Method of Virtual Work Frame Deflection Example Steven Vukazich San Jose State University
|
|
- Lindsey Thornton
- 5 years ago
- Views:
Transcription
1 Method of Virtual Work Frame Deflection xample Steven Vukazich San Jose State University
2 Frame Deflection xample 9 k k D 4 ft θ " # The statically determinate frame from our previous internal force diagram example is made up of columns that are W8x48 (I = 84 in 4 ) members and a beam that is a Wx22 (I = 8 in 4 ). The modulus of elasticity of structural steel is 29, ksi, which yields the following bending stiffnesses: I = 5,33, k-in 2 I D = 3,422, k-in 2 For the loads shown, find the following:
3 Frame Deflection xample ft k δ " D θ % 8 k The statically determinate frame from our previous internal force diagram example is made up of columns that are W8x48 (I = 84 in 4 ) members and a beam that is a Wx22 (I = 8 in 4 ). The modulus of elasticity of structural steel is 29, ksi, which yields the following bending stiffenesses: I = 5,33, k-in 2 I D = 3,422, k-in 2 For the loads shown, find the following: 5 ft ft. The horizontal deflection at point ; 2. The slope at the pin support at.
4 Find the Horizontal Deflection at Point Virtual system to measure δ " D ft 5 ft ft
5 Find Support Reactions for the Virtual System D ft y & M % = + y =.34 x + & F - = x = y 5 ft ft + & F. = y =.34
6 Support Reactions for the Virtual System D ft ft ft
7 hoose Sign onvention for Internal moment For horizontal member D + For vertical member +
8 Moment Diagram for the Virtual System ft D ft 5 ft ft
9 Support Reactions for the Real System Results from our previous module: k D 2 k ft 8 k k k 5 ft ft
10 Moment Diagram for the Real System Results from our previous module: 8 k-ft 8 k-ft ft k-ft D 2 k-ft 5 ft ft
11 valuate the Virtual Work Product Integrals ft M Q 8.3x = 3.9 ft ft D X ft M P 8 k-ft 8 k-ft k-ft D 2 k-ft x X I = 5,33, k-in 2 I D = 3,422, k-in 2 5 ft ft δ " = I 3 M 4 M 7 dx 5 5 ft ft 8 x = 2 5 x Use Table to evaluate product integrals 9 = 3x x = 3 ft
12 Table to valuate Virtual Work Product Integrals ppendix Table.2 and X Table is as useful tool to evaluate product integrals of the form: 5 3 M 4 M 7 dx XD
13 valuate Product Integrals M Q M 2 8 k-ft M 3 L 3 ft X M 3.9 ft X 2 ft 3.9 ft M d L D ft c M P M D + 2M H M L k-ft 3 2 k-ft M 3 M DM L + c k-ft 3
14 valuate Product Integrals M Q M P 3 M DM L L k-ft M M k-ft 3 M ft k-ft M 3 3 M DM L ft L k-ft 3
15 valuate Product Integrals 5 δ " = I 3 M 4 M 7 dx Segment X k-ft 3 Segment XD k-ft 3 5 KRS 3 M 4 M 7 dx = k ft k ft 3 2 in 3 ft 3 = 3,8.3 k in 3 Segment k-ft 3 Segment 7.7 k-ft 3 5 JKL 3 M 4 M 7 dx = k ft 3 2 in 3 ft 3 = 87,92 k in 3
