MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS. On completion of this tutorial you should be able to do the following.


 Ferdinand Joseph
 2 years ago
 Views:
Transcription
1 MECHANICS OF SOLIDS COMPRESSION MEMBERS TUTORIAL 1 STRUTS You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do the following. Define a strut. Extend bending theory to struts. Solve the loads at which struts collapse. Solve the sideways deflection of struts. It is assumed that students doing this tutorial already familiar with the concepts of second moments of area, bending stress, bending moments and deflection of beams. D.J.DUNN 1
2 1. INTRODUCTION COMPRESSION MEMBERS Compression members are divided into three types. 1.1 SHORT In this case the member is called a column and will fail when the ultimate compressive stress of the material is exceeded. Failure will depend upon the type of material. Columns are usually made of brittle material (concrete, stone or cast iron) and failure will be of the brittle type which is basically a crumbling of the material. Columns were studied in Mechanical Science A. 1. LONG Long members are called struts. These bend and bow out when compressed beyond a certain limit. Failure occurs by bending when the maximum tensile stress is exceeded. 1.3 INTERMEDIATE These are short enough to produce failure by bending but also short enough to produce compression failure, especially if the material is brittle This tutorial covers struts. Intermediate and short compression members are covered in the next tutorial. D.J.DUNN
3 . STRUTS.1 DEFINITIONS A strut is a long thin compression member. It may collapse under a compressive load by buckling and bowing out as shown in fig.1. The diagram shows the member with its length horizontal but it is just as likely to be vertical. It is drawn this way so that the xy coordinates are in the normal position at the left end. x measures the distance along the length and y is the deflection. Figure 1. SLENDERNESS RATIO L A strut is usually defined by its slenderness ratio. This is defined as S.R. k L is the effective length and k is the radius of gyration for the cross sectional area..3 RADIUS OF GYRATION k The radius of gyration is defined as k I is the nd moment of area and A is the cross sectional area. I A WORKED EXAMPLE No.1 Derive formulae for the radius of gyration of a circle diameter D and a rectangle width B and depth D. Circle 4 4 πd πd 4D I A k D D 4 Rectangle BD I 1 3 A BD k 3 BD 1BD D 1 D.J.DUNN 3
4 WORKED EXAMPLE No. Calculate the slenderness ratio of a strut made from a hollow tube 0 mm outside diameter and 16 mm inside diameter and 1. metres long. For a hollow tube the second moment of area is πd d π I 4637mm πd d π0 16 A mm 4 4 I 4637 k 6.4 mm A L 100 mm S.R k 6.4 mm SELF ASSESSMENT EXERCISE No.1 1. Find the radius of gyration and the slenderness ratio of a strut made from 5 m length of hollow tube 50 mm outer diameter and 40 mm inner diameter. (Ans 16 mm and 31.3) D.J.DUNN 4
5 . THEORY.1 CRITICAL LOAD The force applied to a strut is in an axial direction (the x direction) and not transversely (y direction) as it is for beams. Consider a long thin strut resting against a solid surface at one end and with a screw device at the other as shown. The distance from the end is x and the deflection is y. When the screw is tightened, the strut is forced to deflect sideways. The more the screw is turned the more the strut deflects. If the strut bends as shown, there must be a bending moment and a bending stress in the material. The applied bending moment is Fy. The force applied by the screw and the distance y will increase as the bending moment increases. At some point it will be found that the screw can be turned with no further increase in the force. This can be explained because the increase in deflection alone is sufficient to produce the required increase in the bending moment. The strut will go on bending until it fails (usually by exceeding the yield stress in the material and leaving it permanently bent). When this point is reached the strut has failed and the critical force F c has been reached. Figure Now consider a vertical strut with weights causing the compression. If the weights are less than the critical force F c the strut is unlikely to deflect very much as it is no longer forced to do so. However when the critical value is reached, the strut collapses suddenly and fails as there is nothing to stop it. This might be explained as follows. If the load is critical, the strut will start to deflect. As the distance y increases so will the bending moment. This in turn makes it deflects even further. This is a run away or unstable condition and the strut keeps on bending and fails. A strut is an unstable structure as collapse is sudden and without warning. Figure 3 D.J.DUNN 5
