Part IB EXPERIMENTAL ENGINEERING MODEL STRUCTURES. 1. To compare the behaviour of various different linear-elastic structures with simple theory.
|
|
- Maximillian Poole
- 6 years ago
- Views:
Transcription
1 Part IB EXPERIMENTAL ENGINEERING SUBJECT: INTEGRATED COURSEWORK LOCATION: STRUCTURES TEACHING LAB EXPERIMENT: A2 (SHORT) MODEL STRUCTURES OBJECTIVES 1. To compare the behaviour of various different linear-elastic structures with simple theory. 2. To give students practice in analysing discrepancies (if any) between theory and experiment, to discover the reasons for them (and so perhaps to improve the theory and/or their understanding of structures). 3. To give students opportunity to verify or disprove certain postulated theorems about linear-elastic structures. 4. To give students practice in oral reporting of their findings briefly but accurately to colleagues, so that the lessons learned may be more widely spread, without the necessity for every student to test every structure. 5. To show to students various aspects of the behaviour of structures that they can explore in more depth as part of an extended exercise. INTRODUCTION This laboratory is part of the Integrated Coursework on Earthquake-resistant structures. To understand the behaviour of a building to an earthquake requires knowledge of the structural mechanics of the building. In the first and second year lecture courses on Structural Mechanics, simplified Engineers theories are presented for the linear-elastic behaviour of structures such as trusses, beams or frameworks. These theories are based on certain simplifying assumptions to reduce the real structure to a theoretical model which can be analysed. For example, in beams each cross-section is assumed to remain plane and undistorted, and normal to the deflected beam centre-line. The question arises, whether these assumptions are always reasonable and if not, whether there are practical circumstances where incorrectness of the assumptions puts the theory into significant error. In this experiment, students compare the results of various tests against standard theory, and attempt to explain discrepancies (if any). A further question on linear-elastic structures is whether there are any general statements which may validly be made for example, on the magnitudes and directions of deflection caused by certain loads. Other groups of students will be given postulated statements or theorems of this type, and asked to verify or disprove them by testing simple models. 1
2 OUTLINE This short 2-hour test session is designed for 6 pairs of students together. Each pair does a different, but related, experiment: in the final 20 minutes, groups describe to others what they have discovered. Four experiments (A D) are essentially on beams. In each case you will be asked to predict the behaviour of a specimen using first - year Engineers Bending Theory. Dimensions and material data will be given to you when you arrive in the laboratory. You will then perform the test, see what actually happens, plot graphs of results, identify shortcomings of the theory (if any), and attempt to explain any discrepancies. Two experiments (E, F) are on bent cantilevers, one with cross-section similar to that of one of the beams (experiment C). Here there will be several statements or potential theorems about deflections. You are asked, by experimenting on the structures in your own way, to disprove or verify these statements (considering for example within what accuracy they might be true, or whether some rewording would be appropriate). In all 6 cases, the magnitude of the applied loads will be limited, so that the structure remains in its elastic range. WRITE-UP Do your preliminary calculations on the lined paper provided, and plot graphs on the squared paper. Follow up with a brief summary and discussion of your findings. Remark upon their implications for practical structures, and on the findings of other groups. DETAILS Further information about the six individual experiments is given below. Before coming to the laboratory, please read these details so as to get a general idea of what is to be done. However, do not attempt beforehand any of the calculations described you will not know until you arrive which of the six experiments is assigned to you. Experiment A: Tubular beam The tube is made from aluminium alloy (E 70 x 10 3 N/mm 2 ). The cross-section is approximately square, with side 50 mm and mean wall thickness 0.83 mm (you may wish to verify these measurements). Calculate I for the cross-section. Hence predict the elastic central deflection (δ = WL 3 /48EI) for each of three spans L (200, 400 and 650 mm) which you will test, for a simply-supported beam with central point load W = 100 N. Plot these on a single graph of W against δ (allowing for max. load 100 N and max. deflection five times that predicted for your longest beam). Draw straight lines to show the expected behaviour as W is increased gradually from zero. Now do the experiment with a truly central point load and four or five load increments. Take some readings as you unload, to see whether behaviour is elastic. There is no need to put down your readings in a table simply plot points on your W-δ graph as you proceed. Compare the theoretical and experimental results and consider the reason(s) for the discrepancy (if any) and how to modify the theory appropriately. Discuss with the demonstrator what to do next. 2
