Thermal expansion of wood and timber-concrete composite members under ISO-fire exposure

Size: px
Start display at page:

Download "Thermal expansion of wood and timber-concrete composite members under ISO-fire exposure"

Transcription

1 Thermal expanson of wood and tmber-concrete composte members under ISO-fre exposure ANDREA FRANGI and MARIO FONTANA Insttute of Structural Engneerng, ETH Zurch, Swtzerland Summary Ths paper dscusses the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre. The frst part of the paper presents a smplfed model to calculate the effects of the thermal expanson, n the second part the calculaton model s compared to fre test results. Keywords Thermal expanson, wood members under ISO-fre exposure, tmber-concrete composte slabs, calculaton model for fre Introducton A research project was carred out at the ETH on the fre behavour of tmber slabs made of hollow elements and tmber-concrete composte slabs, whch consst of tmber members n the tensle zone, a thn concrete layer n the compresson zone and the shear connecton between tmber and concrete. In a seres of small-scale tests the fre behavour of the connectors and the separatng elements was expermentally analysed. A seres of fre tests on slabs looked at the global structural behavour of the tmber slabs and tmberconcrete composte slabs. All fre tests were based on ISO-fre exposure and performed at the Swss Federal Laboratores for Materals Testng and Research n Dübendorf. Detaled expermental results of all fre tests are descrbed n [5] and [6]. The desgn models developed for the calculaton of the fre resstance of tmber slabs and tmberconcrete composte slabs s presented n [7]. The fre tests permtted the study of the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs. Frst a smplfed model to calculate the effects of the thermal expanson s presented, ts results are then compared to the fre tests. Calculaton model The nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre was studed usng a lnear elastc calculaton model. The calculaton model was appled to the tested slabs usng the followng basc assumptons: - lnear elastc materal behavour - Bernoull s hypothess s vald also n the fre stuaton - smply supported member (statcally determnate system) subjected to thermal and mechancal actons Copyrght Internatonal Assocaton for Fre Safety Scence

2 - ISO-fre exposure as thermal acton producng the same temperature feld on each secton along the member - unformly dstrbuted loads and/or concentrated loads as mechancal actons producng only bendng moments M (no axal forces N) The geometres of the tested hollow core tmber slabs and of the tmber-concrete slab wth a wood secton made of tmber planks are shown n Fg. 4. The tmber slabs and the tmber-concrete composte slab were exposed to ISO-fre on one sde. Calculaton model The cross-secton of the structure s dvded nto n hypothetcal longtudnal unconnected layers (see Fg. 1a) wth dfferent stffness and strength propertes as a functon of temperature Θ (t). The temperature of each layer depends on the consdered fre tme and the secton geometry. Fgure 1 Calculaton model: (a) cross-secton composed of dfferent layers, (b) temperature gradent of the cross-secton, (c) thermal strans ε th,, (d) resultng strans ε res, Because of the good nsulatng behavour of charred and uncharred wood, typcal temperature profles through wood members exposed to fre exhbt a steep temperature gradent as presented n Fg. 1b. The steep temperature gradent wll nduce thermal strans ε th,, whch are not lnearly dstrbuted (see Fg. 1c). The thermal strans ε th, are calculated takng nto account the coeffcent of thermal expanson α T as: ε t) = α Θ (t) (1) th, ( T To fulfl the hypothess of Bernoull-Naver of a plane secton, nternal strans ε E, producng resdual thermal stresses σ E, must be ntroduced. The total strans ε res, resultng from the thermal strans ε th, and the nternal strans ε E, may be calculated takng nto account the stran of the upper layer ε 0 and the curvature χ of the cross-secton as (see Fg. 1d): ε t) = ε (t) + ε (t) = ε (t) + χ(t) z (t) () res, ( th, E, 0

3 Therefore the nternal strans ε E, and the resdual thermal stresses σ E, may be calculated n functon of ε 0 and χ as: ε t) = ε (t) ε (t) = ε (t) + χ(t) z (t) ε (t) (3) E,( res, th, 0 th, σ t) = E ( Θ ) ε (t) = E ( Θ ) [ ε (t) + χ(t) z (t) ε (t)] (4) E,( E, 0 th, For a smply supported member whch s not subjected to external loads, the thermal acton does not produce external bendng moments M and external axal forces N. Therefore the stran of the upper layer ε 0 and the curvature χ of the cross-secton can be found from statc equlbrum requrng that the nternal bendng moment force M Θ and nternal axal force N Θ due to the resdual thermal stresses σ E, must be zero: n NΘ (t) = Σ σ (t) A = 0 (5) = 1 n E, MΘ (t) = Σ σ (t) A z (t) = 0 (6) = 1 E, The solutons of equatons 5 and 6 are: ( Σε EA ) ( ΣEA z ) ( ΣEA z ) ( Σε EA z ) th, th, ε 0(t) = (7) ( ΣEA ) ( ΣEA z ) ( ΣEA z) ( ΣEA ) ( Σε EA z ) ( Σε EA ) ( ΣEA z ) th, th, χ (t) = (8) ( ΣEA ) ( ΣEA z ) ( ΣEA z) The deflecton w due to the curvature χ of the cross-secton s calculated accordng to the prncple of vrtual work (see Fg. ) as: l 1 l χ(t) l w(t) = M(x) χ(t) dx = χ(t) l = (9) Fgure Model for the deflecton for a smply supported beam exposed to fre only

