Buckling Analysis of RC Framed Structures with and Without Bracings

Total Page:16

File Type:pdf, Size:1020Kb

Load more

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 10 | Oct -2017 www.irjet.net p-ISSN: 2395-0072 Buckling Analysis of RC Framed Structures With and Without Bracings Sudha S Goudar1 , R.G.Talasadar2 1PG Student department of Civil engineering, B.L.D.E.A’s V.P. Dr P.G. Halakatti College of Engineering and Technology, Vijayapur. 2Associate Professor department of Civil engineering, B.L.D.E.A’s V.P. Dr P.G. Halakatti College of Engineering and Technology, Vijayapur.karnataka, India ---------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - In general, concrete braced reinforced concrete 1.1 Bracings frame is one of the structural systems used to resist buckling loads and buckling of multi-storey structures. The use of Different Story’s are selected like one-storey, three-storey, concrete bracing systems for strengthening buckling five-storey and Ten-storey three bays frames was chosen inadequate reinforced concrete frames is a viable solution for and five different bracing patterns and locations were enhancing buckling resistance. Concrete and steel is selected. Frame was modelled at Bay width as 4m and storey economical, easy to erect and flexible to design for meeting the height as 3.5m. Bracing patterns include single Diagonal, required strength and stiffness. A numerical method for the double diagonal (X), Chevron inverted V, K and V bracings. solution of the elastic stability of fixed frames is presented and the procedure to perform elastic buckling analysis for frame in 1.2 Shear wall use computing buckling loads and buckling modes in frames with fixed columns. For resistance of the earthquake forces shear wall frames and concrete braced frames structural systems used. In this study buckling analysis of reinforced concrete building Generally Reinforced Concrete shear walls have been used as with different types of bracings V, inverted V, X, Diagonal and main lateral load opposing framework in medium & tall K type, bare frame, P-Delta effect, slenderness ratio, and shear structures on account of their high lateral unbending nature. walls studied. The method is illustrated in detail for different cases of single storey, three storey, five storey and ten storey 1.3 Slenderness ratio buildings is analysed for buckling using ETABS, one and three storeys buildings is analysed for buckling using ANSYS Slenderness ratio is the proportion length of a column and software. Comparing the both software’s values, the bracing minimum range of gyration of its cross area shaped by a system improves not only the stiffness capacity but also the plane. If the slenderness ratio is smaller than (kl/r) min buckling of the structure. The main parameters considered are failure happens by crushing. If the slenderness proportion is buckling factor, p-delta effect, slenderness ratio and shear more than (kl/r) min failure happens by buckling, deflection wall. load or stress diminishing for more slenderness. Key Words: Buckling analysis of the structure using 1.4 P-Delta ETABS and ANSYS, performance of slenderness ratio, shear wall, P-delta, stiffness, Bracings. They are second order impacts which increases raise the deformations, member's method for movement and extend 1. INTRODUCTION the effective fundamental period of the structure. P-delta effects in structure may be restrained by increasing its sidely Buckling concept of restrained braces was first introduced rigidity, increasing its strength or by combining of those two. by Wakabayashi in 1973. Buckling can be defined as The basic concept of critical buckling load Pcr the structure 2. MODELLING encounters sudden failure when subjected to compressive load and its length requests of size are greater than both of When considering the presents study, an attempt is made to its separate measurements such a column is known as a quantify the influence of Buckling analysis of RC framed section. we can see there are 2 types of the frames regard to structure With bracing and Without bracing. and its possible side sway where side sway prevented and frames with side to strengthen using shear wall, slenderness ratio, P-Delta sway permitted. In first type of the frame The buckling takes effect and stiffness. For this purpose typical 1,3, 5 and 10 place when the applied load P is equal to critical Pcr storey structures are modelled & analysed using ETABS and columns, and at the top end column is flexibly limited by ANSYS software. beam to which the column is firmly associated, and the critical load of the section depends not only on the column stiffness, additionally depend on rigidity of the beam. © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 607 International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 10 | Oct -2017 www.irjet.net p-ISSN: 2395-0072 