phases do not proceed in a rigid progression , since different materials can be most effective in different schemes , testing can result in change to a design , and a final design is often reached by starting with a rough estimated design , then looping through several cycles of analysis and redesign . Often, several alternative designs will prove quite close in cost, strength, and serviceability. The structural engineer, owner, or end user would then make a selection based on other considerations.Project requirements. Before starting design, the structural engineer must determine the criteria for acceptable performance. The loads or forces to be resisted must be provided. For specialized structures, this may be given directly, as when supporting a known piece of machinery, or a crane of known capacity. For conventional buildings, buildings codes adopted on a municipal, county , or , state level provide minimum design requirements for live loads (occupants and furnishings , snow on roofs , and so on ). The engineer will calculate dead loads (structural and known, permanent installations ) during the design process.For the structural to be serviceable or useful , deflections must also be kept within limits ,since it is possible for safe structural to be uncomfortable “bounce”Very tight deflection limits are set on supports for machinery , since beam sag can cause drive shafts to bend , bearing to burn out , parts to misalign , and overhead cranes to stall . Limitations of sag less than span /1000 ( 1/1000 of the beam length ) are not uncommon . In conventional buildings, beams supporting ceilings often have sag limits of span /360 to avoid plaster cracking, or span /240 to avoid occupant concern (keep visual perception limited ). Beam stiffness also affects floor “bounciness,” which can be annoying if not controlled. In addition , lateral deflection , sway , or drift of tall buildings is often held within approximately height /500 (1/500 of the building height ) to minimize the likelihood of motion discomfort in occupants of upper floors on windy days .Member size limitations often have a major effect on the structural design. For example, a certain type of bridge may be unacceptable because of insufficient under clearance for river traffic, or excessive height endangering aircraft. In building design,ceiling heights and floor-to-floor heights affect the choice of floor framing. Wall thicknesses and column sizes and spacing may also affect the serviceability of various framing schemes.Materials selection. Technological advances have created many novel materials such as carbon fiber and boron fiber-reinforced composites, which have excellent strength, stiffness, and strength-to-weight properties. However, because of the high cost and difficult or unusual fabrication techniques required , they are used only in very limited and specialized applications . Glass-reinforced composites such as fiberglass are more common, but are limited to lightly loaded applications. The main materials used in structural design are more prosaic and include steel, aluminum, reinforced concrete, wood , and masonry .Structural schemes. In an actual structural, various forces are experienced by structural members , including tension , compression , flexure (bending ), shear ,and torsion (twist) . However, the structural scheme selected will influence which of these forces occurs most frequently, and this will influence the process of materials selection.Tension is the most efficient way to resist applied loads ,since the entire member cross section is acting to full capacity and bucking is not a concern . Any tension scheme must also included anchorages for the tension members . In a suspension bridge , for example ,the anchorages are usually massive dead weights at the ends of the main cables . To avoid undesirable changes in geometry under moving or varying loads , tension schemes also generally require stiffening beams or trusses.Compression is the next most efficient method for carrying loads . The full member cross section is used ,but must be designed to avoid bucking ,either by making the member stocky or by adding supplementary bracing . Domed and arched buildings ,arch bridges and columns in buildings frames are common schemes . Arches create lateral outward thrusts which must be resisted . This can be done by designing appropriate foundations or , where the arch occurs above the roadway or floor line , by using tension members along the roadway to tie the arch endstogether ,keeping them from spreading . Compression members weaken drastically when loads are not applied along the member axis , so moving , variable , and unbalanced loads must be carefully considered.Schemes based on flexure are less efficient than tension and compression ,since the flexure or bending is resisted by one side of the member acting in tension while the other side acts in compression . Flexural schemes such as beams , girders , rigid frames , and moment (bending ) connected frames have advantages in requiring