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


 Jordan Cobb
 1 years ago
 Views:
Transcription
1 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: The present dissertation concerns the study of the effects of residual stresses in structures made from tubular hollow sections, specifically steel columns and an arch. It was performed a nonlinear geometrical analysis using the finite element software ABAQUS, in which the main purpose was to evaluate the effect of residual stresses caused by a longitudinal weld along the tube of the columns and the arch. This weld was made during the fabrication of the tube, in order to close the hollow section. The behavior of three columns was evaluated, with the same transversal section but different lengths (4 to 21 m). In this study, several different combinations of residual stresses and the geometrical imperfection were analysed, in order to find the worst cases and to compare them to Eurocode 3 equivalent imperfections. For the study of these effects on the arch was chosen a specific arch with a defined geometry where the variables were the position of the load in the arch, the symmetric and asymmetric loading, the position of the weld in the section and the residual stresses caused, and the geometrical imperfection. The results are compared with the Eurocode 3 equivalent geometrical imperfections. In the end, it was concluded that the residual stresses have an important role in the behavior of this kind of steel structures, and that specifically different positions of the longitudinal weld in relation to the loading and the geometrical imperfection can lead to different behaviors of the structure. Keywords: Column, Arch, Geometrical Imperfections, Residual Stresses. 1
2 1. Introduction and Objectives There are no structural components with a geometry that is exactly the same as the one that the designer conceived. Usually structural members that are assumed to be straight, have deviations from its conceptual axis. The existence of these deviations between the theoretical configurations of parts and their actual geometries justify that, under the current standards of design of steel structures, when assessing the conditions of security of any steel member whose sections are subject (wholly or partially) to compressive stresses, it has to be assumed that its geometry is not the theoretical one but a geometry that it is obtained by introducing the socalled initial geometric imperfections. By introducing such imperfections (or deviations between the theoretical geometry and the geometry of the part assessed), it is intended to take into account not only the possibility of the member being more sensitive to compressive stresses, as well as the existence of the residual stresses and any heterogeneities in the material properties. The geometric imperfections set forth in standards take into account these factors: deviations between the theoretical and the actual geometry of the member and the material imperfections (residual stresses and heterogeneity of the mechanical properties). The principle followed for the definition of the first factor is to seek the actual geometry that produces the most unfavorable effects on its behavior, for example, for a linear compressed member, 2 the "imperfect" axis should have the geometry of the first buckling mode. The amplitude of the imperfections was established based in the results of sampling conducted in a large number of members and taking into account the tolerances specified in the standards for metal structures construction, of which the most wellknown is the EN1090. In regards to the residual stresses, they are converted into geometric imperfections that produce the same effects. Therefore, the standards set different amplitudes to the geometrical imperfection to be considered, according to the manufacturing process of the structural member, like hotrolled or welded components. Within each of these sets, there are also different values depending on the direction of inertia of the section. Residual stresses affect differently the buckling in different directions. It turns out that the regulations do not identify the specific value of each of the two parts of the equivalent geometric imperfections specified. Sometimes it is possible to know the real geometry of the structures before they become subjected to the loading, including of course the permanent actions. This is the case of structures that have secondary structures supporting them only during the assembly. By performing a rigorous survey of the geometry of these structures it is possible to determine the first component of the geometric imperfections. In such cases, which geometric imperfection should be added to the real one, to take into account the effects of residual stress? How important the residual stresses really are?