Table -1: Structural details of the model The analysis is carried out for the bare frame as well as for the braced frames by considering X, V , K, Diagonal,Inverted Number of storey 1,3,5 and 10 V type bracing, slenderness ratio, shear wall, Stiffness and p delta effect for the same model configuration described Storey height 3.5m above. The regular building elevation views with different Number of Bays 3 bays in both types of bracings are shown. directions Spacing of Bays 4 m in both direction 2.2 By using ANSYS Beam Size 230x450 mm Column size 500x500 mm Bracing size 300x300 mm Grade of Materials M25 and Fe 500 Slab Thickness 150mm Load Considered (Dead load 8.2 kN/m2 + Floor finish + Live load ) 2.1 Using ETABS Software Fig-3 Bare model, Diagonal, K type bracing models using Finite element method by using ANSYS Software. The bare frame models considered are described as following Similarly models are prepared for the 1, 3, 5 storeys and 10 storeys. A finite element buckling study determines the lowest buckling factors and their corresponding buckling modes. The bare frame models of 5 different configurations such as Regular, one, three, five and ten are analyzed. Later X, V, Diagonal, V, Inverted V and K bracings are applied to strengthen the structures. The results are compared for structures with and without bracings for 3 storeys structures of all models. The results are basically compared to find which type of bracing will be more effective for different regular structures. Fig-1 Shows models of Regular building without bracing 1, 3, 5 and 10 storeys structures. Buckling Analysis of frames Analytic buckling studies identify additional classes of instability besides Euler buckling. They include lateral buckling, torsion buckling, and other buckling modes. A finite element buckling study determines the lowest buckling factors and their corresponding modes.A buckling, or stability, analysis is an Eigen problem. The size of the scalar Eigen value is known as the “buckling load factor”. The processed displacement Eigen vector is referred to as the "buckling mode" or mode shape. The results of analysis compared include P-delta, slenderness ratio, Stiffness and Buckling of the structures with bracing and without bracings. Fig-2 Shows models of Regular building with bracing 1, 3, 5 and 10 storeys structures, and 3D model of shear wall. © 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 608 International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 04 Issue: 10 | Oct -2017 www.irjet.net p-ISSN: 2395-0072 Table-3 Buckling factor values for storey 3 Buckling 1 2 3 4 5 mode Storey 3 26.686 38.557 79.223 160.2 175.06 The columns sizes for three storey structures considered C300x300. The above graphs shows variations of buckling Fig-4 3D models of buckling modes (first buckling modes factor for different modes. Number of stories increases the of models with bracing and without bracings) buckling factor goes on decreases. Similarly buckling modes for diagonal, X, K, Inverted V type of storey 3 bracings for different stories. 1200 1000 800 2.3 Buckling modes of 3 storey structures by using ANSYS 600 C500x500 400 buckling factor 200 0 Bare f rame diagonal v bracing x bracing inverted v bracing Fig-7 bracing v/s buckling factor. Table-4 Variations of buckling modes values for 3 stroreys. for different bracings by using ETABS software Bare Inv V V X Diagonal K 100.753 942.67 369.979 421.508 726.077 286.075 Fig-5 first buckling modes of 3 storey structures Type of bracing system as lateral load resisting system, Table-2 Variations of buckling modes values for 3 stroreys material of bracing system also increases the stiffness and structures. ductility of the structure. Bracing system is good practice of scheme for high rise RCC structures to strengthen against Bare X Diagonal K buckling. So it can be concluded that Inverted V bracing model system is good practice for implementation in high rise 61.888 327.27 206.96 347.24 structures and reduces the damages in RCC structures during lateral load resisting capacity of the structures. Results of the buckling analysis were compared between the ETABS and ANSYS the variations of buckling factor for bare Mode 1 model 38%, X bracing 22%, K bracing 17% and diagonal 2500 2000 bracing 39%. The average difference between both software 1500 Without shear w all With shear w all values is 25%. 1000 BucklingFactor 500 Similarly the buckling factor results are calculated for one, 0 Storey 1 Storey 3 Storey 5 Storey 10 five and ten storey by using ETABS and buckling factor is Number of Stories calculated for one and three storey using ANSYS. Fig-8 comparison of without shear walls and with shear 2.4 Graphical representation of buckling factor values walls for different stories.
Recommended publications
  • The Effect of Yield Strength on Inelastic Buckling of Reinforcing

