Influence Of Horizontal Curvature Radius And Bent Skew Angle On Seismic .
DOI: https://doi.org/10.14256/JCE.1508.2015Primljen / Received: 6.11.2015.Ispravljen / Corrected: 29.8.2016.Prihvaćen / Accepted: 30.9.2016.Dostupno online / Available online: 10.3.2017.Građevinar 2/2017Influence of horizontal curvature radius and bentskew angle on seismic response of RC bridgesAuthors:Preliminary noteNina Serdar, Mladen Ulićević, Srđan JankovićInfluence of horizontal curvature radius and bent skew angle on seismicresponse of RC bridgesNina Serdar, MSc. CEUniversity of MontenegroFaculty of Civil Engineeringninas@ac.meThe influence of horizontal curvature radius, bridge bents skew angle, and type ofcolumn bents, on the seismic response of bridges is studied in the paper. A total ofeighteen frame-system bridges were analysed. More than 2700 nonlinear dynamicanalyses were conducted for earthquake records matching a particular location by themagnitude, distance from fault, and foundation soil conditions. The response analysisshows that the system’s vulnerability increases with a decrease in curvature radius.Key words:curved bridge, skewed bridge, probabilistic response model, intensity ratingPrethodno priopćenjeNina Serdar, Mladen Ulićević, Srđan JankovićProf. Srđan Janković, PhD. CEUniversity of MontenegroFaculty of Civil Engineeringsrdjan@t-com.meUtjecaj horizontalne krivine i kuta kosine stupova na seizmički odziv abmostovaU radu je analiziran utjecaj radijusa horizontalne krivine, kuta kosine stupova i oblikastupova na seizmički odziv mosta. Ukupno je analizirano 18 mostova okvirnog sustava.Za potresne zapise koji po magnitudi, udaljenosti od rasjeda i uvjetima temeljnog tlaodgovaraju određenoj lokaciji, provedeno je više od 2700 nelinearnih dinamičkih analiza.U analizi odziva uočeno je da manji radijus krivine znači i veću oštetljivost sustava.Ključne riječi:most u krivini, kosi most, probabilistički model odziva, mjera intenzitetaVorherige MitteilungNina Serdar, Mladen Ulićević, Srđan JankovićProf. Mladen Ulićević, PhD. CEUniversity of MontenegroFaculty of Civil Engineeringmladen@t-com.meEinfluss von Horizontalkrümmung und Neigungswinkel der Stützen aufdie seismische Antwort von StahlbetonbrückenIn dieser Arbeit werden Einflüsse von Radius der Horizontalkrümmung, Neigungswinkelder Stützen und Stützenform auf die seismische Antwort von Brücken analysiert.Insgesamt wurden 18 Rahmenbrücken untersucht. Für Erdbebenaufzeichnungen, diein Bezug auf Magnitude, Entfernung von der Verwerfung und Baugrundeigenschafteneiner bestimmter Lokalität entsprechen, wurden über 2700 nichtlineare dynamischeAnalysen durchgeführt. Die Antwortanalyse hat gezeigt, dass einem kleineren Radiusauch eine größere Beschädigung des Systems entspricht.Schlüsselwörter:gekurvte Brücke, schräge Brücke, probabilistisches Antwortmodell, IntensitätsmaßGRAĐEVINAR 69 (2017) 2, 83-9283
Građevinar 2/2017Nina Serdar, Mladen Ulićević, Srđan Janković1. Introductionlimited number of papers currently deals with seismic responseof curved and skewed bridges. In the studies carried out byTondini and Stojadinović [2], it is highlighted that the decreasingradius of curvature results in a higher bridge vulnerability dueto seismic effects. These studies address bridges with a singlecolumn bent of circular cross section, and also involve differentcolumn heights. The effect of the column bent skew angle wasinvestigated for straight bridges [3, 4]. The results show that anincrease in the bridge bent skew angle leads to an increase in thevulnerability of structures, especially in case of straight bridgeswith seat type abutments. Further research, as indicated in theabove references, should include variations of column shapes,impact of skewed angle for curved bridges, analysis of shortbridges, and study of collapse and other damage states.The focus of this paper is on investigation of the effect of threeparameters: bridge deck radius in horizontal plane, bridge bentskew angle, and column cross section shape, on the seismicresponse of a three-span RC box-girder bridge. The aim is toassess the impact of varied parameters on the behaviour ofthe structure through a probabilistic approach. This requiresestablishment of a probabilistic seismic demand model (PSDM),which relates structural