NON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE

Size: px
Start display at page:

Download "NON LINEAR ANALYSIS OF STRUCTURES ACCORDING TO NEW EUROPEAN DESIGN CODE"

Transcription

1 October 1-17, 008, Bejng, Chna NON LINEAR ANALYSIS OF SRUCURES ACCORDING O NEW EUROPEAN DESIGN CODE D. Mestrovc 1, D. Czmar and M. Pende 3 1 Professor, Dept. of Structural Engneerng, Faculty of Cvl Engneerng, Zagreb. Croata Assstant, Dept. of Structural Engneerng, Faculty of Cvl Engneerng, Zagreb. Croata 3 Graduate student, Dept. of Structural Engneerng, Faculty of Cvl Engneerng, Zagreb. Croata Emal: czmardean@yahoo.com, dmestrovc@grad.hr ABSRAC : Structures desgned n sesmcally actve regons must comply wth two basc demands: frst, structure must be desgned for loads durng usage (ultmate lmt state and servceablty lmt state) and second, structure must be sound enough to avod collapse durng earthquake (ultmate lmt state). Except from lnear-elastc calculatons, very often are used non-lnear methods. In ths artcle smple plan frame concrete structure wll be analyzed usng N method from Eurocode 8 (EN :004). N s smple non-lnear method used for calculaton of structures durng earthquakes. It combnes mult degree pushover analyss wth spectrum analyss of equvalent sngle degree of freedom (SDOF) system. It s formulated n acceleraton-dsplacement format, whch s very sutable for vsual overvew of basc varables that account for sesmc response of the structure. N method can be consdered as combnaton of pushover analyss and spectrum analyss. Inelastc demand spectrum s obtaned from elastc spectrum. Results obtaned are accurate enough f structure has domnant frst mode of oscllaton. For now, t s used only for plane structures. hs paper wll gve numercal example of N method. It s concluded that nelastc structural response s crucal n earthquake engneerng. Modern methods, supported wth usage of computers and strct desgn codes ensure better understandng of structural response durng earthquakes and at the same tme sesmc resstant structures. KEYWORDS: sesmc analyss, Eurocode, pushover, non lnear analyss 1. INRODUCION Structures desgned n sesmcally actve regons must comply wth two basc demands: frst, structure must be desgned for loads durng usage (ultmate lmt state and servceablty lmt state) and secondly, structure must be sound enough to avod collapse durng earthquake (ultmate lmt state). For purpose of the sesmc calculaton, we can use both lnear elastc structural analyss and non lnear analyss. In European norm EN :004 calculaton methods are gven n part of [1]. hese two methods are as follows: a) Lateral force method of analyss - ths type of analyss may be appled to structures whose response s not sgnfcantly affected by contrbutons from modes of vbraton hgher than the fundamental mode n each prncpal drecton. b) Modal response spectrum analyss whch can be used for all structures whose respone s/or can be sgnfcantly affected by contrbutons from modes of vbraton hgher than the fundamental mode n each prncpal drecton. Need for the non lnear sesmc analyss dates a long tme ago. It was not used prmarly because of nsuffcent computer power, software lmtatons and nsuffcent research n ths feld. As software and computaton power ncreases rapdly, so ths knd of analyss s becomng more and more popular. New generaton of procedures for desgn of the new and rehabltaton of the damaged structures s now avalable (performance based engneerng concept). It s now evdent that durng desgn phase more attenton must be gven to damage control. hs can not

2 October 1-17, 008, Bejng, Chna be effcently ncorporated f non lnear methods are not used. Except of lnear methods mentoned prevously, non lnear are as follows: c) Non-lnear statc (pushover) analyss mentoned s eurocode part d) Non lnear dnamc analyss (tme hstory) In ths artcle smple plan frame concrete structure wll be analyzed usng N method from Eurocode 8 (EN :004). N s smple non-lnear method used for calculaton of structures durng earthquakes. It combnes mult degree pushover analyss wth spectrum analyss of equvalent sngle degree of freedom (SDOF) system. It s formulated n acceleraton-dsplacement format, whch s very sutable for vsual overvew of basc varables that account for sesmc response of the structure. N method can be consdered as combnaton of pushover analyss and spectrum analyss. Inelastc demanded spectrum s obtaned from elastc spectrum. Results obtaned are accurate enough f structure has domnant frst mode of oscllaton. For now, t s used only for plane structures. Results gven here are based on calculatons and research from []. Sesmc load (demand) n N method s defned n the shape of elastc acceleraton spectrum (fgure 1). For better vsualzaton sesmc demand n N method s defned as elastc spectrum n acceleraton-dsplacement format (fgure 1 rght pcture). Fgure 1 Acceleraton spectrum (N method) As ths method s non lnear, nelastc spectrum must be defned. Only two factors are needed: ductlty factor and reducton factor. hs knd of nelastc spectrum n acceleraton-dsplacement format s called demand spectrum. ypcal demand spectrum s shown n fgure. Fgure Inelastc spectrum Structure s modeled as plan frame model wth multple degrees of freedom (MDOF) model. Wth pushover method

3 October 1-17, 008, Bejng, Chna characterstc non lnear force-dsplacement relaton for MDOF can be calculated (usually base shear and dsplacement n hghest pont are used). Usng transformaton factor Γ transfer to equvalent sngle degree of freedom (SDOF) s made. Non lnear force dsplacement relaton s smplfed usng deal elastc plastc relaton as shown n fgure 3. Fgure 3 Idealzaton of force dsplacement relaton As the fnal result capacty dagram n acceleraton dsplacement format s obtaned (see fgure 4). Demand spectrum and capacty dagram are always on the same fgure. Intersecton of radal lne whch corresponds to elastc perod of dealzed blnear system wth elastc demand spectrum ( =1) defnes demand elastc dsplacement S de. Inelastc demand, related to acceleraton S ay and dsplacement S d corresponds to ntersecton of capacty dagram wth demand spectrum (wth demanded ductlty ). For medum and short range perods structures ( C ) rule of equal dsplacement can be appled (demand nelastc dsplacement S d equals to demand elastc dsplacement S de ). Fgure 4 Elastc and demand spectrum n relaton wth capacty dagram pcture above and for < pcture below) ( C C