6 . EULER'S THEORY FOR COLLAPSE No strut can be perfectly straight and a force applied as shown will make it bend slightly when an axial compression load is applied. The direction in which it moves is random so let s sketch it so that it bows upwards on the diagram. Note that the force is not a transverse force in the y direction but an axial force applied in the x direction. Consider any distance x from the end. The strut has deflected a distance y. The bending moment at this point is M = F y. This will be a maximum at the point where the deflection is greatest so let this maximum value of y be denoted y m. Figure 4 The applied bending moment is M = Fy (minus because it hogs) If the strut does not collapse, the internal bending moment must balance the applied moment and this is given by bending theory as d y M EI Fy dx (minus because it hogs) d y EI Fy dx Rearrange d y Fy 0 dx EI This is a second order differential equation with a standard solution. y Acos(cx) Bsin(cx) F A and B are constant of integration and c represents the expression EI A and B are solved from boundary conditions. We know that for the case illustrated the deflection is zero at the ends and a maximum at the middle. x = 0 y = 0 and at x = L y = 0 First substitute y = 0 and x = 0 into the solution. 0 = Acos(0) + B(sin 0) = A(1) + B(0) hence A = 0 Next substitute y = 0 and x = L 0 = Acos(cL) + Bsin (cl) = 0 cos(cl) + B sin(cl) from which B sin (cl) = 0 If B is zero the solution is always zero and this clearly is not the case. It follows that sin (cl)= 0 and this occurs when cl = 0, 180o, 360o, and so on. In radians this is cl=,, 3 and so on. In general cl = n where n is an integer. D.J.DUNN 6
7 We may state that cl nπ L F EI F n nπ π EI L and thecorresponding deflection is y Bsin(cL) which may be evaluated. If the strut does not have a symmetrical cross section, it will buckle about the axis with least resistance (smallest value of I). For a rectangular section B must always be the larger of the two dimensions. Figure 5 This is the formula usually given in exams and the above derivation should be practised prior to the exam. n is called the mode and its meaning is very real. A node is any point where the strut does not deflect. If the strut is restrained at any point (e.g. guy ropes on a mast) that point will be a node. The diagram shows what happens when the restraints are placed at the middle (n = ) and at equal distances of 1/3 of the length (n = 3). n = 1 is the fundamental mode. Figure 6 This derivation is due to Euler and the value of F is called Euler's critical load. D.J.DUNN 7
8 There are three other modes of importance which are governed by the way the ends are constrained. Half Mode with n = 0.5 occurs when one end is held rigidly and the other is unrestrained. Figure 7 Another double mode with n = occurs when both ends are held rigidly. Figure 8 An unusual mode with n = 1.43 occurs when one end is held rigidly but the other end is pinned (allowed to rotate) but not allowed to move sideways. Figure 9 D.J.DUNN 8
9 WORKED EXAMPLE No.3 A strut is m long and has a rectangular cross section 30 mm x 0 mm. The bottom is built into a ground socket and the top is completely unrestrained. Given E = 00 GPa calculate the buckling load. SOLUTION F = n EI/L This case is as shown in fig. 7 with n = 0.5 I = BD 3 /1 = x 108 m 4 F = 0.5 x00 x 10 9 x x 108 / F = 470 N WORKED EXAMPLE No.4 Repeat the previous problem but with the strut is pinned at the top and bottom and not allowed to move sideways. SOLUTION F = n EI/L This case is as shown in fig. 6 with n = 1 I = BD 3 /1 = x 108 m 4 F = 1 x00 x 10 9 x x 108 / F = 9870 N. D.J.DUNN 9
10 SELF ASSESSMENT EXERCISE No. 1. A steel strut is 0.15 m diameter and 1 m long. It is built in rigidly at the bottom but completely unrestrained at the top. Calculate the buckling load taking E = 05 GPa. (Ans kn).. A steel strut has a solid circular cross section and is 8 m long. It is pinned at the top and bottom but unable to move laterally at the ends. The strut collapses under a load of 00 kn. Taking E = 05 GPa calculate the diameter of the strut. (Ans mm). 3. A shaft is made from alloy tubing 50 mm outer diameter and 30 mm inner diameter. The shaft is placed between bearings 3 m apart so that the ends are constrained to remain horizontal. The shaft also has to take a horizontal axial load. Taking E = 10 GPa determine the maximum axial load before buckling occurs. (Ans. 140 kn). 4. A strut is 0. m diameter and 15 m long. It is pinned at both ends. Calculate Euler's critical load. E = 05 GPa (Ans kn) D.J.DUNN 10