    The Effect of Yield Strength on Inelastic Buckling of Reinforcing

    Mechanics and Mechanical Engineering Vol. 14, No. 2 (2010) 247{255 ⃝c Technical University of Lodz The Effect of Yield Strength on Inelastic Buckling of Reinforcing Bars Jacek Korentz Institute of Civil Engineering University of Zielona G´ora Licealna 9, 65{417 Zielona G´ora, Poland Received (13 June 2010) Revised (15 July 2010) Accepted (25 July 2010) The paper presents the results of numerical analyses of inelastic buckling of reinforcing bars of various geometrical parameters, made of steel of various values of yield strength. The results of the calculations demonstrate that the yield strength of the steel the bars are made of influences considerably the equilibrium path of the compressed bars within the range of postyielding deformations Comparative diagrams of structural behaviour (loading paths) of thin{walled sec- tions under investigation for different strain rates are presented. Some conclusions and remarks concerning the strain rate influence are derived. Keywords: Reinforcing bars, inelastic buckling, yield strength, tensil strength 1. Introduction The impact of some exceptional loads, e.g. seismic loads, on a structure may re- sult in the occurrence of post{critical states. Therefore the National Standards regulations for designing reinforced structures on seismically active areas e.g. EC8 [15] require the ductility of a structure to be examined on a cross{sectional level, and additionally, the structures should demonstrate a suitable level of global duc- tility. The results of the examinations of members of reinforced concrete structures show that inelastic buckling of longitudinal reinforcement bars occurs in the state of post{critical deformations, [1, 2, 4, 7], and in some cases it occurs yet within the range of elastic deformations [8].
  • Lecture 42: Failure Analysis – Buckling of Columns Joshua Pribe Fall 2019 Lecture Book: Ch

    Lecture 42: Failure Analysis – Buckling of Columns Joshua Pribe Fall 2019 Lecture Book: Ch

    ME 323 – Mechanics of Materials Lecture 42: Failure analysis – Buckling of columns Joshua Pribe Fall 2019 Lecture Book: Ch. 18 Stability and equilibrium What happens if we are in a state of unstable equilibrium? Stable Neutral Unstable 2 Buckling experiment There is a critical stress at which buckling occurs depending on the material and the geometry How do the material properties and geometric parameters influence the buckling stress? 3 Euler buckling equation Consider static equilibrium of the buckled pinned-pinned column 4 Euler buckling equation We have a differential equation for the deflection with BCs at the pins: d 2v EI+= Pv( x ) 0 v(0)== 0and v ( L ) 0 dx2 The solution is: P P A = 0 v(s x) = Aco x+ Bsin x with EI EI PP Bsin L= 0 L = n , n = 1, 2, 3, ... EI EI 5 Effect of boundary conditions Critical load and critical stress for buckling: EI EA P = 22= cr L2 2 e (Legr ) 2 E cr = 2 (Lreg) I r = Pinned- Pinned- Fixed- where g Fixed- A pinned fixed fixed is the “radius of gyration” free LLe = LLe = 0.7 LLe = 0.5 LLe = 2 6 Modifications to Euler buckling theory Euler buckling equation: works well for slender rods Needs to be modified for smaller “slenderness ratios” (where the critical stress for Euler buckling is at least half the yield strength) 7 Summary L 2 E Critical slenderness ratio: e = r 0.5 gYc Euler buckling (high slenderness ratio): LL 2 E EI If ee : = or P = 2 rr cr 2 cr L2 gg c (Lreg) e Johnson bucklingI (low slenderness ratio): r = 2 g Lr LLeeA ( eg) If : =−1 rr cr2 Y gg c 2 Lr ( eg)c with radius of gyration 8 Summary Effective length from the boundary conditions: Pinned- Pinned- Fixed- LL= LL= 0.7 FixedLL=- 0.5 pinned fixed e fixede e LL= 2 free e 9 Example 18.1 Determine the critical buckling load Pcr of a steel pipe column that has a length of L with a tubular cross section of inner radius ri and thickness t.
  • 28 Combined Bending and Compression