4 On the other hand, for a smply supported member whch s subjected to external loads producng a bendng moment M(x), the stran of the upper layer ε 0 and the curvature χ of the cross-secton can be found from the condtons of equlbrum by: n NΘ (t) = Σ σ (t) A = 0 (10) = 1 n E, MΘ (t) = Σ σ (t) A z (t) = M(x) (11) = 1 E, The solutons of the equatons 10 and 11 are: ( Σε EA ) ( ΣEA z ) ( ΣEA z ) [( Σε EA z ) + M(x)] th, th, ε 0(x, t) = ( ΣEA ) ( ΣEA z ) ( ΣEA z) (1) ( ΣEA ) [( Σε EA z ) + M(x)] ( Σε EA ) ( ΣEA z ) th, th, χ (x, t) = (13) ( ΣEA ) ( ΣEA z ) ( ΣEA z ) The deflecton w due to the curvature χ of the cross-secton s calculated as: w(x, t) l = M(x) 0 M EI (x, t) l dx = M(x) χ(x, t) dx 0 (14) Materal propertes For the calculaton of the nfluence and effects of thermal expanson on the structural behavour of tmber slabs and tmber-concrete composte slabs exposed to ISO-fre, t s necessary to know the temperature development n the cross-secton n functon of tme as well as the thermal and mechancal materal propertes such as coeffcent of thermal expanson and modulus of elastcty of the dfferent components of the structure (tmber and concrete) n functon of temperature. The thermal expanson of tmber may be calculated accordng to Chrstoph [1] as: ε 6 th, = l = αt Θ = l / Θ (15) The thermal expanson of concrete may be calculated accordng to ENV [3] as: ε th, = l = Θ l / Θ (16) 3 The steep temperature gradent of wood members exposed to ISO-fre can be descrbed as a functon of fre tme and charrng rate. From all temperatures measured durng the ETH fre tests the followng expresson was developed for the calculaton of the temperature profle n a wood member subjected to ISO-fre on one sde [7]:

5 α(t) β t Θ (x) = (17) x α ( t) = 0.05 t (18) Θ: temperature n C n functon of the depth x β: charrng rate n mm/mn t: fre tme n mnutes x: depth measured from the surface of the cross-secton n mm The charrng rate β s the man parameter to descrbe the process of thermal degradaton (pyrolyss) of wood subjected to fre producng combustble gases, accompaned by a loss n weght and cross-secton. The ETH fre tests performed wth wood members exposed to ISO-fre of 30 up to 110 mnutes demonstrated that a constant charrng rate β of about 0.7mm/mn may be assumed. Fre reduces the cross-secton as well as the stffness and strength propertes n functon of temperature. For the concrete slab, the temperature-dependent reduced stffness and strength propertes accordng to ENV [3] are consdered n ths study. Fgure 3 Thermal expanson and modulus of elastcty E of tmber and concrete consdered n ths study n functon of the temperature For the temperature-dependent materal propertes of wood a large and often contradctory varaton of values s gven by dfferent sources [11]. Glos [8] conducted tests on structural tmber members of szes used n practce n bendng, compresson and tenson. The test specmens were heated to a constant temperature and then loaded to falure. The reduced modulus of elastcty obtaned for bendng s shown n Fg. 3 wth E(0.85). Köng [10] conducted extensve expermental research on the fre behavour of lght tmber frame assembles. Especally the performance of tmber frame members n bendng at standard fre exposure was studed [9]. The fre tests were conducted such that the fre-

6 exposed sde was ether n compresson or tenson. Thereby t was possble to separate the effect of temperature on the modulus of elastcty E n tenson and compresson. The reduced modul of elastcty obtaned are shown n Fg. 3 wth E(0.5) for tenson and E(0.35) for compresson. They devate consderably from those gven by Glos wth E(0.85). There are several reasons for ths. One s that t s dffcult to mantan a controlled level of mosture content durng the tests. Another reason s the effect of loadng rate: already consderable at normal temperature, t s much greater at elevated temperatures and senstve to mosture. Fgure 3 shows the thermal and mechancal propertes of tmber and concrete n functon of temperature, used for the followng parametrc study. Comparson wth fre tests The calculated effects of thermal expanson are compared to results of bendng tests performed wth a tmber-concrete composte slab and two tmber slabs made of hollow core elements shown n Fg. 4. All slabs were exposed to ISO-fre from below. Fgure 4 Cross-sectons of the slabs exposed to ISO-fre The tmber-concrete composte slab conssted of sawn spruce tmber planks 100 and 10 mm hgh and a 80 to 100 mm thck concrete layer (see Fg. 4). The composte slab had no connectors between the tmber planks and the concrete layer. The shear connecton between concrete and tmber was realsed by mcro-mechancal nterlock between concrete and the raw sawn surface of the tmber planks wth an alternatng heght of 100 and 10 mm. The slab was loaded wth hydraulc jacks postoned at about a thrd of the span. The load level F fre durng the fre test was set n such a way that the maxmum bendng moment corresponded to that n a slab of 6.5 m span, wth a permanent load of 1.5 kn/m and a reduced accompanyng varable load of 0.3*3.0 kn/m allowng for a reducton of the varable load due to the low probablty of concdence of the maxmum varable load and fre accordng to the Swss acton code SIA 160 [1]. The tmber concrete composte