11 .3 VALIDITY LIMIT OF EULER'S THEORY Euler's theory is inaccurate when the slenderness ratio is small. If the strut is very thin, then the material will simply crush under the axial compression. The slenderness ratio limit depends upon the material but generally if the ratio is less than 10 for steel or less than 80 for aluminium and its alloys, the crushing becomes important and failure will occur at loads smaller than those predicted by Euler. 3. DEFLECTION OF STRUTS It is of interest to know the deflection of a strut at loads less than the buckling value. This can be very complicated work but we do not have to go into full details. When the strut buckles, it fails because it reaches the elastic limit of the material in compression. The strut is put into compression by the load and the direct compressive stress is D = F/A Bending stress is also induced in the strut which tends to be tensile on one side and compressive on the other. This is given by : B = M/I Figure 10 is the distance from the neutral axis to the extreme edge in compression (this is denoted y in beam stress problems but y is unsuited to this case). M is the bending moment Fy. The total compressive stress is hence = F/A + M/I At the point of collapse this is the elastic limit in compression c and the deflection is ym. F Fymδ σ c A I F I y m σ c A Fδ D.J.DUNN 11
12 WORKED EXAMPLE No.5 A strut is made is made from 16 mm diameter steel bar. The buckling load is 400 N. The elastic limit in compression is 30 MPa. Calculate the deflection just prior to collapse. SOLUTION I = D 4 /64 = 3.17 x 109 m4. A =D /4 = 01 x 106 m. c =30 x 10 6 N/m. = D/ = m y m 30 x x x 10 x m or 51.6 mm 400 x D.J.DUNN 1
13 SELF ASSESSMENT EXERCISE No. 3 1.a A uniform slender elastic column of length L is pin jointed at each end and subjected to an axial compression load P. Show that the Euler crippling load occurs when P = EI/L where I is the relevant second moment of area of the column and E is the modulus of elasticity of the material. State any assumptions made. b A straight steel rod 0.5 m long and 0.01 m diameters loaded axially until it buckles. Assuming that the ends of the rod are pin jointed, determine the Euler crippling load. Assume E = 06 GPa. (Ans kn).a The Euler buckling load P for a slender strut of length L and second moment of area I, pin jointed at each end, is given by P = EI/L E is the modulus of elasticity of the material. Using this expression without proof, obtain the formula for the Euler buckling load when the strut is i. fixed (built in) at each end. ii. fixed at one end and pin jointed at the other. b) Fig. 11 shows a vertical pole 6 m long, pinned at the lower end and supported by a wire at the upper end. The pole consists of a tube 50 mm outside diameter and 40 mm inside diameter and the wire has an effective diameter of 6 mm. What is the maximum load P that this system can withstand before failure occurs? For steel assume that the modulus of elasticity E is 06 GPa and for the wire assume that the ultimate stress is 480 MPa. Figure 11 (Answer, the rope breaks before the pole buckles so the maximum value of P is 9.59 kn) D.J.DUNN 13
14 3.a A uniform slender strut of length L which is clamped at one end and free at the other is subjected to an axial compression load P as shown in fig.1. Show that according to EULER'S theory, the strut will buckle when P= (/L)EI where I is the minimum second moment of area of the strut and E is the modulus of elasticity for the material. b A straight steel rod 9 mm diameter is rigidly built into a foundation, the free end protruding 0.5 m normal to the foundation. An axial load is applied to the free end of the rod which deflects as shown in fig.1. Determine the following. i. Euler s buckling load. (636 N) ii. The deflection of the free end of the rod when the total compressive stress reaches the elastic limit. (3.6 mm) For steel assume E = 00GPa and the stress at the elastic limit is 300MPa. Figure 1 D.J.DUNN 14
MECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS
MECHANICS OF SOLIDS  BEAMS TUTORIAL 2 SHEAR FORCE AND BENDING MOMENTS IN BEAMS This is the second tutorial on bending of beams. You should judge your progress by completing the self assessment exercises.
More informationENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P
ENGINEERING SCIENCE H1 OUTCOME 1  TUTORIAL 3 BENDING MOMENTS EDEXCEL HNC/D ENGINEERING SCIENCE LEVEL 4 H1 FORMERLY UNIT 21718P This material is duplicated in the Mechanical Principles module H2 and those
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 1 STRESSES IN BEAMS DUE TO BENDING. On completion of this tutorial you should be able to do the following.
MECHANICS OF SOLIDS  BEAMS TUTOIAL 1 STESSES IN BEAMS DUE TO BENDING This is the first tutorial on bending of beams designed for anyone wishing to study it at a fairly advanced level. You should judge
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS
ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,
More informationKINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK. UNIT I STRESS STRAIN DEFORMATION OF SOLIDS PART A (2 Marks)
KINGS COLLEGE OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING QUESTION BANK SUB CODE/NAME: CE1259 STRENGTH OF MATERIALS YEAR/SEM: II / IV 1. What is Hooke s Law? 2. What are the Elastic Constants?