3 Experiment B: Sandwich beam The beam has aluminium alloy flanges glued to a foam infill. The aluminium sheets (E 70 x 103 N/mm2) are 51 mm wide and 0.75 mm thick. The foam has E 7 N/mm2, and the centre-centre separation of the flanges is 20mm. Calculate I for the composite section transformed to aluminium. Hence calculate the elastic central deflection (δ = WL 3 /48EI) for each of four spans L (range mm) which you intend to test, for a simply-supported beam with central load W = 50 N. Plot these on a single graph of W against δ (max. load 50 N, max. deflection twenty times that predicted for your longest beam). Draw straight lines to show the predicted behaviour as W is increased gradually from zero. Now do the experiment, with a few load increments up to the max. load of 50 N. Take some readings as you unload, to see whether behaviour is elastic. There is no need to put down your readings in a table simply plot points on your W-δ graph as you proceed. Compare the theoretical and experimental results, and consider the reason(s) for the discrepancy (if any) and how to modify the theory appropriately. Discuss with the demonstrator what to do next. Experiment C: Square tube with mitre bend L = 372 mm The specimens are made of steel (E 200 x 10 3 N/mm 2 ) and the cross-section is approx. 25 mm square with 1 mm wall thickness. First test the centrally-loaded simply-supported beam shown in Fig. 2 and plot F against v (max. load 100 N). Is it elastic? (Predicted deflection v = FL 3 /6EI.) Now sketch the bending moment diagram for the two figures, and consider the distorted geometry in the two cases (regarded as two connected cantilevers in each case). Hence predict a relation between the stiffnesses W/u and F/v. Hence, from the measured F/v graph, predict the expected graph of W against u. Plot this prediction on a separate graph, and then perform the test of Fig. 1 (max. load W = 50 N) plotting experimental points on the graph without writing them down in a Table. Consider possible reason(s) for the discrepancy (if any), and how to modify the theory for Fig. 1 appropriately. Discuss with the demonstrator what to do next. 3
4 Experiment D: Slim I-beam The overall dimensions of the cross-section are 12.5 x 29 mm, and pure-bending experiments show that EI = 34.6 Nm 2. Predict the elastic central deflection (δ = WL 3 /48EI) for a centrally-loaded simplysupported beam under 100 N load, for four values of span L you intend to test (range mm). Plot these on a single graph of W against δ (allowing for maximum load 100 N, max. deflection 6 mm). Draw lines to show expected behaviour as W increases from zero. Now do the experiment, starting with the shortest span. Use several load increments, and take some readings as you unload, to check whether behaviour is elastic. There is no need to put down your readings in a table simply plot points on your W-δ graph as you proceed. Increase W until its value reaches 100 N, or the sideways deflection reaches 10 mm, whichever occurs first. Use smaller weight increments in the vicinity of the buckling load, to obtain the buckling load as accurately as possible. Keep careful note of the sideways deflection at each load stage, so that each student can do at least one Southwell plot (see below). Consider how the buckling load (preferably for a perfect beam, from the Southwell plot) varies with span, and discuss with the demonstrator what to do next. Experiment E : Curved cantilevers In this experiment, a curved perspex cantilever with a central plane of symmetry is loaded in that plane by a tip force of constant magnitude but variable direction. The object of the experiment is for you, by making appropriate tests of your own devising, to verify or disprove the various hypotheses listed below. First set up the cantilever and paper sheet with the origin of axes for displacement directly below the hole next to the hole to which force is applied. Displacement of the cantilever under load can then be recorded by pricking through the displaced hole; and the corresponding force direction can be recorded from the cotton thread, again by pricking holes or otherwise. Test the cantilever with the same force (0.4 kgf plus scalepan) in various directions (all parallel to the drawing board) over as near as possible the full 360 range. Observe the tip displacement in each case; draw a curve through the displaced points; and indicate the