# Unit 18 Other Issues In Buckling/Structural Instability

Size: px
Start display at page:

## Transcription

1 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 Mechanics of Composite Materials, Ch. 5 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering Systems

2 Have dealt, thus far, with perfect columns, loading eccentricities, and beam-columns. There are, however, many more issues in buckling/(static) structural instability, most of which will try to touch on. (a) Buckling versus Fracture Have looked at columns that are long enough such that they buckle. However, it is possible that the material compressive ultimate stress may be reached before the static instability occurs. Consider short/ squat column (saw in Unified) Figure 18.1 Representation of short column under compressive load Unit 18 -

3 P σ = A If σ = σ compressive ultimate before P = P cr, then failure occurs by material failure in compression squashing Using the slenderness ratio previously defined: P π cr E σ cr = = A (l ρ ) where: l = l c define a column by its slenderness ratio and can plot the behavior and failure mode of various columns Unit 18-3

4 Figure 18. Summary plot showing general behavior of columns based on stress level versus slenderness ratio Euler curve compressive yield actual behavior Regions of values depend on E and σ cu What happens in the transition region? Unit 18-4

5 (b) Progressive Yielding Figure 18.3 Typical stress-strain plot for a ductile metal (in compression) As the column is loaded, there is some deflection due to slight imperfections. This means the highest load is at the outer part of the beam-column. Unit 18-5

6 Figure 18.4 Representation of region of highest stress in cross-section of beam-column highest compressive stress Thus, this outer part is the first part to yield. As the material yields, the modulus decreases. Figure 18.5 Representation of tangent modulus tangent modulus This changes the location of the centroid Unit 18-6

7 Figure 18.6 Representation of change in location of centroid of crosssection due to local yielding lower modulus, E T < E E This continues and it may eventually squash or buckle (or a combination) --> See Rivello 14.6 (c) Nonuniform Beam-Columns Have looked only at beams with uniform cross-sectional property EI. Now let this vary with x (most likely I, not E). Example: Tapered section Unit 18-7

8 Figure 18.7 Representation of beam-column with tapered cross-section Thus, the governing equation is: d dw EI + P dw = 0 dx dx dx EI = EI(x) must keep this inside the derivative Solve this via numerical techniques: Energy Methods Galerkin Finite Element Method Finite Difference Rayleigh-Ritz --> See Rivello 14.3 Unit 18-8

9 (d) Buckling of Plates Thus far have considered a one-dimensional problem (structural property of main importance is l, besides EI). Now have a two-dimensional structure (a plate ): Figure 18.8 Representation of plate under compressive load Pin-sliding Free Unit 18-9

10 The Poisson s ratio enters into play here. For an isotropic plate get: π EI P cr = l (1 ν ) where: l = a I = 1/1 bh 3 σ = P cr = π E h cr bh 1 1 ν a whereas the column buckling load is P = π EI π EAh = σ = π E h cr l l cr 1 1 l The buckled shape will have components in both directions: Figure 18.9 Representation of deflection of buckled square plate with all sides simply-supported Unit 18-10

11 π w = w sin m x mn a π sin n y b --> can have contributions of many modes. Will depend on boundary conditions on all four sides. --> See Rivello, Ch. 15 Even more complicated for orthotropic plates as the modulus varies in the two directions. (must also look at buckling due to shear loads) --> See Jones, Ch. 5 Note: for some weird anisotropic plates with shear couplings, can get buckling under tension. (Key question: Is there an induced compressive stress in some direction?) think back to basic definition of instability Unit 18-11

12 (e) Cylinders ( thin-walled things, like shells) Have dealt with global instabilities. However, buckling can also be a local instability. Figure Representation of crippling in thin cylinder under axial compressive load local crippling total axial load: P = σ (π) Rh for an isotropic cylinder: σ = E h cr (linear) R Unit 18-1

