11 Locate the centroid of the plane area shown. 12 Determine the location of centroid of the composite area shown.


 Cory Gallagher
 1 years ago
 Views:
Transcription
1 Chapter 1 Review of Mechanics of Materials 11 Locate the centroid of the plane area shown 650 mm 1000 mm 650 x 1 Determine the location of centroid of the composite area shown mm radius 00 mm radius 00 mm 00 mm 600 mm 1 Verif that the radius of gration for a circle of diameter d with respect to a centroidal axis is d/ Determine the moment of inertia of the shaded area with respect to the x axis. 400 mm 600 mm 00 mm 400 mm x 400 mm 400 mm 00
2 15 Determine the product moment of inertia of the triangle with respect to the x and axes. h G b x x 16 Determine the product moment of inertia of the triangle in the previous question with respect to the x and axes. The centroid of the triangle is at G. Answers: 11 x = 76mm, = 08 from the bottom left corner 1 x = 601mm, = 00mm from bottom left corner 1 Hint: find the area moment of inertia and the area m (b h )/ (b h )/7
3 Chapter Basic Elasticit 1 The two dimensional stress state at a point of an element of a material is given as shown. 0 MPa 40 MPa 75 MPa Calculate (a) the axial and shear stress on a plane whose normal is 40 0 clockwise to the xdirection (b) the magnitude and directions of the principal stresses and (c) the maximum shear stress.  A plane element is subjected to a constant axial stress of 50 MPa in the x direction and an axial stress varing from 50 MPa to 50 MPa in the  direction. Plot the maximum shear stress acting in the plane element with respect to the axial stress in the direction. What is the largest shear stress magnitude?  Determine the magnitude and directions of the principal strains and the maximum shear strain on an element with the following strains: ε x = 160 x 106 ; ε = 80 x 106 ; γ x = 10 x The principal strains have been found to be and respectivel. Determine (a) the maximum shear strain and (b) the maximum shear stress given that the shear modulus of elasticit is 6. GPa. 5 The element shown is subject to 50 MPa and 75 MPa compressive stresses in the x and directions respectivel and a shear stress of unknown magnitude but acting in the described sense. When this element is rotated clockwise at 5 o, the shear stress magnitude is equal but acts in the opposite sense; while the axial stress magnitudes are unchanged. Determine the value of the unknown shear stress. 75 MPa unknown 50 MPa
4 6 The element shown is subject to an unknown axial stress in the x direction and zero axial stress in the direction. The shear stress is 0 MPa. When this element is rotated around, the maximum shear stress recorded is 50 MPa. Determine (a) the axial stress in the x direction, and (b) the principal stresses. 0 MPa 0 MPa unknown 7 A pair of strain gages gave the following readings: with 0 o gage = 500 microstrains, with 90 o gage = 100 microstrains. The strain gages register equal values after a 0 o anticlockwise rotation. Determine (a) the maximum shear strain, and (b) the principal strains. 8 A beam of length l with a thin rectangular crosssection is clamped at the end x = 0 and loaded at the tip with vertical force P. Show that the stress distribution can be represented b φ = A + B x + Cx Determine the coefficients A, B, and C. 9 The cantilever beam shown is in a state of plane strain and is rigidl supported at x = L. Examine if the stress function given meets the biharmonic equation and boundar conditions. w 5 φ = (15h x 5x h + ) 0h
5 Answers: 1 (a) 71 MPa 6 MPa MPa (b) 88.5 MPa 4.5 MPa (c) 66 MPa  50 MPa when the axial stress = 50 MPa x 106, 94 x 106, 7 x 106, 1 o 4 (a) (b) MPa MPa 6 (a) 80 MPa (b) 90 MPa, 10 MPa 7 (a) 680 microstrains (b) 540 microstrains, 140 microstrains 8 Pl / td, P/td, P/td
6 Chapter Principles of Aircraft Construction 1 The Ford Trimotor, nicknamed The Tin Goose, was a three engine civil transport aircraft first produced in 195 b Henr Ford and continued until June 7, 19. The structure of the plane consists of a trusswork of U shaped aluminum beams, with a thin skin of aluminum riveted on top, using skin corrugations instead of wing ribs and fuselage stringers. Briefl discuss the benefits and disadvantages with such a construction.  The Gossamer Albatross is a humanpowered aircraft built b American aeronautical engineer Paul B. MacCread. Briefl discuss the merits of the external wire bracing construction used over trusswork or monocoque construction.  Briefl explain wh composite materials have led to huge advances in the monocoque construction of aircrafts.