3 The results presented in this work are intended to help answering these questions. It is not the same for all cross sections and for all structural configurations; so this study concerns only the circular hollow sections, for columns first, and later to the case of a particular tubular arch with a large span. 2. Imperfections Like it was stated in the introduction, there are 2 kinds of imperfections: i) Geometric Imperfections:  Imperfections in the member axis, from its theoretical position (global geometrical imperfections).  Imperfections of the cross section, such as deviations in size and shape geometry (local geometrical imperfections). ii) Material heterogeneity:  Heterogeneity in the yield stress of the steel.  Existence of residual stresses resultant from the manufacturing process Global geometrical imperfections The manufacturing process of the linear elements introduces small random deviations between the real member axis and the theoretical straight axis. These deviations in the theoretical axis can assume a lot of different shapes, but, for simulation it is assumed as a single curvature direction (first buckling mode), with a maximum deflection which produces equivalent effects to the real imperfection. The real imperfection in columns has been studied, and it is assumed that a common value for it is L/1000. The same principle is applied to arches, the first buckling mode is introduced in the analysis as the geometrical imperfection to simulate the deviations in the geometry Local imperfections There are several local imperfections that can appear in circular hollow sections. This work focused only on the main ones, which are listed below:  Outofroundness (Figure 1) Figure 1  Outofroundness, [1]  Dimple imperfections (Figure 2) Figure 2  Dimple caused by a weld, [1] 2.3. Residual stresses The residual stresses found in every type of metal structure can be classified by the phase of the production process in which they appear. Such stresses can arise in the metallurgy (hotrolling, cutting, coldforming, welding) or during assembly of the structure (mainly by welding of the components, in order to assemble them). The causes of the appearance of residual stresses in steel products are: a) time of uneven cooling along the areas of the section, in the case of hotrolled profiles; b) high temperature (fusion of the steel) during the welding process and the temporary yielding of steel for members cold formed; 3
4 c) flamecutting; d) mechanical forming processes; and e) any treatment of steel. During the installation of metal structures, the welds between the elements of the structure are also a source of residual stresses. In simple cases there are methods to estimate the shape and magnitude of these residual stresses. This work aims to study the effect of the longitudinal welds in circular hollow section. Here is presented a way of estimating the residual stresses caused by welding. In Table 1, it is presented the initial bow imperfections proposed in Eurocode 3 for the columns. Table 1  Values of initial bow imperfections, [3] In the part 2 of Eurocode 3, the shape and amplitudes to be considered in plane buckling of arches in steel arch bridges, is presented. 3. Numerical analysis of columns Figure 3  Residual stresses caused by welding, [2], mm (1) A w cross sectional of added weld metal (mm 2 ) Ʃt sum of the plate thickness meeting at the weld (mm) σ r yield stress (MPa) p process efficiency factor 2.4. Equivalent imperfections In the methodology used in Eurocode 3, geometrical imperfections and residual stresses are taken into account by using the buckling curves that depend on the section s geometry and manufacturing process of that structural component. These curves are part of the effects of reductions in strength due to all the imperfections mentioned above, but with emphasis on the geometric imperfections and residual stresses Simulation overview ABAQUS software was used to simulate the effects of residual stresses in a circular tube of Class 4, which allows the performance of geometrically and materially nonlinear analyzes of finite element models. Several analyzes were performed using models with columns s r ss s r ss a r uc s r ss. It w s also carried out a stability analysis, in order to obtain the global and local modes of the columns to be introduced as the settings of the geometrical imperfections. The steel chosen for this analysis was the S355, which has a yield strength of 355 MPa, an elasticity modulus of 210 GPa and Poisson's ratio of 0.3. For simplicity, the perfect elasticplastic behavior of the material was assumed, with a limit of 15% for the ultimate strain. 4
5 The main properties of the cross section are summarized in Table 2. Table 2  Properties of the cross section Diameter D 500 mm Thickness t 8 mm Area A mm² Inertia I 3.93 mm 4 Radius of gyration i mm Normal resistance N pl kn To simulate the columns, finite elements type "S8R5" were used. These are shell elements of reduced thickness with 8 nodes, 5 degrees of freedom per node and reduced integration. The boundary conditions of the column are simply supported in the bottom section with the vertical displacement restrained, and the same for the upper section, but not restrained in the vertical direction. The torsional rotation was also restrained in both ends. The load is concentrated in the upper section with the gravity direction. The selfweight was not considered to simplify the analysis. The amplitude of the geometrical imperfections considered is summarized in Table 3. The local imperfection was obtained from the dimple imperfections. Table 3  Geometrical imperfections Equ v t I p. curv L/250 Equ v t I p. curv c L/150 Global imperfection L/1000 Local imperfection 3 mm The width of tensile residual stresses, caused by the weld, was estimated based on equation (1), and then introduced with the tensile stress of 355 MPa in the software that makes the equilibrium of the stresses, resulting in the diagram of the Figure 4. Figure 4  Residual stresses introduced in the cross section For the simulation of the columns, three relative positions between residual stresses (weld) and the plane of the global imperfection, were considered, and are represented in Figure 5, 6 and 7. Figure 5  Model A Figure 6  Model B Figure 7  Model C Several analyses were performed, combining the types of imperfections. These analyses are listed below: Model 0 No imperfection; Model 1  Global imperfection only (L/1000) 5