More informationCH 4: Deflection and Stiffness
CH 4: Deflection and Stiffness Stress analyses are done to ensure that machine elements will not fail due to stress levels exceeding the allowable values. However, since we are dealing with deformable
More informationStress and Deformation Analysis. Representing Stresses on a Stress Element. Representing Stresses on a Stress Element con t
Stress and Deformation Analysis Material in this lecture was taken from chapter 3 of Representing Stresses on a Stress Element One main goals of stress analysis is to determine the point within a loadcarrying
More informationOUTCOME 3  TUTORIAL 1 STRAIN ENERGY
UNIT 6: Unit code: QCF level: 5 Credit value: 5 STRENGTHS OF MATERIALS K/6/49 OUTCOME  TUTORIAL STRAIN ENERGY Be able to determine the behavioural characteristics of loaded structural members by the consideration
More informationStrength of Materials
FE Review Strength of Materials Problem Statements Copyright 2008 C. F. Zorowski NC State E490 Mechanics of Solids 110 KN 90 KN 13.5 KN A 3 = 4.5x103 m 2 A 2 = 2x103 m 2 A 1 = 5x104 m 2 1. A circular
More informationFigure 12 1 Short columns fail due to material failure
12 Buckling Analysis 12.1 Introduction There are two major categories leading to the sudden failure of a mechanical component: material failure and structural instability, which is often called buckling.
More information1.1 To determine the effect the slenderness ratio has on the load carrying capacity of pin ended columns.
I. OBJECTIVES 1.1 To determine the effect the slenderness ratio has on the load carrying capacity of pin ended columns. 1. To observe short, intermediate and long column behavior under the application
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL 3 THE DEFLECTION OF BEAMS
MECHANICS OF SOLIDS  BEAMS TUTORIAL THE DEECTION OF BEAMS This is the third tutorial on the bending of beams. You should judge your progress by completing the self assessment exercises. On completion
More informationMECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES OF STRESS AND STRAIN
MECHANICAL PRINCIPLES HNC/D PRELIMINARY LEVEL TUTORIAL 1 BASIC STUDIES O STRESS AND STRAIN This tutorial is essential for anyone studying the group of tutorials on beams. Essential prerequisite knowledge
More information10. COMPRESSION AND BUCKLING
10. COMRESSION AND BUCKLING Whenever a structural member is designed, it is necessary that it satisfies specific strength, deflection and stability requirements. Typically strength (or in some cases fracture
More informationMECHANICAL PRINCIPLES HNC/D MOMENTS OF AREA. Define and calculate 1st. moments of areas. Define and calculate 2nd moments of areas.
MECHANICAL PRINCIPLES HNC/D MOMENTS OF AREA The concepts of first and second moments of area fundamental to several areas of engineering including solid mechanics and fluid mechanics. Students who are
More informationENGINEERING COUNCIL CERTIFICATE LEVEL
ENGINEERING COUNCIL CERTIICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL  BASIC STUDIES O STRESS AND STRAIN You should judge your progress by completing the self assessment exercises. These may be sent
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQF LEVEL 3 OUTCOME 2  STRESS AND STRAIN
EDEXCEL NATIONAL CERTIICATE/DIPLOMA URTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11  NQ LEVEL 3 OUTCOME  STRESS AND STRAIN TUTORIAL 1  SHEAR CONTENT Be able to determine the stress in structural
More informationMechanics of Materials StressStrain Curve for Mild Steel
StressStrain Curve for Mild Steel 131 Definitions 132a Hooke s Law Shear Modulus: Stress: Strain: Poisson s Ratio: Normal stress or strain = " to the surface Shear stress = to the surface Definitions
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQF LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS
EDEXCEL NATIONAL CERTIICATE/DIPLOMA MECHANICAL PRINCIPLES AND APPLICATIONS NQ LEVEL 3 OUTCOME 1  LOADING SYSTEMS TUTORIAL 3 LOADED COMPONENTS 1. Be able to determine the effects of loading in static engineering
More informationENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 10  TORSION
ENGINEERING COUNCI IPOMA EVE MECHANICS OF SOIS 20 TUTORIA 10  TORSION You should judge your progress by completing the self assessment exercises. On completion of this tutorial you should be able to do
More informationDesign of Slender Columns
Design of Slender Columns When a stocky column (i.e. one that is not very slender, where slenderness is defined as the ratio between the column s height and width) is subjected to an excessive axial load
More informationMECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS
MECHANICS OF SOLIDS  BEAMS TUTORIAL TUTORIAL 4  COMPLEMENTARY SHEAR STRESS This the fourth and final tutorial on bending of beams. You should judge our progress b completing the self assessment exercises.
More informationcos 2u  t xy sin 2u (Q.E.D.)