16 valuate Product Integrals 5 JKL 3 M 4 M 7 dx = k ft 3 2 in 3 ft 3 = 87,92 k in 3 5 KRS 3 M 4 M 7 dx = k ft k ft 3 2 in 3 ft 3 = 3,8.3 k in 3 5 JKL δ " = 3 M I 4 %U" 5 KRS M 7 dx + 3 M I 4 "VW M 7 dx δ " = 87,92 k in3 3,8.3 k in3 + 5,33, k in2 3,422, k in 2 δ " =.3 in +.38 in =.2 in δ " =.2 inches to the right Positive result, so deflection is in the same direction as the virtual unit load
17 Find the the Rotation at Point Virtual system to measure θ % D ft 5 ft ft
18 Find Support Reactions for the Virtual System D ft x y y & M % = + + & F - = y =.99 x = 5 ft ft + & F. = y =.99
19 Support Reactions for the Virtual System D.99 ft.99 5 ft ft
20 Moment Diagram for the Virtual System ft D 5 ft ft
21 Moment Diagram for the Real System Results from our previous module: 8 k-ft 8 k-ft ft k-ft D 2 k-ft 5 ft ft
22 valuate the Virtual Work Product Integrals ft M Q +.99(3) =.7273 D X ft M P 8 k-ft 8 k-ft k-ft D 2 k-ft 3 ft X 3 ft 5 ft ft 5 ft ft I = 5,33, k-in 2 I D = 3,422, k-in 2 δ " = I 3 M 4 M 7 dx 5 Use Table to evaluate product integrals
23 Table to valuate Virtual Work Product Integrals ppendix Table.2 X Table is as useful tool to evaluate product integrals of the form: 5 3 M 4 M 7 dx XD
24 valuate Product Integrals L 3 ft X X 2 ft M Q M 2 M M M P 8 k-ft M 3 d L D ft c M D + 2M H M L k-ft 2 M 3 2 k-ft M DM L + c k-ft 2
25 valuate Product Integrals M Q M P 8 k-ft M k-ft M 3 2 M DM L ft L 2 5. k-ft 2
26 valuate Product Integrals 5 δ " = I 3 M 4 M 7 dx Segment X k-ft 2 Segment XD k-ft 2 Segment 5. k-ft 2 Segment 5 KRS 3 M 4 M 7 dx = k ft 2 2 H in 2 ft 2 = 2.88 k in 2 5 JKL 3 M 4 M 7 dx = 5 + k ft 2 2 H in 2 ft 2 = 7,2 k in 2
27 5 KRS 3 M 4 valuate Product Integrals M 7 dx = k ft 2 2 H in 2 ft 2 = 2.88 k in 2 5 JKL 3 M 4 M 7 dx = 5 + k ft 2 2 H in 2 ft 2 = 7,2 k in 2 5 JKL θ % = 3 M I 4 %U" 5 KRS M 7 dx + 3 M I 4 UVW M 7 dx θ % = 7,2 k in k in2 + 5,33, k in2 3,422, k in 2 θ % =.349 rad.7 rad =.52 rad θ % =.52 radians clockwise Negative result, so rotation is in the opposite direction of the virtual unit moment
28 Frame Deflection xample Results.2 in k ft D 8 k.52 rad 5 ft ft
k 21 k 22 k 23 k 24 k 31 k 32 k 33 k 34 k 41 k 42 k 43 k 44
CE 6 ab Beam Analysis by the Direct Stiffness Method Beam Element Stiffness Matrix in ocal Coordinates Consider an inclined bending member of moment of inertia I and modulus of elasticity E subjected shear
More information5. What is the moment of inertia about the x - x axis of the rectangular beam shown?
1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D - Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment
More informationBEAM DEFLECTION THE ELASTIC CURVE
BEAM DEFLECTION Samantha Ramirez THE ELASTIC CURVE The deflection diagram of the longitudinal axis that passes through the centroid of each cross-sectional area of a beam. Supports that apply a moment
More informationThis procedure covers the determination of the moment of inertia about the neutral axis.
