Acta Technica Napocensis: Civil Engineering & Architecture Vol. 54 No.1 (2011)

Size: px
Start display at page:

Download "Acta Technica Napocensis: Civil Engineering & Architecture Vol. 54 No.1 (2011)"

Transcription

1 1 Technical University of Cluj-Napoca, Faculty of Civil Engineering. 15 C Daicoviciu Str., , Cluj-Napoca, Romania Received 25 July 2011; Accepted 1 September 2011 The Generalised Beam Theory (GBT) approach was proved to be a valid substitute of the Eurocode methods used for cold-formed steel member design. The conventional GBT is applied for the linear/nonlinear analysis of prismatic thin-walled members, circular and elliptical cylindrical shells and tubes. The authors new formulations etend the GBT for the special case of tapered members. This paper presents an overview of the GBT formulations recently developed by the author and also the software application GBTPower in which these theoretical developments are implemented. GBTPower performs buckling analyses of prismatic and tapered elastic thin-walled members with various types of cross-sections and boundary conditions. At the end a few numerical results are presented and briefly discussed. Abordările specifice Teoriei Generalizate a Grinzii (TGG) pot înlocui cu succes metodele din Eurocode în privinţa proiectării barelor cu pereţi subţiri formate la rece. TGG este utilizată în mod convenţional la analiza liniară şi neliniară a barelor prismatice cu pereţi subţiri şi a tuburilor cilindrice şi eliptice. Noile formulări ale autorului etind TGG pentru cazul special al barelor cu secţiune variabilă. Acest articol face o prezentare de ansamblu ale ultimelor formulări teoretice recent concepute de autor şi de asemenea a programului de calcul GBTPower în care acestea au fost implementate. Programul efectuează analize de tip flambaj prin bifurcare în domeniul elastic pentru bare cu pereţi subţiri cu diferite secţiuni şi rezemări. În final câteva eemple numerice sunt pe scurt prezentate şi discutate.

2 L NL M B M L γ s = M L ε s =

3 = = s ε = u ε = v + w γ = ww & M L M NL M NL s ε = zw ε = zw&& γ = zw& B B B s s B B σ µ ε M M B E B σ = Eε σ s = µ ε s B µ µ B τ s γ s n n IV τ ECikφk GDikφ k + Bikφk λ X jik W j φ k X jki W j φk + X jikw j φ k = τ ( ) ( ) k i = n W j = y z W = N W = M W = M W = B C D B X X τ φ k λ b G s tv ds D

4 C D B X X τ τ ( ) ( ) ( ) ( ) τ E Cikφ k G Dikφ k + Bikφk λ X jikwj φk X jkiw j φk + X jikw j φ k = L y z α g g g θ z a L α θ π z t + t u v w

5 M { } { c} M B M { e} = { } + { } = { } + z{ c} M M L M NL w v ε = ε + ε = ( u ) + + δ M M L M NL v& wc us δ vc w& δ v& + wc εθθ = εθθ + εθθ = r r r r + r M M L M NL u& vs w w& vw c v v& γ θ = γ θ + γ θ = + v δ δ r r + + r r r χ = w w&& w s vc & χθθ = + δ r r r w& ws & c v vs χ θ = + + δ r r r r c = ( α ) s = ( α ) = = θ δ δ δ = δ = δ = δ = δ = δ = M L M L γ = ε = k i θ θθ IV σ σ + + ( + ) + ( + ) σθ τ ( D kk Bkk G kk X jkk X jkk ) φk C φ C φ C D D X φ D D X φ kk k kk k kk kk kk jkk k kk kk jkk k = = n C D D G B X X X σ σθ τ j j j j. λ b σ σ τ o o o θθ θ

6 r < < < < L φ k Matlab R2006b

7 Mihai Nedelcu / Acta Technica Napocensis: Civil Engineering & Architecture Vol. 54 No.1 (2011) Fig. 8. GBTPower input interface Fig.9. GBTPower output interface Each cross-section type and variation law is handled in a different module. GBTPower also accepts different boundary conditions: cantilevers, simple supported, double fied or fied-simplesupported members. The latest developed module deals with the buckling analysis of conical shells. The input interface for opened and constant cross-section is shown in Fig. 8. The output interface displays for 1 st order analysis the displacement and stress field, the shape for each pure deformation 44

8 L = mm β = L = mm β =

9 FEA vs. GBT results for fied members β FEA P cr GBT Pcr kn cbm λ λ P E = GPa ν = t = L = mm r = mm r = λbp λc = λb o σ = P π rtc P = π r knmm kn