7 slab, whch showed no slp between concrete and tmber durng the test, was exposed to 90 mnutes of ISO-fre. The two tmber slabs were made of 00 mm hgh hollow elements of spruce wth a mean densty of 450 kg/m 3. Two dfferent types of slab wth three dfferent types of jont between the tmber elements were desgned for a fre resstance of 60 and 90 mnutes (see Fg. 4). The load level durng the fre tests was set n such a way that the maxmum bendng moment corresponded to that n a slab of about 7.10 m span, wth a permanent load of 1.5 kn/m and a reduced accompanyng lve load of 0.5*3.0 kn/m accordng to ENV []. The tmber slabs were exposed to 70 mnutes and 105 mnutes of ISOfre. No relevant smoke or flame penetraton was observed through the three dfferent types of jont between the tmber elements. In the fre tests the temperatures n selected locatons, the vertcal deflectons and the horzontal deformatons were measured. Detaled expermental results of the fre tests are descrbed n [5] and [6]. Influence of thermal expanson on the deflecton Fgure 5 compares the deflecton measured durng the fre tests wth the deflecton calculated n functon of the three dfferent cases for the temperature-dependent reducton of the modulus of elastcty E of tmber as shown n Fg. 3. The assumed stffness propertes of the slabs at room temperature were calculated from the deflectons measured before the fre tests. Fgure 5 left llustrates the deflecton w th due to the nfluence of the thermal expanson α T accordng to equaton 15 and the deflecton w due to the external mechancal loads. Fgure 5 rght gves the total deflecton w tot. From Fg. 5 the followng conclusons can be drawn: - the sharp ncrease n the deflectons measured at the begnnng of the fre tests shows the nfluence of the thermal expanson of tmber. - the calculated deflectons w due to the external mechancal loads depend strongly on the dfferent materal laws for the temperature-dependent reducton of the modulus of elastcty E of tmber. Further t can be seen that the calculated deflectons w are always smaller than the deflecton measured durng the fre tests. Therefore a calculaton model, whch does not consder the effects of thermal expanson, underestmates the deflectons measured durng the fre tests. - the calculated deflectons w th due to the nfluence of thermal expanson depend only slghtly on the dfferent cases for the temperature-dependent reducton of the modulus of elastcty E of tmber. However the nfluence of thermal expanson leads to a consderable ncrease of the deflecton durng the fre tests. - the calculated deflectons w tot whch consder the effects of thermal expanson are n good agreement wth the deflecton measured durng the fre tests.

8 Fgure 5 Comparson of calculated and measured deflectons for dfferent materal laws accordng to Fg. 3 left and a charrng rate of 0.7 mm/mn.

9 Fgure 6 Influence of the assumed charrng rate and thermal coeffcent on the calculaton model Fgure 6 llustrates the nfluence of the charrng rate β and thermal coeffcent α T assumed for the calculaton model. The deflecton was calculated wth a charrng rate β of 0.70 mm/mn or 0.75 mm/mn and a thermal coeffcent α T of 4*10-6 K -1 or 5*10-6 K -1. Fgure 6 shows that: - the assumed charrng rate of tmber has a consderable nfluence on the calculated deflectons w due to the external mechancal loads. On the other hand, the nfluence of the charrng rate on the calculated deflectons w th due to thermal expanson s small. - the calculated deflectons w th due to the nfluence of thermal expanson depend strongly on the assumed thermal coeffcent α T of tmber. However, as the calculated deflecton w due to the external mechancal loads s consderably hgher than the calculated deflecton w th due to the nfluence of thermal expanson, the nfluence of the assumed thermal coeffcent α T of tmber on the calculated total deflecton w tot s qute small.

10 Influence of resdual thermal stresses Fgure 7 shows the resdual thermal stresses due to the nfluence of thermal expanson calculated after 30, 60 and 90 mnutes for the tmber-concrete composte slab shown n Fg. 4. The resdual thermal stresses were calculated n functon of temperature-dependent reductons of the modulus of elastcty E of tmber E(0.5) and E(0.85) as shown n Fg. 3. Fgure 7 Resdual thermal stresses due to the nfluence of the thermal expanson calculated after 30, 60 and 90 mnutes for the tmber-concrete composte slab From Fg. 7 followng conclusons can be drawn: - the effect of thermal expanson leads to resdual thermal compressve stresses n the upper and lower part of the cross-secton and resdual thermal tensle stresses n the mddle part of the cross-secton. - the resdual thermal compressve stresses slghtly decrease wth ncreasng fre tme, whle the resdual thermal tensle stresses slghtly ncrease. - because of the thermal degradaton of wood, the postons of the greatest compressve and tensle resdual thermal stresses move towards the unexposed sde of the crosssecton wth ncreasng fre tme. - the calculated resdual thermal stresses are qute small. Further t can be seen that the resdual thermal stresses σ E calculated wth E(0.85) are slghtly greater than σ E calculated wth E(0.5).

11 Fgure 8 Resultng stresses calculated wth and wthout the nfluence of the thermal expanson for the cross-secton wth the maxmum bendng moment due to the external mechancal loads Fgure 8 shows the resultng stresses calculated wth and wthout the nfluence of thermal expanson for the cross-secton subjected to the maxmum bendng moment due to the external mechancal loads. The resultng stresses were calculated after 60 and 90 mnutes n functon of the temperature-dependent reducton of the modulus of elastcty E of tmber E(0.5) and E(0.85) as shown n Fg. 3. Fgure 8 shows that the dfferences between the resultng stresses calculated wth and wthout the nfluence of thermal expanson are qute small. For ths reason, the fre resstance t R of a tmber-concrete slab calculated consderng the nfluence of thermal expanson dffers by only few mnutes from t R calculated wthout the nfluence of thermal expanson [7].