no external anchorages or thrust restrains other than normal foundations ,and inherent stiffness and resistance to moving ,variable , and unbalanced loads .Trusses are an interesting hybrid of the above schemes . They are designed to resist loads by spanning in the manner of a flexural member, but act to break up the load into a series of tension and compression forces which are resisted by individually designed tension and have excellent stiffness and resistance to moving and variable loads . Numerous member-to-member connections, supplementary compression braces ,and a somewhat cluttered appearance are truss disadvantages .Plates and shells include domes ,arched vaults ,saw tooth roofs , hyperbolic paraboloids , and saddle shapes .Such schemes attempt to direct all force along the plane of the surface ,and act largely in shear . While potentially very efficient ,such schemes have very strict limitations on geometry and are poor in resisting point ,moving , and unbalanced loads perpendicular to the surface.Stressed-skin and monologue construction uses the skin between stiffening ribs ,spars ,or columns to resist shear or axial forces . Such design is common in airframes for planes and rockets, and in ship hulls . it has also been used to advantage in buildings. Such a design is practical only when the skin is a logical part of the design and is never to be altered or removed .For bridges , short spans are commonly girders in flexure . As spans increase and girder depth becomes unwieldy , trusses are often used ,as well as cablestayed schemes .Longer spans may use arches where foundation conditions ,under clearance ,or headroom requirements are favorable .The longest spans are handled exclusively by suspension schemes ,since these minimize the crucial dead weight andcan be erected wire by wire .For buildings, short spans are handled by slabs in flexure .As spans increase, beams and girders in flexure are used . Longer spans require trusses ,especially in industrial buildings with possible hung loads . Domes ,arches , and cable-suspended and air –supported roofs can be used over convention halls and arenas to achieve clear areas .Structural analysis . Analysis of structures is required to ensure stability (static equilibrium ) ,find the member forces to be resisted ,and determine deflections . It requires that member configuration , approximate member sizes ,and elastic modulus ; linearity ; and curvature and plane sections . Various methods are used to complete the analysis .Final design . once a structural has been analyzed (by using geometry alone if the analysis is determinate , or geometry plus assumed member sizes and materials if indeterminate ), final design can proceed . Deflections and allowable stresses or ultimate strength must be checked against criteria provided either by the owner or by the governing building codes . Safety at working loads must be calculated . Several methods are available ,and the choice depends on the types of materials that will be used .Pure tension members are checked by dividing load by cross-section area .Local stresses at connections ,such as bolt holes or welds ,require special attention . Where axial tension is combined with bending moment ,the sum of stresses is compared to allowance levels . Allowable : stresses in compression members are dependent on the strength of material, elastic modulus ,member slenderness ,and length between bracing points . Stocky members are limited by materials strength ,while slender members are limited by elastic bucking .Design of beams can be checked by comparing a maximum bending stress to an allowable stress , which is generally controlled by the strength of the material, but may be limited if the compression side of the beam is not well braced against bucking .Design of beam-columns ,or compression members with bending moment ,mustconsider two items . First ,when a member is bowed due to an applied moment ,adding axial compression will cause the bow to increase .In effect ,the axial load has magnified the original moment .Second ,allowable stresses for columns and those for beams are often quite different .Members that are loaded perpendicular to their long axis, such as beams and beam-columns, also must carry shear. Shear stresses will occur in a direction to oppose the applied load and also at right angles to it to tie the various elements of the beam together. They are compared to an allowable shear stress. These procedures can also be used to design trusses, which are assemblies of tension and compression members. Lastly, deflections are checked against the project criteria using final member sizes.Once a satisfactory scheme has been analyzed and designed to be within project criteria, the information must be presented for fabrication and construction. This is commonly done through drawings, which indicate all basic dimensions, materials, member sizes, the anticipated loads used in design, and anticipated forces to be carried through connections.结构设计结构设计包含至少5个不同方面的工作：工程要求，材料，结构方案，分析和设计。