7 4 The double riveted joint shown connects two plates. If the failure strength of the rivets in shear is 70 N/mm, and the tensile strength of the plate is 465 N/mm, determine the rivet pitch if the joint is to be designed so that failure due to shear in the rivets and failure due to tension in the plate occur simultaneousl. Find also the joint efficienc. Answers: 4 1mm, 75%
8 Chapter 4 Airframe Loads 41 The aircraft shown weighs 15kN and has landed such that at the instant of impact the ground reaction on each main undercarriage wheel is 00kN and its vertical velocit is.5m/s. Find (i) the acceleration experienced. Each undercarriage wheel weighs.5kn and is attached to a strut. Calculate the (ii) axial load, and (iii) bending moment in the strut. At section AA the wing outboard of this section weighs 6.6kN and the center of gravit is.05m from AA. Calculate the (iv) shear force and (v) bending moment at section AA. 4 An aircraft makes a correctl banked turn at radius 610m at a speed of 168m/s. Find (i) the angle of bank, and (ii) load factor. Immediatel after making the turn and restoring to smmetric flight, the figure shows the relative positions of the center of gravit, aerodnamic center of the complete aircraft less the tailplane, and the tailplane center of pressure at zero lift incidence. The specifications are: Weight (W) = 1,500N; Wing area (S) = 46.5m ; Wing mean cord (c) = m; C D = C L ; C M,O = Find (iii) the lift coefficient, (iv) drag force, and (v) pitching moment. If the change in lift coefficient per wing incidence is 4.5/rad. Determine (vi) the tail load.
9 4 During pullout from a dive with zero thrust at 15m/s, an aircraft weighing 8,000N has the flight path at 40 o to the horizontal with radius of curvature 155m. The distance between the CG and tail is 1.m. The angular velocit of pitch is checked b appling an angular retardation of 0.5 rad/s. The moment of inertia of the aircraft for pitching is 04,000 kgm. Find (i) the additional tail load required to check the angular velocit in pitch. The aircraft has wings 88.5m in area, mean cord of 1m, and the pitching moment coefficient for all parts excluding the tailplane through the CG is given b C M.CG.c = 0.47C L Find (ii) the amount of lift, (iii) the lift coefficient, and (iv) pitching moment, and (v) tail load. (Hint: neglect the tail loads for the first approximation of lift, iterations is sufficient) Answers: m/s 19.kN 9kNm (clockwise) 0.m 19.5kN 59.6kNm o, 4.8, 0.80,,707N, 7,9Nm, 7,160N N, N, 0.59, 0880Nm, 1895N
10 Chapter 5 Torsion of Solid Sections 51 The stress function φ = k(r a ) is applicable to the solution of a solid circular section bar of radius a. Determine the stress distributions τ z, τ zx in the bar in terms of the applied torque, dw/dx, dw/d, and warping of the cross section. 5 A torque T is applied on the section comprising narrow rectangular strips shown. Determine (i) the torsional constant, (ii) the stress distributions τ z, τ zx, and (iii) the maximum shear stress. 5 The stress function φ = m(x a )( b ) is applicable to the solution of the rectangular section bar shown. Determine the stress distributions τ z, τ zx dw/dx, dw/d in the bar in terms of the applied torque. b x a Answers: 51 Tx/πa 4, T/πa 4, 0, 0, 0 (a + b) t d 5, Gx θ T, 0, ± dz (a + b) t 9Tx( b ) 9T( x a ) dw 9T( x a + b ) 5 τ z =, τ zx =, =, 16a b 16a b dx a b dw 9Tx( x a + b ) = d a b
11 Chapter 6 Bending of ThinWalled Beams 61 A bending moment of 000Nm is applied on the section shown at 0 o to the vertical axis. The sense of the bending moment is such that its components M x and M both produce tension in the positive x quadrant. Find the distances of C from edges BC and AB. Deduce the point where the flexural stress is maximum and calculate the amount. 6 A thinwalled cantilever beam of unsmmetrical crosssection supports the shear forces at the free end of the section shown. Calculate the flexural stress midwa along A on the beam. It can be assumed that no twisting of the beam occurs.