10 λc FEM r λ c GBT r

11 λc FEM EUROCODE 3, EN AISI AISI AISI

12 AS/NZS 4600 CUFSM GBTUL Verallgemeinerte Technische Biegetheorie Journal of Thin-Walled Structures Journal of Thin-Walled Structures Journal of Thin-Walled Structures Journal of Thin-Walled Structures International Journal of Solids and Structures, Journal of Thin-Walled Structures Journal of Thin-Walled Structures International Journal of Structural Stability and Dynamics Numerical Solution of Boundary Value Problems for Ordinary Differential Equation AIAA Journal, Stability of thin-walled tubes under torsion Quarterly Journal of Applied Mathematics, Theory of Plates and Shells MathWorks Journal of Computers and Structures, ABAQUS Standard (Version 6.3) Journal of the Structural Division

Dynamic Response of Beams on Elastic Foundation with Axial Load

Dynamic Response of Beams on Elastic Foundation with Axial Load Acta Technica Napocensis: Civil Engineering & Architecture Vol. 56, No. 1, (2013) Journal homepage: http://constructii.utcluj.ro/actacivileng Dynamic Response of Beams on Elastic Foundation with Axial

More information

Nonlinear Vibrations of Elastic Beams

Nonlinear Vibrations of Elastic Beams Acta Technica Napocensis: Civil Engineering & Architecture Vol. 56, No. 1, (2013) Journal homepage: http://constructii.utcluj.ro/actacivileng Nonlinear Vibrations of Elastic Beams Iacob Borş 1, Tudor Milchiş

More information

BUCKLING MODE CLASSIFICATION OF MEMBERS WITH OPEN THIN-WALLED CROSS-SECTIONS

BUCKLING MODE CLASSIFICATION OF MEMBERS WITH OPEN THIN-WALLED CROSS-SECTIONS CIMS 4 Fourth International Conference on Coupled Instabilities in Metal Structures Rome, Italy, 27-29 September, 24 BUCKLING MODE CLASSIFICATION OF MEMBERS WITH OPEN THIN-WALLED CROSS-SECTIONS S. ÁDÁNY,

More information

APPLICATIONS OF PURE AND COMBINED BUCKLING MODE CALCULATION OF THIN-WALLED MEMBERS USING THE FINITE ELEMENT METHOD

APPLICATIONS OF PURE AND COMBINED BUCKLING MODE CALCULATION OF THIN-WALLED MEMBERS USING THE FINITE ELEMENT METHOD SDSS Rio 2010 STABILITY AND DUCTILITY OF STEEL STRUCTURES E. Batista, P. Vellasco, L. de Lima (Eds.) Rio de Janeiro, Brazil, September 8-10, 2010 APPLICATIONS OF PURE AND COMBINED BUCKLING MODE CALCULATION

More information

ERRORS IN CONCRETE SHEAR WALL ELASTIC STRUCTURAL MODELING

ERRORS IN CONCRETE SHEAR WALL ELASTIC STRUCTURAL MODELING BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LVII (LXI), Fasc. 2, 2011 Secţia CONSTRUCŢII. ĂRHITECTURĂ ERRORS IN CONCRETE SHEAR WALL ELASTIC

More information

Direct Strength Design for Cold-Formed Steel Members with Perforations. Progress Report 5 C. Moen and B.W. Schafer AISI-COS Meeting February 2008

Direct Strength Design for Cold-Formed Steel Members with Perforations. Progress Report 5 C. Moen and B.W. Schafer AISI-COS Meeting February 2008 Direct Strength Design for Cold-Formed Steel Members with Perforations Progress Report 5 C. Moen and B.W. Schafer AISI-COS Meeting February 28 outline Objective Summary of past progress Simplified methods

More information

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002

Mechanical Engineering Ph.D. Preliminary Qualifying Examination Solid Mechanics February 25, 2002 student personal identification (ID) number on each sheet. Do not write your name on any sheet. #1. A homogeneous, isotropic, linear elastic bar has rectangular cross sectional area A, modulus of elasticity

More information

Influence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes

Influence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:

More information

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is

External Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the

More information

ACTA TECHNICA NAPOCENSIS

ACTA TECHNICA NAPOCENSIS 101 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Series: Applied Mathematics and Mechanics Vol. 54, Issue I, 2011 MATHEMATICAL MODEL AND PROGRAM FOR ANALYZING THE THERMOREFRACTORY INSULATION

More information

N = Shear stress / Shear strain

N = Shear stress / Shear strain UNIT - I 1. What is meant by factor of safety? [A/M-15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M-15]

More information

Verification Examples

Verification Examples Verification Examples 2008 AxisVM 9 Verification Examples 2 Linear static...3 Supported bar with concentrated loads....4 Thermally loaded bar structure...5 Continously supported beam with constant distributed

More information

GBTUL 1.0. Buckling and Vibration Analysis of Thin-Walled Members GBT THEORETICAL BACKGROUND. Rui Bebiano Nuno Silvestre Dinar Camotim

GBTUL 1.0. Buckling and Vibration Analysis of Thin-Walled Members GBT THEORETICAL BACKGROUND. Rui Bebiano Nuno Silvestre Dinar Camotim GBTUL 1.0 Buckling and Vibration Analysis of Thin-Walled Members GBT THEORETICAL BACKGROUND Rui Bebiano Nuno Silvestre Dinar Camotim Department of Civil Engineering and Architecture, DECivil/IST Technical