13 The actual load where the local instability sets in is less than that predicted from linear theory due to imperfections in both geometry and loading: σ cr( actual ) (015. to 0.9)σ cr( linear ) --> See Rivello, Ch. 15 (f) Reinforced Plates A common design in aerospace structures (and many other structures) is to reinforce a plate with stiffeners: Figure Representation of plate with stiffeners Unit 18-13

14 The buckling can take place at several levels buckling of panels between stiffness buckling of parts of stiffeners (e.g., flange, web) global instability This can occur on a progressive basis. Analysis often uses only stiffness as carrying the load for buckling (axial load) or talk about effective width of skin (this was previously discussed in talking about general shell beams and holds true for buckling) (g) Post-buckling When talked about buckling, talked about bifurcation. In that case w --> as P --> P cr (with imperfections). In reality, a structure can carry load after buckling ( post-buckling behavior). Unit 18-14

15 Figure 18.1 Representation of post-buckling behavior via loaddeflection plot actual behavior w/postbuckling capability perfect linear behavior behavior with imperfection The critical assumption which breaks down is: SMALL DEFORMATIONS Must now account for geometrical nonlinear effects. (Note: material nonlinear effects will also enter in as approach σ cu ) Unit 18-15

16 Consider: Post-Buckling of a beam-column (the issues are the same for a plate) Figure Representation of post-buckling of a beam-column For large deflections, the moment-curvature equation is: Ms () = E I dθ ds where: dθ = curvature ds Look at a beam section: Unit 18-16

17 dw = sinθ ds differentiating: dw ds dθ = cosθ ds or: dθ 1 dw = ds cosθ ds with: dx cosθ = = ds ds dw ds = 1 dw ds or: cosθ = 1 sin θ Unit 18-17

18 So: curvature = d θ 1 = ds 1 dw ds dw ds For moderate angles θ: (via expansion) dθ 1 = 1 + dw ds ds + H.O.T. dw ds nonlinear term In the absence of any primary moment, the moment at any point s is due to the deflection w at that point: Figure Representation of resultants along the beam-column + M = 0 M + Pw = 0 M = -Pw Unit 18-18

19 So the basic Post-Buckling equation becomes: 1 dw dw P 1 + ds + H.O.T. ds + EI w = 0 This can be solved via Numerical Techniques Energy Method --> Effect appears to stiffen the behavior Consider one (numerical) technique known as the Galerkin Method 1. Assume a mode that satisfies the boundary conditions w = q 1 sin πs/l unknown assumed mode shape satisfies all coefficient boundary conditions Unit 18-19

20 . Integrate a weighted average of the solution and the Ordinary Differential Equation (Are minimizing the residuals ) l s Differential q 1 sin π 0 ds = 0 l equation assumed mode shape Here: 1 1 dw dw + ds ds P + w EI This gives: π 3 π 4 Pl q 1 q 1 16 l 3 + q 1 = 0 l EI Solving: π 4 π Pl q 1 q 16 l l EI = 0 Unit 18-0

21 MIT Get: q 1 = q 1 = this latter gives: q 1 = 0 (trivial solution: w = 0) 8l Pl π π EI l P 1 P cr Note: q 1 only for P/P cr > 1 Fall, 00 Plotting P/P cr vs. w c (= q 1 ) gives: Figure Representation of load versus center deflection for postbuckled beam-column based on Galerkin Method Unit 18-1

22 For w c / l > 0.3, include more terms: 4 1 dw 3 dw K ds 8 ds See: Rivello, Timoshenko & Gere --> Postscript: Buckling and Failure When is a structure that buckles considered to have failed? Recall discussion of failure at beginning of term. There is not (physically only mathematically) a point of buckling. What happens is that deflection increases with load very rapidly. If failure is deflection-based, look at deflection; if stress/strainbase, look at that Unit 18 -

23 Must consider: pre-buckling behavior: imperfections cause deflections and stresses. These may cause failure before buckling post-buckling behavior: extra stiffening at large deflections may result in ability to carry deflections and stresses such that failure is after buckling Unit 18-3