327 Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the T-beam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination
More information8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam 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 informationSoftware Verification
EXAMPLE 1-026 FRAME MOMENT AND SHEAR HINGES EXAMPLE DESCRIPTION This example uses a horizontal cantilever beam to test the moment and shear hinges in a static nonlinear analysis. The cantilever beam has
More informationAssumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are
*12.4 SLOPE & DISPLACEMENT BY THE MOMENT-AREA METHOD Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are very small,
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 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 informationTruss Analysis Method of Joints. Steven Vukazich San Jose State University
Truss nalysis Method of Joints Steven Vukazich San Jose State University General Procedure for the nalysis of Simple Trusses using the Method of Joints 1. raw a Free Body iagram (FB) of the entire truss
More informationChapter 8 Supplement: Deflection in Beams Double Integration Method
Chapter 8 Supplement: Deflection in Beams Double Integration Method 8.5 Beam Deflection Double Integration Method In this supplement, we describe the methods for determining the equation of the deflection
More informationChapter 11. Displacement Method of Analysis Slope Deflection Method
Chapter 11 Displacement ethod of Analysis Slope Deflection ethod Displacement ethod of Analysis Two main methods of analyzing indeterminate structure Force method The method of consistent deformations
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 informationShear Force and Bending Moment Diagrams for a Beam Steven Vukazich San Jose State University
Shear Force and Bending oment Diagrams for a Beam Steven ukazich San Jose State University General procedure for the construction of internal force diagrams 1. Find all of the eternal forces and draw 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 informationP.E. Civil Exam Review:
P.E. Civil Exam Review: Structural Analysis J.P. Mohsen Email: jpm@louisville.edu Structures Determinate Indeterminate STATICALLY DETERMINATE STATICALLY INDETERMINATE Stability and Determinacy of Trusses
More informationMECE 3321: Mechanics of Solids Chapter 6
MECE 3321: Mechanics of Solids Chapter 6 Samantha Ramirez Beams Beams are long straight members that carry loads perpendicular to their longitudinal axis Beams are classified by the way they are supported
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 informationInternal Internal Forces Forces
Internal Forces ENGR 221 March 19, 2003 Lecture Goals Internal Force in Structures Shear Forces Bending Moment Shear and Bending moment Diagrams Internal Forces and Bending The bending moment, M. Moment
More information3 Relation between complete and natural degrees of freedom
Stiffness matrix for D tapered beams by ouie. Yaw, PhD, PE, SE Walla Walla University March 9, 9 Introduction This article presents information necessary for the construction of the stiffness matrix of
More informationChapter 7 FORCES IN BEAMS AND CABLES
hapter 7 FORES IN BEAMS AN ABLES onsider a straight two-force member AB subjected at A and B to equal and opposite forces F and -F directed along AB. utting the member AB at and drawing the free-body B
More informationANSWERS September 2014
NSWERS September 2014 nswers to selected questions: Sheet # (1) (2) () (4) SCE-55 D SCE-86 D SCE-88 D C MCM-21 MCM-12 D MMC-80 C C D MCM-52 D D MCM-1 C D D MCM-51 D D MCM-57 D D MCM-60 D MLS-12 C D NS
More informationModule 3. Analysis of Statically Indeterminate Structures by the Displacement Method
odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 21 The oment- Distribution ethod: rames with Sidesway Instructional Objectives After reading this chapter the student
More informationMethod of Consistent Deformation
Method of onsistent eformation Structural nalysis y R.. Hibbeler Theory of Structures-II M Shahid Mehmood epartment of ivil Engineering Swedish ollege of Engineering and Technology, Wah antt FRMES Method
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 11 The Force Method of Analysis: Frames Instructional Objectives After reading this chapter the student will be
More informationDEFLECTION CALCULATIONS (from Nilson and Nawy)
DEFLECTION CALCULATIONS (from Nilson and Nawy) The deflection of a uniformly loaded flat plate, flat slab, or two-way slab supported by beams on column lines can be calculated by an equivalent method that
More informationDeflections. Deflections. Deflections. Deflections. Deflections. Deflections. dx dm V. dx EI. dx EI dx M. dv w
CIVL 311 - Conjugate eam 1/5 Conjugate beam method The development of the conjugate beam method has been atributed to several strucutral engineers. any credit Heinrich üller-reslau (1851-195) with the
More informationExperiment Instructions. Deformation of Frames
Experiment Instructions SE 0.20 Deformation of Frames Experiment Instructions This manual must be kept by the unit. Before operating the unit: - Read this manual. - All participants must be instructed
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 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 informationBEAM A horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam
BEM horizontal or inclined structural member that is designed to resist forces acting to its axis is called a beam INTERNL FORCES IN BEM Whether or not a beam will break, depend on the internal resistances
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 informationModule 3. Analysis of Statically Indeterminate Structures by the Displacement Method
odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Lesson 16 The Slope-Deflection ethod: rames Without Sidesway Instructional Objectives After reading this chapter the student
More informationstructural analysis Excessive beam deflection can be seen as a mode of failure.