corresponding force directions. Consider hypotheses (a), (b) and (d) in the light of these observations; note whether each hypotheses is true, false or badly worded, giving reason(s) why you reach this conclusion from the results. [Note for (d) that this is a 2- not 3-dimensional structure]. You have effectively measured the elastic flexibility of the cantilever (i.e. the displacement for unit force) for forces in varying directions. Now resolve each measured displacement (or flexibility) into directions parallel and perpendicular to the corresponding applied force, using an appropriate sign convention. On a separate piece of graph paper, to an appropriate scale, plot (displacement-in-the-force-direction) horizontally, and vertically the corresponding (displacement-perpendicular-to-the-applied-force). If you can, draw a curve through these points, and comment, in the light of hypothesis (d). Finally, by studying the observations already made, or by carrying out further special tests, consider hypothesis (c), especially version (i). How general can your conclusions be, and to what accuracy are various verified hypotheses true? 4
5 Experiment F : Right-angled cantilever tube The tube is of steel, with wall thickness 1 mm and a square section of side 25 mm. (A similar tube is being tested by another group of students). Your rig allows load (max. 50 N) to be applied in three directions at a point near the tip of the cantilever, and displacements to be measured at much the same point. Load can be applied in a wide range of directions in the cantilever plane; and load can be applied or deflections read at a second point, on the beam. The object of the experiment is for you, by making appropriate tests of your own devising on this bent cantilever, to verify or disprove the hypotheses listed below. First apply the three in-plane loads in turn. In each case, cycle the load once or twice between 0.2 and 4.2 kg in the scale pan : then take readings of the four dial gauges at 0.2, 4.2, 0.2, 4.2 kg etc. until you are satisfied with consistency. To eliminate the effect of friction on loads applied via pulleys, ensure that the load has been increased by at least 0.2 kgf just before you take each set of readings. Finally, take readings of the dial gauges with the out-of-plane load at 0.2, 2.2, 0.2 kgf etc. Estimate flexibilities or compliances in mm/n. If you have time later, take some intermediate readings to check on linearity. Then consider the hypotheses in the order given, and see whether your results prove or disprove them. If your experiments suggest that a hypothesis is true, or nearly so, devise a way of stating its accuracy. In some cases, rewording a hypothesis may be necessary. From some tests, you may obtain the 3 x 3 flexibility matrix F at a point, defined by the relation d = Fp between displacement d and applied load p. Calculate the eigenvalues and eigenvectors of F using Matlab. Then consider, consulting the demonstrator, what further experiments to do to verify the hypotheses. Note: For a right-angle bent cantilever with uniform members of length h, bending in plane only, with flexural modulus EI1 for the column and EL2 for the beam, the tip deflections according to simple Engineers Bending Theory are horiz. load H : Hh 3 /3EI 1 horiz. ; Hh 3 /2EI 1 vertical vert. load V : Vh 3 /2EI 1 horiz. ; V h vertical EI1 3EI2 Hypotheses (for experiments E and F) The following hypotheses are put forward as applying to all structures in the linear-elastic range of behaviour. (a) If a force is applied to the structure at any point A, the displacement of A is in the same direction as the force. (b) If a force is applied to the structure at any point A, the displacement of A in the force direction is greater than its displacement in any perpendicular direction. (c) A force is applied at point A on a structure in direction i and the displacement of point B in direction j is measured. This displacement is the same as that caused at A in direction i by the same force magnitude applied at B in direction j: (i) if A and B are the same point, or (ii) if A and B are any two points (the same, or distinct). (d) If a force is applied at any point A, and is to cause A to displace in the same direction as the force, the force must be applied in one of three definite mutually-perpendicular directions. One of these directions will show the maximum, and one the minimum, flexibility. 5