### Unit 15 Shearing and Torsion (and Bending) of Shell Beams

Unit 15 Shearing and Torsion (and Bending) of Shell Beams Readings: Rivello Ch. 9, section 8.7 (again), section 7.6 T & G 126, 127 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering

### Unit 13 Review of Simple Beam Theory

MIT - 16.0 Fall, 00 Unit 13 Review of Simple Beam Theory Readings: Review Unified Engineering notes on Beam Theory BMP 3.8, 3.9, 3.10 T & G 10-15 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics

### Chapter 12 Elastic Stability of Columns

Chapter 12 Elastic Stability of Columns Axial compressive loads can cause a sudden lateral deflection (Buckling) For columns made of elastic-perfectly plastic materials, P cr Depends primarily on E and

### Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012

Lecture Slides Chapter 4 Deflection and Stiffness The McGraw-Hill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration

### 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

### Accordingly, the nominal section strength [resistance] for initiation of yielding is calculated by using Equation C-C3.1.

C3 Flexural Members C3.1 Bending The nominal flexural strength [moment resistance], Mn, shall be the smallest of the values calculated for the limit states of yielding, lateral-torsional buckling and distortional

### 9.1 Introduction to bifurcation of equilibrium and structural

Module 9 Stability and Buckling Readings: BC Ch 14 earning Objectives Understand the basic concept of structural instability and bifurcation of equilibrium. Derive the basic buckling load of beams subject

### ME 354, MECHANICS OF MATERIALS LABORATORY COMPRESSION AND BUCKLING

ME 354, MECHANICS OF MATERIALS LABATY COMPRESSION AND BUCKLING PURPOSE 01 January 2000 / mgj The purpose of this exercise is to study the effects of end conditions, column length, and material properties

### Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6.2, 6.3

M9 Shafts: Torsion of Circular Shafts Reading: Crandall, Dahl and Lardner 6., 6.3 A shaft is a structural member which is long and slender and subject to a torque (moment) acting about its long axis. We

### Mechanics of Materials Primer

Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus

### EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 10 Columns

EMA 370 Mechanics & Materials Science (Mechanics of Materials) Chapter 10 Columns Columns Introduction Columns are vertical prismatic members subjected to compressive forces Goals: 1. Study the stability

### Lecture 15 Strain and stress in beams

Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME

### INFLUENCE OF FLANGE STIFFNESS ON DUCTILITY BEHAVIOUR OF PLATE GIRDER

International Journal of Civil Structural 6 Environmental And Infrastructure Engineering Research Vol.1, Issue.1 (2011) 1-15 TJPRC Pvt. Ltd.,. INFLUENCE OF FLANGE STIFFNESS ON DUCTILITY BEHAVIOUR OF PLATE

### March 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE

Chapter 4 Deflection and Stiffness 1 2 Chapter Outline Spring Rates Tension, Compression, and Torsion Deflection Due to Bending Beam Deflection Methods Beam Deflections by Superposition Strain Energy Castigliano

### NON LINEAR BUCKLING OF COLUMNS Dr. Mereen Hassan Fahmi Technical College of Erbil

Abstract: NON LINEAR BUCKLING OF COLUMNS Dr. Mereen Hassan Fahmi Technical College of Erbil The geometric non-linear total potential energy equation is developed and extended to study the behavior of buckling

### Laboratory 4 Topic: Buckling

Laboratory 4 Topic: Buckling Objectives: To record the load-deflection response of a clamped-clamped column. To identify, from the recorded response, the collapse load of the column. Introduction: Buckling

### Lecture 4 Honeycombs Notes, 3.054

Honeycombs-In-plane behavior Lecture 4 Honeycombs Notes, 3.054 Prismatic cells Polymer, metal, ceramic honeycombs widely available Used for sandwich structure cores, energy absorption, carriers for catalysts

### Optimization of Thin-Walled Beams Subjected to Bending in Respect of Local Stability and Strenght

Mechanics and Mechanical Engineering Vol. 11, No 1 (2007) 37 48 c Technical University of Lodz Optimization of Thin-Walled Beams Subjected to Bending in Respect of Local Stability and Strenght Tadeusz

### Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties

Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties DR. ŞEREF DOĞUŞCAN AKBAŞ Civil Engineer, Şehit Muhtar Mah. Öğüt Sok. No:2/37, 34435 Beyoğlu- Istanbul,

### ENG2000 Chapter 7 Beams. ENG2000: R.I. Hornsey Beam: 1

ENG2000 Chapter 7 Beams ENG2000: R.I. Hornsey Beam: 1 Overview In this chapter, we consider the stresses and moments present in loaded beams shear stress and bending moment diagrams We will also look at

OPTI Buckling Buckling and Stability: As we learned in the previous lectures, structures may fail in a variety of ways, depending on the materials, load and support conditions. We had two primary concerns:

### ENCE 455 Design of Steel Structures. III. Compression Members

ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland Compression Members Following subjects are covered:

### 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

### On Nonlinear Buckling and Collapse Analysis using Riks Method

Visit the SIMULIA Resource Center for more customer examples. On Nonlinear Buckling and Collapse Analysis using Riks Method Mingxin Zhao, Ph.D. UOP, A Honeywell Company, 50 East Algonquin Road, Des Plaines,

### UNIT- I Thin plate theory, Structural Instability:

UNIT- I Thin plate theory, Structural Instability: Analysis of thin rectangular plates subject to bending, twisting, distributed transverse load, combined bending and in-plane loading Thin plates having

### 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

### STRUCTURAL SURFACES & FLOOR GRILLAGES

STRUCTURAL SURFACES & FLOOR GRILLAGES INTRODUCTION Integral car bodies are 3D structures largely composed of approximately subassemblies- SSS Planar structural subassemblies can be grouped into two categories

### Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7

Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...

### BEAMS AND PLATES ANALYSIS

BEAMS AND PLATES ANALYSIS Automotive body structure can be divided into two types: i. Frameworks constructed of beams ii. Panels Classical beam versus typical modern vehicle beam sections Assumptions:

### MODULE C: COMPRESSION MEMBERS

MODULE C: COMPRESSION MEMBERS This module of CIE 428 covers the following subjects Column theory Column design per AISC Effective length Torsional and flexural-torsional buckling Built-up members READING:

### five Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2017 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS

### Longitudinal buckling of slender pressurised tubes

Fluid Structure Interaction VII 133 Longitudinal buckling of slender pressurised tubes S. Syngellakis Wesse Institute of Technology, UK Abstract This paper is concerned with Euler buckling of long slender

### ε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram

CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case

### COLUMNS: BUCKLING (DIFFERENT ENDS)

COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pin-connected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43

### Compression Members. ENCE 455 Design of Steel Structures. III. Compression Members. Introduction. Compression Members (cont.)

ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland Compression Members Following subjects are covered:

### 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

### Unit III Theory of columns. Dr.P.Venkateswara Rao, Associate Professor, Dept. of Civil Engg., SVCE, Sriperumbudir

Unit III Theory of columns 1 Unit III Theory of Columns References: Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength of Materials", Tata

### 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:

### 2766. Differential quadrature method (DQM) for studying initial imperfection effects and pre- and post-buckling vibration of plates

2766. Differential quadrature method (DQM) for studying initial imperfection effects and pre- and post-buckling vibration of plates Hesam Makvandi 1, Shapour Moradi 2, Davood Poorveis 3, Kourosh Heidari

### Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

### Chapter 4 Deflection and Stiffness

Chapter 4 Deflection and Stiffness Asst. Prof. Dr. Supakit Rooppakhun Chapter Outline Deflection and Stiffness 4-1 Spring Rates 4-2 Tension, Compression, and Torsion 4-3 Deflection Due to Bending 4-4 Beam

### 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

### Chapter 6: Cross-Sectional Properties of Structural Members

Chapter 6: Cross-Sectional Properties of Structural Members Introduction Beam design requires the knowledge of the following. Material strengths (allowable stresses) Critical shear and moment values Cross