4 October 1-17, 008, Bejng, Chna. N MEHOD For the purpose of better understandng of N method wll be gven n steps..1. Step 1 Besde the data needed for usual elastc analyss, data concernng non lnear relaton force dsplacement must be gven. Blnear or tr-lnear dagram are often used. Sesmc demand s defned n the shape of elastc spectrum. Spectral acceleraton s gven n relaton to perod ()... Step For elastc system wth sngle degree of freedom followng relaton apples: = Sae (.1) 4π Sde ω Sae = where S ae S de are values from elastc spectrum (acceleraton and dsplacement) for perod and correspondng dampng. For nonlnear SDOF wth blnear relatonshp spectral acceleraton S a and spectral dsplacement S d can be calculated as n Eqns.. and.3: Sae Sa = (.) R = S (.3) S d Sde = Sae = R R 4π 4π a where s ductlty factor (defned as rato between maxmal dsplacement and yeld dsplacement) and reducton factor R. For reducton factor several propostons are gven as n Eqns..4 and.5. R = ( 1) + 1, C C < (.4) R =, C (.5) where C s characterstc perod defned as ntermedate value between short and medum perods (between constant acceleraton and constant velocty). Startng from elastc spectrum and usng equatons defned prevously demand spectrum can be calculated (see fgure 5)..3. Step 3 Pushover s conducted n a way that structure s subjected to monotone lateral loads, whch correspond to nertal forces durng sesmc actons. By gradually ncreasng lateral forces, constructve elements are falng consecutvely and stffness of the structure decreases. Due to lmtaton of ths artcle equatons wll be omtted. All equatons can be found n []. Base shear wll correspond to force and roof dsplacement wll correspond to dsplacement..4. Step 4 Sesmc demand must be obtaned form spectrum whch s usually made for SDOF system. hat mples that

5 October 1-17, 008, Bejng, Chna structure must be modeled as equvalent SDOF system and than ths two model must be compared. For the purpose of obtanng SDOF system varous procedures are avalable. One of them wll be gven n short n ths chapter. Start pont s the equaton of shear buldng (only translatons are taken nto account as n Eqn..6). Fgure 5 Demand spectrums for constant ductlty values m u'' + R= m 1α (.6) In Eqn..6. u and R are vectors (dsplacements and nternal forces), 1 s unt vector whle α. Dampng s not ncluded n ths Eqn. but t wll be ncluded n desgn spectrum. V s shear force (see Eqn..8). Constant Γ can be obtaned as n Eqn..9. Elastc perod of SDOF system ( ) can be calculated as n Eqn..10., where F and D are yeld strength and yeld dsplacement, respectvely. Eqn..11 represents capacty dagram whch s gven as force and equvalent mass rato. V F = (.7) Γ V = P = m Φ m1 Γ = = Φ mφ Φ m1p = p m Φ = p (.8) m Φ m Φ = m m Φ y (.9) y π = π ω = m D y Fy (.10) F S a = (.11) m.5. Step 5 Sesmc demand for equvalent SDOF system can be obtaned graphcally as n fgure 6 for structures wth short and medum perods. Fgure 6 represents demand and capacty spectrum. For structures wth short perods fgure 4 mples. Intersecton of radal lne whch corresponds to elastc perod of dealzed blnear system, wth

6 October 1-17, 008, Bejng, Chna elastc demand, defnes demand acceleraton (strength) S ae for elastc behavor and correspondng elastc dsplacement S de. Acceleraton at yeld strength represents both demand acceleraton and capacty of nelastc system. Fgure 6 Demand and capacty spectrum.6. Steps 6 and 7 Demand dsplacement of SDOF model S d s transformed nto global demanded maxmal dsplacement D t usng transform equatons. hat maxmal dsplacement D t corresponds to target dsplacement (part B of []). Local sesmc demand can also be obtaned by means of pushover analyss. Due to monotoncally ncrease of lateral loads, structure s pushed untl target dsplacement s not reached..7. Step 8 In the last step, predcted behavor of the structure can be estmated by comparson of local and global sesmc demands from chapter 7 wth the capactes of dfferent levels. Global behavor can also be estmated by comparson of dsplacement capacty and dsplacements accordng to sesmc demand. 3. NUMERICAL EXAMPLE As example, response of four story renforced concrete plane frame wll be gven. Structure s subjected to three dfferent earthquakes. Buldng s also tested n European Laboratory for Structural Assessment (ELSA). Results of experment are used to verfy mathematcal model. Structure s desgned accordng to European norms as structure wth peak ground acceleraton of 0,3g. Masses of floors (from frst floor) are 87, 86, 86 and 83 tons. Resultng shear factor has a value of 0,15. Addtonal detals are gven n []. Fgure 7 represents bearng structure. In fgure 8 same curve defne two relatons: V D t for MDOF system and F D rato of equvalent SDOF system. In must be noted that scales are dfferent, however ( Γ = 1, 34 ). Blnear representaton of the pushover curve s represented n fgure 8 (left part of the pcture, see thck lne) and values of strength and dsplacement at yeld pont can be determned: ( F = y 830kN and D y = 6,1 cm ). Elastc perod can be calculated as n Eqn. 3.1: m Dy π = 0,79s (3.1) F = y Capacty dagram (fgure 8, left part) s determned by Eqn. 3.:

7 October 1-17, 008, Bejng, Chna Fy S 830 ay = = = 3,8ms 0, 39g m 17 = (3.) Capacty dagram and demanded spectrum are compared n fgure 8 (rght part of the pcture). Fgure 7 Overvew of the structure Fgure 8 Pushover curve and capacty dagram (left part of the pcture); demand spectrum for 3 dfferent ground acceleratons and capacty dagram (rght part of the pcture) Pushover analyss preformed on MDOF model, wth maxmal dsplacement D t (roof) provdes dsplacements for whole structure, local sesmc demands (n term of relatve floor dsplacements and jont rotatons) as gven n fgure 9. Maxmal rotaton n fgure 9 s,%. Other rotatons are proportonal to maxmal. Resultng envelopes are obtaned by pushover from left to rght and vce versa. Expermental results from ELSA are smlar to ths model.