本科生外文译文课程设计

本科生外文译文课程设计一、课程目标知识目标：1. 学生能够理解并掌握外文课文中的主要知识点，包括专业词汇、语法结构和文章组织。

2. 学生能够准确翻译外文课文，理解其深层含义，并能进行相关领域的知识拓展。

3. 学生能够对外文课文进行批判性阅读，分析文章的论证方式和逻辑结构。

技能目标：1. 学生能够运用所学翻译技巧，对外文课文进行准确、流畅的翻译。

2. 学生能够通过小组讨论、课堂展示等形式，提高自己的表达能力和团队合作能力。

3. 学生能够运用批判性思维，对外文课文进行深入分析，提高自己的思辨能力。

情感态度价值观目标：1. 学生能够增强对所学专业的兴趣和热情，培养自主学习的能力。

2. 学生能够尊重不同文化背景，培养跨文化交际的意识。

3. 学生能够通过外文译文的学习，拓宽国际视野，增强国家意识和责任感。

课程性质：本课程为专业选修课，旨在提高学生的外文翻译能力和跨文化交际能力。

学生特点：本科生已经具备一定的外语基础，但翻译技巧和批判性思维能力有待提高。

教学要求：教师应注重理论与实践相结合，充分调动学生的主观能动性，引导学生进行自主、合作、探究式学习。

同时，关注学生的个体差异，因材施教，提高课程教学效果。

通过本课程的学习，使学生达到上述课程目标，并为后续相关课程的学习打下坚实基础。

二、教学内容本课程教学内容主要包括以下几部分：1. 外文课文翻译基本技巧：包括词汇、语法、句型结构等方面的翻译方法，以及翻译过程中的常见问题与对策。

2. 外文课文分析与解读：对教材中的精选文章进行深度剖析，理解文章的论证方式、逻辑结构和作者观点。

3. 批判性阅读与思考：培养学生对外文课文进行批判性思考，分析文章的优点和不足，提高学生的思辨能力。

4. 跨文化交际能力培养：通过对比分析中外文化差异，提高学生在实际翻译中的跨文化交际能力。

教学内容安排如下：第一周：外文课文翻译基本技巧介绍与练习。

第二周：分析教材第一章文章，进行翻译实践和讨论。

外文翻译---高层建筑及结构设计

外文翻译---高层建筑及结构设计High-rise XXX to define。

Generally。

a low-rise building is considered to be een 1 to 2 stories。

while a medium-rise building ranges from 3 or 4 stories up to 10 or 20 stories or more。

While the basic principles of vertical and horizontal subsystem design remain the same for low-。

medium-。

or high-rise buildings。

the vertical subsystems XXX high-XXX requiring larger columns。

walls。

XXX。

XXX.The design of high-rise buildings must take into account the unique XXX by their height and the need to withstand lateral forces such as wind and earthquakes。

One important aspect of high-rise design is the framework shear system。

XXX。

braced frames。

or XXX the appropriate system depends on the specific building characteristics and the seismicity of the n in which it is located.Another key n in high-rise design is the seismic system。

图书馆框架结构设计外文翻译六

图书馆框架结构设计外文翻译六文档编制序号：[KK8UY-LL9IO69-TTO6M3-MTOL89-FTT688]南京理工大学紫金学院毕业设计(论文)外文资料翻译系：机械工程系专业：土木工程姓名：袁洲学号： 0外文出处： Design of prestressed concrete structures附件： 1.外文资料翻译译文；2.外文原文。

注：请将该封面与附件装订成册。

(用外文写)附件1：外文资料翻译译文8-2简支梁布局一个简单的预应力混凝土梁由两个危险截面控制：最大弯矩截面和端截面。

这两部分设计好之后，中间截面一定要单独检查，必要时其他部位也要单独调查。

最大弯矩截面在以下两种荷载阶段为控制情况，即传递时梁受最小弯矩MG 的初始阶段和最大设计弯矩MT时的工作荷载阶段。

而端截面则由抗剪强度、支承垫板、锚头间距和千斤顶净空所需要的面积来决定。

所有的中间截面是由一个或多个上述要求，根它们与上述两种危险截面的距离来控制。

对于后张构件的一种常见的布置方式是在最大弯矩截面采用诸如I形或T形的截面，而在接近梁端处逐渐过渡到简单的矩形截面。

这就是人们通常所说的后张构件的端块。

对于用长线法生产的先张构件，为了便于生产，全部只用一种等截面，其截面形状则可以为I形、双T形或空心的。

在第5 、6 和7章节中已经阐明了个别截面的设计，下面论述简支梁钢索的总布置。

梁的布置可以用变化混凝土和钢筋的办法来调整。

混凝土的截面在高度、宽度、形状和梁底面或者顶面的曲率方面都可以有变化。

而钢筋只在面积方面有所变化，不过在相对于混凝土重心轴线的位置方面却多半可以有变化。

通过调整这些变化因素，布置方案可能有许多组合，以适应不同的荷载情况。

这一点是与钢筋混凝土梁是完全不同的，在钢筋混凝土梁的通常布置中，不是一个统一的矩形截面便是一个统一的T形，而钢筋的位置总是布置得尽量靠底面纤维。

首先考虑先张梁，如图 8-7，这里最好采用直线钢索，因为它们在两个台座之间加力比较容易。

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在混凝土框架结构下膜的影响—在框架结构的设计变化的一个建议A.W. Beeby 利兹大学，土木工程学院摘要本文关注的是框架的行动或钢筋混凝土框架的行为的影响。