More information

A COMPARATIVE ANALYSIS OF WEB BUCKLING RESISTANCE: STEEL PLATE GIRDERS GIRDERS WITH CORRUGATED WEBS

A COMPARATIVE ANALYSIS OF WEB BUCKLING RESISTANCE: STEEL PLATE GIRDERS GIRDERS WITH CORRUGATED WEBS BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIX (LXIII), Fasc. 1, 013 Secţia CONSTRUCŢII. ARHITECTURĂ A COMPARATIVE ANALYSIS OF WEB BUCKLING

More information

Module 2 Stresses in machine elements

Module 2 Stresses in machine elements Module 2 Stresses in machine elements Lesson 3 Strain analysis Instructional Objectives At the end of this lesson, the student should learn Normal and shear strains. 3-D strain matri. Constitutive equation;

More information

THE BEHAVIOUR OF ELASTOMERIC BEARINGS UNDER LOAD COMBINATIONS

THE BEHAVIOUR OF ELASTOMERIC BEARINGS UNDER LOAD COMBINATIONS BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LX (LXIV), Fasc. 3, 2014 Secţia CONSTRUCŢII. ARHITECTURĂ THE BEHAVIOUR OF ELASTOMERIC BEARINGS

More information

Eurocode 3: Design of steel structures. Part 1-6: Strength and Stability of Shell Structures National Annex

Eurocode 3: Design of steel structures. Part 1-6: Strength and Stability of Shell Structures National Annex ICS 91.010.30, 91.080.10 SR EN 1993-1-6/NA STANDARD ROMÂN 2011 Eurocode 3: Design of steel structures. Part 1-6: Strength and Stability of Shell Structures National Annex Eurocod 3: Proiectarea structurilor

More information

CONFERINŢA INTERNAŢIONALĂ DEDUCON 70

CONFERINŢA INTERNAŢIONALĂ DEDUCON 70 CONFERINŢA INTERNAŢIONALĂ DEDUCON 70 DEZVOLTARE DURABILĂ ÎN CONSTRUCŢII Iaşi, 11 noiembrie 011 Conferinţă dedicată aniversării a 70 ani de învăţământ superior în construcţii la Iaşi A14 STABILITY ANALYSIS

More information

Example 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60.

Example 3.7 Consider the undeformed configuration of a solid as shown in Figure 3.60. 162 3. The linear 3-D elasticity mathematical model The 3-D elasticity model is of great importance, since it is our highest order hierarchical model assuming linear elastic behavior. Therefore, it provides

More information

Spiral Cylindrical Torsion Spring Analysis

Spiral Cylindrical Torsion Spring Analysis Spiral Cylindrical Torsion Spring Analysis Theory & FEA JingheSu: alwjybai@gmail.com Introduction A torsion spring is a spring that works by torsion or twisting; that is, a fleible elastic object that

More information

The University of Melbourne Engineering Mechanics

The University of Melbourne Engineering Mechanics The University of Melbourne 436-291 Engineering Mechanics Tutorial Four Poisson s Ratio and Axial Loading Part A (Introductory) 1. (Problem 9-22 from Hibbeler - Statics and Mechanics of Materials) A short

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. D : SOLID MECHANICS Q. 1 Q. 9 carry one mark each. Q.1 Find the force (in kn) in the member BH of the truss shown. Q.2 Consider the forces of magnitude F acting on the sides of the regular hexagon having

More information

FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH

FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH Journal of Engineering Science and Technology Vol. 12, No. 11 (2017) 2839-2854 School of Engineering, Taylor s University FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING

More information

Verification Examples. FEM-Design. version

Verification Examples. FEM-Design. version FEM-Design 6.0 FEM-Design version. 06 FEM-Design 6.0 StruSoft AB Visit the StruSoft website for company and FEM-Design information at www.strusoft.com Copyright 06 by StruSoft, all rights reserved. Trademarks

More information

Civil. Engineering INELASTIC BENDING CAPACITY IN COLD-FORMED STEEL MEMBERS Annual Stability Conference New Orleans, Louisiana

Civil. Engineering INELASTIC BENDING CAPACITY IN COLD-FORMED STEEL MEMBERS Annual Stability Conference New Orleans, Louisiana Civil Engineering at JOHNS HOPKINS UNIVERSITY at JOHNS HOPKINS UNIVERSITY INELASTIC BENDING CAPACITY IN COLD-FORMED STEEL MEMBERS 2007 Annual Stability Conference New Orleans, Louisiana April 2007 Y.Shifferaw