6 NOTE ON MATRICES In the elasticity experiment, you effectively measure the terms of the 3 x 3 matrix F relating displacement d to the applied load P at the same point, ie. D = FP. From Part IA Mathematics, if d is to be the same direction as P, ie d = λ P where λ is scalar, then [F - λ I] P = 0 (1) where I is the unit matrix. Obviously (1) is satisfied trivially when P = 0, but there may be some special cases when P is not zero but (1) is nevertheless satisfied. Then the determinant of [F - λ I] must be zero, giving a cubic equation for λ whose roots are the eigenvalues (here the flexibility of the structure in the special directions). To each eigenvalue there corresponds a special direction, the eigenvector. Each eigenvector can be obtained by substituting an eigenvalue into (1) and regarding P as unknown (but with one arbitrarily-chosen component set to unity). Eigenvalues and eigenvectors can be found using the command eig in Matlab (type help eig to learn more). NOTE ON SOUTHWELL PLOT The Southwell plot is a method of estimating the buckling load P cr for a perfect strut from the increase of sideways deflection of an imperfect specimen as the load P approaches P cr. All struts will have some initial imperfection in the eventual buckling mode, say e o at midspan. According to simple strut theory, this is magnified to w = e o (1 P/P cr ) as P P cr (leaving other shapes of imperfection insignificant). A gauge placed to measure sideways movement at midspan will record = w e o = e P o cr 1. A graph, the Southwell Plot of the ratio P /P against should then have slope 1/P cr. So P cr may be estimated, usually with good accuracy, from the slope of the best-fit line through experimental points. This applies strictly to pin-ended struts, and so will apply here if the top flange of the beam is regarded as similar to a pin-ended strut. If proper account is to be taken of the lateraltorsional behaviour here, with restraint of warping, the Southwell plot should be of /P n against giving slope 1/P cr n, where n is between 1 and 2 depending on the geometry of the beam. S.D. Guest F.A. McRobie September
7 7
8 8
9 9
10 10
Structures. Shainal Sutaria
Structures ST Shainal Sutaria Student Number: 1059965 Wednesday, 14 th Jan, 011 Abstract An experiment to find the characteristics of flow under a sluice gate with a hydraulic jump, also known as a standing
More informationStructural Analysis Laboratory. Michael Storaker, Sam Davey and Rhys Witt. JEE 332 Structural Analysis. 4 June 2012.
Structural Analysis Laboratory Michael Storaker, Sam Davey and Rhys Witt JEE 332 Structural Analysis 4 June 2012 Lecturer/Tutor Shinsuke Matsuarbara 1 Contents Statically Indeterminate Structure Objective...
More informationMAAE 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
More informationStructural Analysis III Compatibility of Displacements & Principle of Superposition
Structural Analysis III Compatibility of Displacements & Principle of Superposition 2007/8 Dr. Colin Caprani, Chartered Engineer 1 1. Introduction 1.1 Background In the case of 2-dimensional structures
More informationLATERAL STABILITY OF BEAMS WITH ELASTIC END RESTRAINTS
LATERAL STABILITY OF BEAMS WITH ELASTIC END RESTRAINTS By John J. Zahn, 1 M. ASCE ABSTRACT: In the analysis of the lateral buckling of simply supported beams, the ends are assumed to be rigidly restrained
More information2012 MECHANICS OF SOLIDS
R10 SET - 1 II B.Tech II Semester, Regular Examinations, April 2012 MECHANICS OF SOLIDS (Com. to ME, AME, MM) Time: 3 hours Max. Marks: 75 Answer any FIVE Questions All Questions carry Equal Marks ~~~~~~~~~~~~~~~~~~~~~~
More informationLevel 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method
9210-203 Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method You should have the following for this examination one answer book No additional data is attached
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 informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING. BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS
TW21 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BEng (HONS) CIVIL ENGINEERING SEMESTER 1 EXAMINATION 2016/2017 MATHEMATICS & STRUCTURAL ANALYSIS MODULE NO: CIE4011 Date: Wednesday 11 th January 2017 Time:
More informationBending Load & Calibration Module
Bending Load & Calibration Module Objectives After completing this module, students shall be able to: 1) Conduct laboratory work to validate beam bending stress equations. 2) Develop an understanding of
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method
Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 8 The Force Method of Analysis: Beams Instructional Objectives After reading this chapter the student will be
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 informationto 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,
More informationExperimental Lab. Principles of Superposition
Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you
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 informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CE-NEW)/SEM-3/CE-301/ SOLID MECHANICS
Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers
More informationChapter 2 Basis for Indeterminate Structures
Chapter - Basis for the Analysis of Indeterminate Structures.1 Introduction... 3.1.1 Background... 3.1. Basis of Structural Analysis... 4. Small Displacements... 6..1 Introduction... 6.. Derivation...