09 Solutions 46060 6/8/10 3:13 PM Page 619 010 Pearson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 9 1. Prove that
More informationMECHANICS OF MATERIALS
2009 The McGrawHill Companies, Inc. All rights reserved. Fifth SI Edition CHAPTER 4 MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf David F. Mazurek Pure Bending Lecture
More informationStructures and Stiffness
Structures and Stiffness ENGR 10 Introduction to Engineering Ken Youssefi/Thalia Anagnos Engineering 10, SJSU 1 Wind Turbine Structure The Goal The support structure should be optimized for weight and
More informationStresses in Beam (Basic Topics)
Chapter 5 Stresses in Beam (Basic Topics) 5.1 Introduction Beam : loads acting transversely to the longitudinal axis the loads create shear forces and bending moments, stresses and strains due to V and
More informationCOMPLEX STRESS TUTORIAL 5 STRAIN ENERGY
COMPLEX STRESS TUTORIAL 5 STRAIN ENERGY This tutorial covers parts of the Engineering Council Exam D Structural Analysis and further material useful students of structural engineering. You should judge
More informationElastic Buckling Loads of Hinged Frames by the Newmark Method
International Journal of Applied Science and Technology Vol. 1 No. 3; June 011 Abstract Elastic Buckling Loads of Hinged Frames by the Newmark Method Ashraf Badir Department of Environmental and Civil
More informationChapter 12 Elasticity
If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences
More informationEnd Restraint and Effective Lengths of Columns
CHAPTER Structural Steel Design LRFD Method Third Edition INTRODUCTION TO AXIALLY LOADED COMPRESSION MEMBERS A. J. Clark School of Engineering Department of Civil and Environmental Engineering Part II
More informationCOMPLEX STRESS TUTORIAL 3 COMPLEX STRESS AND STRAIN
COMPLX STRSS TUTORIAL COMPLX STRSS AND STRAIN This tutorial is not part of the decel unit mechanical Principles but covers elements of the following sllabi. o Parts of the ngineering Council eam subject
More informationDesign of crossgirders and slabs in ladder deck bridges
130 Chris R Hendy Head of Bridge Design and Technology Highways & Transportation Atkins Jessica Sandberg Senior Engineer Highways & Transportation Atkins David Iles Steel Construction Institute Design
More information6 1. Draw the shear and moment diagrams for the shaft. The bearings at A and B exert only vertical reactions on the shaft.
06 Solutions 46060_Part1 5/27/10 3:51 PM Page 329 6 1. Draw the shear and moment diagrams for the shaft. The bearings at and exert only vertical reactions on the shaft. 250 mm 800 mm 24 kn 6 2. Draw the
More informationUnit 48: Structural Behaviour and Detailing for Construction. Chapter 13. Reinforced Concrete Beams
Chapter 13 Reinforced Concrete Beams Concrete is a material strong in its resistance to compression, but very weak indeed in tension. good concrete will safely take a stress upwards of 7 N/mm 2 in compression,
More informationOUTCOME 1  TUTORIAL 1 COMPLEX STRESS AND STRAIN
UNIT 6: STRNGTHS OF MATRIALS Unit code: K/60/409 QCF level: 5 Credit value: 5 OUTCOM  TUTORIAL COMPLX STRSS AND STRAIN. Be able to determine the behavioural characteristics of engineering components subjected
More informationDesign of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column
Design of reinforced concrete columns Type of columns Failure of reinforced concrete columns Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend
More informationUnit M4.7 The Column and Buckling
Unit M4.7 The Column and Buckling Readings: CDL 9.19.4 CDL 9.5, 9.6 16.003/004  Unified Engineering Department of Aeronautics and Astronautics Massachusetts Institute of Technology LEARNING OBJECTIVES
More informationENGINEERING COUNCIL CERTIFICATE LEVEL ENGINEERING SCIENCE C103 TUTORIAL 3  TORSION
ENGINEEING COUNCI CETIFICATE EVE ENGINEEING SCIENCE C10 TUTOIA  TOSION You should judge your progress by completing the self assessment exercises. These may be sent for marking or you may request copies
More informationStatics and Mechanics of Materials
Statics and Mechanics of Materials Chapter 4 Stress, Strain and Deformation: Axial Loading Objectives: Learn and understand the concepts of internal forces, stresses, and strains Learn and understand the
More informationModule 6 Power Screws. Version 2 ME, IIT Kharagpur
Module 6 Power Screws Lesson Design of power screws Instructional Objectives At the end of this lesson, the students should have the knowledge of Stresses in power screw. Design procedure of a power screw.
More information10 Space Truss and Space Frame Analysis
10 Space Truss and Space Frame Analysis 10.1 Introduction One dimensional models can be very accurate and very cost effective in the proper applications. For example, a hollow tube may require many thousands
More informationIII. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.)
ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University it of Maryland Compression Members Following subjects are covered:
More informationChapter 4: Summary and Conclusions
Chapter 4: Summary and Conclusions 4.1 Summary Three different models are presented and analyzed in this research for the purpose of studying the potential of using postbuckled or prebent elastic struts
More informationCourse 1 Laboratory. Second Semester. Experiment: Young s Modulus
Course 1 Laboratory Second Semester Experiment: Young s Modulus 1 Elasticity Measurements: Young Modulus Of Brass 1 Aims of the Experiment The aim of this experiment is to measure the elastic modulus with
More informationOptimising plate girder design
Optimising plate girder design NSCC29 R. Abspoel 1 1 Division of structural engineering, Delft University of Technology, Delft, The Netherlands ABSTRACT: In the design of steel plate girders a high degree
More informationBending Beam. Louisiana State University. Joshua Board
Bending Beam Louisiana State University Joshua Board Table of Contents: Table of Figures:... 4 Purpose... 5 Introduction... 5 Apparatus and Test Procedures... 11 Summary of Data... 14 Discussion of Results...