6 Model 2 Residual stresses only Model 3 Global and local imperfections Model 4 Geometrical imperfections and residual stresses Model 5 Equivalent imperfections from Eur c 3 curv L 5 curv c (L/150) 3.2. Results The results are presented in form of the ultimate normal resistance supported by the columns, and is summarized in Table 4. Table 4  Results of the analysis of columns L=4m L=14m L=21m Modelo N u (kn) N u (kn) N u (kn) Model Model Model Model Model 4  A Model 4  B Model 4  C Model 5  curve a Model 5  curve c Conclusions It seems evident that the residual stresses in tubular columns influence their ultimate strength. This influence can be favorable (increases in resistance) which occurs generally in the models A, in which the longitudinal weld is executed on the same side where the curvature of the global geometrical imperfection is considered. However it can often be unfavorable (decrease in resistance), as it is shown in the other models, in which there was a combination of the effects of eccentricities resulting from global geometric imperfection with the one resultant from the process of welding (residual stresses). It is possible to conclude that in columns in which the bearing capacity is conditioned by the occurrence of overall buckling  long columns  the design curve "c" proves to be suitable for design, even having in consideration the size of the sample analyzed. The same cannot be said about short columns, in which local buckling precedes the global. Another possible conclusion is that, the less slender is the column, the lower is the significance of the relative position of the residual stresses over the plane of initial curvature. This can be important because it allows greater predictability of the effects on short columns. 4. Numerical analysis of an arch 4.1. Introduction To understand the importance of the residual stresses on the strength and behavior of an arch it was used the ABAQUS software, as for the columns analyzed in the previous chapter. The program performs the geometrically nonlinear analysis of the behavior of the arch subjected to a set of predefined loads. The geometry of the arch was defined such that it may simulate, by its dimensions, an arch suspending cover of a stadium bench. This is the typical case of an arch that is fully supported until nearly all of the permanent loads are applied. These arches are usually supported, by temporary structures, throughout its length until the whole structure of the cover is assembled. The loads were also representative of the loads existent in the cover of a stadium. 6
7 These loads are transmitted to the arch through hangers, consequently, the permanent loads have two parts: i) concentrated loads applied by vertical hangers; ii) the weight of the arch tube, that is a load distributed over its length. The variable action considered has an intensity of 0.3 kn/m 2. Finally it should be noted that the configuration chosen for the axis of the arc is such that it approximately corresponds to the antifunicular of permanent loads. It is not exactly the antifunicular of the permanent loads, because in the case of an arch made with 2.0 meters of diameter tube, it must be manufactured with straight segments which are then welded to each t r s. For this reason, small bending moments arise in the sections of the arch, even only with permanent loads. The analysis refers only to the behavior of the arc in his plan Geometry and model The arch analysis is only made for inplane behavior. The axis of the arch is formed by a sequence of straight sections, with lengths from 6 m to 9.3 m. The properties of the arch are summarized in Table 5. Table 5  Properties of the arch (geometry, material and cross section) Geometry span m bow 31.4 m Material S355 Section (CHS) class 4 f y 355 Mpa D 2000 mm f u 490 Mpa t 30 mm E 210 GPa A mm 2 ε y 0.17% I 90.1x10 4 mm 4 ε u 2.54% N rd kn 0.3 M el,rd kn.m To simulate the arch, finite elements type "S8R5" were used, as in the columns. The arch boundary conditions consist of restraining the displacements in all directions, in both ends. The amplitude of the geometrical imperfections considered is summarized in Table 6. The local imperfections were not considered. Table 6  Global geometrical imperfections Equivalent L/ mm I p r ct curv Equivalent L/ mm I p r ct curv c Global imperfection L/ mm Figure 8  Pattern of residual stresses (MPa) The pattern of residual stresses originated during the longitudinal welding of the tube is represented in Figure 8. Five different positions of the weld in the cross section were considered, which are shown in Table 7. 7
8 Table 7  Positions of the weld in the section Weld position Diagram Position 1 Position 2 Position 3 Figure 91 st buckling mode (global geometrical imperfection) The study consisted in combining the several positions of residual stresses in the section, global imperfection and position of the variable load, and find out the resistance in each combination Results It is shown in Figure 10 the results for the load parameter in each case. The load parameter is the multiplicative factor of the variable load, which could be resisted by the structure. Position 4 Position 5 Another variable in the study was the positioning of the variable load in the arch, for which three positions were considered.. In the first case, the variable load is distributed along the whole length of the arch, the second in the left half and the third in the right half of the arch. The global geometrical imperfection was always introduced as it is shown in Figure 9, which corresponds to the geometry of the first buckling mode, so the variable load introduced in the left part leads to increases in the resistance, so it is not shown here. Figure 10  Results for the load parameter 4.4. Conclusions The first conclusion is that the stresses which produce the collapse of the tube are the compressions caused by bending. Whether bending is generated by asymmetric loads applied on the arch or the second order moments caused by compressive stresses in a geometry already deformed and asymmetric yield of the sections, with consequent variation of the neutral axis position. 8