8 October 1-17, 008, Bejng, Chna Fgure 9 Dsplacements, relatve dsplacements and rotatons of frame 4. CONCLUSION In ths paper overvew of N method s gven. hs s smple non-lnear method used for calculaton of structures durng earthquakes. It combnes mult degree pushover analyss wth spectrum analyss of equvalent sngle degree of freedom (SDOF) system. It s formulated n acceleraton-dsplacement format, whch s very sutable for vsual overvew of basc varables that account for sesmc response of the structure. he nelastc structural response s crucal n earthquake engneerng as all concrete buldngs behave nelastc durng sesmc extaton. Modern methods lke N, supported wth usage of computers and strct desgn codes wll ensure better understandng of structural response durng earthquakes and at the same tme sesmc resstant structures. REFERENCES [1] Eurocode 8: Desgn of Structures for Earthquake Resstance - Part 1: General Rules, Sesmc Actons Rules for Buldngs (004). CEN, Brussels, Belgum. [] Zahenter, E. Non lnear sesmc analyss of structures accordng to European norm EN :004. (006). MS thess, Unversty of Rjeka, Rjeka, Croata. [3] Chopra, A. K. (1995). Dynamcs of Structures, heory and Applcatons to Earthquake Engneerng, New Yersey: Prentce Hall, USA [4] M. Causevc. (001). Earthquake Engneerng, Unversty of Rjeka, Rjeka, Croata. [5] Eurocode : Desgn of concrete structures - Part 1-1: Basc rules and regulatons for buldngs (HRN ENV ). (004), Zagreb, Croata. [6] Radć, J., (006), Concrete structures manual, Croatan Unversty Press, Zagreb, Croata

Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Structural Dynamcs and Earthuake Engneerng Course 9 Sesmc-resstant desgn of structures (1) Sesmc acton Methods of elastc analyss Course notes are avalable for download at http://www.ct.upt.ro/users/aurelstratan/

More information

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion

Assessment of Site Amplification Effect from Input Energy Spectra of Strong Ground Motion Assessment of Ste Amplfcaton Effect from Input Energy Spectra of Strong Ground Moton M.S. Gong & L.L Xe Key Laboratory of Earthquake Engneerng and Engneerng Vbraton,Insttute of Engneerng Mechancs, CEA,

More information

SEISMIC ANALYSIS AND DESIGN OF BUILDING STRUCTURES WITH SUPPLEMENTAL LEAD DAMPERS

SEISMIC ANALYSIS AND DESIGN OF BUILDING STRUCTURES WITH SUPPLEMENTAL LEAD DAMPERS SEISMIC ANALYSIS AND DESIGN OF BUILDING STUCTUES WITH SUPPLEMENTAL LEAD DAMPES X LIN 1, Peter J MOSS And Athol J CA 3 SUMMAY The response behavour of buldng structures ncorporatng a new type of dampng

More information

CHAPTER 9 CONCLUSIONS

CHAPTER 9 CONCLUSIONS 78 CHAPTER 9 CONCLUSIONS uctlty and structural ntegrty are essentally requred for structures subjected to suddenly appled dynamc loads such as shock loads. Renforced Concrete (RC), the most wdely used

More information

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE

CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng

More information

9.2 Seismic Loads Using ASCE Standard 7-93

9.2 Seismic Loads Using ASCE Standard 7-93 CHAPER 9: Wnd and Sesmc Loads on Buldngs 9.2 Sesmc Loads Usng ASCE Standard 7-93 Descrpton A major porton of the Unted States s beleved to be subject to sesmc actvty suffcent to cause sgnfcant structural

More information

November 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project

November 5, 2002 SE 180: Earthquake Engineering SE 180. Final Project SE 8 Fnal Project Story Shear Frame u m Gven: u m L L m L L EI ω ω Solve for m Story Bendng Beam u u m L m L Gven: m L L EI ω ω Solve for m 3 3 Story Shear Frame u 3 m 3 Gven: L 3 m m L L L 3 EI ω ω ω

More information

Study on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI

Study on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI 2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,

More information

, + &. / / 0 # 1) (5

, + &. / / 0 # 1) (5 ! # % # & & + + +, + &. / / 0 # 23 4 55 006 2 54223 7 / / 2 8 Hajrasoulha I & Doostan A 200 A smplfed model for sesmc response predcton of concentrcally braced frames. Advances n Engneerng Software, 43,

More information

Indeterminate pin-jointed frames (trusses)

Indeterminate pin-jointed frames (trusses) Indetermnate pn-jonted frames (trusses) Calculaton of member forces usng force method I. Statcal determnacy. The degree of freedom of any truss can be derved as: w= k d a =, where k s the number of all

More information

AN EFFECTIVE METHOD FOR DISPLACEMENT-BASED EARTHQUAKE DESIGN OF BUILDINGS

AN EFFECTIVE METHOD FOR DISPLACEMENT-BASED EARTHQUAKE DESIGN OF BUILDINGS 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 004 Paper o. 151 A EECTIVE ETHOD OR DISPLACEET-BASED EARTHQUAKE DESIG O BUILDIGS Jorge GUTIERREZ 1 and aurco ALPIZAR SUARY