More informationStrength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 29 Stresses in Beams IV
Strength of Materials Prof: S.K.Bhattacharya Dept of Civil Engineering, IIT, Kharagpur Lecture no 29 Stresses in Beams IV Welcome to the fourth lesson of the sixth module on Stresses in Beams part 4.
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA ADVANCED MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 18 NQF LEVEL 3
EEXCE NATIONA CETIFICATE/IPOMA AVANCE MECHANICA PINCIPES AN APPICATIONS UNIT 18 NQF EVE OUTCOME 2 BE ABE TO ETEMINE THE STESS UE TO BENING IN BEAMS AN TOSION IN POWE TANSMISSION SHAFTS TUTOIA  SHEA STESS
More informationMECHANICS OF MATERIALS Plastic Deformations of Members With a Single Plane of Symmetry
Plastic Deformations of Members With a Single Plane of Smmetr Full plastic deformation of a beam with onl a vertical plane of smmetr. The neutral axis cannot be assumed to pass through the section centroid.
More information11 Vibration Analysis
11 Vibration Analysis 11.1 Introduction A spring and a mass interact with one another to form a system that resonates at their characteristic natural frequency. If energy is applied to a spring mass system,
More informationR A = R B = = 3.6 kn. ΣF y = 3.6 V = 0 V = 3.6 kn. A similar calculation for any section through the beam at 3.7 < x < 7.
ENDNG STRESSES & SHER STRESSES N EMS (SSGNMENT SOLUTONS) Question 1: 89 mm 3 mm Parallam beam has a length of 7.4 m and supports a concentrated load of 7.2 kn, as illustrated below. Draw shear force and
More informationChapter 4 Strain and Material Relations
CIVL 222 STRENGTH OF MATERIALS Chapter 4 Strain and Material Relations Terminology 1. Displacement 2. Deformation 3. Strain 4. Average Axial Strain 5. Shearing Strain 6. Poisson s Ratio 7. Mechanical Properties
More informationCHAPTER MECHANICS OF MATERIALS
CHPTER 4 Pure MECHNCS OF MTERLS Bending Pure Bending Pure Bending Other Loading Tpes Smmetric Member in Pure Bending Bending Deformations Strain Due to Bending Stress Due to Bending Beam Section Properties
More informationCHAPTER 4 TENSILE TESTING
CHAPTER 4 TENSILE TESTING EXERCISE 28, Page 7 1. What is a tensile test? Make a sketch of a typical load/extension graph for a mild steel specimen to the point of fracture and mark on the sketch the following:
More informationB.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) TermEnd Examination December, 2011 BAS010 : MACHINE DESIGN
No. of Printed Pages : 7 BAS01.0 B.TECH. (AEROSPACE ENGINEERING) PROGRAMME (BTAE) CV CA CV C:) O TermEnd Examination December, 2011 BAS010 : MACHINE DESIGN Time : 3 hours Maximum Marks : 70 Note : (1)
More informationThe elements used in commercial codes can be classified in two basic categories:
CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for
More informationCHAPTER 1 INTRODUCTION
CHAPTER 1 INTRODUCTION 1.1 Background of the research Beam is a main element in structural system. It is horizontal member that carries load through bending (flexure) action. Therefore, beam will deflect
More informationCE 1252 STRENGTH OF MATERIALS
CE 1252 STRENGTH OF MATERIALS TWO MARK QUESTION & ANSWERS Prepared by K.J.Jegidha, M.E. Lecturer, Civil UNIT : I ENERGY METHODS 1.Define: Strain Energy When an elastic body is under the action of external
More informationMechanics of Materials Qualifying Exam Study Material
Mechanics of Materials Qualifying Exam Study Material The candidate is expected to have a thorough understanding of mechanics of materials topics. These topics are listed below for clarification. Not all
More informationSheet metal operations  Bending and related processes
Sheet metal operations  Bending and related processes R. Chandramouli Associate DeanResearch SASTRA University, Thanjavur613 401 Table of Contents 1.QuizKey... Error! Bookmark not defined. 1.Bending
More informationPOWER SCREWS (ACME THREAD) DESIGN
POWER SCREWS (ACME THREAD) DESIGN There are at least three types of power screw threads: the square thread, the Acme thread, and the buttress thread. Of these, the square and buttress threads are the most
More informationStrength of materials Lab. Manual. Production Engineering
1 Strength of materials Lab. Manual Production Engineering 2 Strength of materials lab. manual Contents S.No. Title Pg.no 1. Rockwell Hardness test 3 2. Brinell hardness test. 5 3. Impact test 8 4. Tension
More informationSimple design method
method Aim of the design method 2 3 Content of presentation in a fire situation method of reinforced concrete slabs at 20 C Floor slab model Failure modes method of at Extension to fire behaviour Membrane
More informationDesign of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar. Fig. 7.21 some of the trusses that are used in steel bridges
7.7 Truss bridges Fig. 7.21 some of the trusses that are used in steel bridges Truss Girders, lattice girders or open web girders are efficient and economical structural systems, since the members experience
More informationDr. Seshu Adluri. Structural Steel Design Compression Members
Dr. Seshu Adluri Structural Steel Design Compression Members Columns in Buildings Columns in Buildings Column supports Compression members in trusses Compression members in trusses Compression members