9 Another important conclusion is that the position of the longitudinal weld is relevant to the strength of the arch. When the welding causes compressive residual stresses on the upper and lower parts of section, there are significant decreases in the overall resistance of the arc, since the bending moments yield these areas where there are compressive stresses, reducing considerably the rigidity and bending resistance, and increasing the eccentricities of second order. Despite this, it appears that the arch almost always behaves within the elastic range, except locally and for load levels near the ultimate load. Therefore, the collapse is always due to the loss of stability or the arch. Finally, it appears that the residual stresses represent a significant part of the initial imperfections that Eurocode 3 recommends for arches. The most adverse case found for the resistance is equivalent to a geometric imperfection of L/290 (763.8 mm). This means that the actual geometrical imperfections (L/1000) part is only 29%, while the effect of residual stresses is 71%. 5. Analysis of an arch with a stiffness beam 5.1. Introduction In the previous section we analyzed the structural behavior of a single arch. It is known that the load carrying capacity of the arch is very sensitive to factors causing bending moments, such as the asymmetric loads and/or the existence of asymmetric geometrical imperfections. 9 In general, the purpose of an arch is to support other secondary structures that work together with it. The stiffness of these structures, however minimal, can improve the behavior of the arches, mainly because it decreases the asymmetric displacements. Typical cases of the importance of flexural stiffness elements are the arch bridges. The higher the stiffness of the bridge deck, the smaller bending moments in the arch. The same situation happens in the coverage of large areas. The secondary structure can decisively contribute to the reduction of displacements in the arch where it is suspended. The objective of this part of the study is to evaluate the benefits that an element with relatively high bending stiffness can bring to the arch behavior and especially to its ultimate capacity. As a result of some research in projects carried out in arched covers of stadiums, it was decided to choose a stiffness beam whose bending stiffness is equal to half the bending stiffness of the arch Results The results for the load parameter are shown in Table 8. Table 8  Results for the load parameter In the Table 9, a comparison is made between the parts of each imperfection for the arch with and without the beam, with
10 the Eurocode recommended imperfections for the curv s c. Table 9  Importance of the two main imperfections in the equivalent imperfection 5.3. Conclusions The introduction of the stiffness beam benefits the behavior of the arc in terms of gaining strength and ductility. This benefit results from the redistribution of applied loads provided by the beam, which results in a considerable reduction of the values of the maximum bending moment. With the beam, the compressive stress increases and this causes larger yielded areas of material. The behavior changes from the elastic regime as it happened in general when the arch was simulated separately, to a more plastic behavior. This increase of the compressive stresses causes yield and local instability in the tubes, the undulation of the walls of the tube and the outroundness of the section. These effects turn out to be the cause of the failure for some of the cases studied. With regard to the load capacity of the arc, the residual stress pattern that simulates a longitudinal welding, along the lateral part of the section (positions 2 and 5), is more favorable, opposing to what was found when the arch was modeled isolated. The most unfavorable situation, with respect to the bearing capacity of the arch, is the weld made on top of the section of the tube (position 1), also the opposite of 10 what happened when the analysis was made without the beam. In general, the equivalent geometric imperfection established for the curve "c" in Part 2 of Eurocode 3 is a good simulation of the effects of real imperfections (geometrical and residual stresses) corresponding to an initial geometric imperfection of L/1000, plus the effects of residual stresses considered. Therefore, if the deformed geometry of the bow is known precisely, in theory, to simulate the effect of residual stress should be added to this an imperfection of L/667, which represents the difference between L/400 (equivalent imperfection) and L/1000 (real geometrical imperfection). An exception to the above stated is made, considering the results obtained in the model with residual stresses in the position 1, which has a continuous longitudinal weld at the top of the arch, in which the load parameter is lower than that obtained from the analysis results of the model with the equivalent geometrical imperfection corresponding to curve "c". For this case it is concluded that the appropriate equivalent imperfection is equal to L/365 (less than L/400 value of the curve "c"). Overall, it is confirmed that the part of global equivalent geometrical imperfections proposed by the Eurocode 3, which corresponds to the residual stresses, is higher than the part of real geometric imperfection.