More information

Buckling Resistance Assessment of a Slender Cylindrical Shell Axially Compressed

Buckling Resistance Assessment of a Slender Cylindrical Shell Axially Compressed Mechanics and Mechanical Engineering Vol. 14, No. 2 (2010) 309 316 c Technical University of Lodz Buckling Resistance Assessment of a Slender Cylindrical Shell Axially Compressed Jakub Marcinowski Institute

More information

ACTA TECHNICA NAPOCENSIS

ACTA TECHNICA NAPOCENSIS 599 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Series: Applied Mathematics and Mechanics Vol. 55, Issue III, SIZE EFFECT ON THE DYNAMICAL BEHAVIOUR OF ELECTROSTATICALLY ACTUATED MEMS

More information

FINITE ELEMENT ANALYSIS OF FRICTIONAL CONTACTS

FINITE ELEMENT ANALYSIS OF FRICTIONAL CONTACTS BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică Gheorghe Asachi din Iaşi Tomul LIV (LVIII), Fasc. 3, 2011 Secţia CONSTRUCŢII. ARHITECTURĂ FINITE ELEMENT ANALYSIS OF FRICTIONAL

More information

Cone-shaped socket connections for cylindrical members

Cone-shaped socket connections for cylindrical members NSCC2009 Cone-shaped socket connections for cylindrical members H. Kuwamura 1 & T. Ito 2 1 Department of Architecture, The University of Tokyo, Tokyo, Japan 2 Department of Architecture, Tokyo University

More information

Analysis of Axially Loaded Non-prismatic Beams with General End Restraints Using Differential Quadrature Method

Analysis of Axially Loaded Non-prismatic Beams with General End Restraints Using Differential Quadrature Method ISBN 978-93-84422-56-1 Proceedings of International Conference on Architecture, Structure and Civil Engineering (ICASCE'15 Antalya (Turkey Sept. 7-8, 2015 pp. 1-7 Analysis of Axially Loaded Non-prismatic

More information

2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft

2. (a) Explain different types of wing structures. (b) Explain the advantages and disadvantages of different materials used for aircraft Code No: 07A62102 R07 Set No. 2 III B.Tech II Semester Regular/Supplementary Examinations,May 2010 Aerospace Vehicle Structures -II Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE

More information

Analytical Strip Method for Thin Isotropic Cylindrical Shells

Analytical Strip Method for Thin Isotropic Cylindrical Shells IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 4 Ver. III (Jul. Aug. 2017), PP 24-38 www.iosrjournals.org Analytical Strip Method for

More information

CALCULUS OF SHAFT LINE FROM SHIPS USING FEM METHOD

CALCULUS OF SHAFT LINE FROM SHIPS USING FEM METHOD THE ANNALS OF "DUNAREA DE JOS UNIVERSITY OF GALATI REFRIGERATING TECHNIQUE, INTERNAL COMBUSTION ENGINES, BOILERS AND TURBINES,05, ISSN -4558 CALCULUS OF SHAFT LINE FROM SHIPS USING FEM METHOD Mihai SIMIONOV

More information

STRUCTURAL ANALYSIS OF THE LIFTING DEVICE DETECTOR SUPPORTS FOR THE LHCb VERTEX LOCATOR (VELO)

STRUCTURAL ANALYSIS OF THE LIFTING DEVICE DETECTOR SUPPORTS FOR THE LHCb VERTEX LOCATOR (VELO) National Institute for Nuclear Physics and High Energy Physics Kruislaan 409 1098 SJ Amsterdam The Netherlands NIKHEF Reference no.: MT-VELO 04-2 EDMS no: 466608 OF THE LIFTING DEVICE DETECTOR SUPPORTS

More information

AN APPROACH TO THE NONLINEAR LOCAL PROBLEMS IN MECHANICAL STRUCTURES

AN APPROACH TO THE NONLINEAR LOCAL PROBLEMS IN MECHANICAL STRUCTURES U.P.B. Sci. Bull., Series D, Vol. 74, Iss. 3, 2012 ISSN 1454-2358 AN APPROACH TO THE NONLINEAR LOCAL PROBLEMS IN MECHANICAL STRUCTURES Marius-Alexandru GROZEA 1, Anton HADĂR 2 Acest articol prezintă o

More information

EE C245 ME C218 Introduction to MEMS Design

EE C245 ME C218 Introduction to MEMS Design EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy

More information

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics

PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [ ] Introduction, Fundamentals of Statics Page1 PDDC 1 st Semester Civil Engineering Department Assignments of Mechanics of Solids [2910601] Introduction, Fundamentals of Statics 1. Differentiate between Scalar and Vector quantity. Write S.I.