More informationEQUILIBRIUM AND ELASTICITY
Chapter 12: EQUILIBRIUM AND ELASTICITY 1 A net torque applied to a rigid object always tends to produce: A linear acceleration B rotational equilibrium C angular acceleration D rotational inertia E none
More informationDESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,
DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared
More information3. AXIALLY LOADED MEMBERS
3 AXIALLY LOADED MEMBERS 31 Reading Assignment: Section 19 and Sections 81 and 82 of text Most axially loaded structural members carry some moment in addition to axial load  for this discussion, restrict
More informationCOLUMNS: BUCKLING (PINNED ENDS)
LECTURE Third Edition COLUMNS: BUCKLNG (PNNED ENDS) A. J. Clark School of Engineering Department of Civil and Environmental Engineering 6 Chapter 10.1 10.3 b Dr. brahim A. Assakkaf SPRNG 003 ENES 0 Mechanics
More informationSAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN
SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN 1.1 Stress & Strain Stress is the internal resistance offered by the body per unit area. Stress is represented as force per unit area. Typical
More informationP4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections
4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 4 Stresses on Inclined Sections Shear stress and shear strain. Equality of shear stresses on perpendicular planes. Hooke s law in shear. Normal and shear
More information3. Decide on the span or total length of the truss based on the length of each member of the truss.
Truss building project: Objective: Build a truss made of straws to a desired length and predict the maximum amount of weight it will hold (for a minimum of 20 seconds) when the weight is placed in the
More informationSection 16: Neutral Axis and Parallel Axis Theorem 161
Section 16: Neutral Axis and Parallel Axis Theorem 161 Geometry of deformation We will consider the deformation of an ideal, isotropic prismatic beam the cross section is symmetric about yaxis All parts
More informationObjectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.
Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity
More informationTorsion Testing. Objectives
Laboratory 4 Torsion Testing Objectives Students are required to understand the principles of torsion testing, practice their testing skills and interpreting the experimental results of the provided materials
More informationMCE380: Measurements and Instrumentation Lab. Chapter 9: Force, Torque and Strain Measurements
MCE380: Measurements and Instrumentation Lab Chapter 9: Force, Torque and Strain Measurements Topics: Elastic Elements for Force Measurement Dynamometers and Brakes Resistance Strain Gages Holman, Ch.
More informationPin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify.
4. FORCES in PIN JOINTED STRUCTURES Pin jointed structures are often used because they are simple to design, relatively inexpensive to make, easy to construct, and easy to modify. They can be fixed structures
More informationSTRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION
Chapter 11 STRESS AND DEFORMATION ANALYSIS OF LINEAR ELASTIC BARS IN TENSION Figure 11.1: In Chapter10, the equilibrium, kinematic and constitutive equations for a general threedimensional solid deformable
More informationThe Mathematics of Simple Beam Deflection
The Mathematics of Simple Beam Laing O Rourke Civil Engineering INTRODUCTION Laing O Rourke plc is the largest privately owned construction firm in the UK. It has offices in the UK, Germany, India, Australia
More information16. BeamandSlab Design
ENDP311 Structural Concrete Design 16. BeamandSlab Design BeamandSlab System How does the slab work? L beams and T beams Holding beam and slab together University of Western Australia School of Civil
More informationDesign of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
Problem 1 Design a hand operated overhead crane, which is provided in a shed, whose details are: Capacity of crane = 50 kn Longitudinal spacing of column = 6m Center to center distance of gantry girder
More informationDesign Analysis and Review of Stresses at a Point
Design Analysis and Review of Stresses at a Point Need for Design Analysis: To verify the design for safety of the structure and the users. To understand the results obtained in FEA, it is necessary to
More informationWorked Examples of mathematics used in Civil Engineering
Worked Examples of mathematics used in Civil Engineering Worked Example 1: Stage 1 Engineering Surveying (CIV_1010) Tutorial  Transition curves and vertical curves. Worked Example 1 draws from CCEA Advanced
More informationDESIGN OF SLABS. Department of Structures and Materials Engineering Faculty of Civil and Environmental Engineering University Tun Hussein Onn Malaysia
DESIGN OF SLABS Department of Structures and Materials Engineering Faculty of Civil and Environmental Engineering University Tun Hussein Onn Malaysia Introduction Types of Slab Slabs are plate elements
More informationProblem P5.2: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable?