12 6 A thin walled beam has the crosssection shown. If the beam is subjected to a bending moment Mx in the plane of web, calculate the distribution of flexural stress in the beam cross section. Answers: mm, 8.4mm, C, 6.N/mm N/mm σ z,1 = Mx, σ Mx z, =, σ z, = Mx, σ z,4 = Mx h t h t h t h t
13 Chapter 7 Shear of ThinWalled Beams 71 A beam has singl smmetrical thinwalled cross section shown. The thickness of the walls is constant throughout. Show that the distance of the shear centre from the web is given b ρ sin α cosα ξ s = d for ρ = d / h 1+ 6ρ + ρ sin α 7 A beam has singl smmetrical thinwalled cross section shown. Each wall of the section is flat and has the same length a and thickness t. Calculate the distance of the shear centre from point.
14 7 A uniform thin walled beam of thickness t has a crosssection in the shape of an isosceles triangle. It is loaded b a vertical shear force S applied at the apex. Calculate the shear flow over the cross section. Answers: 71 Tx/πa 4, T/πa 4, 0, 0, θ a a x x dz d G, + θ a x dz d G, dz d a x θ, dz d a a x θ +, dz d x a θ ) ( 1 7 ) ( ) / ( 1 1 d h h d h d s S q + =, ) ( ) 6 6 ( d h h h hs s S q + + =
15 Chapter 8 Virtual Work & Energ Methods 81 During a routine manufacturing operation, rod AB must acquire an elastic strain energ of 1 J. Determine the ield strength of the steel if the factor of safet = 5 and E = 00 GPa. B 18 mm diameter A P 1.5 m 8 Evaluate the strain energ of the prismatic beam for the loading shown. A P D B a L b 8 The element shown is taken from part of a bar subjected to axial stresses in x and axis. The shear stress is zero. Find the strain energ stored in the bar of volume.75 x 105 m. The modulus of elasticit is 00 GPa and the Poisson s ratio is 0.8. x 10 MPa 60 MPa 84 Determine the force in member AB in the truss shown in (a) using the principle of virtual work given the deformation described in (b).
16 85 Determine the slope A of the beam ABC at A using the principle of virtual work. 86 Calculate the vertical displacements of B and C in the simpl supported beam of length L and flexural rigidit EI using the energ method. 87 Calculate the loads in the members of the singl redundant pinjointed framework using the energ method. The members AC and BD are 0mm in cross section and all other members are 0mm in cross section. The members AD, BC, and DC are 800mm long. E = 00,000N/mm.
17 Answers: MPa 8 Pab ( a+ b) 6EIL J kn 85 WL 16EI wL 5wL, 4576EI 84EI 87 R =.1 N
18 Chapter 9 Matrix Methods 91 The square smmetrical pinjointed truss is pinned to rigid supports at and 4; whilst loaded at 1. The axial rigidit for all members is EA. Use the matrix method to (a) find the displacements in 1 and and (b) solve for all internal member forces and support reactions. 9 The displacement at node 4 of the pinjointed frame is zero. Use the matrix method to find (a) the ratio H/P and the (b) displacements of nodes and. Answers: PL 91 v1 =, AE H 9 = , v P 0.9PL P v =, s 1 = s14 =, s = s4 = 0. 07P AE 4Pl 6Pl =, v = (9 + ) AE (9 + ) AE
19 Chapter 10 Stress/Strain Measurement 101 A cantilever bar is to be loaded as shown and the strain axial strain measured at midspan with strain gages. Briefl suggest a readout scheme wherein the highest voltage is obtained for the load applied. P L 10 In certain strain gage applications, it is necessar to record strains over a long period of time without having the opportunit to recheck the zero reading. The strain indicator will have an effect of the zero position drifting. Suggest how the measuring method can be done in order to eliminate the strain indicator drifting effect and how the instrumentation drift amount can be determined. 10 A birefringent disk of thickness of 5mm and material fringe value of 1.5 N/mm is viewed under a circular polariscope. Along a horizontal section in the middle, the outer ends have zero relative retardation. Find the principal stress difference at the middle of the disk. Answers: 1015N/mm
Module 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 informationExternal Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is
Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the
More informationUnit 15 Shearing and Torsion (and Bending) of Shell Beams
Unit 15 Shearing and Torsion (and Bending) of Shell Beams Readings: Rivello Ch. 9, section 8.7 (again), section 7.6 T & G 126, 127 Paul A. Lagace, Ph.D. Professor of Aeronautics & Astronautics and Engineering
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 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 information2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at A and supported at B by rod (1). What is the axial force in rod (1)?