response (EDP - Engineering DemandParameter) to earthquake intensity measure (IM - IntensityMeasure). In the literature, this methodology is known as thePBEE methodology [5]. The analysis of seismic response wasperformed for a total of eighteen bridge prototypes. Threebridge bent skew angles were considered (0 , 20 , and 30 )along with two values of horizontal curvature (straight bridge which corresponds to an infinite value of curvature radius, andbridge curvature value of R 150 m - which is larger than theprescribed minimum value on roads with the relevant designspeed of up to 60 km/h) and three types of the bridge columncross-section shape. Bridges are classified into three types A,B, and C according to the shape of the column cross-section:hollow box column, double column bent with circular crosssection, and rectangular column cross-section, respectively.Bridges rank among the weakest links in transport networkin terms of vulnerability when exposed to earthquake action.According to modern guidelines, bridges should be designedin such a way that their collapse is prevented during strongearthquake motions (earthquakes with a return period of475 years according to EN 1998-2). If significant damage toa bridge occurs, direct economic losses associated with thecost of reconstruction will certainly be incurred. However,indirect losses caused by loss of bridge function, or by itsfunctioning at a reduced capacity, cannot be neglected. It canbe said that predicting seismic response of a bridge structure,and identifying the parameters that affect the vulnerability ofa bridge, with the aim of avoiding collapse in case of strongearthquakes, and bringing damage to an acceptable level incase of minor earthquakes, is an important task that has to beproperly addressed in research work.The focus of this paper is on the analysis of seismic response ofreinforced curved bridges and bridges with the skewed bridgebent. These structures are highly desirable and sometimesnecessary as a means to facilitate traffic transition. Theyare usually the elements of major freeway interchanges,highway access ramps, overpasses, etc. Experience from pastearthquakes has shown that even if curved and skewed bridgesare suitable for smooth traffic flow, their response to seismiceffects is less predictable and certainly different from theresponse of straight bridges. In the past, after several strongearthquakes (Northridge (1994), Wenchuan-China (2008), Chile(2010), etc.) such structures have experienced some unexpectedtypes of failure and damage.Specific behaviour of curved and skewed bridges during seismicexcitation is due to their significant coupling between responsesin two orthogonal horizontal directions. Columns are subjectedto simultaneous bi-axial bending and torsion. An increase inaxial, shear and torsional effects can be prompted by torsionalvibration modes [1]. Larger in-plane deck rotations inducelarger displacements of deck over abutments. In addition tothe column-bent failure, the abutment unseating and shear keyfailure due to large longitudinal and transverse displacementsare also important types of failure of skewed and curved bridges.Consequently, they must be further investigated and studied inorder to ensure better understanding of their seismic response.After an overview of relevant literature, it can be seen that a very2. Description of bridge prototypesThe investigated bridge prototype is a three-span frame bridgewith individual spans measuring 32 m, 40 m, and 32 m (see Figure1). For a curved bridge, span length refers to an appropriate circulararch length. The superstructure is a one cell box girder measuring10 m in total width and 2.5 m in height. The column height,Figure 1. a) Plan view and longitudinal configuration of bridge; b) bridge deck cross-section; c) column cross-section for bridge types A; B and C84GRAĐEVINAR 69 (2017) 2, 83-92