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
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads
More informationExperimental 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 12, 2015, University of
More informationChapter 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 elasticperfectly plastic materials, P cr Depends primarily on E and
More informationAn 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: 24555703 An Increase in Elastic Buckling Strength of Plate Girder by the Influence of Transverse Stiffeners
More informationPES Institute of Technology
PES Institute of Technology Bangalore south campus, Bangalore5460100 Department of Mechanical Engineering Faculty name : Madhu M Date: 29/06/2012 SEM : 3 rd A SEC Subject : MECHANICS OF MATERIALS Subject
More informationQUESTION 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 informationSECTION 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 information3. Stability of builtup members in compression
3. Stability of builtup members in compression 3.1 Definitions Buildup members, made out by coupling two or more simple profiles for obtaining stronger and stiffer section are very common in steel structures,
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode 3 Module 7 : Worked Examples Lecture 20 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or builtin beams are commonly used in building construction because they possess high rigidity in comparison to simply supported beams. When a simply supported
More informationEngineering Science OUTCOME 1  TUTORIAL 4 COLUMNS
Unit 2: Unit code: QCF Level: Credit value: 15 Engineering Science L/601/10 OUTCOME 1  TUTORIAL COLUMNS 1. Be able to determine the behavioural characteristics of elements of static engineering systems
More informationFinite 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 postyield behaviour in one or more degrees of freedom. Hinges only
More informationFundamentals of Structural Design Part of Steel Structures
Fundamentals of Structural Design Part of Steel Structures Civil Engineering for Bachelors 133FSTD Teacher: Zdeněk Sokol Office number: B619 1 Syllabus of lectures 1. Introduction, history of steel structures,
More informationFINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING WEB DEPTH
Journal of Engineering Science and Technology Vol. 12, No. 11 (2017) 28392854 School of Engineering, Taylor s University FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NONLINEAR VARYING
More informationKINGS 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)
More informationQUESTION BANK SEMESTER: III SUBJECT NAME: MECHANICS OF SOLIDS
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 Hooke s law. 3. Define modular ratio,
More information: 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
More informationOUTCOME 1  TUTORIAL 3 BENDING MOMENTS. You should judge your progress by completing the self assessment exercises. CONTENTS
Unit 2: Unit code: QCF Level: 4 Credit value: 15 Engineering Science L/601/1404 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS 1. Be able to determine the behavioural characteristics of elements of static engineering
More informationPushover Seismic Analysis of Bridge Structures
Pushover Seismic Analysis of Bridge Structures Bernardo Frère Departamento de Engenharia Civil, Arquitectura e Georrecursos, Instituto Superior Técnico, Technical University of Lisbon, Portugal October
More informationLecture 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
More informationExperimental investigation on monotonic performance of steel curved knee braces for weldfree beamtocolumn connections
Experimental investigation on monotonic performance of steel curved knee braces for weldfree beamtocolumn connections *Zeyu Zhou 1) Bo Ye 2) and Yiyi Chen 3) 1), 2), 3) State Key Laboratory of Disaster
More informationDownloaded from Downloaded from / 1
PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION2002 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 informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a crosssection of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationPLASTIC COLLAPSE MECHANISMS IN COMPRESSED ELLIPTICAL HOLLOW SECTIONS
SDSS Rio 010 STABILITY AND DUCTILITY OF STEEL STRUCTURES E. Batista, P. Vellasco, L. de Lima (Eds.) Rio de Janeiro, Brazil, September 810, 010 PLASTIC COLLAPSE MECHANISMS IN COMPRESSED ELLIPTICAL HOLLOW
More informationPOSTBUCKLING CAPACITY OF BIAXIALLY LOADED RECTANGULAR STEEL PLATES
POSTBUCKLING CAPACITY OF BIAXIALLY LOADED RECTANGULAR STEEL PLATES Jeppe Jönsson a and Tommi H. Bondum b a,b DTU Civil Engineering, Technical University of Denmark Abstract: Results from a detailed numerical
More informationCOURSE 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
More information3 Hours/100 Marks Seat No.