12 Conclusons A research project was carred out at the ETH on the fre behavour of tmber slabs and tmber-concrete composte slabs. The fre tests permtted studyng the effects of thermal expanson on the structural behavour of the slabs. The frst part of the paper presented a smplfed lnear elastc model to calculate the effects of thermal expanson on deflectons and stresses, n the second part ths calculaton model was compared to fre test results. From the study the followng conclusons can be drawn: - the effect of thermal expanson leads to an ncrease of the deflecton. Therefore calculaton models, whch do not consder ths nfluence, underestmate the deflecton measured durng fre tests. - the effect of thermal expanson leads to resdual thermal stresses. However, the calculaton model showed that the resdual thermal stresses are small n comparson to the stresses due to external mechancal loads and may therefore be neglected n the calculaton of the fre resstance tme of beams and slabs. References 1. Chrstoph N., Brettel G., Untersuchungen zur Wärmedehnung von Holz n Abhänggket von Rohdchte und Temperatur, Holz als Roh- und Werkstoff 35, ENV (Eurocode 1), Bass of desgn and actons on structures Part 1: Bass of desgn, CEN, Brussels, ENV (Eurocode 4), Desgn of composte steel and concrete structures Part 1-: General rules Structural fre desgn, CEN, Brussels, ENV (Eurocode 5), Desgn of tmber structures Part 1-: General rules Structural fre desgn, CEN, Brussels, Frang A., Fontana M., Zum Brandverhalten von Holzdecken aus Hohlkastenelementen, Insttute of Structural Engneerng (IBK). ETH Zurch, IBK Report No. 44, Brkhäuser Basle, Frang A., Fontana M., Versuche zum Tragverhalten von Holz-Beton-Verbunddecken be Raumtemperatur und Normbrandbedngungen, Insttute of Structural Engneerng, ETH Zurch, IBK Report No. 49, Brkhäuser Basle, Frang A., Fontana M., Brandverhalten von Holz-Beton-Verbunddecken, Insttute of Structural Engneerng, ETH Zurch, IBK Report No. 69, Brkhäuser Basle, Glos P., Henrc D., Festgket von Bauholz be hohen Temperaturen, Fnal report 87505, Insttut für Holzforschung der Unverstät München, Köng J., Fre resstance of tmber josts and load bearng wall frames, Swedsh Insttute for Wood Technology Research, Rapport I , Stockholm, Köng J., Wallej L., Tmber frame assembles exposed to standard and parametrc fres. Part : a desgn model for standard fre exposure, Swedsh Insttute for Wood Technology Research (Trätek), Rapport I , Stockholm, Köng J., Källsner B., Thermal and mechancal propertes of tmber and some other materals used n lght tmber frame constructon, CIB-W18, Paper , Meetng 33, Delft, SIA 160 (Code), Enwrkung auf Tragwerke, Schwez. Ingeneur- und Archtektenveren, Zürch, 1989.

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

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

EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES

EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES EVALUATION OF THE VISCO-ELASTIC PROPERTIES IN ASPHALT RUBBER AND CONVENTIONAL MIXES Manuel J. C. Mnhoto Polytechnc Insttute of Bragança, Bragança, Portugal E-mal: mnhoto@pb.pt Paulo A. A. Perera and Jorge

More information

THE EFFECT OF BEAM TO COLUMN CONNECTION IN ARC PORTAL FRAME

THE EFFECT OF BEAM TO COLUMN CONNECTION IN ARC PORTAL FRAME THE EFFECT OF BEAM TO COLUMN CONNECTON N ARC PORTAL FRAME Asko Keronen Rakenteden Mekankka, Vol. 26 No 2 1993, ss. 35-5 SUMMARY A full scale rc (renforced concrete) portal frame has been bult n order to

More information

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION

STATIC ANALYSIS OF TWO-LAYERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION STATIC ANALYSIS OF TWO-LERED PIEZOELECTRIC BEAMS WITH IMPERFECT SHEAR CONNECTION Ákos József Lengyel István Ecsed Assstant Lecturer Emertus Professor Insttute of Appled Mechancs Unversty of Mskolc Mskolc-Egyetemváros

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

FUZZY FINITE ELEMENT METHOD

FUZZY FINITE ELEMENT METHOD FUZZY FINITE ELEMENT METHOD RELIABILITY TRUCTURE ANALYI UING PROBABILITY 3.. Maxmum Normal tress Internal force s the shear force, V has a magntude equal to the load P and bendng moment, M. Bendng moments

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

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp.

ORIGIN 1. PTC_CE_BSD_3.2_us_mp.mcdx. Mathcad Enabled Content 2011 Knovel Corp. Clck to Vew Mathcad Document 2011 Knovel Corp. Buldng Structural Desgn. homas P. Magner, P.E. 2011 Parametrc echnology Corp. Chapter 3: Renforced Concrete Slabs and Beams 3.2 Renforced Concrete Beams -

More information

DUE: WEDS FEB 21ST 2018

DUE: WEDS FEB 21ST 2018 HOMEWORK # 1: FINITE DIFFERENCES IN ONE DIMENSION DUE: WEDS FEB 21ST 2018 1. Theory Beam bendng s a classcal engneerng analyss. The tradtonal soluton technque makes smplfyng assumptons such as a constant

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: Instructor s Name and Secton: (Crcle Your Secton) Sectons:

More information

Frame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments.

Frame element resists external loads or disturbances by developing internal axial forces, shear forces, and bending moments. CE7 Structural Analyss II PAAR FRAE EEET y 5 x E, A, I, Each node can translate and rotate n plane. The fnal dsplaced shape has ndependent generalzed dsplacements (.e. translatons and rotatons) noled.