IDE 110 S08 Test 1 Name: 1. Determine the internal axial forces in segments (1), (2) and (3). (a) N 1 = kn (b) N 2 = kn (c) N 3 = kn 2. Rigid bar ABC supports a weight of W = 50 kn. Bar ABC is pinned at
More informationσ = Eα(T T C PROBLEM #1.1 (4 + 4 points, no partial credit)
PROBLEM #1.1 (4 + 4 points, no partial credit A thermal switch consists of a copper bar which under elevation of temperature closes a gap and closes an electrical circuit. The copper bar possesses a length
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 informationLECTURE 14 Strength of a Bar in Transverse Bending. 1 Introduction. As we have seen, only normal stresses occur at cross sections of a rod in pure
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 14 Strength of a Bar in Transverse Bending 1 ntroduction s we have seen, onl normal stresses occur at cross sections of a rod in pure bending. The corresponding
More informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 4 Pure Bending
EA 3702 echanics & aterials Science (echanics of aterials) Chapter 4 Pure Bending Pure Bending Ch 2 Aial Loading & Parallel Loading: uniform normal stress and shearing stress distribution Ch 3 Torsion:
More informationThe example of shafts; a) Rotating Machinery; Propeller shaft, Drive shaft b) Structural Systems; Landing gear strut, Flap drive mechanism
TORSION OBJECTIVES: This chapter starts with torsion theory in the circular cross section followed by the behaviour of torsion member. The calculation of the stress stress and the angle of twist will be
More informationOutline. Organization. Stresses in Beams
Stresses in Beams B the end of this lesson, ou should be able to: Calculate the maimum stress in a beam undergoing a bending moment 1 Outline Curvature Normal Strain Normal Stress Neutral is Moment of
More informationUnit III Theory of columns. Dr.P.Venkateswara Rao, Associate Professor, Dept. of Civil Engg., SVCE, Sriperumbudir
Unit III Theory of columns 1 Unit III Theory of Columns References: Punmia B.C.,"Theory of Structures" (SMTS) Vol II, Laxmi Publishing Pvt Ltd, New Delhi 2004. Rattan.S.S., "Strength of Materials", Tata
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationSample Problems for Exam II
Sample Problems for Exam 1. Te saft below as lengt L, Torsional stiffness GJ and torque T is applied at point C, wic is at a distance of 0.6L from te left (point ). Use Castigliano teorem to Calculate
More informationMECHANICS OF MATERIALS. Prepared by Engr. John Paul Timola
MECHANICS OF MATERIALS Prepared by Engr. John Paul Timola Mechanics of materials branch of mechanics that studies the internal effects of stress and strain in a solid body. stress is associated with the
More informationQuestion 1. Ignore bottom surface. Solution: Design variables: X = (R, H) Objective function: maximize volume, πr 2 H OR Minimize, f(x) = πr 2 H
Question 1 (Problem 2.3 of rora s Introduction to Optimum Design): Design a beer mug, shown in fig, to hold as much beer as possible. The height and radius of the mug should be not more than 20 cm. The
More informationReview of Strain Energy Methods and Introduction to Stiffness Matrix Methods of Structural Analysis
uke University epartment of Civil and Environmental Engineering CEE 42L. Matrix Structural Analysis Henri P. Gavin Fall, 22 Review of Strain Energy Methods and Introduction to Stiffness Matrix Methods
More informationBeams. Beams are structural members that offer resistance to bending due to applied load
Beams Beams are structural members that offer resistance to bending due to applied load 1 Beams Long prismatic members Nonprismatic sections also possible Each crosssection dimension Length of member
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 informationPractice Test 3. Name: Date: ID: A. Multiple Choice Identify the choice that best completes the statement or answers the question.
Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20
More informationSpherical Pressure Vessels
Spherical Pressure Vessels Pressure vessels are closed structures containing liquids or gases under essure. Examples include tanks, pipes, essurized cabins, etc. Shell structures : When essure vessels
More informationChapter 2: Deflections of Structures
Chapter 2: Deflections of Structures Fig. 4.1. (Fig. 2.1.) ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 1 (2.1) (4.1) (2.2) Fig.4.2 Fig.2.2 ASTU, Dept. of C Eng., Prepared by: Melkamu E. Page 2
More informationStress Transformation Equations: u = +135 (Fig. a) s x = 80 MPa s y = 0 t xy = 45 MPa. we obtain, cos u + t xy sin 2u. s x = s x + s y.