设计实验探讨在框架极限条件。

结果表明该框架梁、柱的延性破坏脆性破坏的程度取决于端部约束的柱梁设置。

其中对于膜的最显著的影响是框架是施加于该柱的弯曲力矩。

因为膜的里的改变，在柱子或框架破坏的瞬间，力的分布和大小不同于用正常分析方法所预测的。

钢塑性分析是用接近理论破坏的方法。

这种方法再加上柱子的极限刚度估算，能够预估出破坏条件。

试验与理论的结合下提出了一种允许在框架薄膜效应下的设计方法。

1. 景区简介人们已经认识到从实验和理论研究认识到，如果约束增强不足，梁被加载到任意截面开裂或以上的水平，这将导致轴向力增加。

由于混凝土是薄弱的张力，裂缝发生在最大压力构件的部分，甚至在很小变形。

最初在的中和轴，中层深度的成员，将朝着压缩产生的水平延伸区的重心移动。

如果这个扩展受到抑制，轴向压缩力增加。

由于变形相对于构件的深度很小，压缩力作用在中间的行为凌驾于压缩力在末端并且那种拱形发展将支持一个显著的外部负载。

从图1中可以看出这一点。

塑性理论的发展和其他更严格的的分析方法可能导致工程师认为，目前的设计方法做了合理的最终行为准确地反映。

然而，这些方法忽略压缩膜行动。

在过去的30年，压缩膜行动已经若干学者研究的课题，试图产生更经济的设计方法，特别是对砖。

此现象显然是公认的板建设先驱。

如Gvozdev[1]。

在随后几年中，已进行实验研究出[2-4]一个完整的建筑，板系列在实验室的研究方案和未加固砖梁之间的刚性支撑限制。

他们都表现为弯曲破坏的极限荷载超过正常的设计方法预测。

在基础研究的弹性和塑性方法板设计，木材[5]确定了修改屈服准则横向内敛板坯上的相互作用是从硬质塑料理论根据膜力和弯矩而得。

这一理论标志着真正的研究一个合理的方法将压缩薄膜效应分析钢筋混凝土板的开始。

其他理论研究遵循并且特性克制，砖现在能够合理地理解。

对于板克制，扩展可能会提供周围板面板或由硬质元素，如核心壁结构，强度的增加产生的约束可以是非常大。

在梁钢架结构，可以增强实力预计将一般比较小，约束通常是只由柱提供，这个一般相当灵活。

图1 负载下变形的钢筋混凝土梁工作守则一般都没有引进膜行动的设计，因为难以界定的约束条件由于所加的复杂性引入设计。

然而，压缩膜量比简单的提高板坯的行为更有效果：如果横向力发展那么他们必须支持柱。

柱也必须适应任何扩大并且无不良影响（图2）。

图2. 框架膜力的开发图3 多面板钢筋混凝土框架2实验方案一个设计来测试试样的端跨度建模在一个多面板钢筋混凝土框架（图3）。

该方案的主要目的是建立数据上的力分布在一个简单的框架时，在框架的梁被加载到破坏。

影响钢筋混凝土框架结构行为的主要变量可以概括如下：（1）在梁的钢筋将被装载到破坏的量（2）结构的刚度。

这将取决于的横截面尺寸和跨度，柱尺寸和柱上的负载（3）混凝土和钢筋性质（4）柱和梁的跨度深入比（5）加载性质在本研究中，考虑的主要变量加固在梁的量和不同的柱的开裂弯矩将修改刚性柱荷载。