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

CLT - Cross Laminated Timber Fire protection.

CLT - Cross Laminated Timber Fire protection. CLT - Cross Lamnated Tmber Fre protecton www.clt.nfo www.storaenso.com C O N T E N T S Verson 01/2014 AG It should be noted that ths fact sheet on fre protecton s merely ntended to support the user. Stora

More information

LAB 4: Modulus of elasticity

LAB 4: Modulus of elasticity LAB 4: Modulus of elastcty 1. Preparaton: modulus of elastcty (chapter15, p.79) Hook s law graphcal determnaton of modulus of elastcty (p.8) determnaton of modulus of elastcty n tenson and flexural stress

More information

OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES

OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES ICAMS 204 5 th Internatonal Conference on Advanced Materals and Systems OFF-AXIS MECHANICAL PROPERTIES OF FRP COMPOSITES VLAD LUPĂŞTEANU, NICOLAE ŢĂRANU, RALUCA HOHAN, PAUL CIOBANU Gh. Asach Techncal Unversty

More information

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Summer 2014 Fnal Exam NAME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam

APPENDIX F A DISPLACEMENT-BASED BEAM ELEMENT WITH SHEAR DEFORMATIONS. Never use a Cubic Function Approximation for a Non-Prismatic Beam APPENDIX F A DISPACEMENT-BASED BEAM EEMENT WITH SHEAR DEFORMATIONS Never use a Cubc Functon Approxmaton for a Non-Prsmatc Beam F. INTRODUCTION { XE "Shearng Deformatons" }In ths appendx a unque development

More information

One Dimensional Axial Deformations

One Dimensional Axial Deformations One Dmensonal al Deformatons In ths secton, a specfc smple geometr s consdered, that of a long and thn straght component loaded n such a wa that t deforms n the aal drecton onl. The -as s taken as the

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

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests

Simulated Power of the Discrete Cramér-von Mises Goodness-of-Fit Tests Smulated of the Cramér-von Mses Goodness-of-Ft Tests Steele, M., Chaselng, J. and 3 Hurst, C. School of Mathematcal and Physcal Scences, James Cook Unversty, Australan School of Envronmental Studes, Grffth

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

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Fall 2013 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

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

Principle of virtual work

Principle of virtual work Ths prncple s the most general prncple n mechancs 2.9.217 Prncple of vrtual work There s Equvalence between the Prncple of Vrtual Work and the Equlbrum Equaton You must know ths from statc course and dynamcs

More information

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls

A Mechanics-Based Approach for Determining Deflections of Stacked Multi-Storey Wood-Based Shear Walls A Mechancs-Based Approach for Determnng Deflectons of Stacked Mult-Storey Wood-Based Shear Walls FPINNOVATIONS Acknowledgements Ths publcaton was developed by FPInnovatons and the Canadan Wood Councl based

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

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS Fourth Edton CHTER MECHNICS OF MTERIS Ferdnand. Beer E. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech Unversty Stress and Stran xal oadng Contents Stress & Stran: xal oadng

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

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

Please review the following statement: I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Sprng 2014 Fnal Exam NME (Last, Frst): Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS

More information

Plan: Fuselages can. multideck

Plan: Fuselages can. multideck Lecture 22(18). TRENGTH ANALY OF FUELAGE Plan: 1. tructurally - power fuselage schemes. 2. trength analyss of fuselages cross-sectons. 3. emmonocoque fuselage cross-secton calculaton. Calculaton from external

More information

Torsion Stiffness of Thin-walled Steel Beams with Web Holes

Torsion Stiffness of Thin-walled Steel Beams with Web Holes Torson Stffness of Thn-walled Steel Beams wth Web Holes MARTN HORÁČEK, JNDŘCH MELCHER Department of Metal and Tmber Structures Brno Unversty of Technology, Faculty of Cvl Engneerng Veveří 331/95, 62 Brno

More information

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods

Chapter Eight. Review and Summary. Two methods in solid mechanics ---- vectorial methods and energy methods or variational methods Chapter Eght Energy Method 8. Introducton 8. Stran energy expressons 8.3 Prncpal of statonary potental energy; several degrees of freedom ------ Castglano s frst theorem ---- Examples 8.4 Prncpal of statonary

More information

Buckling analysis of single-layered FG nanoplates on elastic substrate with uneven porosities and various boundary conditions

Buckling analysis of single-layered FG nanoplates on elastic substrate with uneven porosities and various boundary conditions IOSR Journal of Mechancal and Cvl Engneerng (IOSR-JMCE) e-issn: 78-1684,p-ISSN: 30-334X, Volume 15, Issue 5 Ver. IV (Sep. - Oct. 018), PP 41-46 www.osrjournals.org Bucklng analyss of sngle-layered FG nanoplates

More information

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH

Turbulence classification of load data by the frequency and severity of wind gusts. Oscar Moñux, DEWI GmbH Kevin Bleibler, DEWI GmbH Turbulence classfcaton of load data by the frequency and severty of wnd gusts Introducton Oscar Moñux, DEWI GmbH Kevn Blebler, DEWI GmbH Durng the wnd turbne developng process, one of the most mportant

More information

Computer Simulations of Parallel-to-Series Conversion in Solid State Frame Transfer Image Sensors. J. Bisschop

Computer Simulations of Parallel-to-Series Conversion in Solid State Frame Transfer Image Sensors. J. Bisschop 207 SIMULATION OF SEMICONDUCTOR DEVICES AND PROCESSES Vol. 3 Edted by G. Baccaran, M. Rudan - Bologna (Italy) September 26-28,988 - Tecnoprnt Computer Smulatons of Parallel-to-Seres Converson n Sold State

More information

I have not received unauthorized aid in the completion of this exam.