Influence of horizontal curvature radius and bent skew angle on seismic response of RC bridgesGrađevinar 2/2017measured from foundations to the bridgeTable 1. Geometric characteristics and bridge descriptiondeck, is 10 m. Columns are fully restrainedStructural bearing system3 span frame , with central span of 40 m, and with 32 m end spansin foundations. The bridge deck is rigidlyBent skew angle0 , 20 ,30 connected to columns. The column crossRadius of curvature insection is a hollow box, double bentStraight bridge: R inf; Curved bridge: R 150 mhorizontal planeeither with circular piers or with piers ofDeck cross-section geometricEA 1,97·108 kN;rectangular cross-section, depending onEIx 1,8·108 kNm2; EIy 1,3·109 kNm2; GJ 1.55·108 kNm2characteristicthe type of bridge (A, B or C). Bridge deckType A: Hollow box b x d 2 x 4 m; dzida 0.4 mis supported over seat-type abutmentsShape and size of columnsType B: Double column bent circular section diameter of 1.4 mwith four elastomeric bearings, movableType C: Rectangular wall type column 1 x 4.4 min longitudinal direction. The concreteType A: qlongitudinal qtransversal 3.2class is assumed to be C30/37, and theBehavior factor qType B: qlongitudinal qtransversal 3.5quality of reinforcing steel is B500B.Type C: qlongitudinal 3,5; qtransversal 3Bridges were designed in accordanceType A: ρ L 2 % (2 x 2x 14 φ28 along width and 2 x 2 x 21 φ28with European standards EN 1991-2Longitudinal reinforcement inalong depth)[6] EN 1992-1-1 [7] and EN 1998-2 [8].columns (number of bars x bar Type B: ρL 2.7 % (40 φ36)diameter φ)Type C: ρL 3.3 % (2 x 24 φ36 along width and 2 x 48 φ36The three-dimensional span model withalong depth)line elements of appropriate geometricType A: ρ Tx 0.4 % (longitudinally); ρTy 0.55 % (transversely)characteristics was used for linearTransverse reinforcement(φ10/15)analysis, which was conducted using thein columns (bar diameter φ/Type B: ρT 1,21 % (φ20/8)software package SAP 2000 v.14. [9].longitudinal space)Type C: ρTx 1.5 % (longitudinally); ρTy 0.7 % (transversely)Geometric properties of an uncracked(φ16/11.5)cross section are taken for modellingbridge deck, while the effective flexuralTable 2. Characteristic of confined and unconfined concrete and reinforcementstiffness of columns is estimatedConfined concreteaccording to Annex C EN 1998-2 [8]. Eachfcm,c - maximum compressive strength based on mean value for57-57-54 MPaspan is modelled by ten straight elementscompressive strength fcm, according to [7] (typeA-typeB-typeC)to an approximated horizontal curvature ofεc1,c - strain at fcm,c (typeA-typeB-typeC)0.008-0.008-0.007the bridge. Columns are fully fixed in themaximumstrain0.033εcu,cbase and all movements and rotations areVlačna čvrstoća0restrained. Deck movements at abutmentsin the vertical and transverse directions areUnconfined concreterestrained, and rotation around the axisfcm - mean value for compressive strength38 MPaperpendicular to the longitudinal plane ofεc1 - strain at fcm0.0022the bridge deck is allowed.maximumstrain0.,0035εcu,1Seismic analysis was performed usingTensile strength0the multimodal spectral analysis. Firsttwelve vibration tones were taken intoElasticity modulus33 GPaaccount, which was sufficient for theReinforcing steelsum of effective modal masses to befym - mean value for yield strength575 MPahigher than 90 % of the total mass. TheElasticitymodulus200 GPahorizontal seismic action was specifiedthrough the design response spectrumfor B category soil and the design ground acceleration of ag Many authors addressed the issue of structure and material0.4 g. Ductile behaviour of the structure and the correspondingmodelling, and so recommendations given in the correspondingbehaviour factor q were adopted. The corresponding valuesliterature [10] will be applied in the present study. The bridgeare given in Table 1. The vertical seismic load was not takenmodelling and analysis were conducted in the program forinto account in column design. Reinforcement percentages innonlinear analysis SeismoStruct version 7.0.3 [11]. The bridgecolumns are given in Table 1.deck was modelled using linear elements located at the centreof gravity of deck cross-sections. Elastic frame elements wereused because non-linear behaviour is not expected to occur3. Non-linear modelling of bridgein deck during earthquake action. Geometric properties of anuncracked deck cross-section were used for elastic elements,Main aspects of bridge modelling for the purpose of conductingaccording to relevant recommendations given in Europeannon-linear dynamic analysis (NDA) are presented in this section.GRAĐEVINAR 69 (2017) 2, 83-9285