测试计划包括6个钢筋混凝土试件。

以下测试程序的纲要：2.1测试样本的选择和钻机的设计试样的目标是在模型条件的端部和矩形的钢筋混凝土柱框架跨度端。

由于可用的测试框架容量限制，标本的设计大约半音阶模型的实际框架。

点与点之间的整体高度选择为3.6米，梁的长度，对应约2/3的跨度，为2.2米。

在这个规模，规模效应不显著。

有关的列于表1和表2和图 4和5。

试验台的设计的主要要求从图3中可以看出。

这些是：（1）上端和下端的列被假定为固定，但能够传递垂直载荷和剪力（2）梁的端部的模拟禁止弯曲点进一步从端支承，并且需要再固定，但能传递轴向力和剪切。

它也不含一些有限程度偏转钻机详细信息示于图 4。

图4 详细的测试图5 试验片的详细信息（I-1）2.2 仪器仪表梁和柱的挠曲测定在13分，使要建立的试样的形状偏转。

横梁钻机的偏转也要被测量。

这一点，与借助提供前校准的钻机，为测得的负载单元提供了检测。

千分表被固定在轻钢结构桥从测试框架获得独立支撑。

混凝土的质量，测定压缩和张力面的梁，并柱的两面上使用一个千分表。

所有测试点的定位是相同的。

2.3 测试铸造一个星期后，从模板移除试样，过了些日子，在钻机上被定位。

手压泵用于操作液压千斤顶。

在每次试验的开始，参考应变计和千分表的读数记录。

加载进行如下两个阶段：在第一个阶段，所需的轴向施加载荷的增量的柱和柱的挠曲和应变测量，梁的行为也需要检查。

在第二阶段中，负载逐渐施加给梁。

在负载中的每个增量后采取一套完整的读数。

载荷为最初在5千牛顿的增量，然后在10千牛后递增到裂缝出现。

接近屈服时缓慢增加负载，直到递增达到破坏荷载。

在每一个载荷增量的测试标本检查是否有裂纹，通常第三或第四的载荷增量后出现。

3 试样性能研究3.1 开裂模式和破坏模式监测每一个试样开裂的传播。

在测试过程中标本裂缝发展可分为两组。

第一组包括所有受弯而出现裂缝的梁和柱，第二组由轴向力导致横梁裂缝甚至破坏和梁上的横向力导致柱子破坏。

在所有的框架，六个开裂阶段之前确认破坏（图6）。

两种类型的破坏的发生：1 梁破坏：这种情况发生在试样的I-1，I-2和1-3柱上具有较低的轴向载荷。

破坏是由钢筋的拉伸屈服在试样I-1和I-2中，首先在该点梁的最大正弯矩区和附近的支撑。

最后的破坏导致从破碎的混凝土的末端，跨中。

这些试样破坏发生导致在梁形成两个是非常韧性的塑性铰。

2 这种情况发生在试样脆性破坏的柱：II-1，II-2和II-3，它在柱上有较高的轴向载荷。

出现这种破坏模式像一个梁柱节点破坏然而产生破坏表明斜裂缝在组合中是次要的，只有后形成的混凝土已开始粉碎。

共同的破坏将启动具体的组合斜裂缝和破碎的混凝土支柱之间的缝隙[6]。

在所观察到的破坏模式和开裂的混凝土的基础上,这很明显可以看出，无论是框架中的柱的较高的轴向载荷脆性破坏还是在该框架中较低的轴向载荷对柱柱的断裂机理，压缩膜的行动有显著影响最终的标本行为。

破坏的试样的裂缝模式示于图II-3和I-1。

图7（a-c）3.2 分布在柱子上时整个试验过程，同时在顶部和底部柱反应记录。

柱的瞬间从产品的端反应获得和从支撑柱测量长度。

最显著的膜力的效果的是施加在柱上的弯曲力矩，示于图 8。

与此相比，在柱上获得的弯矩图中弹性分析忽略了膜力和那些测量的上梁的最大负载。

这可以看出，实际柱可能高达七次忽略膜力矩的计算值。

较高的柱负载是有较大的影响。

3.3 极限载荷所有试样的极限载荷列于表3中。

预测值进行计算，框架和截面使用弹性分析的方法BS8110忽略膜力实际故障负荷的预测值的比率范围在1.04-1.63。

图7 （a）II-3试样试验后的开裂的详细信息（b）I-1 试样中试验后的开裂详细信息（c）测试试样I-1和II-3样品的开裂详细信息4 钢筋混凝土框架结构新的设计方法这种方法几乎普遍使用在钢筋混凝土框架结构的设计最初的开发设计方法时有效地承担钢筋混凝土脆性材料的弹性正如我们了解在钢筋混凝土开发，设计方法已经有点改变，但没有真正改变。