More information

The 5rd International Conference on. COMEC OCTOBER 2013, Brasov, Romania

The 5rd International Conference on. COMEC OCTOBER 2013, Brasov, Romania The 5rd International Conference on Computational Mechanics and Virtual Engineering COMEC 2013 24 25 OCTOBER 2013, Brasov, Romania THEORETICAL STUDIES AND EXPERIMENTAL RESEARCH FOR THE INCREASE OF THE

More information

Downloaded from Downloaded from / 1

Downloaded from   Downloaded from   / 1 PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their

More information

CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS

CHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a cross-sectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress

More information

Aim of the study Experimental determination of mechanical parameters Local buckling (wrinkling) Failure maps Optimization of sandwich panels

Aim of the study Experimental determination of mechanical parameters Local buckling (wrinkling) Failure maps Optimization of sandwich panels METNET Workshop October 11-12, 2009, Poznań, Poland Experimental and numerical analysis of sandwich metal panels Zbigniew Pozorski, Monika Chuda-Kowalska, Robert Studziński, Andrzej Garstecki Poznan University

More information

Validation of the Advanced Calculation Model SAFIR Through DIN EN Procedure

Validation of the Advanced Calculation Model SAFIR Through DIN EN Procedure Validation of the Advanced Calculation Model SAFIR Through DIN EN 1991-1-2 Procedure Raul Zaharia Department of Steel Structures and Structural Mechanics The Politehnica University of Timisoara, Ioan Curea

More information

JEPPIAAR ENGINEERING COLLEGE

JEPPIAAR ENGINEERING COLLEGE JEPPIAAR ENGINEERING COLLEGE Jeppiaar Nagar, Rajiv Gandhi Salai 600 119 DEPARTMENT OFMECHANICAL ENGINEERING QUESTION BANK VI SEMESTER ME6603 FINITE ELEMENT ANALYSIS Regulation 013 SUBJECT YEAR /SEM: III

More information

Experimental Study and Numerical Simulation on Steel Plate Girders With Deep Section

Experimental Study and Numerical Simulation on Steel Plate Girders With Deep Section 6 th International Conference on Advances in Experimental Structural Engineering 11 th International Workshop on Advanced Smart Materials and Smart Structures Technology August 1-2, 2015, University of

More information

Question 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H

Question 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H Question 1 (Problem 2.3 of rora s Introduction to Optimum Design): Design a beer mug, shown in fig, to hold as much beer as possible. The height and radius of the mug should be not more than 20 cm. The

More information

Lecture 8. Stress Strain in Multi-dimension

Lecture 8. Stress Strain in Multi-dimension Lecture 8. Stress Strain in Multi-dimension Module. General Field Equations General Field Equations [] Equilibrium Equations in Elastic bodies xx x y z yx zx f x 0, etc [2] Kinematics xx u x x,etc. [3]

More information

Open Access Prediction on Deflection of V-core Sandwich Panels in Weak Direction

Open Access Prediction on Deflection of V-core Sandwich Panels in Weak Direction Send Orders for Reprints to reprints@benthamscience.net The Open Ocean Engineering Journal, 2013, 6, Suppl-1, M5) 73-81 73 Open Access Prediction on Deflection of V-core Sandwich Panels in Weak Direction

More information

Advanced Analysis of Steel Structures

Advanced Analysis of Steel Structures Advanced Analysis of Steel Structures Master Thesis Written by: Maria Gulbrandsen & Rasmus Petersen Appendix Report Group B-204d M.Sc.Structural and Civil Engineering Aalborg University 4 th Semester Spring

More information

3.5 STRESS AND STRAIN IN PURE SHEAR. The next element is in a state of pure shear.

3.5 STRESS AND STRAIN IN PURE SHEAR. The next element is in a state of pure shear. 3.5 STRESS AND STRAIN IN PURE SHEAR The next element is in a state of pure shear. Fig. 3-20 Stresses acting on a stress element cut from a bar in torsion (pure shear) Stresses on inclined planes Fig. 3-21

More information

ACTA TECHNICA NAPOCENSIS

ACTA TECHNICA NAPOCENSIS 471 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Series: Applied Mathematics, Mechanics, and Engineering Vol. 57, Issue III, September, 2014 THEORETICAL DETERMINATION OF A VEHICLE VIBRATIONS

More information

EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING

EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Journal of MECHANICAL ENGINEERING Strojnícky časopis, VOL 67 (217), NO 1, 5-22 EFFECT OF LAMINATION ANGLE AND THICKNESS ON ANALYSIS OF COMPOSITE PLATE UNDER THERMO MECHANICAL LOADING Arnab Choudhury 1,

More information

of I Section Members

of I Section Members IMPROVED DESIGN ASSESSMENT OF LTB OF I-SECTION MEMBERS VIA MODERN COMPUTATIONAL METHODS Improved Design Assessment of LTB of I Section Members Donald W. White (with credits to Dr. Woo Yong Jeong & Mr.