Građevinar 2/2017Nina Serdar, Mladen Ulićević, Srđan Janković(1)An elastic ideal-plastic behaviour wasadopted for the link element forcedisplacement diagram in longitudinaldirection [14].86 C1500 0.6080.5460.31920 0.6440.5110.31330 06720.4860.3060 0.6080.5370.32320 0.6580.4980.31530 0.6780.4860.311Transverse directionTransverse directionLongitudinal directionIn transverse direction, zero-length link elements are alsostandards [8]. Each span is modelled by eight straight elementsmodelled to represent soil stiffness. These elements representto an approximated bridge curvature in horizontal plane.resistance of the embankment fill and wing wall. For simplicityMander’s uniaxial nonlinear concrete model was used for thereasons, contribution of stiffness of the protecting wall andconfined concrete modelling [12]. The behaviour under cyclicbearings was ignored. The transverse stiffness is obtainedloading was modelled according to the suggestion given in [13].by multiplying the stiffness in longitudinal direction, shownThe properties of steel were taken according to [8]. Materialin equation (1), the wing wall efficiency coefficient (CL 2/3),characteristic are given in Table 2.As substantially plastic behaviour is expected in columns, aparticipation factor (CW 4/3), and the aspect ratio of wing wallcolumn has been modelled as a single inelastic element startingand back wall width [15]. As two link elements are assigned inat the foundation and ending at the bottom of the deck. Thetransverse direction, one at each end, the associated stiffnessdistributed nonlinearity along the length of the column wasfor one element is equal to a half of the above calculated value.assumed. The cross-section was divided into the material ofIn vertical direction, the stiffness that matches soil stiffnessthe concrete core - confined concrete, concrete of the protectiveunder the foundation was assigned to elastic link elements.layer - unconfined concrete, and reinforcing steel. At the level ofThe effect of the vertical embankment stiffness and verticalcross section, the stress-strain state was obtained by integratingstiffness of elastomeric bearings is not accounted for.non-linear uniaxial stress-strain responses of individual "fibres"Modal damping is considered with the value of 5 %.into which the cross-section was divided. The number of crosssections in which the integration was conducted was five. An4. Modal analysis resultselastic rigid element was used to model the column to deckconnection. The cap-beam for two column bent was modelledModal analysis was conducted for all investigated bridges. Firstas an elastic frame element with an increased torsion stiffnesstwelve vibration periods and mode shapes were calculated.because of the influence of high flexural superstructure stiffness.The first three vibration periods for bridges type A, B, and C areA simplified model was used for abutment modelling. Abutmentsshown in Table 3. Short columns, ten meters in height (aspectwere modelled as infinitely rigid linear elements without weight,ratio of span to column height amounts to L / H 4), resultedusing width of the span structure. The weight of the abutmentsin a rather stiff structure with the relatively low vibration modewas neglected because it is assumed that it has no greaterperiods. For all bridge types, the fundamental vibration modeimpact on the overall response of longerbridges. Zero-length link elements wereTable 3. First three periods of vibration for bridges A, B and Cmodelled at each end of the element,Periods of vibrations T [s]in vertical and horizontal directions, soCurvatureBridgeBent skew1st mode2nd moderadiusas to represent soil characteristics andtypeangle(transverse(longitudinal3rd mode[m]embankment fill characteristics. Zerodirection)direction)length link elements were assigned in0 0.5960.3270.230longitudinal direction, with no tensile 20 0.6000.3260.235stiffness, to represent the back-wall andembankment fill response where passive30 0.6060.3250.241Apressure is activated after closing the0 0.5960.3280.231gap. The link element stiffness (Kabt, L)15020 0.6040.3270.239was calculated according to Caltrans30 0.6090.3260.242recommendations [14], and it depends0 0.8670.7490.431on the initial soil stiffness (Ki), the height 20 0.8820.7290.433of the abutment (h), and the width of theabutment (w), using the expression in30 0.8920.7100.435BEquation (1). As two link elements are0 0.8490.7310.438assigned at each end, the associated15020 0.8670.7060.437stiffness for one element is equal to one30 0.8770.6960.438half of the above calculated value.GRAĐEVINAR 69 (2017) 2, 83-92