I have not received unauthorized aid in the completion of this exam. ME 270 Sprng 2013 Fnal Examnaton Please read and respond to the followng statement, I have not receved unauthorzed ad n the completon of ths exam. Agree Dsagree Sgnature INSTRUCTIONS Begn each problem

More information

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

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

MODELLING OF ELASTO-STATICS OF POWER LINES BY NEW COMPOSITE BEAM FINITE ELEMENT Bratislava

MODELLING OF ELASTO-STATICS OF POWER LINES BY NEW COMPOSITE BEAM FINITE ELEMENT Bratislava ODING OF ASTO-STATICS OF POW INS BY NW COPOSIT BA FINIT NT urín Justín 1 rabovský Jura 1 Gogola oman 1 utš Vladmír 1 Paulech Jura 1 1 Insttute of Automotve echatroncs FI STU n Bratslava Ilkovčova 3 812

More information

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t

Description of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set

More information

Chapter 12. Ordinary Differential Equation Boundary Value (BV) Problems

Chapter 12. Ordinary Differential Equation Boundary Value (BV) Problems Chapter. Ordnar Dfferental Equaton Boundar Value (BV) Problems In ths chapter we wll learn how to solve ODE boundar value problem. BV ODE s usuall gven wth x beng the ndependent space varable. p( x) q(

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

Please initial the statement below to show that you have read it

Please initial the statement below to show that you have read it EN0: Structural nalyss Exam I Wednesday, March 2, 2005 Dvson of Engneerng rown Unversty NME: General Instructons No collaboraton of any nd s permtted on ths examnaton. You may consult your own wrtten lecture

More information

The optimal delay of the second test is therefore approximately 210 hours earlier than =2.

The optimal delay of the second test is therefore approximately 210 hours earlier than =2. THE IEC 61508 FORMULAS 223 The optmal delay of the second test s therefore approxmately 210 hours earler than =2. 8.4 The IEC 61508 Formulas IEC 61508-6 provdes approxmaton formulas for the PF for smple

More information

Lecture Note 3. Eshelby s Inclusion II

Lecture Note 3. Eshelby s Inclusion II ME340B Elastcty of Mcroscopc Structures Stanford Unversty Wnter 004 Lecture Note 3. Eshelby s Incluson II Chrs Wenberger and We Ca c All rghts reserved January 6, 004 Contents 1 Incluson energy n an nfnte

More information

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1

Physics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1 P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the

More information

Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur

Module 11 Design of Joints for Special Loading. Version 2 ME, IIT Kharagpur Module 11 Desgn o Jonts or Specal Loadng Verson ME, IIT Kharagpur Lesson 1 Desgn o Eccentrcally Loaded Bolted/Rveted Jonts Verson ME, IIT Kharagpur Instructonal Objectves: At the end o ths lesson, the

More information

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam.

I certify that I have not given unauthorized aid nor have I received aid in the completion of this exam. ME 270 Fall 2012 Fnal Exam Please revew the followng statement: I certfy that I have not gven unauthorzed ad nor have I receved ad n the completon of ths exam. Sgnature: INSTRUCTIONS Begn each problem

More information

Influential Factors Affecting Inherent Deformation during Plate Forming by Line Heating (Report 1)

Influential Factors Affecting Inherent Deformation during Plate Forming by Line Heating (Report 1) Transactons of JWRI, Vol.36 (2007), No.1 Influental Factors Affectng Inherent Deformaton durng Plate Formng by Lne Heatng (Report 1) The Effect of Plate Sze and Edge Effect VEGA Adan*, RASHED Sherf**,

More information

INDETERMINATE STRUCTURES METHOD OF CONSISTENT DEFORMATIONS (FORCE METHOD)

INDETERMINATE STRUCTURES METHOD OF CONSISTENT DEFORMATIONS (FORCE METHOD) INETNTE STUTUES ETHO OF ONSISTENT EFOTIONS (FOE ETHO) If all the support reactons and nternal forces (, Q, and N) can not be determned by usng equlbrum equatons only, the structure wll be referred as STTIY

More information

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models

More information

Nordic Insulation Symposium - Nord-IS 13 - Trondheim, Norway, June 9-12, 2013

Nordic Insulation Symposium - Nord-IS 13 - Trondheim, Norway, June 9-12, 2013 Nordc Insulaton Symposum - Nord-IS - Trondhem, Norway, June 9-2, 2 Dpl.-Ing. D. Geßler (danel.gessler@kt.edu), Prof. Dr.-Ing. T. Lebfred Insttute of Electrc Energy Systems and Hgh Voltage Technology Karlsruhe

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

Actual behaviour of composite externally CFRP-reinforced timber beams stress analysis

Actual behaviour of composite externally CFRP-reinforced timber beams stress analysis Actual behavour of composte externally CFRP-renforced tmber beams stress analyss Marcela Karmazínová Abstract The paper s focused on the problems of composte CFRP-renforced tmber beams. CFRP renforcement

More information

Determining the Temperature Distributions of Fire Exposed Reinforced Concrete Cross-Sections with Different Methods

Determining the Temperature Distributions of Fire Exposed Reinforced Concrete Cross-Sections with Different Methods Research Journal of Envronmental and Earth Scences 4(8): 782-788, 212 ISSN: 241-492 Maxwell Scentfc Organzaton, 212 Submtted: May 21, 212 Accepted: June 23, 212 Publshed: August 2, 212 Determnng the Temperature