    28 Combined Bending and Compression

    CE 479 Wood Design Lecture Notes JAR Combined Bending and Compression (Sec 7.12 Text and NDS 01 Sec. 3.9) These members are referred to as beam-columns. The basic straight line interaction for bending and axial tension (Eq. 3.9-1, NDS 01) has been modified as shown in Section 3.9.2 of the NDS 01, Eq. (3.9-3) for the case of bending about one or both principal axis and axial compression. This equation is intended to represent the following conditions: • Column Buckling • Lateral Torsional Buckling of Beams • Beam-Column Interaction (P, M). The uniaxial compressive stress, fc = P/A, where A represents the net sectional area as per 3.6.3 28 CE 479 Wood Design Lecture Notes JAR The combination of bending and axial compression is more critical due to the P-∆ effect. The bending produced by the transverse loading causes a deflection ∆. The application of the axial load, P, then results in an additional moment P*∆; this is also know as second order effect because the added bending stress is not calculated directly. Instead, the common practice in design specifications is to include it by increasing (amplification factor) the computed bending stress in the interaction equation. 29 CE 479 Wood Design Lecture Notes JAR The most common case involves axial compression combined with bending about the strong axis of the cross section. In this case, Equation (3.9-3) reduces to: 2 ⎡ fc ⎤ fb1 ⎢ ⎥ + ≤ 1.0 F' ⎡ ⎛ f ⎞⎤ ⎣ c ⎦ F' 1 − ⎜ c ⎟ b1 ⎢ ⎜ F ⎟⎥ ⎣ ⎝ cE 1 ⎠⎦ and, the amplification factor is a number greater than 1.0 given by the expression: ⎛ ⎞ ⎜ ⎟ ⎜ 1 ⎟ Amplification factor for f = b1 ⎜ ⎛ f ⎞⎟ ⎜1 − ⎜ c ⎟⎟ ⎜ ⎜ F ⎟⎟ ⎝ ⎝ E 1 ⎠⎠ 30 CE 479 Wood Design Lecture Notes JAR Example of Application: The general interaction formula reduces to: 2 ⎡ fc ⎤ fb1 ⎢ ⎥ + ≤ 1.0 F' ⎡ ⎛ f ⎞⎤ ⎣ c ⎦ F' 1 − ⎜ c ⎟ b1 ⎢ ⎜ F ⎟⎥ ⎣ ⎝ cE 1 ⎠⎦ where: fc = actual compressive stress = P/A F’c = allowable compressive stress parallel to the grain = Fc*CD*CM*Ct*CF*CP*Ci Note: that F’c includes the CP adjustment factor for stability (Sec.
  • “Linear Buckling” Analysis Branch

    “Linear Buckling” Analysis Branch

    Appendix A Eigenvalue Buckling Analysis 16.0 Release Introduction to ANSYS Mechanical 1 © 2015 ANSYS, Inc. February 27, 2015 Chapter Overview In this Appendix, performing an eigenvalue buckling analysis in Mechanical will be covered. Mechanical enables you to link the Eigenvalue Buckling analysis to a nonlinear Static Structural analysis that can include all types of nonlinearities. This will not be covered in this section. We will focused on Linear buckling. Contents: A. Background On Buckling B. Buckling Analysis Procedure C. Workshop AppA-1 2 © 2015 ANSYS, Inc. February 27, 2015 A. Background on Buckling Many structures require an evaluation of their structural stability. Thin columns, compression members, and vacuum tanks are all examples of structures where stability considerations are important. At the onset of instability (buckling) a structure will have a very large change in displacement {x} under essentially no change in the load (beyond a small load perturbation). F F Stable Unstable 3 © 2015 ANSYS, Inc. February 27, 2015 … Background on Buckling Eigenvalue or linear buckling analysis predicts the theoretical buckling strength of an ideal linear elastic structure. This method corresponds to the textbook approach of linear elastic buckling analysis. • The eigenvalue buckling solution of a Euler column will match the classical Euler solution. Imperfections and nonlinear behaviors prevent most real world structures from achieving their theoretical elastic buckling strength. Linear buckling generally yields unconservative results
  • Buckling Failure Boundary for Cylindrical Tubes in Pure Bending