More informationStructural Mechanics Column Behaviour
Structural Mechanics Column Behaviour 008/9 Dr. Colin Caprani, 1 Contents 1. Introduction... 3 1.1 Background... 3 1. Stability of Equilibrium... 4. Buckling Solutions... 6.1 Introduction... 6. Pinned-Pinned
More information1C8 Advanced design of steel structures. prepared by Josef Machacek
1C8 Advanced design of steel structures prepared b Josef achacek List of lessons 1) Lateral-torsional instabilit of beams. ) Buckling of plates. 3) Thin-walled steel members. 4) Torsion of members. 5)
More informationBy Dr. Mohammed Ramidh
Engineering Materials Design Lecture.6 the design of beams By Dr. Mohammed Ramidh 6.1 INTRODUCTION Finding the shear forces and bending moments is an essential step in the design of any beam. we usually
More informationModule 4 : Deflection of Structures Lecture 4 : Strain Energy Method
Module 4 : Deflection of Structures Lecture 4 : Strain Energy Method Objectives In this course you will learn the following Deflection by strain energy method. Evaluation of strain energy in member under
More informationENG1001 Engineering Design 1
ENG1001 Engineering Design 1 Structure & Loads Determine forces that act on structures causing it to deform, bend, and stretch Forces push/pull on objects Structures are loaded by: > Dead loads permanent
More informationAERO 214. Lab II. Measurement of elastic moduli using bending of beams and torsion of bars
AERO 214 Lab II. Measurement of elastic moduli using bending of beams and torsion of bars BENDING EXPERIMENT Introduction Flexural properties of materials are of interest to engineers in many different
More informationComputational Stiffness Method
Computational Stiffness Method Hand calculations are central in the classical stiffness method. In that approach, the stiffness matrix is established column-by-column by setting the degrees of freedom
More informationStructural Steelwork Eurocodes Development of A Trans-national Approach
Structural Steelwork Eurocodes Development of A Trans-national Approach Course: Eurocode Module 7 : Worked Examples Lecture 0 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic Loads
More informationLevel 3 Cambridge Technical in Engineering
Oxford Cambridge and RSA Level 3 Cambridge Technical in Engineering 05822/05823/05824/05825 Unit 3: Principles of mechanical engineering Sample Assessment Material Date - Morning/Afternoon Time allowed:
More informationShear force and bending moment of beams 2.1 Beams 2.2 Classification of beams 1. Cantilever Beam Built-in encastre' Cantilever
CHAPTER TWO Shear force and bending moment of beams 2.1 Beams A beam is a structural member resting on supports to carry vertical loads. Beams are generally placed horizontally; the amount and extent of
More informationC6 Advanced design of steel structures
C6 Advanced design of steel structures prepared b Josef achacek List of lessons 1) Lateral-torsional instabilit of beams. ) Buckling of plates. 3) Thin-walled steel members. 4) Torsion of members. 5) Fatigue
More informationDEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS).