More information

Application to Plane (rigid) frame structure

Application to Plane (rigid) frame structure Advanced Computatonal echancs 18 Chapter 4 Applcaton to Plane rgd frame structure 1. Dscusson on degrees of freedom In case of truss structures, t was enough that the element force equaton provdes onl

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

Total Strain Behavior of Mortar under Freeze-Thaw Cycles in Consideration of the in Coefficient of Thermal Expansion of Frost Damaged Mortar

Total Strain Behavior of Mortar under Freeze-Thaw Cycles in Consideration of the in Coefficient of Thermal Expansion of Frost Damaged Mortar Total Stran Behavor of Mortar under Freeze-Thaw Cycles n Consderaton of the n Coeffcent of Thermal Expanson of Frost Damaged Mortar Evdon Scat 1, Fuyuan Gong 1*, Ueda Tamon 2 and Zhang Dawe 3 1 Graduate

More information

System in Weibull Distribution

System in Weibull Distribution Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co

More information

Lifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model

Lifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model ECCMR, Prague, Czech Republc; September 3 th, 2015 Lfetme predcton of EP and NBR rubber seal by thermos-vscoelastc model Kotaro KOBAYASHI, Takahro ISOZAKI, Akhro MATSUDA Unversty of Tsukuba, Japan Yoshnobu

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

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

ME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints

ME 307 Machine Design I. Chapter 8: Screws, Fasteners and the Design of Nonpermanent Joints Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts Dr.. zz Bazoune Chapter 8: Screws, Fasteners and the Desgn of Nonpermanent Jonts CH-8 LEC 35 Slde 2 Dr.. zz Bazoune Chapter

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

Virtual Work 3rd Year Structural Engineering

Virtual Work 3rd Year Structural Engineering Vrtual Work 3rd Year Structural Engneerng 2/ Dr. Coln Capran Contents. Introducton... 4. General... 4.2 Background... 5 2. The Prncple of Vrtual Work... 4 2. Defnton... 4 2.2 Vrtual Dsplacements... 7 2.3

More information

Tensor Smooth Length for SPH Modelling of High Speed Impact

Tensor Smooth Length for SPH Modelling of High Speed Impact Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru

More information

Calculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption

Calculating the Quasi-static Pressures of Confined Explosions Considering Chemical Reactions under the Constant Entropy Assumption Appled Mechancs and Materals Onlne: 202-04-20 ISS: 662-7482, ol. 64, pp 396-400 do:0.4028/www.scentfc.net/amm.64.396 202 Trans Tech Publcatons, Swtzerland Calculatng the Quas-statc Pressures of Confned

More information

Transactions of the VŠB Technical University of Ostrava, Mechanical Series. article No. 1907

Transactions of the VŠB Technical University of Ostrava, Mechanical Series. article No. 1907 Transactons of the VŠB Techncal Unversty of Ostrava, Mechancal Seres No., 0, vol. LVIII artcle No. 907 Marek NIKODÝM *, Karel FYDÝŠEK ** FINITE DIFFEENCE METHOD USED FO THE BEAMS ON ELASTIC FOUNDATION

More information

General displacement arch-cantilever element method for stress analysis of arch dam

General displacement arch-cantilever element method for stress analysis of arch dam Water Scence and Engneerng, 009, (): 3-4 do:0.388/j.ssn.674-370.009.0.004 http://kkb.hhu.edu.cn e-mal: wse@hhu.edu.cn General dsplacement arch-cantlever element method for stress analyss of arch dam Hao

More information

ANALYSIS OF TIMOSHENKO BEAM RESTING ON NONLINEAR COMPRESSIONAL AND FRICTIONAL WINKLER FOUNDATION

ANALYSIS OF TIMOSHENKO BEAM RESTING ON NONLINEAR COMPRESSIONAL AND FRICTIONAL WINKLER FOUNDATION VOL. 6, NO., NOVEMBER ISSN 89-668 6- Asan Research Publshng Network (ARPN). All rghts reserved. ANALYSIS OF TIMOSHENKO BEAM RESTING ON NONLINEAR COMPRESSIONAL AND FRICTIONAL WINKLER FOUNDATION Adel A.

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

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding.

Physics 53. Rotational Motion 3. Sir, I have found you an argument, but I am not obliged to find you an understanding. Physcs 53 Rotatonal Moton 3 Sr, I have found you an argument, but I am not oblged to fnd you an understandng. Samuel Johnson Angular momentum Wth respect to rotatonal moton of a body, moment of nerta plays

More information

STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES

STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES STUDY OF A THREE-AXIS PIEZORESISTIVE ACCELEROMETER WITH UNIFORM AXIAL SENSITIVITIES Abdelkader Benchou, PhD Canddate Nasreddne Benmoussa, PhD Kherreddne Ghaffour, PhD Unversty of Tlemcen/Unt of Materals

More information

DESIGN METHODS OF A TIMBER-CONCRETE T-CROSS-SECTION UDC : (045)=20

DESIGN METHODS OF A TIMBER-CONCRETE T-CROSS-SECTION UDC : (045)=20 FACTA UNIVERSITATIS Seres: Archtecture and Cvl Engneerng Vol., N o 5, 3, pp. 39-338 DESIGN METHODS OF A TIMBER-CONCRETE T-CROSS-SECTION UDC 64.6:64..+64..3(45)= Radovan Cvetkovć, Dragoslav Stojć Faculty