    Buckling Failure Boundary for Cylindrical Tubes in Pure Bending

    Brigham Young University BYU ScholarsArchive Theses and Dissertations 2012-03-14 Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller Brigham Young University - Provo Follow this and additional works at: https://scholarsarchive.byu.edu/etd Part of the Mechanical Engineering Commons BYU ScholarsArchive Citation Miller, Daniel Peter, "Buckling Failure Boundary for Cylindrical Tubes in Pure Bending" (2012). Theses and Dissertations. 3131. https://scholarsarchive.byu.edu/etd/3131 This Thesis is brought to you for free and open access by BYU ScholarsArchive. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of BYU ScholarsArchive. For more information, please contact [email protected], [email protected]. Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller A thesis submitted to the faculty of Brigham Young University in partial fulfillment of the requirements for the degree of Master of Science Kenneth L. Chase, Chair Carl D. Sorenson Brian D. Jensen Department of Mechanical Engineering Brigham Young University April 2012 Copyright © 2012 Daniel P. Miller All Rights Reserved ABSTRACT Buckling Failure Boundary for Cylindrical Tubes in Pure Bending Daniel Peter Miller Department of Mechanical Engineering Master of Science Bending of thin-walled tubing to a prescribed bend radius is typically performed by bending it around a mandrel of the desired bend radius, corrected for spring back. By eliminating the mandrel, costly setup time would be reduced, permitting multiple change of radius during a production run, and even intermixing different products on the same line. The principal challenge is to avoid buckling, as the mandrel and shoe are generally shaped to enclose the tube while bending.
  • Column Analysis and Design

    Column Analysis and Design

    Chapter 9: Column Analysis and Design Introduction Columns are usually considered as vertical structural elements, but they can be positioned in any orientation (e.g. diagonal and horizontal compression elements in a truss). Columns are used as major elements in trusses, building frames, and sub-structure supports for bridges (e.g. piers). • Columns support compressive loads from roofs, floors, or bridge decks. • Columns transmit the vertical forces to the foundations and into the subsoil. The work of a column is simpler than the work of a beam. • The loads applied to a column are only axial loads. • Loads on columns are typically applied at the ends of the member, producing axial compressive stresses. • However, on occasion the loads acting on a column can include axial forces, transverse forces, and bending moments (e.g. beam-columns). Columns are defined by the length between support ends. • Short columns (e.g. footing piers). • Long columns (e.g. bridge and freeway piers). Virtually every common construction material is used for column construction. • Steel, timber, concrete (reinforced and pre-stressed), and masonry (brick, block, and stone). The selection of a particular material may be made based on the following. • Strength (material) properties (e.g. steel vs. wood). • Appearance (circular, square, or I-beam). • Accommodate the connection of other members. • Local production capabilities (i.e. the shape of the cross section). Columns are major structural components that significantly affect the building’s overall performance and stability. • Columns are designed with larger safety factors than other structural components. 9.1 • Failure of a joist or beam may be localized and may not severely affect the building’s integrity (e.g.
  • Local Buckling Analysis of Steel Truss Bridge Under Seismic Loading