More information

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle

More information

829. An adaptive method for inertia force identification in cantilever under moving mass

829. An adaptive method for inertia force identification in cantilever under moving mass 89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,

More information

THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD

THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS OF A TELESCOPIC HYDRAULIC CYLINDER SUBJECTED TO EULER S LOAD Journal of Appled Mathematcs and Computatonal Mechancs 7, 6(3), 7- www.amcm.pcz.pl p-issn 99-9965 DOI:.75/jamcm.7.3. e-issn 353-588 THE EFFECT OF TORSIONAL RIGIDITY BETWEEN ELEMENTS ON FREE VIBRATIONS

More information

MEEM 3700 Mechanical Vibrations

MEEM 3700 Mechanical Vibrations MEEM 700 Mechancal Vbratons Mohan D. Rao Chuck Van Karsen Mechancal Engneerng-Engneerng Mechancs Mchgan echnologcal Unversty Copyrght 00 Lecture & MEEM 700 Multple Degree of Freedom Systems (ext: S.S.

More information

In this section is given an overview of the common elasticity models.

In this section is given an overview of the common elasticity models. Secton 4.1 4.1 Elastc Solds In ths secton s gven an overvew of the common elastcty models. 4.1.1 The Lnear Elastc Sold The classcal Lnear Elastc model, or Hooean model, has the followng lnear relatonshp

More information

NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA.

NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA. The 4 th October 2-7, 28, Bejng, Chna NEAR-FIELD PULSE-TYPE MOTION OF SMALL EVENTS IN DEEP GOLD MINES: OBSERVATIONS, RESPONSE SPECTRA AND DRIFT SPECTRA ABSTRACT: Artur Cchowcz Dr, Sesmology Unt, Councl

More information

PERFORMANCE-BASED SEISMIC DESIGN OF SUPPLEMENTAL DAMPERS IN INELASTIC SYSTEM

PERFORMANCE-BASED SEISMIC DESIGN OF SUPPLEMENTAL DAMPERS IN INELASTIC SYSTEM 4th Internatonal Conference on Earthquake Engneerng Tape, Tawan October -3, 6 Paper No. 8 PERFORMANCE-BASE SEISMIC ESIGN OF SUPPLEMENTAL AMPERS IN INELASTIC SYSTEM Bo L and Xng-wen Lang ABSTRACT A smplfed

More information

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading

Experimental Study on Ultimate Strength of Flexural-Failure-Type RC Beams under Impact Loading xpermental Study on Ultmate Strength of Flexural-Falure-Type RC Beams under Impact Loadng N. Ksh 1), O. Nakano 2~, K. G. Matsuoka 1), and T. Ando 1~ 1) Dept. of Cvl ngneerng, Muroran Insttute of Technology,

More information

Second Order Analysis

Second Order Analysis Second Order Analyss In the prevous classes we looked at a method that determnes the load correspondng to a state of bfurcaton equlbrum of a perfect frame by egenvalye analyss The system was assumed to

More information

Uncertainty in measurements of power and energy on power networks

Uncertainty in measurements of power and energy on power networks Uncertanty n measurements of power and energy on power networks E. Manov, N. Kolev Department of Measurement and Instrumentaton, Techncal Unversty Sofa, bul. Klment Ohrdsk No8, bl., 000 Sofa, Bulgara Tel./fax:

More information

Chapter 3. Estimation of Earthquake Load Effects

Chapter 3. Estimation of Earthquake Load Effects Chapter 3. Estmaton of Earthquake Load Effects 3.1 Introducton Sesmc acton on chmneys forms an addtonal source of natural loads on the chmney. Sesmc acton or the earthquake s a short and strong upheaval

More information

Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed

Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed (2) 4 48 Irregular vbratons n mult-mass dscrete-contnuous systems torsonally deformed Abstract In the paper rregular vbratons of dscrete-contnuous systems consstng of an arbtrary number rgd bodes connected

More information

The equation of motion of a dynamical system is given by a set of differential equations. That is (1)

The equation of motion of a dynamical system is given by a set of differential equations. That is (1) Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence

More information

PRATICAL STATIC CALCULATION METHOD FOR ESTIMATING ELASTO-PLASTIC DYNAMIC RESPONSES OF SPACE FRAMES

PRATICAL STATIC CALCULATION METHOD FOR ESTIMATING ELASTO-PLASTIC DYNAMIC RESPONSES OF SPACE FRAMES th World Congress on Computatonal Mechancs (WCCM XI) 5th European Conference on Computatonal Mechancs (ECCM V) 6th European Conference on Computatonal lud ynamcs (EC VI) E. Oñate, J. Olver and A. Huerta

More information

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD

COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,

More information

DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS

DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 2004 Paper No. 539 DESIGN SPECTRUM-BASED SCALING OF STRENGTH REDUCTION FACTORS Arndam CHAKRABORTI 1 and Vnay K. GUPTA

More information

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS Avalable onlne at http://sck.org J. Math. Comput. Sc. 3 (3), No., 6-3 ISSN: 97-537 COMPARISON OF SOME RELIABILITY CHARACTERISTICS BETWEEN REDUNDANT SYSTEMS REQUIRING SUPPORTING UNITS FOR THEIR OPERATIONS

More information

Modeling of Dynamic Systems

Modeling of Dynamic Systems Modelng of Dynamc Systems Ref: Control System Engneerng Norman Nse : Chapters & 3 Chapter objectves : Revew the Laplace transform Learn how to fnd a mathematcal model, called a transfer functon Learn how

More information

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM

ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look

More information

Seismic Performance Enhancement Methodology for Framed Structures using Supplemental Damping

Seismic Performance Enhancement Methodology for Framed Structures using Supplemental Damping Vol., Issue.1, pp-134-140 ISSN: 49-6645 Sesmc Performance Enhancement Methodology for Framed Structures usng Supplemental Dampng K. SAHISH KUMAR 1, R. SUNDARARAJAN, C. ANONY JEYASEHAR 3,. RADHA KRISHNAN