### SERVICEABILITY OF BEAMS AND ONE-WAY SLABS

CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach - Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONE-WAY SLABS A. J. Clark School of Engineering Department of Civil

### Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 17

Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil engineering Indian Institute of Technology, Madras Module - 01 Lecture - 17 In the last class, we were looking at this general one-dimensional

### CHAPTER 5. Beam Theory

CHPTER 5. Beam Theory SangJoon Shin School of Mechanical and erospace Engineering Seoul National University ctive eroelasticity and Rotorcraft Lab. 5. The Euler-Bernoulli assumptions One of its dimensions

### MATERIALS. Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle?

MATERIALS Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: A. Composition

### LINEAR AND NONLINEAR BUCKLING ANALYSIS OF STIFFENED CYLINDRICAL SUBMARINE HULL

LINEAR AND NONLINEAR BUCKLING ANALYSIS OF STIFFENED CYLINDRICAL SUBMARINE HULL SREELATHA P.R * M.Tech. Student, Computer Aided Structural Engineering, M A College of Engineering, Kothamangalam 686 666,

### to introduce the principles of stability and elastic buckling in relation to overall buckling, local buckling

to introduce the principles of stability and elastic buckling in relation to overall buckling, local buckling In the case of elements subjected to compressive forces, secondary bending effects caused by,

### How materials work. Compression Tension Bending Torsion

Materials How materials work Compression Tension Bending Torsion Elemental material atoms: A. Composition a) Nucleus: protons (+), neutrons (0) b) Electrons (-) B. Neutral charge, i.e., # electrons = #

### Experimental investigation on monotonic performance of steel curved knee braces for weld-free beam-to-column connections

Experimental investigation on monotonic performance of steel curved knee braces for weld-free beam-to-column connections *Zeyu Zhou 1) Bo Ye 2) and Yiyi Chen 3) 1), 2), 3) State Key Laboratory of Disaster

### Bending of Simply Supported Isotropic and Composite Laminate Plates

Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,

### Computational Analysis for Composites

Computational Analysis for Composites Professor Johann Sienz and Dr. Tony Murmu Swansea University July, 011 The topics covered include: OUTLINE Overview of composites and their applications Micromechanics

### Johns Hopkins University What is Engineering? M. Karweit MATERIALS

Why do things break? Why are some materials stronger than others? Why is steel tough? Why is glass brittle? What is toughness? strength? brittleness? Elemental material atoms: MATERIALS A. Composition

### ANALYSIS OF THE INTERACTIVE BUCKLING IN STIFFENED PLATES USING A SEMI-ANALYTICAL METHOD

EUROSTEEL 2014, September 10-12, 2014, Naples, Italy ANALYSIS OF THE INTERACTIVE BUCKLING IN STIFFENED PLATES USING A SEMI-ANALYTICAL METHOD Pedro Salvado Ferreira a, Francisco Virtuoso b a Polytechnic

### Esben Byskov. Elementary Continuum. Mechanics for Everyone. With Applications to Structural Mechanics. Springer

Esben Byskov Elementary Continuum Mechanics for Everyone With Applications to Structural Mechanics Springer Contents Preface v Contents ix Introduction What Is Continuum Mechanics? "I Need Continuum Mechanics

### Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

### 7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment

7.6 Stress in symmetrical elastic beam transmitting both shear force and bending moment à It is more difficult to obtain an exact solution to this problem since the presence of the shear force means that

### INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad

NSTTUTE OF AERONAUTCAL ENGNEERNG (Autonomous) Dundigal, Hyderabad - 00 043 AERONAUTCAL ENGNEERNG TUTORAL QUESTON BANK Course Name : ARCRAFT VEHCLES STRUCTURES Course Code : A2109 Class : B. Tech Semester

### two structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS

APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture two structural analysis (statics & mechanics) Analysis 1 Structural Requirements strength serviceability

### needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods used to design concentric and eccentric columns.

CHAPTER OBJECTIVES Discuss the behavior of columns. Discuss the buckling of columns. Determine the axial load needed to buckle an ideal column. Analyze the buckling with bending of a column. Discuss methods

### Reports RESEARCH REPORT RP00-3 RESEARCH REPORT RP01-1 OCTOBER REVISION 2006 REVISION

research report A AISI Design Sponsored Approach Resear for ch Complex Reports AISI Sponsored Stiffeners Research Reports RESEARCH REPORT RP00-3 RP01-1 RESEARCH REPORT RP01-1 OCTOBER 2001 2000 REVISION

### 7.5 Elastic Buckling Columns and Buckling

7.5 Elastic Buckling The initial theory of the buckling of columns was worked out by Euler in 1757, a nice example of a theory preceding the application, the application mainly being for the later invented

### A study of the critical condition of a battened column and a frame by classical methods

University of South Florida Scholar Commons Graduate Theses and Dissertations Graduate School 003 A study of the critical condition of a battened column and a frame by classical methods Jamal A.H Bekdache

### Chapter 3. Load and Stress Analysis

Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3

### BUCKLING OF VARIABLE CROSS-SECTIONS COLUMNS IN THE BRACED AND SWAY PLANE FRAMES

ROCZNIKI INŻYNIERII BUDOWLANEJ ZESZYT 16/016 Komisja Inżynierii Budowlanej Oddział Polskiej Akademii Nauk w Katowicach BUCKLING OF VARIABLE CROSS-SECTIONS COLUMNS IN THE BRACED AND SWAY PLANE FRAMES Ružica

### 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

Buckling of Columns Buckling of Columns Critical Load Some member may be subjected to compressive loadings, and if these members are long enough to cause the member to deflect laterally or sideway. To

### An Increase in Elastic Buckling Strength of Plate Girder by the Influence of Transverse Stiffeners

GRD Journals- Global Research and Development Journal for Engineering Volume 2 Issue 6 May 2017 ISSN: 2455-5703 An Increase in Elastic Buckling Strength of Plate Girder by the Influence of Transverse Stiffeners

### COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5

COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4017 COURSE CATEGORY : A PERIODS/WEEK : 6 PERIODS/ SEMESTER : 108 CREDITS : 5 TIME SCHEDULE MODULE TOPICS PERIODS 1 Simple stresses

### Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2

Lecture M1 Slender (one dimensional) Structures Reading: Crandall, Dahl and Lardner 3.1, 7.2 This semester we are going to utilize the principles we learnt last semester (i.e the 3 great principles and

### Automatic Scheme for Inelastic Column Buckling

Proceedings of the World Congress on Civil, Structural, and Environmental Engineering (CSEE 16) Prague, Czech Republic March 30 31, 2016 Paper No. ICSENM 122 DOI: 10.11159/icsenm16.122 Automatic Scheme

### Comparison of Euler Theory with Experiment results

Comparison of Euler Theory with Experiment results Limitations of Euler's Theory : In practice the ideal conditions are never [ i.e. the strut is initially straight and the end load being applied axially

### Basic principles of steel structures. Dr. Xianzhong ZHAO

Basic principles of steel structures Dr. Xianzhong ZHAO.zhao@mail.tongji.edu.cn www.sals.org.cn 1 Introduction Resistance of cross-section Compression members Outlines Overall stabilit of uniform (solid

### UNIVERSITY OF SASKATCHEWAN ME MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich

UNIVERSITY OF SASKATCHEWAN ME 313.3 MECHANICS OF MATERIALS I FINAL EXAM DECEMBER 13, 2008 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS For Marker s Use Only LAST NAME (printed): FIRST

### MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

### NUMERICAL EVALUATION OF THE ROTATIONAL CAPACITY OF STEEL BEAMS AT ELEVATED TEMPERATURES

8 th GRACM International Congress on Computational Mechanics Volos, 12 July 15 July 2015 NUMERICAL EVALUATION OF THE ROTATIONAL CAPACITY OF STEEL BEAMS AT ELEVATED TEMPERATURES Savvas Akritidis, Daphne