    Local Buckling Analysis of Steel Truss Bridge Under Seismic Loading

    LOCAL BUCKLING ANALYSIS OF STEEL TRUSS BRIDGE UNDER SEISMIC LOADING Eiki Yamaguchi1, Keita Yamada2 Abstract In the 2004 Mid Niigata Prefecture Earthquake, a steel truss bridge was damaged: the lower chord member underwent local buckling. The axial force in that member is not necessarily compression-dominant: tensile axial force is also expected. Since many steel bridge piers were subjected to local buckling in the 1995 Kobe Earthquake, the criterion for local bucking in the member under axial compression has been studied rather extensively. However, the local buckling in the member under the other states of axial force has not. In the present study, the local buckling in the lower chord member of a truss bridge is to be looked into. To that end, the existing criterion for local buckling in terms of average strain is tested for the case when tensile yielding precedes compression, failing to confirm its applicability. Then the criterion is modified by introducing the updated average strain. The seismic response analysis is then conducted to show the significance of the proposed criterion. Introduction One of the largest earthquakes in the recorded history, the Tohoku Earthquake, just hit Japan in March, 2011, causing very serious damage in the eastern part of Japan. Yet the memory of the damage to structures in the 1995 Kobe Earthquake is still fresh and vivid for many structural engineers. Between the two large earthquakes, numerous earthquakes occurred as well, some of which were quite large and comparable to the 1995 Kobe Earthquake. The damage in each big earthquake has posed a new challenge for engineers; some of them are yet to be solved.
  • Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis

    Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis

    Impact of Ballast Fouling on the Mechanical Properties of Railway Ballast: Insights from Discrete Element Analysis By Luyu Wang Department of Civil Engineering and Applied Mechanics McGill University Montréal, Québec, Canada July 2020 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Master of Engineering © Luyu Wang, 2020 Abstract Ballast fouling is a major factor that contributes to the reduction of the shear strength of railway ballast, which can further influence the stability of railway equipment. Depending on the railway function and location, the major sources of ballast fouling are the infiltration of foreign fine material and ballast material degradation. The discrete element method (DEM) is an efficient way to capture the mechanical behavior of particles under various loading conditions. It has been successfully applied to investigate the mechanical behavior of ballast assembly and fouled ballast in the previous practices. In this study, a discrete element model is developed in PFC3D to simulate the stress-strain behavior of fresh ballast assembly tested in the direct shear test. A series of sensitivity analyses of the different parameters are conducted to better understand the corresponding effect on the stress- strain behavior of ballast assembly. An efficient approach to simulate the foreign material induced fouling of ballast and capture the mechanical behavior of the material at various levels of void contamination index (VCI) is proposed. The approach is based on the concept that the foreign fouling material will not only change the inter-particle friction angle but also the inter-particle contact stiffness. Therefore, both the effective modulus and the inter-particle friction coefficient are adjusted based on the validated fresh ballast contact model.
  • Residual Ultimate Buckling Strength of Steel Stiffened Panels Subjected

    Residual Ultimate Buckling Strength of Steel Stiffened Panels Subjected

    RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED TO CORROSION DAMAGE A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment Of the Requirements for the Degree Master of Science Elijah Fox May, 2017 RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED TO CORROSION DAMAGE Elijah Fox Thesis Approved: Accepted: Advisor Department Chair Dr. Anil Patnaik Dr. Wieslaw K. Binienda Committee Member Interim Dean of the College Dr. Craig Menzemer Dr. Donald J. Visco Committee Member Dean of the Graduate School Dr. Ping Yi Dr. Chand Midha Date 2 ACKNOWLEDGEMENTS I would like to thank my mother, Janice, and my siblings, Kivie and Nakita. Without my families support over all of these years, I would not have been able to complete my degree. My mother has always been strong and has taught me so many fundamentals which I live by; I just want to thank her for making me the man I am today. My family has always been so supportive, loving, and has done anything they could to help me succeed and because of this, I am forever grateful. I owe a special thank you to my amazing life partner, Marisa. She has been in my life since my first day of college and I would not have been able to make it without her love and support throughout these years. She is still by my side through all of the trials and tribulations life has thrown at me over the past seven years and words could not express how appreciative I am of all of her help.
  • Buckling Analysis of a Column