Problem P5.: A 1 Mg container hangs from a 15 mm diameter steel cable. What is the stress in the cable? Find the cross sectional area in terms of diameter using Equation (5.1). Calculate the tensile stress
More informationSOLID MECHANICS DYNAMICS TUTORIAL NATURAL VIBRATIONS ONE DEGREE OF FREEDOM
SOLID MECHANICS DYNAMICS TUTORIAL NATURAL VIBRATIONS ONE DEGREE OF FREEDOM This work covers elements of the syllabus for the Engineering Council Exam D5 Dynamics of Mechanical Systems, C05 Mechanical and
More informationIntroduction to Beam. Area Moments of Inertia, Deflection, and Volumes of Beams
Introduction to Beam Theory Area Moments of Inertia, Deflection, and Volumes of Beams Horizontal structural member used to support horizontal loads such as floors, roofs, and decks. Types of beam loads
More informationTechnical Notes 3B  Brick Masonry Section Properties May 1993
Technical Notes 3B  Brick Masonry Section Properties May 1993 Abstract: This Technical Notes is a design aid for the Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 40292) and Specifications
More informationTensile Testing Laboratory
Tensile Testing Laboratory By Stephan Favilla 0723668 ME 354 AC Date of Lab Report Submission: February 11 th 2010 Date of Lab Exercise: January 28 th 2010 1 Executive Summary Tensile tests are fundamental
More informationSTRENGTH OF MATERIALS  II
STRENGTH OF MATERIALS  II DEPARTMENT OF CIVIL ENGINEERING INSTITUTE OF AERONAUTICAL ENGINEERING UNIT 1 TORSION TORSION OF HOLLOW SHAFTS: From the torsion of solid shafts of circular x section,
More informationStressStrain Relationship
(Strength of Materials) Dave Morgan StressStrain Relationship p. 1/21 The tension test: StressStrain Relationship p. 2/21 The tension test: Is a common standardised test that can
More informationModule 4 Fasteners. Version 2 ME, IIT Kharagpur
Module 4 Fasteners Lesson 1 Types of fasteners: Pins and keys Instructional Objectives At the end of this lesson, the students should have the knowledge of Fasteners and their types: permanent and detachable
More informationDesign of Steel Structures Prof. S.R.Satish Kumar and Prof. A.R.Santha Kumar
6.3 Behaviour of steel beams Laterally stable steel beams can fail only by (a) Flexure (b) Shear or (c) Bearing, assuming the local buckling of slender components does not occur. These three conditions
More information5 Steel elements. 5.1 Structural design At present there are two British Standards devoted to the design of strucof tural steel elements:
5 Steel elements 5.1 Structural design At present there are two British Standards devoted to the design of strucof steelwork tural steel elements: BS 449 The use of structural steel in building. BS 5950
More informationTHREE DIMENSIONAL ACES MODELS FOR BRIDGES
THREE DIMENSIONAL ACES MODELS FOR BRIDGES Noel Wenham, Design Engineer, Wyche Consulting Joe Wyche, Director, Wyche Consulting SYNOPSIS Plane grillage models are widely used for the design of bridges,
More informationEffect of Oblique Loading on Energy Absorption Capacity of Rectangular Tube
Effect of Oblique Loading on Energy Absorption Capacity of Rectangular Tube Prashant Hupare 1 1 M.E. Student, Mechanical Engineering Department, Walchand Institute of Technology, Solapur University, Solapur413006,
More informationRC Expert. User Manual
Software Package Design Expert version 2.7 Structural Design and Detailing to Eurocode RC Expert All rights reserved 2014 TABLE OF CONTENTS About the program... 2 Data input... 2 Files... 3 New file...
More informationUnit 24: Applications of Pneumatics and Hydraulics
Unit 24: Applications of Pneumatics and Hydraulics Unit code: J/601/1496 QCF level: 4 Credit value: 15 OUTCOME 2 TUTORIAL 2 HYDRAULIC AND PNEUMATIC CYLINDERS The material needed for outcome 2 is very extensive
More informationImpact Load Factors for Static Analysis
Impact Load Factors for Static Analysis Often a designer has a mass, with a known velocity, hitting an object and thereby causing a suddenly applied impact load. Rather than conduct a dynamic analysis
More informationAluminium systems profile selection
Aluminium systems profile selection The purpose of this document is to summarise the way that aluminium profile selection should be made, based on the strength requirements for each application. Curtain
More information