More information

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE Prof. J. N. Mandal Department of cvl engneerng, IIT Bombay, Powa, Mumba 400076, Inda. Tel.022-25767328 emal: cejnm@cvl.tb.ac.n Module - 9 LECTURE - 48

More information

OPTIMUM STRENGTH RATIO OF BUCKLING-RESTRAINED BRACES AS HYSTERETIC ENERGY DISSIPATION DEVICES INSTALLED IN R/C FRAMES

OPTIMUM STRENGTH RATIO OF BUCKLING-RESTRAINED BRACES AS HYSTERETIC ENERGY DISSIPATION DEVICES INSTALLED IN R/C FRAMES The th World Conference on arthquake ngneerng October -,, Bejng, Chna OPTIMUM STRNGTH RATIO OF BUCKLING-RSTRAIND BRACS AS HYSTRTIC NRGY DISSIPATION DVICS INSTALLD IN R/C FRAMS Juan Andrés Ovedo A., Mtsumasa

More information

APPLICATION OF LQR CONTROL TECHNIQUE TO OFFSHORE JACKET PLATFORM SUBJECTED TO EARTHQUAKE

APPLICATION OF LQR CONTROL TECHNIQUE TO OFFSHORE JACKET PLATFORM SUBJECTED TO EARTHQUAKE APPICAIO OF QR CORO ECHIQUE O OFFSHORE JACKE PAFORM SUBJECED O EARHQUAKE Abbas Ahmed Syed Khaja and Deepak Kumar Departmental of Ocean Engg. II-Madras, Chenna, Inda E-Mal: abbasgtl@yahoo.co.uk ABSRAC Offshore

More information

APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS

APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS 6th ICPT, Sapporo, Japan, July 008 APPROXIMATE ANALYSIS OF RIGID PLATE LOADING ON ELASTIC MULTI-LAYERED SYSTEMS James MAINA Prncpal Researcher, Transport and Infrastructure Engneerng, CSIR Bult Envronment

More information

SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES

SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES 13 th World Conference on Earthquake Engneerng Vancouver, B.C., Canada August 1-6, 4 Paper No. 371 SIMPLIFIED PREDICTION METHOD FOR SEISMIC RESPONSE OF ROCKING STRUCTURAL SYSTEMS WITH YIELDING BASE PLATES

More information

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger

JAB Chain. Long-tail claims development. ASTIN - September 2005 B.Verdier A. Klinger JAB Chan Long-tal clams development ASTIN - September 2005 B.Verder A. Klnger Outlne Chan Ladder : comments A frst soluton: Munch Chan Ladder JAB Chan Chan Ladder: Comments Black lne: average pad to ncurred

More information

An Algorithm to Solve the Inverse Kinematics Problem of a Robotic Manipulator Based on Rotation Vectors

An Algorithm to Solve the Inverse Kinematics Problem of a Robotic Manipulator Based on Rotation Vectors An Algorthm to Solve the Inverse Knematcs Problem of a Robotc Manpulator Based on Rotaton Vectors Mohamad Z. Al-az*, Mazn Z. Othman**, and Baker B. Al-Bahr* *AL-Nahran Unversty, Computer Eng. Dep., Baghdad,

More information

MR Damper in Reducing Pounding Effect of Base- Isolated RC Highway Bridges

MR Damper in Reducing Pounding Effect of Base- Isolated RC Highway Bridges Australan Earthquake Engneerng Socety 21 Conference, Perth, Western Australa MR Damper n Reducng Poundng Effect of Base- Isolated RC Hghway Brdges M. Neaz Shekh 1, Jngya Xong 2, and Wehua L 3 1. Senor

More information

Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances

Annexes. EC.1. Cycle-base move illustration. EC.2. Problem Instances ec Annexes Ths Annex frst llustrates a cycle-based move n the dynamc-block generaton tabu search. It then dsplays the characterstcs of the nstance sets, followed by detaled results of the parametercalbraton

More information

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA

Statistical Energy Analysis for High Frequency Acoustic Analysis with LS-DYNA 14 th Internatonal Users Conference Sesson: ALE-FSI Statstcal Energy Analyss for Hgh Frequency Acoustc Analyss wth Zhe Cu 1, Yun Huang 1, Mhamed Soul 2, Tayeb Zeguar 3 1 Lvermore Software Technology Corporaton

More information

Operating conditions of a mine fan under conditions of variable resistance

Operating conditions of a mine fan under conditions of variable resistance Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety

More information

Chapter 13: Multiple Regression

Chapter 13: Multiple Regression Chapter 13: Multple Regresson 13.1 Developng the multple-regresson Model The general model can be descrbed as: It smplfes for two ndependent varables: The sample ft parameter b 0, b 1, and b are used to

More information

DYNAMIC BEHAVIOR OF PILE GROUP CONSIDERING SOIL-PILE-CAP INTERACTION

DYNAMIC BEHAVIOR OF PILE GROUP CONSIDERING SOIL-PILE-CAP INTERACTION October 1-17, 8, Bejng, Chna DYNAMIC BEHAVIOR OF PILE GROUP CONSIDERING SOIL-PILE-CAP INTERACTION A. M. Halaban 1 and M. Malek 1 Professor, Faculty of Cvl Engneerng, Isfahan Unversty of Technology, Isfahan,

More information

/ n ) are compared. The logic is: if the two

/ n ) are compared. The logic is: if the two STAT C141, Sprng 2005 Lecture 13 Two sample tests One sample tests: examples of goodness of ft tests, where we are testng whether our data supports predctons. Two sample tests: called as tests of ndependence

More information

Lecture 8 Modal Analysis

Lecture 8 Modal Analysis Lecture 8 Modal Analyss 16.0 Release Introducton to ANSYS Mechancal 1 2015 ANSYS, Inc. February 27, 2015 Chapter Overvew In ths chapter free vbraton as well as pre-stressed vbraton analyses n Mechancal