DEPARTMENT OF MECHANICAL ENIGINEERING, UNIVERSITY OF ENGINEERING & TECHNOLOGY LAHORE (KSK CAMPUS). Lab Director: Coordinating Staff: Mr. Muhammad Farooq (Lecturer) Mr. Liaquat Qureshi (Lab Supervisor)
More informationPh.D. Preliminary Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2017 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 1 - STATIC AND DYNAMIC FORCES TUTORIAL 3 STRESS AND STRAIN 1 Static and dynamic forces Forces: definitions of: matter, mass, weight,
More informationPh.D. Preliminary Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.
More information= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200
Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength
More informationMoment Area Method. 1) Read
Moment Area Method Lesson Objectives: 1) Identify the formulation and sign conventions associated with the Moment Area method. 2) Derive the Moment Area method theorems using mechanics and mathematics.
More information3.032 Problem Set 1 Fall 2007 Due: Start of Lecture,
3.032 Problem Set 1 Fall 2007 Due: Start of Lecture, 09.14.07 1. The I35 bridge in Minneapolis collapsed in Summer 2007. The failure apparently occurred at a pin in the gusset plate of the truss supporting
More informationStructural Steelwork Eurocodes Development of A Trans-national Approach
Structural Steelwork Eurocodes Development of A Trans-national Approach Course: Eurocode 3 Module 7 : Worked Examples Lecture 20 : Simple braced frame Contents: 1. Simple Braced Frame 1.1 Characteristic
More informationChapter 7: Internal Forces
Chapter 7: Internal Forces Chapter Objectives To show how to use the method of sections for determining the internal loadings in a member. To generalize this procedure by formulating equations that can
More informationPhysics 8 Monday, November 20, 2017
Physics 8 Monday, November 20, 2017 Pick up HW11 handout, due Dec 1 (Friday next week). This week, you re skimming/reading O/K ch8, which goes into more detail on beams. Since many people will be traveling
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 information1 332 Laboratories 1. 2 Computational Exercises 1 FEA of a Cantilever Beam... 1 Experimental Laboratory: Tensile Testing of Materials...
1 332 Laboratories Contents 1 332 Laboratories 1 2 Computational Exercises 1 FEA of a Cantilever Beam.......................................... 1 Experimental Laboratory: Tensile Testing of Materials..........................
More 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 informationWorkshop 8. Lateral Buckling
Workshop 8 Lateral Buckling cross section A transversely loaded member that is bent about its major axis may buckle sideways if its compression flange is not laterally supported. The reason buckling occurs
More informationEntrance exam Master Course
- 1 - Guidelines for completion of test: On each page, fill in your name and your application code Each question has four answers while only one answer is correct. o Marked correct answer means 4 points
More informationA 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
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 cross-section 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 informationENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3 - SHEAR FORCE AND BENDING MOMENTS IN BEAMS
ENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3 - SHEAR FORCE AND BENDING MOMENTS IN BEAMS You should judge your progress by completing the self assessment exercises. On completion
More informationCHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES
CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES 14.1 GENERAL REMARKS In structures where dominant loading is usually static, the most common cause of the collapse is a buckling failure. Buckling may
More informationNational Exams May 2015
National Exams May 2015 04-BS-6: Mechanics of Materials 3 hours duration Notes: If doubt exists as to the interpretation of any question, the candidate is urged to submit with the answer paper a clear
More informationCIVIL DEPARTMENT MECHANICS OF STRUCTURES- ASSIGNMENT NO 1. Brach: CE YEAR:
MECHANICS OF STRUCTURES- ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes X-X and Y-Y of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationUsing the finite element method of structural analysis, determine displacements at nodes 1 and 2.
Question 1 A pin-jointed plane frame, shown in Figure Q1, is fixed to rigid supports at nodes and 4 to prevent their nodal displacements. The frame is loaded at nodes 1 and by a horizontal and a vertical
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 elastic-perfectly plastic materials, P cr Depends primarily on E and
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 informationNAME: Given Formulae: Law of Cosines: Law of Sines:
NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.
More informationTable of Contents. Preface...xvii. Part 1. Level
Preface...xvii Part 1. Level 1... 1 Chapter 1. The Basics of Linear Elastic Behavior... 3 1.1. Cohesion forces... 4 1.2. The notion of stress... 6 1.2.1. Definition... 6 1.2.2. Graphical representation...