More information

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

More information

CHAPTER 5 PROPOSED WARPING CONSTANT

CHAPTER 5 PROPOSED WARPING CONSTANT 122 CHAPTER 5 PROPOSED WARPING CONSTANT 5.1 INTRODUCTION Generally, lateral torsional buckling is a major design aspect of flexure members composed of thin-walled sections. When a thin walled section is

More information

Comb Resonator Design (2)

Comb Resonator Design (2) Lecture 6: Comb Resonator Design () -Intro. to Mechanics of Materials Sh School of felectrical ti lengineering i and dcomputer Science, Si Seoul National University Nano/Micro Systems & Controls Laboratory

More information

Torsion of Shafts Learning objectives

Torsion of Shafts Learning objectives Torsion of Shafts Shafts are structural members with length significantly greater than the largest cross-sectional dimension used in transmitting torque from one plane to another. Learning objectives Understand

More information

Advanced stability analysis and design of a new Danube archbridge. DUNAI, László JOÓ, Attila László VIGH, László Gergely

Advanced stability analysis and design of a new Danube archbridge. DUNAI, László JOÓ, Attila László VIGH, László Gergely Advanced stability analysis and design of a new Danube archbridge DUNAI, László JOÓ, Attila László VIGH, László Gergely Subject of the lecture Buckling of steel tied arch Buckling of orthotropic steel

More information

PES Institute of Technology

PES Institute of Technology PES Institute of Technology Bangalore south campus, Bangalore-5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject

More information

The Local Web Buckling Strength of Coped Steel I-Beam. ABSTRACT : When a beam flange is coped to allow clearance at the

The Local Web Buckling Strength of Coped Steel I-Beam. ABSTRACT : When a beam flange is coped to allow clearance at the The Local Web Buckling Strength of Coped Steel I-Beam Michael C. H. Yam 1 Member, ASCE Angus C. C. Lam Associate Member, ASCE, V. P. IU and J. J. R. Cheng 3 Members, ASCE ABSTRACT : When a beam flange

More information

INTRODUCTION TO STRAIN

INTRODUCTION TO STRAIN SIMPLE STRAIN INTRODUCTION TO STRAIN In general terms, Strain is a geometric quantity that measures the deformation of a body. There are two types of strain: normal strain: characterizes dimensional changes,

More information

Types of Structures & Loads

Types of Structures & Loads Structure Analysis I Chapter 4 1 Types of Structures & Loads 1Chapter Chapter 4 Internal lloading Developed in Structural Members Internal loading at a specified Point In General The loading for coplanar

More information

Direct Strength Method of Design for Shear of Cold-formed Channels Based on a Shear Signature Curve

Direct Strength Method of Design for Shear of Cold-formed Channels Based on a Shear Signature Curve Missouri University of Science and Technology Scholars' Mine International Specialty Conference on Cold- Formed Steel Structures (2012) - 21st International Specialty Conference on Cold-Formed Steel Structures

More information

Mechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total

Mechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total Mechanics of Materials MENG 70 Fall 00 Eam Time allowed: 90min Name. Computer No. Q.(a) Q. (b) Q. Q. Q.4 Total Problem No. (a) [5Points] An air vessel is 500 mm average diameter and 0 mm thickness, the

More information

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is

More information

FINAL EXAMINATION. (CE130-2 Mechanics of Materials)

FINAL EXAMINATION. (CE130-2 Mechanics of Materials) UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,

More information

Iraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk

Iraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-015 1678 Study the Increasing of the Cantilever Plate Stiffness by Using s Jawdat Ali Yakoob Iesam Jondi Hasan Ass.

More information

TWO BOUNDARY ELEMENT APPROACHES FOR THE COMPRESSIBLE FLUID FLOW AROUND A NON-LIFTING BODY

TWO BOUNDARY ELEMENT APPROACHES FOR THE COMPRESSIBLE FLUID FLOW AROUND A NON-LIFTING BODY U.P.B. Sci. Bull., Series A, Vol. 7, Iss., 9 ISSN 3-77 TWO BOUNDARY ELEMENT APPROACHES FOR THE COMPRESSIBLE FLUID FLOW AROUND A NON-LIFTING BODY Luminiţa GRECU, Gabriela DEMIAN, Mihai DEMIAN 3 În lucrare

More information

Chapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson

Chapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. El-kashif Civil Engineering Department, University

More information

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?

2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)? IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at

More information

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship

Chapter 5 Elastic Strain, Deflection, and Stability 1. Elastic Stress-Strain Relationship Chapter 5 Elastic Strain, Deflection, and Stability Elastic Stress-Strain Relationship A stress in the x-direction causes a strain in the x-direction by σ x also causes a strain in the y-direction & z-direction

More information

1 332 Laboratories 1. 2 Computational Exercises 1 FEA of a Cantilever Beam... 1 Experimental Laboratory: Tensile Testing of Materials...

1 332 Laboratories 1. 2 Computational Exercises 1 FEA of a Cantilever Beam... 1 Experimental Laboratory: Tensile Testing of Materials... 1 332 Laboratories Contents 1 332 Laboratories 1 2 Computational Exercises 1 FEA of a Cantilever Beam.......................................... 1 Experimental Laboratory: Tensile Testing of Materials..........................