More information

Physics 181. Particle Systems

Physics 181. Particle Systems Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system

More information

AGC Introduction

AGC Introduction . Introducton AGC 3 The prmary controller response to a load/generaton mbalance results n generaton adjustment so as to mantan load/generaton balance. However, due to droop, t also results n a non-zero

More information

NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS

NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc

More information

Chapter 11: Simple Linear Regression and Correlation

Chapter 11: Simple Linear Regression and Correlation Chapter 11: Smple Lnear Regresson and Correlaton 11-1 Emprcal Models 11-2 Smple Lnear Regresson 11-3 Propertes of the Least Squares Estmators 11-4 Hypothess Test n Smple Lnear Regresson 11-4.1 Use of t-tests

More information

Identification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model

Identification of Instantaneous Modal Parameters of A Nonlinear Structure Via Amplitude-Dependent ARX Model Identfcaton of Instantaneous Modal Parameters of A Nonlnear Structure Va Ampltude-Dependent ARX Model We Chh Su(NCHC), Chung Shann Huang(NCU), Chng Yu Lu(NCU) Outlne INRODUCION MEHODOLOGY NUMERICAL VERIFICAION

More information

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems

Chapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons

More information

SIMPLIFIED APPROACH TO THE NON-LINEAR BEHAVIOR OF RC MEMBERS

SIMPLIFIED APPROACH TO THE NON-LINEAR BEHAVIOR OF RC MEMBERS SIMPLIFIED APPROACH TO THE NON-LINEAR BEHAVIOR OF RC MEMBERS Shahd NASIR 1, Supratc GUPTA 2 And Hdetaka UMEHARA 3 SUMMARY In ths paper, a smplfed one-dmensonal analytcal tool based on fnte dfference technque

More information

Constitutive Modelling of Superplastic AA-5083

Constitutive Modelling of Superplastic AA-5083 TECHNISCHE MECHANIK, 3, -5, (01, 1-6 submtted: September 19, 011 Consttutve Modellng of Superplastc AA-5083 G. Gulano In ths study a fast procedure for determnng the constants of superplastc 5083 Al alloy

More information

DESIGN OF STEEL PLATE SHEAR WALLS CONSIDERING BOUNDARY FRAME MOMENT RESISTING ACTION. B. Qu 1 and M.Bruneau 2 ABSTRACT

DESIGN OF STEEL PLATE SHEAR WALLS CONSIDERING BOUNDARY FRAME MOMENT RESISTING ACTION. B. Qu 1 and M.Bruneau 2 ABSTRACT Proceedngs of the 9th U.S. Natonal and 0th Canadan Conference on Earthquake Engneerng Compte Rendu de la 9ème Conférence Natonale Amércane et 0ème Conférence Canadenne de Géne Parassmque July 5-9, 00,

More information

STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION

STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION CAO Wanln 1, CHANG Wehua 2, ZHANG Janwe 1 1 College of archtecture and Cvl Engneerng, Bejng

More information

Note 10. Modeling and Simulation of Dynamic Systems

Note 10. Modeling and Simulation of Dynamic Systems Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada

More information

REINFORCED CONCRETE STRUCTURE DESIGN ANALYSIS UNDER EARTHQUAKE LOADING (LATERAL LOAD)

REINFORCED CONCRETE STRUCTURE DESIGN ANALYSIS UNDER EARTHQUAKE LOADING (LATERAL LOAD) REINFORCE CONCRETE STRUCTURE ESIGN ANALYSIS UNER EARTHQUAKE LOAING (LATERAL LOA) r. Muzaffer BÖREKÇİ SUMMARY FOR ANALYSIS UNER EARTQUAKE etermne the buldng parameters gven n Turksh Sesmc Code for Buldngs

More information

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis

Part C Dynamics and Statics of Rigid Body. Chapter 5 Rotation of a Rigid Body About a Fixed Axis Part C Dynamcs and Statcs of Rgd Body Chapter 5 Rotaton of a Rgd Body About a Fxed Axs 5.. Rotatonal Varables 5.. Rotaton wth Constant Angular Acceleraton 5.3. Knetc Energy of Rotaton, Rotatonal Inerta

More information

x = , so that calculated

x = , so that calculated Stat 4, secton Sngle Factor ANOVA notes by Tm Plachowsk n chapter 8 we conducted hypothess tests n whch we compared a sngle sample s mean or proporton to some hypotheszed value Chapter 9 expanded ths to

More information

Finite Element Modelling of truss/cable structures

Finite Element Modelling of truss/cable structures Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures

More information

INCREMENTAL DYNAMIC ANALYSIS AND PUSHOVER ANALYSIS. A PROBABILISTIC COMPARISON

INCREMENTAL DYNAMIC ANALYSIS AND PUSHOVER ANALYSIS. A PROBABILISTIC COMPARISON COMPDYN 2 III ECCOMAS Thematc Conference on Computatonal Metho n Structural Dynamcs and Earthquake Engneerng M. Papadrakaks, M. Fragadaks, V. Plevrs (e.) Corfu, Greece, 25 28 May 2 INCREMENTAL DYNAMIC

More information

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram

Adiabatic Sorption of Ammonia-Water System and Depicting in p-t-x Diagram Adabatc Sorpton of Ammona-Water System and Depctng n p-t-x Dagram J. POSPISIL, Z. SKALA Faculty of Mechancal Engneerng Brno Unversty of Technology Techncka 2, Brno 61669 CZECH REPUBLIC Abstract: - Absorpton

More information

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering

Proceedings of the 11th WSEAS International Conference on Sustainability in Science Engineering 4,50m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 4,00m 40,50m 7,50m 7,50m 7,50m Proceedngs of the 11th WSEAS Internatonal Conference on Sustanablty n Scence Engneerng OERSTREGTH DEMADS I MULTISTOREY