### 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

### Design of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar

5.4 Beams As stated previousl, the effect of local buckling should invariabl be taken into account in thin walled members, using methods described alread. Laterall stable beams are beams, which do not

### 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

### Symmetric Bending of Beams

Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications

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

### BUCKLING STRENGTH ANALYSIS OF BARS AND FRAMES, AND SPHERICAL SHELLS

CLASSIFICATION NOTES No. 30.1 BUCKLING STRENGTH ANALYSIS OF BARS AND FRAMES, AND SPHERICAL SHELLS APRIL 004 Veritasveien 1, NO-13 Høvik, Norway Tel.: +47 67 57 99 00 Fax: +47 67 57 99 11 FOREWORD is an

### Some Aspects Of Dynamic Buckling of Plates Under In Plane Pulse Loading

Mechanics and Mechanical Engineering Vol. 12, No. 2 (2008) 135 146 c Technical University of Lodz Some Aspects Of Dynamic Buckling of Plates Under In Plane Pulse Loading Katarzyna Kowal Michalska, Rados

### Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics)

Week 7, 14 March Mechanics in Energy Resources Engineering - Chapter 5 Stresses in Beams (Basic topics) Ki-Bok Min, PhD Assistant Professor Energy Resources Engineering i Seoul National University Shear

### CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR

CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR 2014-2015 UNIT - 1 STRESS, STRAIN AND DEFORMATION OF SOLIDS PART- A 1. Define tensile stress and tensile strain. The stress induced

### 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.

### 3. BEAMS: STRAIN, STRESS, DEFLECTIONS

3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets

### : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE

COURSE TITLE : APPLIED MECHANICS & STRENGTH OF MATERIALS COURSE CODE : 4021 COURSE CATEGORY : A PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 75 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Simple stresses

### KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV

KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Subject code/name: ME2254/STRENGTH OF MATERIALS Year/Sem:II / IV UNIT I STRESS, STRAIN DEFORMATION OF SOLIDS PART A (2 MARKS)

### Part D: Frames and Plates

Part D: Frames and Plates Plane Frames and Thin Plates A Beam with General Boundary Conditions The Stiffness Method Thin Plates Initial Imperfections The Ritz and Finite Element Approaches A Beam with

### A *69>H>N6 #DJGC6A DG C<>C::G>C<,8>:C8:H /DA 'D 2:6G - ( - ) +"' ( + -"( (' (& -+" % '('%"' +"-2 ( -!"',- % )% -.C>K:GH>IN D; AF69>HH>6,-+

The primary objective is to determine whether the structural efficiency of plates can be improved with variable thickness The large displacement analysis of steel plate with variable thickness at direction

### Unit M1.5 Statically Indeterminate Systems

Unit M1.5 Statically Indeterminate Systems Readings: CDL 2.1, 2.3, 2.4, 2.7 16.001/002 -- Unified Engineering Department of Aeronautics and Astronautics Massachusetts Institute of Technology LEARNING OBJECTIVES

### Finite Element Modelling with Plastic Hinges

01/02/2016 Marco Donà Finite Element Modelling with Plastic Hinges 1 Plastic hinge approach A plastic hinge represents a concentrated post-yield behaviour in one or more degrees of freedom. Hinges only

### 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

### A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,

### MECHANICS OF SOLIDS. (For B.E. Mechanical Engineering Students) As per New Revised Syllabus of APJ Abdul Kalam Technological University

MECHANICS OF SOLIDS (For B.E. Mechanical Engineering Students) As per New Revised Syllabus of APJ Abdul Kalam Technological University Dr. S.Ramachandran, M.E., Ph.D., Mr. V.J. George, M.E., Mr. S. Kumaran,

### Mechanics of Earthquakes and Faulting

Mechanics of Earthquakes and Faulting www.geosc.psu.edu/courses/geosc508 Overview Milestones in continuum mechanics Concepts of modulus and stiffness. Stress-strain relations Elasticity Surface and body