Influence of horizontal curvature radius and bent skew angle on seismic response of RC bridgeswas in transverse direction, with mode periods ranging from 0.6to 0.9 s.Vibration periods shown in Table 3 are periods with the highestmagnitude in a particular direction. Effective modal massparticipation factors are not presented in this paper, and so itcan be concluded that the influence of higher vibration modesis significant for bridges type A and C (those with relativelystiff piers compared to the deck). Bridges type A and C do notdominantly oscillate in the first mode shape.It was found that the period of vibration in longitudinal directiondecreases with an increase in the bridge bent skew angle. This wasfound for both curved and straight bridges. A significant decrease inperiods occurred in bridge types B and C, while this effect was lesspronounced in bridge type A. Also, vibration periods in transversedirection increase with an increase in skewness.A decrease in the radius of curvature of the bridge type B led toreduction in vibration periods in the transverse and longitudinaldirections, as well as to reduction in vibration periods of thebridge type C in longitudinal direction, for all skew anglesinvestigated. The bridge type A has relatively stiff piers in bothdirections compared to the deck, as well as the bridge type C intransverse direction. This caused a decrease in the bridge deckdominance over dynamic response of the bridge, and pointedout the influence of higher vibration modes and stiffnessof the columns. Thus, reduction in the radius of curvature isnot reflected in the same way in the change of fundamentalvibration period for bridge A and bridge C in transverse direction,compared to the effect of the radius of curvature reduction onfundamental periods of the bridge type B.Modal mass participation factors for significant modes ofvibrations, vibration mode shapes and modal displacementswill not be presented in this paper, due to space limitations.However, these values were analysed and it was concludedthat the coupling between modal responses in longitudinal andtransversal directions increases with an increase in the bridgebent skewness. Transverse vibration mode shapes do not quitecorrespond to the transverse horizontal motion, but they havea significant component of longitudinal displacement. The mostpronounced coupling of longitudinal and transverse vibrationmodes was found in the bridge type B (bridges with doublecircular columns) compared to the other two bridge types. Forcurved bridges, there was a noticeable increase in the contributionof torsion mode.5. Selection of ground motion and earthquakeintensity measuresSelection of earthquake records for the nonlinear dynamicanalysis is carried out according to the pre-defined earthquakescenario and soil conditions. The values of magnitude M 7 anddistance from fault RL 20 km, are the values that are consideredfor the location. Near fault effects are not considered in thispaper. Soil site conditions coincide with the ground category B,as it is defined in European standards EN 1998-1.GRAĐEVINAR 69 (2017) 2, 83-92Građevinar 2/2017The most accurate way to assess a structure’s response toearthquake action would be to choose a large number ofearthquakes with a consistent earthquake scenario, and to usethem unscaled as an input for the non-linear dynamic analysis.This approach is not practically possible. Namely, the numberof records with the magnitude, distance and soil conditionsthat are consistent with the earthquake scenario is insufficient.Therefore, search conditions are loose, which resulted in theselection of a larger number of earthquake records.Figure 2. Resulting spectra for scaled and unscaled recordsThis means that earthquakes that satisfy the following conditions:6.2 M 7.6, 15 km RL 30 km and 360 m / s vs, 30 800 m /s (where vs, 30 is the speed of shear waves in the ground down tothe depth of 30 m) were extracted from the available earthquakedatabases (European Strong Motion Database and PEER StrongMotion Database). The search resulted in the selection of a total of38 records (one record consists of a pair of orthogonal horizontalcomponents of ground motion acceleration records). Earthquakerecords were scaled only in amplitude without changing theirfrequency content. The records were scaled up by factors of 1,2, 4, and 8, which resulted in two hundred and fifty earthquakerecords for input in NDA. Both horizontal components of motionwere applied to the structure at the same time, one in the globalX direction, and the other in the global Y direction. Scaling wasnecessary to ensure non-linear behaviour of the structure. Onlythose structural responses obtained from NDA, in which ductilitydisplacements did not exceed 4, were considered in furtheranalysis. Several authors consider that this ductility displacementvalue represents the limit between the limit state correspondingto a major damage in columns and the collapse limit state [16,17]. In other words, this paper investigates only the no-collapsecases. The resulting acceleration spectra for selected earthquakerecords, obtained as a vector sum of two horizontal components87
Građevinar 2/2017of acceleration spectra, are given in Figure 2. The resultingacceleration spectrum, representative of seismic action on bridges,is also applied in European regulations EN 1998-2.Selection of the earthquake intensity measure - IM (IM-IntensityMeasure), which effectively quantifies seismic action, is a verysensitive issue in the seismic analysis of structures. An efficientintensity measure is a measure that has a small dispersion(Equation (3)), in correlation with the considered structuralresponse. Measures such as PGA (Peak Ground Acceleration) orPGD (Peak Ground Displacement) have been widely representedin previous studies. The PGA is a measure that is stillpredominantly represented in seismic regulations. Subsequentstudies have shown that there is no universal intensity measurethat would be suitable for all types of structures, and thatthe measures such as the spectral acceleration, velocity, anddisplacement can be considered as relatively appropriate fromthe aspect of efficiency [18].Table 4. Analysed seismic intensity measuresMeasure (IMs)Descriptiontrans PGAPeak ground acceleration from the componentapplied in transverse directiontrans PGVPeak ground velocity from the component appliedin transverse directiontrans Sa(T1)Spectral acceleration for period of fundamentalvibration mode of the component applied intransverse directionrez PGAResultant peak ground acceleration calculatedfrom two horizontal componentsrez PGVResultant peak ground velocity calculated fromtwo horizontal componentsrez Sa(T1)Spectral acceleration for period of fund. vib. modeof the resultant spectrumrez Sv(T1)Spectral velocity for period of fund. vib. mode ofthe resultant spectrumrez Sd(T1)Spectral displacement for period of fund. vib. modeof the resultant spectrumrez CordovaIntensity measure [20] calculated from resultantspectra:S (2T )Sa Sa (T1) a 1Sa (T1)From the list of intensity measures recommended in theliterature [19], this paper presents results for those measuresthat have proven to be effective, but also for the measures thatare in use in common practice, such as the PGA. Furthermore,in addition to measures obtained from the individual horizontalcomponents of motion (trans prefix before the name of measure),the measures arising from the resultant acceleration, velocity anddisplacement records and the resultant spectra were also usedin this study (prefix rez before the name of the measures). Theresultant record/spectrum was obtained as the vector sum oftwo records / spectra of horizontal components. Other authors[4] investigated resultant measures such as the PGA and PGV88Nina Serdar, Mladen Ulićević, Srđan Jankovićfor skewed bridges, and concluded that the resultant PGV hasproven to be a suitable measure. This approach (considerationof resulting measures) is extended in this paper to all spectralmeasures as well as to measures that directly depend on spectralmeasures (rez Sa (T1), rez Sv (T1), rez Cordova etc.). The finallist of analysed intensity measures is given in Table 4.6. Analysis of seismic response of structuresThe analysis of