Structure Analysis I Chapter 8 Deflections Introduction Calculation of deflections is an important part of structural analysis Excessive beam deflection can be seen as a mode of failure. Extensive glass
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 informationMECHANICS OF MATERIALS
Third E CHAPTER 6 Shearing MECHANCS OF MATERALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University Stresses in Beams and Thin- Walled Members Shearing
More informationDeterminate portal frame
eterminate portal frame onsider the frame shown in the figure below with the aim of calculating the bending moment diagram (M), shear force diagram (SF), and axial force diagram (F). P H y R x x R y L
More informationProblem 1: Calculating deflection by integration uniform load. Problem 2: Calculating deflection by integration - triangular load pattern
Problem 1: Calculating deflection by integration uniform load Problem 2: Calculating deflection by integration - triangular load pattern Problem 3: Deflections - by differential equations, concentrated
More informationPurpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.
ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th in-class Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on
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 information14. *14.8 CASTIGLIANO S THEOREM
*14.8 CASTIGLIANO S THEOREM Consider a body of arbitrary shape subjected to a series of n forces P 1, P 2, P n. Since external work done by forces is equal to internal strain energy stored in body, by
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 informationSteel Post Load Analysis
Steel Post Load Analysis Scope The steel posts in 73019022, 73019024, and 73019025, are considered to be traditional building products. According to the 2015 International Building Code, this type of product
More informationChapter 7: Bending and Shear in Simple Beams
Chapter 7: Bending and Shear in Simple Beams Introduction A beam is a long, slender structural member that resists loads that are generally applied transverse (perpendicular) to its longitudinal axis.
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 7 INTERNAL FORCES
Chapter 7 INTERNAL FORCES READING QUIZ 1. In a multiforce member, the member is generally subjected to an internal. A) normal force B) shear force C) bending moment D) All of the above. 2. In mechanics,
More informationSteel Cross Sections. Structural Steel Design
Steel Cross Sections Structural Steel Design PROPERTIES OF SECTIONS Perhaps the most important properties of a beam are the depth and shape of its cross section. There are many to choose from, and there
More information2 marks Questions and Answers
1. Define the term strain energy. A: Strain Energy of the elastic body is defined as the internal work done by the external load in deforming or straining the body. 2. Define the terms: Resilience and
More informationSTRUCTURAL ANALYSIS BFC Statically Indeterminate Beam & Frame
STRUCTURA ANAYSIS BFC 21403 Statically Indeterminate Beam & Frame Introduction Analysis for indeterminate structure of beam and frame: 1. Slope-deflection method 2. Moment distribution method Displacement
More informationShear Force V: Positive shear tends to rotate the segment clockwise.
INTERNL FORCES IN EM efore a structural element can be designed, it is necessary to determine the internal forces that act within the element. The internal forces for a beam section will consist of a shear
More informationDesign of a Bi-Metallic Strip for a Thermal Switch. Team Design Project 2. Dr. William Slaughter. ENGR0145 Statics and Mechanics of Materials II
Design of a Bi-Metallic Strip for a Thermal Switch Team Design Project 2 Dr. William Slaughter ENGR0145 Statics and Mechanics of Materials II April 10, 2015 Jacob Feid Derek Nichols ABSTRACT The goal of
More information[5] Stress and Strain
[5] Stress and Strain Page 1 of 34 [5] Stress and Strain [5.1] Internal Stress of Solids [5.2] Design of Simple Connections (will not be covered in class) [5.3] Deformation and Strain [5.4] Hooke s Law
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 informationSide Note (Needed for Deflection Calculations): Shear and Moment Diagrams Using Area Method
Side Note (Needed for Deflection Calculations): Shear and Moment Diagrams Using Area Method How do we draw the moment and shear diagram for an arbitrarily loaded beam? Is there a easier and faster way