014 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently 9 7. Determine the normal stress and shear stress acting
More informationMECHANICAL PROPERTIES OF SOLIDS
Chapter Nine MECHANICAL PROPERTIES OF SOLIDS MCQ I 9.1 Modulus of rigidity of ideal liquids is (a) infinity. (b) zero. (c) unity. (d) some finite small nonzero constant value. 9. The maximum load a wire
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 informationEMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading
MA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain  Axial Loading MA 3702 Mechanics & Materials Science Zhe Cheng (2018) 2 Stress & Strain  Axial Loading Statics
More informationLab Exercise #3: Torsion
Lab Exercise #3: Prelab 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 informationME 101: Engineering Mechanics
ME 0: Engineering Mechanics Rajib Kumar Bhattacharja Department of Civil Engineering ndian nstitute of Technolog Guwahati M Block : Room No 005 : Tel: 8 www.iitg.ernet.in/rkbc Area Moments of nertia Parallel
More informationAPPENDIX A Thickness of Base Metal
APPENDIX A Thickness of Base Metal For uncoated steel sheets, the thickness of the base metal is listed in Table A.1. For galvanized steel sheets, the thickness of the base metal can be obtained by subtracting
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More information7.4 The Elementary Beam Theory
7.4 The Elementary Beam Theory In this section, problems involving long and slender beams are addressed. s with pressure vessels, the geometry of the beam, and the specific type of loading which will be
More informationMECHANICS OF MATERIALS
Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:
More informationChapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING )
Chapter 5 CENTRIC TENSION OR COMPRESSION ( AXIAL LOADING ) 5.1 DEFINITION A construction member is subjected to centric (axial) tension or compression if in any cross section the single distinct stress
More informationFor more Stuffs Visit Owner: N.Rajeev. R07
Code.No: 43034 R07 SET1 JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II.B.TECH  I SEMESTER REGULAR EXAMINATIONS NOVEMBER, 2009 FOUNDATION OF SOLID MECHANICS (AERONAUTICAL ENGINEERING) Time: 3hours
More informationStrength of Material. Shear Strain. Dr. Attaullah Shah
Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume
More informationTorsion Stresses in Tubes and Rods
Torsion Stresses in Tubes and Rods This initial analysis is valid only for a restricted range of problem for which the assumptions are: Rod is initially straight. Rod twists without bending. Material is
More informationLecture 8: Flexibility Method. Example
ecture 8: lexibility Method Example The plane frame shown at the left has fixed supports at A and C. The frame is acted upon by the vertical load P as shown. In the analysis account for both flexural and
More informationMaterials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon.
Modes of Loading (1) tension (a) (2) compression (b) (3) bending (c) (4) torsion (d) and combinations of them (e) Figure 4.2 1 Standard Solution to Elastic Problems Three common modes of loading: (a) tie
More informationUNITV MOMENT DISTRIBUTION METHOD
UNITV MOMENT DISTRIBUTION METHOD Distribution and carryover of moments Stiffness and carry over factors Analysis of continuous beams Plane rigid frames with and without sway Neylor s simplification. Hardy
More informationBasic Energy Principles in Stiffness Analysis
Basic Energy Principles in Stiffness Analysis StressStrain Relations The application of any theory requires knowledge of the physical properties of the material(s) comprising the structure. We are limiting
More informationCHAPTER OBJECTIVES CHAPTER OUTLINE. 4. Axial Load
CHAPTER OBJECTIVES Determine deformation of axially loaded members Develop a method to find support reactions when it cannot be determined from euilibrium euations Analyze the effects of thermal stress
More informationElasticity: Term Paper. Danielle Harper. University of Central Florida
Elasticity: Term Paper Danielle Harper University of Central Florida I. Abstract This research was conducted in order to experimentally test certain components of the theory of elasticity. The theory was
More informationMechanics of Materials MENG 270 Fall 2003 Exam 3 Time allowed: 90min. Q.1(a) Q.1 (b) Q.2 Q.3 Q.4 Total
Mechanics of Materials MENG 70 Fall 00 Eam Time allowed: 90min Name. Computer No. Q.(a) Q. (b) Q. Q. Q.4 Total Problem No. (a) [5Points] An air vessel is 500 mm average diameter and 0 mm thickness, the
More informationInitial Stress Calculations
Initial Stress Calculations The following are the initial hand stress calculations conducted during the early stages of the design process. Therefore, some of the material properties as well as dimensions
More informationram reports in applied measurement
ram reports in applied measurement Introduction In the last decades, strain gage technology has developed into a standard procedure for experimental stress analysis. It is generally the case that three
More informationIndeterminate Analysis Force Method 1
Indeterminate Analysis Force Method 1 The force (flexibility) method expresses the relationships between displacements and forces that exist in a structure. Primary objective of the force method is to
More informationBOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE 2 ND YEAR STUDENTS OF THE UACEG
BOOK OF COURSE WORKS ON STRENGTH OF MATERIALS FOR THE ND YEAR STUDENTS OF THE UACEG Assoc.Prof. Dr. Svetlana LilkovaMarkova, Chief. Assist. Prof. Dimitar Lolov Sofia, 011 STRENGTH OF MATERIALS GENERAL
More information4. SHAFTS. A shaft is an element used to transmit power and torque, and it can support
4. SHAFTS A shaft is an element used to transmit power and torque, and it can support reverse bending (fatigue). Most shafts have circular cross sections, either solid or tubular. The difference between
More informationPractice Test 3. Multiple Choice Identify the choice that best completes the statement or answers the question.
Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s. During
More informationMECHANICS OF SOLIDS Credit Hours: 6
MECHANICS OF SOLIDS Credit Hours: 6 Teaching Scheme Theory Tutorials Practical Total Credit Hours/week 4 0 6 6 Marks 00 0 50 50 6 A. Objective of the Course: Objectives of introducing this subject at second
More informationCivil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7
Civil Engineering Design (1) Design of Reinforced Concrete Columns 2006/7 Dr. Colin Caprani, Chartered Engineer 1 Contents 1. Introduction... 3 1.1 Background... 3 1.2 Failure Modes... 5 1.3 Design Aspects...
More informationSolid Mechanics Homework Answers
Name: Date: Solid Mechanics Homework nswers Please show all of your work, including which equations you are using, and circle your final answer. Be sure to include the units in your answers. 1. The yield
More informationtwo structural analysis (statics & mechanics) APPLIED ACHITECTURAL STRUCTURES: DR. ANNE NICHOLS SPRING 2017 lecture STRUCTURAL ANALYSIS AND SYSTEMS
APPLIED ACHITECTURAL STRUCTURES: STRUCTURAL ANALYSIS AND SYSTEMS DR. ANNE NICHOLS SPRING 2017 lecture two structural analysis (statics & mechanics) Analysis 1 Structural Requirements strength serviceability
More informationAPPENDIX 1 MODEL CALCULATION OF VARIOUS CODES
163 APPENDIX 1 MODEL CALCULATION OF VARIOUS CODES A1.1 DESIGN AS PER NORTH AMERICAN SPECIFICATION OF COLD FORMED STEEL (AISI S100: 2007) 1. Based on Initiation of Yielding: Effective yield moment, M n
More informationMET 301 EXPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES
MET 301 EPERIMENT # 2 APPLICATION OF BONDED STRAIN GAGES 1. Objective To understand the working principle of bonded strain gauge and to study the stress and strain in a hollow cylindrical shaft under bending,
More informationMECH 401 Mechanical Design Applications
MECH 401 Mechanical Design Applications Dr. M. O Malley Master Notes Spring 008 Dr. D. M. McStravick Rice University Updates HW 1 due Thursday (11708) Last time Introduction Units Reliability engineering
More informationTHEME IS FIRST OCCURANCE OF YIELDING THE LIMIT?
CIE309 : PLASTICITY THEME IS FIRST OCCURANCE OF YIELDING THE LIMIT? M M  N N + + σ = σ = + f f BENDING EXTENSION Ir J.W. Welleman page nr 0 kn Normal conditions during the life time WHAT HAPPENS DUE TO
More informationName. ME 270 Fall 2005 Final Exam PROBLEM NO. 1. Given: A distributed load is applied to the top link which is, in turn, supported by link AC.