seismic response of curved and skewed bridgesis presented in this section. The aim was to identify the effectof the radius of horizontal curvature, angle of skewness, andcolumn shape, on seismic response of the structure. With thispurpose, non-linear dynamic analyses (NDA) were conducted onbridges described in section 2. Maximum relative displacementof top of the column divided by column height (CDR - ColumnDrift Ratio) was recorded in each NDA and selected for theengineering demand parameter (EDP). The CDR in transversedirection (global Y direction) and the resulting CDR derived fromthe transversal and longitudinal CDR (global Y and X directions)are considered. The results obtained by analysis of the seismicIMs efficiency in correlation with EDP are presented anddiscussed in this section. Derived EDP-IM curves are based onlyon pairs of EDP and IM where the displacement ductility doesnot exceed the value of 4.The spectra of those earthquakes that caused structuralductility displacements greater than 4 are plotted in colourline in Figure 2. It can be noted that these spectra have higherspectral acceleration values on wider range of periods, whichunderlines the importance of the so-called softening of thestructure and extension of vibration periods when the structureenters nonlinear behaviour due to seismic action.In the probabilistic seismic analysis it is assumed that structuralresponse (EDP) is log-normally distributed when conditioned onintensity measure (IM) l and that this relationship can be writtenas in equation (3):ln(EPD) a bln(IM)(3)Coefficients a and b, as well as dispersion of the results σEDP IM areobtained from the regression analysis. Dispersion is calculatedas the square root of the sum of squares of errors divided by thenumber of samples (results) minus one. The dispersion value for allbridges and analysed intensity measures are given in Table 5. Themeasures calculated from records/spectra in transverse directionare correlated to structural response in transverse direction, andthe resultant measures are correlated to resultant response.From the results shown, it can be concluded that among themeasures that do not depend on structural characteristics theintensity measures trans PGV stand out as efficient by the criteriaof dispersion, with values ranging from 0.315 to 0.418. The biggestdispersion for this IM occurs in the bridge type B (two-column bent).It is precisely for this bridge type B that the intensity measure rezPGV, with dispersion values ranging from 0.317 to 0.347, shows ahigher efficiency compared to trans PGV. Intensity measures relatedGRAĐEVINAR 69 (2017) 2, 83-92
Influence of horizontal curvature radius and bent skew angle on seismic response of RC bridgesGrađevinar 2/2017Table 5. Dispersion of results of investigated intensity measuresBridgetypeIntensity measureR[m]α0 0.5560.3910.3500.4850.4030.3070.2800.3070.344 20 0.5270.3480.3150.4820.3890.2840.2720.2840.318A150 B150 C150Trans PGATrans PGVTrans Sa(T1)rez PGArez PGVrez Sa(T1)rez Sv(T1)rez Sd(T1)rez cordσEDP IM30 0.4950.3280.3230.4950.3970.3060.2970.3060.3190 0.5340.3440.3710.4590.3570.2950.2700.2960.32520 0.4960.3410.3250.4870.3270.2790.2550.2790.30630 0.5060.3640.360.4670.3850.2690.2470.2700.2850 0.5790.4180.4120.510.3210.2630.2760.2630.24720 0.5890.4250.4110.5690.3180.2620.2790.2610.25430 0.5780.3960.3800.5650.3170.2690.2810.2680.2510 0.5730.4080.4100.5770.3470.2660.2780.2660.26120 0.5470.3570.3910.530.3420.2740.2950.2740.25430 0.5370.3660.3740.5750.3110.2650.2830.2650.2480 0.4870.3580.3360.5170.4090.2820.3050.2880.26120 0.5480.3730.3740.530.4440.3740.3310.3020.28030 0.5430.3470.3540.570.4740.3310.3380.3320.2820 0.5040.3470.3210.5340.4150.3080.3220.3080.28620 0.4270.3150.3780.5460.4440.310.3140.3100.24930 0.5010.340.3910.6150.4770.3580.3650.3580.293to acceleration are characterized by a considerable dissipation, whichis expected considerig the value of the fundamental vibration period.These results are consistent with research results of other authors[21] obtained for different types of structures that had higher valuesof fundamental vibration periods.From the measures that depend on structural characteristics,for example vibration period, the intensity measure proposed byCordov
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