More informationMoment of a force (scalar, vector ) Cross product Principle of Moments Couples Force and Couple Systems Simple Distributed Loading
Chapter 4 Moment of a force (scalar, vector ) Cross product Principle of Moments Couples Force and Couple Systems Simple Distributed Loading The moment of a force about a point provides a measure of the
More informationTORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES)
Page1 TORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES) Restrained warping for the torsion of thin-wall open sections is not included in most commonly used frame analysis programs. Almost
More informationSLOPE-DEFLECTION METHOD
SLOPE-DEFLECTION ETHOD The slope-deflection method uses displacements as unknowns and is referred to as a displacement method. In the slope-deflection method, the moments at the ends of the members are
More informationQuizzam Module 1 : Statics
Structural Steel Design Quizzam odule : Statics NAE Draw shear and moment diagrams for the following loading conditions. Note the reactions. Calculate the maximum amount of internal bending moment. 0 500
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 information8.3 Shear and Bending-Moment Diagrams Constructed by Areas
8.3 Shear and ending-moment Diagrams Constructed by reas 8.3 Shear and ending-moment Diagrams Constructed by reas Procedures and Strategies, page 1 of 3 Procedures and Strategies for Solving Problems Involving
More informationExternal work and internal work
External work and internal work Consider a load gradually applied to a structure. Assume a linear relationship exists between the load and the deflection. This is the same assumption used in Hooke s aw
More informationBeams are bars of material that support. Beams are common structural members. Beams can support both concentrated and distributed loads
Outline: Review External Effects on Beams Beams Internal Effects Sign Convention Shear Force and Bending Moment Diagrams (text method) Relationships between Loading, Shear Force and Bending Moments (faster
More information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shear-stress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationBEAMS: SHEAR AND MOMENT DIAGRAMS (FORMULA)
LETURE Third Edition BEMS: SHER ND MOMENT DGRMS (FORMUL). J. lark School of Engineering Department of ivil and Environmental Engineering 1 hapter 5.1 5. b Dr. brahim. ssakkaf SPRNG 00 ENES 0 Mechanics
More informationME 323 Examination #2 April 11, 2018
ME 2 Eamination #2 April, 2 PROBLEM NO. 25 points ma. A thin-walled pressure vessel is fabricated b welding together two, open-ended stainless-steel vessels along a 6 weld line. The welded vessel has an
More informationME325 EXAM I (Sample)
ME35 EXAM I (Sample) NAME: NOTE: COSED BOOK, COSED NOTES. ONY A SINGE 8.5x" ORMUA SHEET IS AOWED. ADDITIONA INORMATION IS AVAIABE ON THE AST PAGE O THIS EXAM. DO YOUR WORK ON THE EXAM ONY (NO SCRATCH PAPER
More information1 of 12. Given: Law of Cosines: C. Law of Sines: Stress = E = G
ES230 STRENGTH OF MATERIALS FINAL EXAM: WEDNESDAY, MAY 15 TH, 4PM TO 7PM, AEC200 Closed book. Calculator and writing supplies allowed. Protractor and compass required. 180 Minute Time Limit You must have
More informationSymmetric Bending of Beams
Symmetric Bending of Beams beam is any long structural member on which loads act perpendicular to the longitudinal axis. Learning objectives Understand the theory, its limitations and its applications
More informationME C85/CE C30 Fall, Introduction to Solid Mechanics ME C85/CE C30. Final Exam. Fall, 2013
Introduction to Solid Mechanics ME C85/CE C30 Fall, 2013 1. Leave an empty seat between you and the person (people) next to you. Unfortunately, there have been reports of cheating on the midterms, so we
More information1 of 12. Law of Sines: Stress = E = G. Deformation due to Temperature: Δ
NAME: ES30 STRENGTH OF MATERIALS FINAL EXAM: FRIDAY, MAY 1 TH 4PM TO 7PM Closed book. Calculator and writing supplies allowed. Protractor and compass allowed. 180 Minute Time Limit GIVEN FORMULAE: Law
More informationSupplement: Statically Indeterminate Frames
: Statically Indeterminate Frames Approximate Analysis - In this supplement, we consider another approximate method of solving statically indeterminate frames subjected to lateral loads known as the. Like