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

APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE

APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE APPLICATION OF EDDY CURRENT PRINCIPLES FOR MEASUREMENT OF TUBE CENTERLINE DEFLECTION E. J. Chern Martn Maretta Laboratores 1450 South Rollng Road Baltmore, MD 21227 INTRODUCTION Tubes are a vtal component

More information

Uniformity of Deformation in Element Testing

Uniformity of Deformation in Element Testing Woousng Km, Marc Loen, ruce hadbourn and Joseph Labu Unformt of Deformaton n Element Testng Abstract Unform deformaton s a basc assumpton n element testng, where aal stran tpcall s determned from dsplacement

More information

Increase Decrease Remain the Same (Circle one) (2 pts)

Increase Decrease Remain the Same (Circle one) (2 pts) ME 270 Sample Fnal Eam PROBLEM 1 (25 ponts) Prob. 1 questons are all or nothng. PROBLEM 1A. (5 ponts) FIND: A 2000 N crate (D) s suspended usng ropes AB and AC and s n statc equlbrum. If θ = 53.13, determne

More information

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications

Durban Watson for Testing the Lack-of-Fit of Polynomial Regression Models without Replications Durban Watson for Testng the Lack-of-Ft of Polynomal Regresson Models wthout Replcatons Ruba A. Alyaf, Maha A. Omar, Abdullah A. Al-Shha ralyaf@ksu.edu.sa, maomar@ksu.edu.sa, aalshha@ksu.edu.sa Department

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

NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM

NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM Advanced Steel Constructon Vol. 5, No., pp. 59-7 (9) 59 NONLINEAR NATURAL FREQUENCIES OF A TAPERED CANTILEVER BEAM M. Abdel-Jaber, A.A. Al-Qasa,* and M.S. Abdel-Jaber Department of Cvl Engneerng, Faculty

More information

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure.

An influence line shows how the force in a particular member changes as a concentrated load is moved along the structure. CE 331, Fall 2010 Influence Les for Trusses 1 / 7 An fluence le shows how the force a partcular member changes as a concentrated load s moved along the structure. For eample, say we are desgng the seven

More information

One-sided finite-difference approximations suitable for use with Richardson extrapolation

One-sided finite-difference approximations suitable for use with Richardson extrapolation Journal of Computatonal Physcs 219 (2006) 13 20 Short note One-sded fnte-dfference approxmatons sutable for use wth Rchardson extrapolaton Kumar Rahul, S.N. Bhattacharyya * Department of Mechancal Engneerng,

More information

Lecture Notes on Linear Regression

Lecture Notes on Linear Regression Lecture Notes on Lnear Regresson Feng L fl@sdueducn Shandong Unversty, Chna Lnear Regresson Problem In regresson problem, we am at predct a contnuous target value gven an nput feature vector We assume

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

EURAMET.M.D-S2 Final Report Final report

EURAMET.M.D-S2 Final Report Final report Fnal report on ERAMET blateral comparson on volume of mass standards Project number: 1356 (ERAMET.M.D-S2) Volume of mass standards of 10g, 20 g, 200 g, 1 kg Zoltan Zelenka 1 ; Stuart Davdson 2 ; Cslla

More information

Chapter 8. Potential Energy and Conservation of Energy

Chapter 8. Potential Energy and Conservation of Energy Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and non-conservatve forces Mechancal Energy Conservaton of Mechancal

More information

Temperature. Chapter Heat Engine

Temperature. Chapter Heat Engine Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the

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

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body

χ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown

More information

Determinationn of gasket load drop at welding neck flange joints operating at medium high temperature

Determinationn of gasket load drop at welding neck flange joints operating at medium high temperature Determnatonn of gasket load drop at large sze weldng neck flange onts operatng at medum hgh temperature A. agy * and B. Dudnszky * * Department of Buldng Servces and Process Engneerng, aculty of Mechancal

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

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur

Dr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur Analyss of Varance and Desgn of Experment-I MODULE VII LECTURE - 3 ANALYSIS OF COVARIANCE Dr Shalabh Department of Mathematcs and Statstcs Indan Insttute of Technology Kanpur Any scentfc experment s performed

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

FATIGUE LIFE PREDICTION OF UMBILICALS CONSIDERING NON-LINEAR STRESS

FATIGUE LIFE PREDICTION OF UMBILICALS CONSIDERING NON-LINEAR STRESS POLISH MARITIME RESEARCH Specal Issue 2017 S2 (94) 2017 Vol. 24; pp. 154-163 10.1515/pomr-2017-0078 FATIGUE LIFE PREDICTION OF UMBILICALS CONSIDERING NON-LINEAR STRESS Lu Qngzhen 1, Lecturer Yn Yuanchao

More information

DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM

DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI

More information

Code_Aster. Identification of the model of Weibull

Code_Aster. Identification of the model of Weibull Verson Ttre : Identfcaton du modèle de Webull Date : 2/09/2009 Page : /8 Responsable : PARROT Aurore Clé : R70209 Révson : Identfcaton of the model of Webull Summary One tackles here the problem of the

More information

A Modified Neuber Method Avoiding Artefacts Under Random Loads

A Modified Neuber Method Avoiding Artefacts Under Random Loads A Modfed Neuber Method Avodng Artefacts Under Random Loads T. Herbland a,b, G. Calletaud a, J. L. Chaboche c, S. Qulc a, F. Gallerneau c a Mnes Pars Pars Tech, CNRS UMR 7633, P 87, 91003 vry cedex, France

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