    Buckling Analysis of a Column

    Buckling Analysis of a Column Title Euler Buckling Analysis of a pin-ended column Description A column with both ends pinned has to be checked for buckling instability i) Find out the buckling mode shapes, ii) Find the critical buckling compressive load on the column Assume Column to be an I-section i.e. a Universal Column UC 203x203x60. The material of the column is S355 as per Eurocode. Height of the column, L= 5 m. Vertical Load acting on the column, P= 1000 kN. Structural geometry and analysis model 1 Finite Element Modelling: Analysis Type: 2-D static analysis (X-Z plane) Step 1: Go to File>New Project and then go to File>Save to save the project with any name Step 2: Go to Model>Structure Type to set the analysis mode to 2D (X-Z plane) Unit System: kN,m Step 3: Go to Tools>Unit System and change the units to kN and m. 2 Geometry generation: Step 4: Go to Model>Structure Wizard>Column and enter Distance as 0.50 m and Repeat times = 10. Press Add. This will create a column of height 5 m which is composed of 10 finite elements. A column should be divided into several finite elements before performing the buckling analysis in the software. Select pin as the boundary condition. Enter Material and Section ID as 1. Click OK. Switch to the Front view by clicking on as shown below. 3 Material: S355 (Eurocode). E=2.1x108 kN/m2 Step 7: Go to Model>Properties>Material>Add. Select Steel in the Type of Design and select Standard as EN(05)S.
  • Fracture, Delamination, and Buckling of Elastic Thin Films on Compliant Substrates

    Fracture, Delamination, and Buckling of Elastic Thin Films on Compliant Substrates

    FRACTURE, DELAMINATION, AND BUCKLING OF ELASTIC THIN FILMS ON COMPLIANT SUBSTRATES Haixia Mei, Yaoyu Pang, Se Hyuk Im, Rui Huang Department of Aerospace Engineering and Engineering Mechanics University of Texas at Austin 1 University Station, C0600 Austin, Texas 78712 Phone: (512) 471-7558 Fax: (512) 471-5500 Email: [email protected] ABSTRACT Greek symbols A series of studies have been conducted for mechanical fracture toughness (J/m2) behavior of elastic thin films on compliant substrates. Under first Dundurs parameter (dimensionless) tension, the film may fracture by growing channel cracks. The second Dundurs parameter (dimensionless) driving force for channel cracking (i.e., the energy release opening displacement (m) rate) increases significantly for compliant substrates. phase angle of mode mix (radian) Moreover, channel cracking may be accompanied by Poisson’s ratio (dimensionless) interfacial delamination. For a film on a relatively compliant 2 substrate, a critical interface toughness is predicted, which stress (N/m ) separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with Subscripts no delamination when the interface toughness is greater than a f film critical value. An effective energy release rate for the steady- i interface state growth of a channel crack is defined to account for the s substrate influence of interfacial delamination on both the fracture ss steady state driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. Alternatively, when the film is under compression, it tends to INTRODUCTION buckle. Two buckling modes have been observed, one with interfacial delamination (i.e., buckle-delamination) and the Integrated structures with mechanically soft components have other without delamination (i.e., wrinkling).
  • DNVGL-CG-0128 Buckling

    DNVGL-CG-0128 Buckling

    CLASS GUIDELINE DNVGL-CG-0128 Edition October 2015 Buckling The electronic pdf version of this document, available free of charge from http://www.dnvgl.com, is the officially binding version. DNV GL AS FOREWORD DNV GL class guidelines contain methods, technical requirements, principles and acceptance criteria related to classed objects as referred to from the rules. © DNV GL AS Any comments may be sent by e-mail to [email protected] If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of DNV GL, then DNV GL shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million. In this provision "DNV GL" shall mean DNV GL AS, its direct and indirect owners as well as all its affiliates, subsidiaries, directors, officers, employees, agents and any other acting on behalf of DNV GL. CHANGES – CURRENT This is a new document. Changes - current Class guideline — DNVGL-CG-0128. Edition October 2015 Page 3 Buckling DNV GL AS CONTENTS Changes – current...................................................................................................... 3 Contents Section 1 Introduction............................................................................................... 7 1 Objective.................................................................................................7 2 Buckling methods..................................................................................