*17304* 17304 14115 3 Hours/100 Marks Seat No. Instructions : (1) All questions are compulsory. (2) Illustrate your answers with neat sketches wherever necessary. (3) Figures to the right indicate full
More informationNORMAL 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 informationBridge deck modelling and design process for bridges
EURussia Regulatory Dialogue Construction Sector Subgroup 1 Bridge deck modelling and design process for bridges Application to a composite twingirder bridge according to Eurocode 4 Laurence Davaine
More informationResearch Collection. Numerical analysis on the fire behaviour of steel plate girders. Conference Paper. ETH Library
Research Collection Conference Paper Numerical analysis on the fire behaviour of steel plate girders Author(s): Scandella, Claudio; Knobloch, Markus; Fontana, Mario Publication Date: 14 Permanent Link:
More informationDesign of AAC wall panel according to EN 12602
Design of wall panel according to EN 160 Example 3: Wall panel with wind load 1.1 Issue Design of a wall panel at an industrial building Materials with a compressive strength 3,5, density class 500, welded
More informationDesign of reinforced concrete sections according to EN and EN
Design of reinforced concrete sections according to EN 199211 and EN 19922 Validation Examples Brno, 21.10.2010 IDEA RS s.r.o. South Moravian Innovation Centre, U Vodarny 2a, 616 00 BRNO tel.: +420511
More informationEquivalent Uniform Moment Factor for Lateral Torsional Buckling of Steel Beams
University of Alberta Department of Civil & Environmental Engineering Master of Engineering Report in Structural Engineering Equivalent Uniform Moment Factor for Lateral Torsional Buckling of Steel Beams
More informationStructural Analysis I Chapter 4  Torsion TORSION
ORSION orsional stress results from the action of torsional or twisting moments acting about the longitudinal axis of a shaft. he effect of the application of a torsional moment, combined with appropriate
More informationSabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in
Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are
More informationAim of the study Experimental determination of mechanical parameters Local buckling (wrinkling) Failure maps Optimization of sandwich panels
METNET Workshop October 1112, 2009, Poznań, Poland Experimental and numerical analysis of sandwich metal panels Zbigniew Pozorski, Monika ChudaKowalska, Robert Studziński, Andrzej Garstecki Poznan University
More informationUltimate shear strength of FPSO stiffened panels after supply vessel collision
Ultimate shear strength of FPSO stiffened panels after supply vessel collision Nicolau Antonio dos Santos Rizzo PETROBRAS Rio de Janeiro Brazil Marcelo Caire SINTEF do Brasil Rio de Janeiro Brazil Carlos
More informationCHAPTER 4. ANALYSIS AND DESIGN OF COLUMNS
4.1. INTRODUCTION CHAPTER 4. ANALYSIS AND DESIGN OF COLUMNS A column is a vertical structural member transmitting axial compression loads with or without moments. The cross sectional dimensions of a column
More informationCOURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 3013 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6
COURSE TITLE : THEORY OF STRUCTURES I COURSE CODE : 0 COURSE CATEGORY : B PERIODS/WEEK : 6 PERIODS/SEMESTER: 90 CREDITS : 6 TIME SCHEDULE Module Topics Period Moment of forces Support reactions Centre
More informationWhere and are the factored end moments of the column and >.
11 LIMITATION OF THE SLENDERNESS RATIO( ) 1Nonsway (braced) frames: The ACI Code, Section 6.2.5 recommends the following limitations between short and long columns in braced (nonsway) frames: 1. The
More informationDesign 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
More informationInteractive Buckling of ColdFormed Steel Sections Applied in Pallet Rack Upright Members
Interactive Buckling of ColdFormed Steel Sections Applied in Pallet Rack Upright Members D. Dubina, V. Ungureanu, A. Crisan Politehnica University of Timişoara Peculiarities of coldformed thinwalled
More informationD : 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 Ns/m. To make the system
More informationD : 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 informationUNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation.
UNIT 1 STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define stress. When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The magnitude
More informationCHAPTER 4: BENDING OF BEAMS
(74) CHAPTER 4: BENDING OF BEAMS This chapter will be devoted to the analysis of prismatic members subjected to equal and opposite couples M and M' acting in the same longitudinal plane. Such members are
More informationEffective stress method to be used in beam finite elements to take local instabilities into account
Effective stress method to be used in beam finite elements to take local instabilities into account JEANMARC FRANSSEN, BAPTISTE COWEZ and THOMAS GERNAY ArgencoDepartment University of Liège Chemin des
More informationAccordingly, the nominal section strength [resistance] for initiation of yielding is calculated by using Equation CC3.1.