More informationSummative Practical: Motion down an Incline Plane
Summative Practical: Motion down an Incline Plane In the next lesson, your task will be to perform an experiment to investigate the motion of a ball rolling down an incline plane. For an incline of 30,
More informationA RATIONAL BUCKLING MODEL FOR THROUGH GIRDERS
A RATIONAL BUCKLING MODEL FOR THROUGH GIRDERS (Hasan Santoso) A RATIONAL BUCKLING MODEL FOR THROUGH GIRDERS Hasan Santoso Lecturer, Civil Engineering Department, Petra Christian University ABSTRACT Buckling
More informationCOLUMNS: 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
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 informationPreliminaries: Beam Deflections Virtual Work
Preliminaries: Beam eflections Virtual Work There are several methods available to calculate deformations (displacements and rotations) in beams. They include: Formulating moment equations and then integrating
More informationPart IB Paper 2: Structures. Examples Paper 2/3 Elastic structural analysis
ISSUEB 011 15 NOV 2013 1 Engineering Tripos Part IB SECOND YEAR Part IB Paper 2: Structures Examples Paper 2/3 Elastic structural analysis Straightforward questions are marked by t; Tripos standard questions
More informationCE 320 Structures Laboratory 1 Flexure Fall 2006
CE 320 Structures Laboratory 1 Flexure Fall 2006 General Note: All structures labs are to be conducted by teams of no more than four students. Teams are expected to meet to decide on an experimental design
More informationUNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded
More informationChapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd
Chapter Objectives To generalize the procedure by formulating equations that can be plotted so that they describe the internal shear and moment throughout a member. To use the relations between distributed
More informationLecture 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
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 informationA 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,
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 (1987-018) Office : F-16, (Lower Basement), Katwaria Sarai, New Delhi-110016 Phone : 011-65064 Mobile : 81309090, 9711853908 E-mail: info@iesmasterpublications.com,
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 N-s/m. To make the system
More informationIshik University / Sulaimani Architecture Department. Structure. ARCH 214 Chapter -5- Equilibrium of a Rigid Body
Ishik University / Sulaimani Architecture Department 1 Structure ARCH 214 Chapter -5- Equilibrium of a Rigid Body CHAPTER OBJECTIVES To develop the equations of equilibrium for a rigid body. To introduce
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 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 informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
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 informationIntroduction to Structural Member Properties
Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I): a mathematical property of a cross-section (measured in inches 4 or in 4 ) that gives important information
More informationMoment Distribution Method
Moment Distribution Method Lesson Objectives: 1) Identify the formulation and sign conventions associated with the Moment Distribution Method. 2) Derive the Moment Distribution Method equations using mechanics
More informationISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING
ISHIK UNIVERSITY DEPARTMENT OF MECHATRONICS ENGINEERING QUESTION BANK FOR THE MECHANICS OF MATERIALS-I 1. A rod 150 cm long and of diameter 2.0 cm is subjected to an axial pull of 20 kn. If the modulus
More informationStructural Analysis II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 38
Structural Analysis II Prof. P. Banerjee Department of Civil Engineering Indian Institute of Technology, Bombay Lecture 38 Good morning. We have been looking at influence lines for the last couple of lectures
More informationM.S Comprehensive Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... M.S Comprehensive
More informationChapter 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
More informationFIXED BEAMS IN BENDING
FIXED BEAMS IN BENDING INTRODUCTION Fixed or built-in 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 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 informationDeflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering
Deflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering 008/9 Dr. Colin Caprani 1 Contents 1. Introduction... 3 1.1 General... 3 1. Background... 4 1.3 Discontinuity Functions...