开发和引进极限荷载设计的理由是它提供了一个明确的实际发生了破坏模型并因此允许更可靠的设计事实上，它是没有必要因为我们的行为模式是准确的，只是它不应该是不安全的。

然而经济压力的行为以改进模型，使其更精确，这样一个可以实现更均匀的安全水平。

它已被证明在这项研究中，分析常用模型被用来预测力的分布包括破坏附近的结构，在某些情况下，的确是非常不准确的。

因此，有必要考虑当前的方法是否充分的或是否需要改善，这个问题不可能会那么简单，因为。

考虑到框架端部的行为，很显然，柱中的瞬间力可以在梁的破坏显著的超过由电流计算方法。

但是，增强梁的强度由压缩膜作用的影响。

因此，破坏载荷必须大于实际，以满足当前的安全要求。

这是可能的论证，因此，分布的矩最终非常不同的实际上是不重要的。

但是，这种说法困难。

在设计极限荷载，柱瞬间力基本上大于计算，这会似乎会增加破坏的概率的柱上述所隐含经典方法。

考虑的另一个因素是破坏的模式是可以接受的。

它已经看到，在那里柱子的设计承受沉重的轴向载荷，可能导致梁的端柱产生脆性破坏。

这反过来，可能会导致破坏的不支持荷载。

因此，一个跨度的梁的有限破坏可能有比期望后果更严重的。

BS8110中的稳健性规则的基本概念：如果一个成员破坏，那么，剩余的成员应该是能够站立，虽然有些可能处于损坏状态。

捆扎规则的目的是确保能做到这一点。

可以说，如果破坏的梁，在任何负载，在一个附加的柱脆性破坏的结果，那么这项基本要求的稳定被破坏并且结构不会坚固。

如果这种说法被接受，那么必要的手段必须找到确定的情况下的超负荷的的梁导致破坏的柱和一个设计提出的方法，以确保它不会发生。

即使它可以表明，过早的破坏不会发生，留下一个不可避免的结论目前的分析方法不这样做，以较大优势：给出一个准确的图片濒临绝境的条件。

我们目前的整个逻辑似乎质疑框架程序设计以来：如果最终的负载的方法并不能合理地预测实际行为，似乎有一点优势，其使用过旧的服务负载的方法。

也许我们应该：或者（1）开发设计/分析方法模型的实际行为；或：（2）弃极限荷载的设计，并转移到可维护性的方法。

这第二种方法已被建议在最近的文献[7]。

第一种方法可以实现以下阶段：（1）制定一个简单的程序来查明情况列可能会破坏（2）制定这些情况下，设计一个简单的设计过程，可以采取要求的形式, 反过来施加到每个部分的水平载荷设计表3 实验和分析的极限载荷的比较5 推导的设计方法我们的目标是开发和验证模型，被用来预测经受垂直和水平载荷的框架的最终行为。

由于我们只考虑在最终大变形的条件正在发生的变形的刚性塑料的分析，扩展允许支承刚度，似乎是一个方便的起点。

完整的分析，提出了参考。

图[8]图8 弯曲实验瞬间力分布的比较在柱破坏的附近和弹性分析忽略膜效果（阴影区表示计算出的弯矩大小）5.1 预测的破坏模式在本部分中考虑预测是否崩溃的方法因为有柱或梁的破坏。

这将首先通过分析一个横向钢筋混凝土约束崩溃的行为的梁作为一个功能的克制柱其次是估计柱的端部的最终偏转并且估计柱崩溃的瞬间刚度。

分析中给出的参考[8]给出了以下在梁的膜力计算公式为：一个边界条件并且对应的偏转为零的轴向载荷。

其他研究人员已经假设n = 0时的偏转0.5-0.7的有效深度D。

在这项研究中，早期发展膜力是更重要的，它似乎更好地假设n= 0时的开裂弯矩达到并因此偏转计算此条件。

Su是约束梁最终提供的柱的刚度。

这是来自通过估计的柱的最终偏转。

崩溃的柱假设发生的压缩应变的关键部分在柱达到欧盟（假定0.0035）。