More information

CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES

CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES 14.1 GENERAL REMARKS In structures where dominant loading is usually static, the most common cause of the collapse is a buckling failure. Buckling may

More information

Optimal Shapes of the Cylindrical Pressurized Fuel Tanks

Optimal Shapes of the Cylindrical Pressurized Fuel Tanks Optimal Shapes of the Cylindrical Pressurized Fuel Tanks Prof. PhD. Eng. Marin BICĂ 1, Assoc. Prof. PhD. Eng. Mihai ŢĂLU 2,*, Assoc. Prof. PhD. Eng. Ștefan ŢĂLU 3 1 University of Craiova, Faculty of Mechanics,

More information

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A

QUESTION BANK DEPARTMENT: CIVIL SEMESTER: III SUBJECT CODE: CE2201 SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A DEPARTMENT: CIVIL SUBJECT CODE: CE2201 QUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS UNIT 1- STRESS AND STRAIN PART A (2 Marks) 1. Define longitudinal strain and lateral strain. 2. State

More information

Free Body Diagram: Solution: The maximum load which can be safely supported by EACH of the support members is: ANS: A =0.217 in 2

Free Body Diagram: Solution: The maximum load which can be safely supported by EACH of the support members is: ANS: A =0.217 in 2 Problem 10.9 The angle β of the system in Problem 10.8 is 60. The bars are made of a material that will safely support a tensile normal stress of 8 ksi. Based on this criterion, if you want to design the

More information

Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength of Material. Shear Strain. Dr. Attaullah Shah Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume

More information

Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives

Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Experimentally Calibrating Cohesive Zone Models for Structural Automotive Adhesives Mark Oliver October 19, 2016 Adhesives and Sealants Council Fall Convention contact@veryst.com www.veryst.com Outline

More information

A GENERALIZATION OF A CLASSICAL MONTE CARLO ALGORITHM TO ESTIMATE π

A GENERALIZATION OF A CLASSICAL MONTE CARLO ALGORITHM TO ESTIMATE π U.P.B. Sci. Bull., Series A, Vol. 68, No., 6 A GENERALIZATION OF A CLASSICAL MONTE CARLO ALGORITHM TO ESTIMATE π S.C. ŞTEFĂNESCU Algoritmul Monte Carlo clasic A1 estimeazează valoarea numărului π bazându-se

More information

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each.

D : SOLID MECHANICS. Q. 1 Q. 9 carry one mark each. GTE 2016 Q. 1 Q. 9 carry one mark each. D : SOLID MECHNICS Q.1 single degree of freedom vibrating system has mass of 5 kg, stiffness of 500 N/m and damping coefficient of 100 N-s/m. To make the system

More information

BUCKLING OF CYLINDRICAL COMPOSITE SHELLS UNDER DEFORMATION-RELATED LOADS BY USING FINITE STRIP METHOD

BUCKLING OF CYLINDRICAL COMPOSITE SHELLS UNDER DEFORMATION-RELATED LOADS BY USING FINITE STRIP METHOD BUCKLING OF CYLINDRICAL COMPOSITE SHELLS UNDER DEFORMATION-RELATED LOADS BY USING FINITE STRIP METHOD Arman Amini Safir-E-Andisheh Language Academy, Iran Abstract Current advances in today s industries

More information

Comb resonator design (2)

Comb resonator design (2) Lecture 6: Comb resonator design () -Intro Intro. to Mechanics of Materials School of Electrical l Engineering i and Computer Science, Seoul National University Nano/Micro Systems & Controls Laboratory

More information

UNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2

UNIT-I STRESS, STRAIN. 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 UNIT-I STRESS, STRAIN 1. A Member A B C D is subjected to loading as shown in fig determine the total elongation. Take E= 2 x10 5 N/mm 2 Young s modulus E= 2 x10 5 N/mm 2 Area1=900mm 2 Area2=400mm 2 Area3=625mm

More information

FACULTY OF ELECTRONICS, TELECOMMUNICATIONS AND INFORMATION TECHNOLOGY. Ing. Nicolae-Cristian PAMPU. PhD. THESIS

FACULTY OF ELECTRONICS, TELECOMMUNICATIONS AND INFORMATION TECHNOLOGY. Ing. Nicolae-Cristian PAMPU. PhD. THESIS Investeşte în oameni! FONDUL SOCIAL EUROPEAN Proiect cofinanţat din Fondul Social European prin Programul Operaţional Sectorial pentru Dezvoltarea Resurselor Umane 2007-2013 Axa prioritară 1 : Educaţia

More information

Plates and Shells: Theory and Computation. Dr. Mostafa Ranjbar

Plates and Shells: Theory and Computation. Dr. Mostafa Ranjbar Plates and Shells: Theory and Computation Dr. Mostafa Ranjbar Outline -1-! This part of the module consists of seven lectures and will focus on finite elements for beams, plates and shells. More specifically,