More information

Reliability Analysis of Bearing Capacity of Large-Diameter Piles under Osterberg Test

Reliability Analysis of Bearing Capacity of Large-Diameter Piles under Osterberg Test Research Journal of Appled Scences, Engneerng and Technology 5(2): 4878-4883, 213 ISSN: 24-7459; e-issn: 24-7467 Maxwell Scentfc Organzaton, 213 Submtted: September 27, 212 Accepted: December 13, 212 Publshed:

More information

Spin-rotation coupling of the angularly accelerated rigid body

Spin-rotation coupling of the angularly accelerated rigid body Spn-rotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 E-mal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s

More information

PART II IMPLEMENTATION OF THE DIRECT DISPLACEMENT- BASED DESIGN METHOD FOR SEISMIC DESIGN OF HIGHWAY BRIDGES

PART II IMPLEMENTATION OF THE DIRECT DISPLACEMENT- BASED DESIGN METHOD FOR SEISMIC DESIGN OF HIGHWAY BRIDGES PART II IMPLEMENTATION OF THE DIRECT DISPLACEMENT- BASED DESIGN METHOD FOR SEISMIC DESIGN OF HIGHWAY BRIDGES Vnco A. Suarez and Mervyn J. Kowalsky Department of Cvl, Constructon and Envronmental Engneerng,

More information

FEASIBILITY STUDY OF ACTIVE MICRO-VIBRATION CONTROL SYSTEM USING PIEZOELECTRIC ACTUATORS FOR FLOOR STRUCTURE OF PRECISION MANUFACTURING FACILITIES

FEASIBILITY STUDY OF ACTIVE MICRO-VIBRATION CONTROL SYSTEM USING PIEZOELECTRIC ACTUATORS FOR FLOOR STRUCTURE OF PRECISION MANUFACTURING FACILITIES October -7, 8, Bejng, Chna FEASIBILITY STUDY OF ACTIVE MICRO-VIBRATION CONTROL SYSTEM USING PIEZOELECTRIC ACTUATORS FOR FLOOR STRUCTURE OF PRECISION MANUFACTURING FACILITIES Hrokazu Hora, Masash Yasuda,

More information

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force.

First Law: A body at rest remains at rest, a body in motion continues to move at constant velocity, unless acted upon by an external force. Secton 1. Dynamcs (Newton s Laws of Moton) Two approaches: 1) Gven all the forces actng on a body, predct the subsequent (changes n) moton. 2) Gven the (changes n) moton of a body, nfer what forces act

More information

Week 9 Chapter 10 Section 1-5

Week 9 Chapter 10 Section 1-5 Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,

More information

GLOBAL SEISMIC RELIABILITY ANALYSIS OF BUILDING STRUCTURES BASED ON SYSTEM-LEVEL LIMIT STATES

GLOBAL SEISMIC RELIABILITY ANALYSIS OF BUILDING STRUCTURES BASED ON SYSTEM-LEVEL LIMIT STATES GLOBAL SEISMIC RELIABILITY ANALYSIS OF BUILDING STRUCTURES BASED ON SYSTEM-LEVEL LIMIT STATES Da-Gang Lu, Peng-Yan Song, Xao-Hu Yu 3 and Guang-Yuan Wang 4 Professor, School of Cvl Engneerng, Harbn Insttute

More information

An Interactive Optimisation Tool for Allocation Problems

An Interactive Optimisation Tool for Allocation Problems An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents

More information

MULTIBODY DYNAMICS METHOD FOR IMMERSED TUNNEL SUBJECTED TO LONGITUDINAL SEISMIC LOADING

MULTIBODY DYNAMICS METHOD FOR IMMERSED TUNNEL SUBJECTED TO LONGITUDINAL SEISMIC LOADING th World Congress on Computatonal Mechancs (WCCM XI) 5th European Conference on Computatonal Mechancs (ECCM V) 6th European Conference on Computatonal Flud Dynamcs (ECFD VI) E. Oñate, J. Olver and A. Huerta

More information

Benefits of Vertically Distributed Isolation Devices for an 8-storey Structure with Complex Geometry

Benefits of Vertically Distributed Isolation Devices for an 8-storey Structure with Complex Geometry Benefts of Vertcally Dstrbuted Isolaton Devces for an 8-storey Structure wth Complex Geometry T.J. Sullvan Unversty of Pava, Pava, Italy A. Lago Skdmore, Owngs and Merrll LLP, S.F., USA, formerly ROSE

More information

Inductance Calculation for Conductors of Arbitrary Shape

Inductance Calculation for Conductors of Arbitrary Shape CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors

More information

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2

Week 8: Chapter 9. Linear Momentum. Newton Law and Momentum. Linear Momentum, cont. Conservation of Linear Momentum. Conservation of Momentum, 2 Lnear omentum Week 8: Chapter 9 Lnear omentum and Collsons The lnear momentum of a partcle, or an object that can be modeled as a partcle, of mass m movng wth a velocty v s defned to be the product of

More information

Rehabilitation of existing structures by optimal placement of viscous dampers

Rehabilitation of existing structures by optimal placement of viscous dampers Lfe-Cycle and Sustanablty of Cvl Infrastructure Systems Strauss, Frangopol & Bergmester (Eds) 3 Taylor & Francs Group, London, ISBN 978--45-66-7 Rehabltaton of exstng structures by optmal placement of

More information

So far: simple (planar) geometries

So far: simple (planar) geometries Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector

More information

Physics 207: Lecture 20. Today s Agenda Homework for Monday

Physics 207: Lecture 20. Today s Agenda Homework for Monday Physcs 207: Lecture 20 Today s Agenda Homework for Monday Recap: Systems of Partcles Center of mass Velocty and acceleraton of the center of mass Dynamcs of the center of mass Lnear Momentum Example problems