More informationDECLARATION. Supervised by: Prof Stephen Mutuli
DECLARATION The work presented in this project is the original work, which to the best of our knowledge has never been produced and presented elsewhere for academic purposes... EYSIMGOBANAY K. J F18/1857/006
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 informationSRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA
SRI CHANDRASEKHARENDRA SARASWATHI VISWA MAHAVIDHYALAYA (Declared as Deemed-to-be University under Section 3 of the UGC Act, 1956, Vide notification No.F.9.9/92-U-3 dated 26 th May 1993 of the Govt. of
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 informationCHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 2. Discontinuity functions
1. Deflections of Beams and Shafts CHAPTER OBJECTIVES Use various methods to determine the deflection and slope at specific pts on beams and shafts: 1. Integration method. Discontinuity functions 3. Method
More informationDesign of Steel Structures Dr. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati
Design of Steel Structures Dr. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 6 Flexural Members Lecture 5 Hello today I am going to deliver the lecture
More informationLab Exercise #3: Torsion
Lab Exercise #3: Pre-lab assignment: Yes No Goals: 1. To evaluate the equations of angular displacement, shear stress, and shear strain for a shaft undergoing torsional stress. Principles: testing of round
More informationDeflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering
Deflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering 009/10 Dr. Colin Caprani 1 Contents 1. Introduction... 4 1.1 General... 4 1. Background... 5 1.3 Discontinuity Functions...
More information1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine Spring 2004 LABORATORY ASSIGNMENT NUMBER 6
1.103 CIVIL ENGINEERING MATERIALS LABORATORY (1-2-3) Dr. J.T. Germaine MIT Spring 2004 LABORATORY ASSIGNMENT NUMBER 6 COMPRESSION TESTING AND ANISOTROPY OF WOOD Purpose: Reading: During this laboratory
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 1 - FRAMES AND BEAMS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 1 - FRAMES AND BEAMS TUTORIAL 2 - BEAMS CONTENT Be able to determine the forces acting
More informationMARKS DISTRIBUTION AS PER CHAPTER (QUESTION ASKED IN GTU EXAM) Name Of Chapter. Applications of. Friction. Centroid & Moment.
Introduction Fundamentals of statics Applications of fundamentals of statics Friction Centroid & Moment of inertia Simple Stresses & Strain Stresses in Beam Torsion Principle Stresses DEPARTMENT OF CIVIL
More informationVirtual distortions applied to structural modelling and sensitivity analysis. Damage identification testing example
AMAS Workshop on Smart Materials and Structures SMART 03 (pp.313 324) Jadwisin, September 2-5, 2003 Virtual distortions applied to structural modelling and sensitivity analysis. Damage identification testing
More informationENGINEERING TRIPOS PART IIA 3C7: EXPERIMENTAL STRESS ANALYSIS
ENGINEERING TRIPOS PART IIA 3C7: EXPERIMENTAL STRESS ANALYSIS Experiment takes place in BNB-06 (follow downward stairs opposite Baker Building reception). OBJECTIVES To develop an appreciation of two different
More informationDesign of Steel Structures Prof. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati
Design of Steel Structures Prof. Damodar Maity Department of Civil Engineering Indian Institute of Technology, Guwahati Module 7 Gantry Girders and Plate Girders Lecture - 3 Introduction to Plate girders
More information1.050: Beam Elasticity (HW#9)
1050: Beam Elasticity (HW#9) MIT 1050 (Engineering Mechanics I) Fall 2007 Instructor: Markus J BUEHER Due: November 14, 2007 Team Building and Team Work: We strongly encourage you to form Homework teams
More information1.105 Solid Mechanics Laboratory Fall 2003
1.105 Solid Mechanics Laboratory Fall 200 Experiment 7 Elastic Buckling. The objectives of this experiment are To study the failure of a truss structure due to local buckling of a compression member. To
More information3. 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
More informationCALCULUS APPLICATIONS OF DIFFERENTIATION LESSON PLAN. C3 Topic Overview
CALCULUS C3 Topic Overview C3 APPLICATIONS OF DIFFERENTIATION Differentiation can be used to investigate the behaviour of a function, to find regions where the value of a function is increasing or decreasing
More information