More information

The example of shafts; a) Rotating Machinery; Propeller shaft, Drive shaft b) Structural Systems; Landing gear strut, Flap drive mechanism

The example of shafts; a) Rotating Machinery; Propeller shaft, Drive shaft b) Structural Systems; Landing gear strut, Flap drive mechanism TORSION OBJECTIVES: This chapter starts with torsion theory in the circular cross section followed by the behaviour of torsion member. The calculation of the stress stress and the angle of twist will be

More information

Interactive Buckling of Cold-Formed Steel Sections Applied in Pallet Rack Upright Members

Interactive Buckling of Cold-Formed Steel Sections Applied in Pallet Rack Upright Members Interactive Buckling of Cold-Formed Steel Sections Applied in Pallet Rack Upright Members D. Dubina, V. Ungureanu, A. Crisan Politehnica University of Timişoara Peculiarities of cold-formed thin-walled

More information

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

More information

TORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES)

TORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES) Page1 TORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES) Restrained warping for the torsion of thin-wall open sections is not included in most commonly used frame analysis programs. Almost

More information

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS

VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS The 4 th World Conference on Earthquake Engineering October -7, 008, Beijing, China VORONOI APPLIED ELEMENT METHOD FOR STRUCTURAL ANALYSIS: THEORY AND APPLICATION FOR LINEAR AND NON-LINEAR MATERIALS K.

More information

Outline. Organization. Stresses in Beams

Outline. Organization. Stresses in Beams Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of

More information

Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double cantilever beam (DCB) specimens.

Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double cantilever beam (DCB) specimens. a). Cohesive Failure b). Interfacial Failure c). Oscillatory Failure d). Alternating Failure Fig. 1. Different locus of failure and crack trajectories observed in mode I testing of adhesively bonded double

More information

Parametric Instability and Snap-Through of Partially Fluid- Filled Cylindrical Shells

Parametric Instability and Snap-Through of Partially Fluid- Filled Cylindrical Shells Available online at www.sciencedirect.com Procedia Engineering 14 (011) 598 605 The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction Parametric Instability and Snap-Through

More information

Practice Final Examination. Please initial the statement below to show that you have read it

Practice Final Examination. Please initial the statement below to show that you have read it EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use

More information

Durability of Steel Fiber Reinforced Concrete Filled Steel Tubes under Eccentric Loads

Durability of Steel Fiber Reinforced Concrete Filled Steel Tubes under Eccentric Loads Durability of Steel Fiber Reinforced Concrete Filled Steel Tubes under Eccentric Loads Eltobgy, H. H. 1,*, Abdallah, S. 1, and Shaaban, I. 1 1 Civil Engineering Department, Faculty of Eng. at Shoubra,

More information

Unit 18 Other Issues In Buckling/Structural Instability

Unit 18 Other Issues In Buckling/Structural Instability Unit 18 Other Issues In Buckling/Structural Instability Readings: Rivello Timoshenko Jones 14.3, 14.5, 14.6, 14.7 (read these at least, others at your leisure ) Ch. 15, Ch. 16 Theory of Elastic Stability

More information

Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition

Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition Fluid Structure Interaction and Moving Boundary Problems IV 63 Hydroelastic vibration of a rectangular perforated plate with a simply supported boundary condition K.-H. Jeong, G.-M. Lee, T.-W. Kim & J.-I.

More information

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering

Mechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected

More information

SECTION 7 DESIGN OF COMPRESSION MEMBERS

SECTION 7 DESIGN OF COMPRESSION MEMBERS SECTION 7 DESIGN OF COMPRESSION MEMBERS 1 INTRODUCTION TO COLUMN BUCKLING Introduction Elastic buckling of an ideal column Strength curve for an ideal column Strength of practical column Concepts of effective

More information

Sheathing Braced Design of Wall Studs July 2011 Update. for

Sheathing Braced Design of Wall Studs July 2011 Update.  for Civil Engineering at JOHNS HOPKINS UNIVERSITY Sheathing Braced Design of Wall Studs July 2011 Update www.ce.jhu.edu/bschafer/sheathedwalls for AISI Committee on Framing Standards Design Methods Subcommittee

More information

INFLUENCE OF THE FRICTION COEFICIENT ON SPRINGBACK EFFECT OF A U-SHAPED PART MANUFACTURED BY TAILOR WELDED STRIPES

INFLUENCE OF THE FRICTION COEFICIENT ON SPRINGBACK EFFECT OF A U-SHAPED PART MANUFACTURED BY TAILOR WELDED STRIPES U.P.B. Sci. Bull., Series D, Vol. 68, No. 3, 2006 INFLUENCE OF THE FRICTION COEFICIENT ON SPRINGBACK EFFECT OF A U-SHAPED PART MANUFACTURED BY TAILOR WELDED STRIPES A. ALBUŢ Geometria finală a unei piesei

More information