More information

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st

EN40: Dynamics and Vibrations. Homework 4: Work, Energy and Linear Momentum Due Friday March 1 st EN40: Dynamcs and bratons Homework 4: Work, Energy and Lnear Momentum Due Frday March 1 st School of Engneerng Brown Unversty 1. The fgure (from ths publcaton) shows the energy per unt area requred to

More information

DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS

DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Munch, Germany, 26-30 th June 2016 1 DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School

More information

AP Physics 1 & 2 Summer Assignment

AP Physics 1 & 2 Summer Assignment AP Physcs 1 & 2 Summer Assgnment AP Physcs 1 requres an exceptonal profcency n algebra, trgonometry, and geometry. It was desgned by a select group of college professors and hgh school scence teachers

More information

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1

Physics 141. Lecture 14. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Frank L. H. Wolfs Department of Physcs and Astronomy, Unversty of Rochester, Lecture 14, Page 1 Physcs 141. Lecture 14. Course Informaton: Lab report # 3. Exam # 2. Mult-Partcle

More information

Difference Equations

Difference Equations Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1

More information

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient

Lab 2e Thermal System Response and Effective Heat Transfer Coefficient 58:080 Expermental Engneerng 1 OBJECTIVE Lab 2e Thermal System Response and Effectve Heat Transfer Coeffcent Warnng: though the experment has educatonal objectves (to learn about bolng heat transfer, etc.),

More information

COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN

COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN Int. J. Chem. Sc.: (4), 04, 645654 ISSN 097768X www.sadgurupublcatons.com COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN R. GOVINDARASU a, R. PARTHIBAN a and P. K. BHABA b* a Department

More information

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations

1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys

More information

Study on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component

Study on Non-Linear Dynamic Characteristic of Vehicle. Suspension Rubber Component Study on Non-Lnear Dynamc Characterstc of Vehcle Suspenson Rubber Component Zhan Wenzhang Ln Y Sh GuobaoJln Unversty of TechnologyChangchun, Chna Wang Lgong (MDI, Chna [Abstract] The dynamc characterstc

More information

Polynomial Regression Models

Polynomial Regression Models LINEAR REGRESSION ANALYSIS MODULE XII Lecture - 6 Polynomal Regresson Models Dr. Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Test of sgnfcance To test the sgnfcance

More information

GEO-SLOPE International Ltd, Calgary, Alberta, Canada Vibrating Beam

GEO-SLOPE International Ltd, Calgary, Alberta, Canada   Vibrating Beam GEO-SLOPE Internatonal Ltd, Calgary, Alberta, Canada www.geo-slope.com Introducton Vbratng Beam Ths example looks at the dynamc response of a cantlever beam n response to a cyclc force at the free end.

More information

Construction of Serendipity Shape Functions by Geometrical Probability

Construction of Serendipity Shape Functions by Geometrical Probability J. Basc. Appl. Sc. Res., ()56-56, 0 0, TextRoad Publcaton ISS 00-0 Journal of Basc and Appled Scentfc Research www.textroad.com Constructon of Serendpty Shape Functons by Geometrcal Probablty Kamal Al-Dawoud

More information

NUMERICAL RESULTS QUALITY IN DEPENDENCE ON ABAQUS PLANE STRESS ELEMENTS TYPE IN BIG DISPLACEMENTS COMPRESSION TEST

NUMERICAL RESULTS QUALITY IN DEPENDENCE ON ABAQUS PLANE STRESS ELEMENTS TYPE IN BIG DISPLACEMENTS COMPRESSION TEST Appled Computer Scence, vol. 13, no. 4, pp. 56 64 do: 10.23743/acs-2017-29 Submtted: 2017-10-30 Revsed: 2017-11-15 Accepted: 2017-12-06 Abaqus Fnte Elements, Plane Stress, Orthotropc Materal Bartosz KAWECKI

More information

Problem Set 9 Solutions

Problem Set 9 Solutions Desgn and Analyss of Algorthms May 4, 2015 Massachusetts Insttute of Technology 6.046J/18.410J Profs. Erk Demane, Srn Devadas, and Nancy Lynch Problem Set 9 Solutons Problem Set 9 Solutons Ths problem

More information

Structure and Drive Paul A. Jensen Copyright July 20, 2003

Structure and Drive Paul A. Jensen Copyright July 20, 2003 Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.

More information

SIMPLE LINEAR REGRESSION

SIMPLE LINEAR REGRESSION Smple Lnear Regresson and Correlaton Introducton Prevousl, our attenton has been focused on one varable whch we desgnated b x. Frequentl, t s desrable to learn somethng about the relatonshp between two

More information

Uncertainty and auto-correlation in. Measurement

Uncertainty and auto-correlation in. Measurement Uncertanty and auto-correlaton n arxv:1707.03276v2 [physcs.data-an] 30 Dec 2017 Measurement Markus Schebl Federal Offce of Metrology and Surveyng (BEV), 1160 Venna, Austra E-mal: markus.schebl@bev.gv.at

More information

Linear Regression Analysis: Terminology and Notation

Linear Regression Analysis: Terminology and Notation ECON 35* -- Secton : Basc Concepts of Regresson Analyss (Page ) Lnear Regresson Analyss: Termnology and Notaton Consder the generc verson of the smple (two-varable) lnear regresson model. It s represented

More information

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009

College of Computer & Information Science Fall 2009 Northeastern University 20 October 2009 College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:

More information

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng

More information

2016 Wiley. Study Session 2: Ethical and Professional Standards Application

2016 Wiley. Study Session 2: Ethical and Professional Standards Application 6 Wley Study Sesson : Ethcal and Professonal Standards Applcaton LESSON : CORRECTION ANALYSIS Readng 9: Correlaton and Regresson LOS 9a: Calculate and nterpret a sample covarance and a sample correlaton

More information