Name ME 270 Fall 2005 Final Exam PROBLEM NO. 1 Given: A distributed load is applied to the top link which is, in turn, supported by link AC. Find: a) Draw a free body diagram of link BCDE and one of link
More informationME 202 STRENGTH OF MATERIALS SPRING 2014 HOMEWORK 4 SOLUTIONS
ÇANKAYA UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 202 STRENGTH OF MATERIALS SPRING 2014 Due Date: 1 ST Lecture Hour of Week 12 (02 May 2014) Quiz Date: 3 rd Lecture Hour of Week 12 (08 May 2014)
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 informationCHAPTER 6 BENDING Part 1
Ishik University / Sulaimani Civil Engineering Department Mechanics of Materials CE 211 CHAPTER 6 BENDING Part 11 CHAPTER 6 Bending Outlines of this chapter: 6.1. Chapter Objectives 6.2. Shear and
More informationEE C245 ME C218 Introduction to MEMS Design
EE C245 ME C218 Introduction to MEMS Design Fall 2007 Prof. Clark T.C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 94720 Lecture 16: Energy
More informationDESIGN OF BEAMCOLUMNS  II
DESIGN OF BEACOLUNSII 14 DESIGN OF BEACOLUNS  II 1.0 INTRODUCTION Beamcolumns are members subjected to combined bending and axial compression. Their behaviour under uniaxial bending, biaxial bending
More informationSERVICEABILITY LIMIT STATE DESIGN
CHAPTER 11 SERVICEABILITY LIMIT STATE DESIGN Article 49. Cracking Limit State 49.1 General considerations In the case of verifications relating to Cracking Limit State, the effects of actions comprise
More information8. Combined Loadings
CHAPTER OBJECTIVES qanalyze the stress developed in thinwalled pressure vessels qreview the stress analysis developed in previous chapters regarding axial load, torsion, bending and shear qdiscuss the
More informationInfluence of residual stresses in the structural behavior of. tubular columns and arches. Nuno Rocha Cima Gomes
October 2014 Influence of residual stresses in the structural behavior of Abstract tubular columns and arches Nuno Rocha Cima Gomes Instituto Superior Técnico, Universidade de Lisboa, Portugal Contact:
More informationStructural Analysis III The Moment Area Method Mohr s Theorems
Structural Analysis III The Moment Area Method Mohr s Theorems 009/10 Dr. Colin Caprani 1 Contents 1. Introduction... 4 1.1 Purpose... 4. Theory... 6.1 asis... 6. Mohr s First Theorem (Mohr I)... 8.3 Mohr
More informationStrength Of Materials/Mechanics of Solids
Table of Contents Stress, Strain, and Energy 1. Stress and Strain 2. Change in length 3. Determinate Structure  Both ends free 4. Indeterminate Structure  Both ends fixed 5. Composite Material of equal
More informationSteel Structures Design and Drawing Lecture Notes
Steel Structures Design and Drawing Lecture Notes INTRODUCTION When the need for a new structure arises, an individual or agency has to arrange the funds required for its construction. The individual or
More information3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture,
3.032 Problem Set 2 Solutions Fall 2007 Due: Start of Lecture, 09.21.07 1. In the beam considered in PS1, steel beams carried the distributed weight of the rooms above. To reduce stress on the beam, it
More informationCHAPTER 1 ENGINEERING MECHANICS I
CHAPTER 1 ENGINEERING MECHANICS I 1.1 Verification of Lame s Theorem: If three concurrent forces are in equilibrium, Lame s theorem states that their magnitudes are proportional to the sine of the angle
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationParametric analysis and torsion design charts for axially restrained RC beams
Structural Engineering and Mechanics, Vol. 55, No. 1 (2015) 127 DOI: http://dx.doi.org/10.12989/sem.2015.55.1.001 1 Parametric analysis and torsion design charts for axially restrained RC beams Luís F.A.
More informationChapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements
CIVL 7/8117 Chapter 12  Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness
More informationML (B) The homogeneous state of stress for a metal part undergoing plastic deformation is K
CHAPTER STRENGTH OF MATERIALS YEAR 0 ONE MARK MCQ. MCQ. MCQ. A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by % and the thickness is reduced
More informationTask 1  Material Testing of Bionax Pipe and Joints
Task 1  Material Testing of Bionax Pipe and Joints Submitted to: Jeff Phillips Western Regional Engineer IPEX Management, Inc. 20460 Duncan Way Langley, BC, Canada V3A 7A3 Ph: 6045348631 Fax: 6045347616
More informationLecture 1617, Sandwich Panel Notes, 3.054
Sandwich Panels Two stiff strong skins separated by a lightweight core Separation of skins by core increases moment of inertia, with little increase in weight Efficient for resisting bending and buckling
More informationLATERALLY RESTRAINED BEAMS
9 1.0 INTRODUCTION Beams are structural members frequentl used to carr loads that are transverse to their longitudinal axis. The transfer loads primaril b bending and shear. In a rectangular building frame,
More informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More information7.5 Elastic Buckling Columns and Buckling
7.5 Elastic Buckling The initial theory of the buckling of columns was worked out by Euler in 1757, a nice example of a theory preceding the application, the application mainly being for the later invented
More informationBasis of Structural Design
Basis of Structural Design Course 2 Structural action: cables and arches Course notes are available for download at http://www.ct.upt.ro/users/aurelstratan/ Structural action Structural action: the way
More informationDiscontinuous Distributions in Mechanics of Materials
Discontinuous Distributions in Mechanics of Materials J.E. Akin, Rice University 1. Introduction The study of the mechanics of materials continues to change slowly. The student needs to learn about software
More informationEquilibrium & Elasticity
PHYS 101 Previous Exam Problems CHAPTER 12 Equilibrium & Elasticity Static equilibrium Elasticity 1. A uniform steel bar of length 3.0 m and weight 20 N rests on two supports (A and B) at its ends. A block
More informationChapter 8 BIAXIAL BENDING
Chapter 8 BAXAL BENDN 8.1 DEFNTON A cross section is subjected to biaial (oblique) bending if the normal (direct) stresses from section are reduced to two bending moments and. enerall oblique bending is
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
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 informationSLOPEDEFLECTION METHOD
SLOPEDEFLECTION ETHOD The slopedeflection method uses displacements as unknowns and is referred to as a displacement method. In the slopedeflection method, the moments at the ends of the members are
More informationRigid and Braced Frames
RH 331 Note Set 12.1 F2014abn Rigid and raced Frames Notation: E = modulus of elasticit or Young s modulus F = force component in the direction F = force component in the direction FD = free bod diagram
More informationBeam Bending Stresses and Shear Stress
Beam Bending Stresses and Shear Stress Notation: A = name or area Aweb = area o the web o a wide lange section b = width o a rectangle = total width o material at a horizontal section c = largest distance
More informationA Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers H. Ozbasaran
Vol:8, No:7, 214 A Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers H. Ozbasaran Abstract IPN and IPE sections, which are commonly used European I shapes, are widely used
More informationSimulation of Nonlinear Behavior of WallFrame Structure during Earthquakes
Simulation of Nonlinear Behavior of WallFrame Structure during Earthquakes b Masaomi Teshigawara 1, Hiroshi Fukuama 2, Hiroto Kato 2, Taiki Saito 2, Koichi Kusunoki 2, Tomohisa Mukai 2 ABSTRACT The reinforced
More informationD e s i g n o f R i v e t e d J o i n t s, C o t t e r & K n u c k l e J o i n t s
D e s i g n o f R i v e t e d J o i n t s, C o t t e r & K n u c k l e J o i n t s 1. Design of various types of riveted joints under different static loading conditions, eccentrically loaded riveted joints.
More informationModule 3. Analysis of Statically Indeterminate Structures by the Displacement Method
odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 14 The SlopeDeflection ethod: An Introduction Introduction As pointed out earlier, there are two distinct methods
More informationDistributed Forces: Moments of Inertia
Distributed Forces: Moments of nertia Contents ntroduction Moments of nertia of an Area Moments of nertia of an Area b ntegration Polar Moments of nertia Radius of Gration of an Area Sample Problems Parallel
More information85 ConjugateBeam method. 85 ConjugateBeam method. 85 ConjugateBeam method. 85 ConjugateBeam method
The basis for the method comes from the similarity of eqn.1 &. to eqn 8. & 8. To show this similarity, we can write these eqn as shown dv dx w d θ M dx d M w dx d v M dx Here the shear V compares with
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. BernoulliEuler Beams.
More informationTHE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE
Journal of Applied Mathematics and Computational Mechanics 013, 1(4), 131 THE INFLUENCE OF THERMAL ACTIONS AND COMPLEX SUPPORT CONDITIONS ON THE MECHANICAL STATE OF SANDWICH STRUCTURE Jolanta Błaszczuk
More informationTheory and Analysis of Structures
7 Theory and nalysis of Structures J.Y. Richard iew National University of Singapore N.E. Shanmugam National University of Singapore 7. Fundamental Principles oundary Conditions oads and Reactions Principle
More informationAE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF HOOP STRESSES FOR A THINWALL PRESSURE VESSEL
Objective AE3610 Experiments in Fluid and Solid Mechanics TRANSIENT MEASUREMENTS OF OOP STRESSES FOR A TINWA PRESSURE VESSE This experiment will allow you to investigate hoop and axial stress/strain relations
More information