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, lateraltorsional buckling and distortional
More informationLecture Slides. Chapter 4. Deflection and Stiffness. The McGrawHill Companies 2012
Lecture Slides Chapter 4 Deflection and Stiffness The McGrawHill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration
More informationSTRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS
1 UNIT I STRESS STRAIN AND DEFORMATION OF SOLIDS, STATES OF STRESS 1. Define: Stress When an external force acts on a body, it undergoes deformation. At the same time the body resists deformation. The
More informationSEISMIC BASE ISOLATION
SEISMIC BASE ISOLATION DESIGN OF BASE ISOLATION SYSTEMS IN BUILDINGS FILIPE RIBEIRO DE FIGUEIREDO SUMMARY The current paper aims to present the results of a study for the comparison of different base isolation
More informationMarch 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
More informationWhat to expect when you re expecting FEA A guide to good practice
What to expect when you re expecting FEA A guide to good practice 1. Background Finite Element Analysis (FEA) has transformed design procedures for engineers. Allowing more complex geometry, loading and
More informationMechanics 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
More information[8] Bending and Shear Loading of Beams
[8] Bending and Shear Loading of Beams Page 1 of 28 [8] Bending and Shear Loading of Beams [8.1] Bending of Beams (will not be covered in class) [8.2] Bending Strain and Stress [8.3] Shear in Straight
More informationDesign of Beams (Unit  8)
Design of Beams (Unit  8) Contents Introduction Beam types Lateral stability of beams Factors affecting lateral stability Behaviour of simple and built  up beams in bending (Without vertical stiffeners)
More informationSeismic design of bridges
NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour
More informationENG2000 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
More informationFEA A Guide to Good Practice. What to expect when you re expecting FEA A guide to good practice
FEA A Guide to Good Practice What to expect when you re expecting FEA A guide to good practice 1. Background Finite Element Analysis (FEA) has transformed design procedures for engineers. Allowing more
More informationPERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK
PERIYAR CENTENARY POLYTECHNIC COLLEGE PERIYAR NAGAR  VALLAM  613 403  THANJAVUR. DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK Sub : Strength of Materials Year / Sem: II / III Sub Code : MEB 310
More informationMechanics 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
More informationCritical Load columns buckling critical load
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
More informationFLANGE CURLING IN COLD FORMED PROFILES
Nordic Steel Construction Conference 22 Hotel Bristol, Oslo, Norway 57 September 22 FLANGE CURLING IN COLD FORMED PROFILES Jeppe Jönsson, Gediminas Ramonas DTU Civil Engineering, Technical University
More informationAutomatic 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
More informationneeded 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
More informationStructural Steelwork Eurocodes Development of A Transnational Approach
Structural Steelwork Eurocodes Development of A Transnational Approach Course: Eurocode Module 7 : Worked Examples Lecture 22 : Design of an unbraced sway frame with rigid joints Summary: NOTE This example
More informationThe Local Web Buckling Strength of Coped Steel IBeam. ABSTRACT : When a beam flange is coped to allow clearance at the
The Local Web Buckling Strength of Coped Steel IBeam 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 informationA METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECONDORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES
A METHOD OF LOAD INCREMENTS FOR THE DETERMINATION OF SECONDORDER LIMIT LOAD AND COLLAPSE SAFETY OF REINFORCED CONCRETE FRAMED STRUCTURES Konuralp Girgin (Ph.D. Thesis, Institute of Science and Technology,
More informationStress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 3 ME 276 Spring 20172018 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 informationProblem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323
Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine
More informationfive 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
More informationfive Mechanics of Materials 1 ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture five mechanics www.carttalk.com of materials Mechanics of Materials 1 Mechanics of Materials MECHANICS MATERIALS
More informationExternal Pressure... Thermal Expansion in unrestrained pipeline... The critical (buckling) pressure is calculated as follows:
External Pressure... The critical (buckling) pressure is calculated as follows: P C = E. t s ³ / 4 (1  ν ha.ν ah ) R E ³ P C = Critical buckling pressure, kn/m² E = Hoop modulus in flexure, kn/m² t s
More informationShear Behaviour of Fin Plates to Tubular Columns at Ambient and Elevated Temperatures
Shear Behaviour of Fin Plates to Tubular Columns at Ambient and Elevated Temperatures Mark Jones Research Student, University of Manchester, UK Dr. Yong Wang Reader, University of Manchester, UK Presentation
More information4.MECHANICAL PROPERTIES OF MATERIALS
4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stressstrain diagram
More informationINFLUENCE 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) 115 TJPRC Pvt. Ltd.,. INFLUENCE OF FLANGE STIFFNESS ON DUCTILITY BEHAVIOUR OF PLATE
More information7.6 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
More informationUnit 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 informationSTRESS, STRAIN AND DEFORMATION OF SOLIDS
VELAMMAL COLLEGE OF ENGINEERING AND TECHNOLOGY, MADURAI 625009 DEPARTMENT OF CIVIL ENGINEERING CE8301 STRENGTH OF MATERIALS I 
More informationFailure in Flexure. Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas
Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE VIII Dr. Jason E. Charalambides Failure in Flexure!
More informationTORSION 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 thinwall open sections is not included in most commonly used frame analysis programs. Almost
More informationCO~RSEOUTL..INE. revisedjune 1981 by G. Frech. of..a.pqij~t(..~ttsa.fidteconol.q.gy. Sault ",Ste'...:M~ri,e.: SAUl. ir.ft\,nl~t';~l' G ". E b:.
/ 1/ /.. SAUl. ir.ft\,nl~t';~l' G ". E b:.~~~~~, of..a.pqij~t(..~ttsa.fidteconol.q.gy. Sault ",Ste'...:M~ri,e.: ',' .\'~. ~ ;:T.., CO~RSEOUTL..INE ARCHITECTURAL ENGINEERING II ARC 2004 revisedjune 1981
More informationENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 4 COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL COLUMNS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those studying
More informationC C JTS 16:00 17:30. Lebet
24 1 27 ()16001730 C C JTS 21 ( ) 16:0017:30 Lebet SGST // Branson Bridge, Martigny, 2006 LéopoldSédarSenghor Bridge, Nantes (F), 2009 Taulhac Bridge, PuyenVelay (F), 2012 Langensand Bridge Lucerne,
More informationUNITI 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
UNITI 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 informationSENSITIVITY ANALYSIS OF LATERAL BUCKLING STABILITY PROBLEMS OF HOTROLLED STEEL BEAMS
2005/2 PAGES 9 14 RECEIVED 18.10.2004 ACCEPTED 18.4.2005 Z. KALA, J. KALA SENSITIVITY ANALYSIS OF LATERAL BUCKLING STABILITY PROBLEMS OF HOTROLLED STEEL BEAMS ABSTRACT Doc. Ing. Zdeněk KALA, PhD. Brno
More informationMechanical Design in Optical Engineering
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:
More informationTuesday, February 11, Chapter 3. Load and Stress Analysis. Dr. Mohammad Suliman Abuhaiba, PE
1 Chapter 3 Load and Stress Analysis 2 Chapter Outline Equilibrium & FreeBody Diagrams Shear Force and Bending Moments in Beams Singularity Functions Stress Cartesian Stress Components Mohr s Circle for
More informationPLATE GIRDERS II. Load. Web plate Welds A Longitudinal elevation. Fig. 1 A typical Plate Girder
16 PLATE GIRDERS II 1.0 INTRODUCTION This chapter describes the current practice for the design of plate girders adopting meaningful simplifications of the equations derived in the chapter on Plate Girders
More informationJob No. Sheet No. Rev. CONSULTING Engineering Calculation Sheet. Member Design  Steel Composite Beam XX 22/09/2016
CONSULTING Engineering Calculation Sheet jxxx 1 Member Design  Steel Composite Beam XX Introduction Chd. 1 Grade 50 more common than Grade 43 because composite beam stiffness often 3 to 4 times non composite
More informationCE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR
CE6306 STRENGTH OF MATERIALS TWO MARK QUESTIONS WITH ANSWERS ACADEMIC YEAR 20142015 UNIT  1 STRESS, STRAIN AND DEFORMATION OF SOLIDS PART A 1. Define tensile stress and tensile strain. The stress induced
More informationANALYSIS OF THE INTERACTIVE BUCKLING IN STIFFENED PLATES USING A SEMIANALYTICAL METHOD
EUROSTEEL 2014, September 1012, 2014, Naples, Italy ANALYSIS OF THE INTERACTIVE BUCKLING IN STIFFENED PLATES USING A SEMIANALYTICAL METHOD Pedro Salvado Ferreira a, Francisco Virtuoso b a Polytechnic
More informationGATE SOLUTIONS E N G I N E E R I N G
GATE SOLUTIONS C I V I L E N G I N E E R I N G From (1987018) Office : F16, (Lower Basement), Katwaria Sarai, New Delhi110016 Phone : 01165064 Mobile : 81309090, 9711853908 Email: info@iesmasterpublications.com,
More informationSTEEL JOINTS  COMPONENT METHOD APPLICATION
Bulletin of the Transilvania University of Braşov Vol. 5 (54)  2012 Series 1: Special Issue No. 1 STEEL JOINTS  COPONENT ETHOD APPLICATION D. RADU 1 Abstract: As long as the rotation joint stiffness
More informationEffective stress method to be used in beam finite elements to take local instabilities into account
Effective stress method to be used in beam finite elements to take local instabilities into account JEANMARC FRANSSEN, BAPTISTE COWEZ ans THOMAS GERNAY Argenco Department University of Liège Chemin des
More informationBuckling 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 informationN = Shear stress / Shear strain
UNIT  I 1. What is meant by factor of safety? [A/M15] It is the ratio between ultimate stress to the working stress. Factor of safety = Ultimate stress Permissible stress 2. Define Resilience. [A/M15]
More information