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 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 informationSupport Idealizations
IVL 3121 nalysis of Statically Determinant Structures 1/12 nalysis of Statically Determinate Structures nalysis of Statically Determinate Structures The most common type of structure an engineer will analyze
More informationREVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002
REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental
More informationCHAPTER 7 DEFLECTIONS OF BEAMS
CHPTER 7 DEFLECTIONS OF EMS OJECTIVES Determine the deflection and slope at specific points on beams and shafts, using various analytical methods including: o o o The integration method The use of discontinuity
More informationFINITE ELEMENT ANALYSIS OF ARKANSAS TEST SERIES PILE #2 USING OPENSEES (WITH LPILE COMPARISON)
FINITE ELEMENT ANALYSIS OF ARKANSAS TEST SERIES PILE #2 USING OPENSEES (WITH LPILE COMPARISON) Ahmed Elgamal and Jinchi Lu October 07 Introduction In this study, we conduct a finite element simulation
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 informationCITY AND GUILDS 9210 UNIT 135 MECHANICS OF SOLIDS Level 6 TUTORIAL 5A - MOMENT DISTRIBUTION METHOD
Outcome 1 The learner can: CITY AND GUIDS 910 UNIT 15 ECHANICS OF SOIDS evel 6 TUTORIA 5A - OENT DISTRIBUTION ETHOD Calculate stresses, strain and deflections in a range of components under various load
More informationPortal Frame Calculations Lateral Loads
Portal Frame Calculations Lateral Loads Consider the following multi-story frame: The portal method makes several assumptions about the internal forces of the columns and beams in a rigid frame: 1) Inflection
More informationProperties of Sections
ARCH 314 Structures I Test Primer Questions Dr.-Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body
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 informationMECHANICS OF MATERIALS
STATICS AND MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr, John T. DeWolf David E Mazurek \Cawect Mc / iur/» Craw SugomcT Hilt Introduction 1 1.1 What is Mechanics? 2 1.2 Fundamental
More informationModule 3. Analysis of Statically Indeterminate Structures by the Displacement Method. Version 2 CE IIT, Kharagpur
odule 3 Analysis of Statically Indeterminate Structures by the Displacement ethod Version CE IIT, Kharagpur Lesson The ultistory Frames with Sidesway Version CE IIT, Kharagpur Instructional Objectives
More informationFree Body Diagram: Solution: The maximum load which can be safely supported by EACH of the support members is: ANS: A =0.217 in 2
Problem 10.9 The angle β of the system in Problem 10.8 is 60. The bars are made of a material that will safely support a tensile normal stress of 8 ksi. Based on this criterion, if you want to design the
More informationStress Analysis Lecture 4 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy
Stress Analysis Lecture 4 ME 76 Spring 017-018 Dr./ Ahmed Mohamed Nagib Elmekawy Shear and Moment Diagrams Beam Sign Convention The positive directions are as follows: The internal shear force causes a
More informationProblem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323
Problem 9.1 Two beam segments, AC and CD, are connected together at C by a frictionless pin. Segment CD is cantilevered from a rigid support at D, and segment AC has a roller support at A. a) Determine
More 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 informationUNIT IV FLEXIBILTY AND STIFFNESS METHOD
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : SA-II (13A01505) Year & Sem: III-B.Tech & I-Sem Course & Branch: B.Tech
More information[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21
[7] Torsion Page 1 of 21 [7] Torsion [7.1] Torsion [7.2] Statically Indeterminate Torsion [7] Torsion Page 2 of 21 [7.1] Torsion SHEAR STRAIN DUE TO TORSION 1) A shaft with a circular cross section is
More informationIDE 110 Mechanics of Materials Spring 2006 Final Examination FOR GRADING ONLY
Spring 2006 Final Examination STUDENT S NAME (please print) STUDENT S SIGNATURE STUDENT NUMBER IDE 110 CLASS SECTION INSTRUCTOR S NAME Do not turn this page until instructed to start. Write your name on
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 Lilkova-Markova, Chief. Assist. Prof. Dimitar Lolov Sofia, 011 STRENGTH OF MATERIALS GENERAL
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 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 Slope-Deflection ethod: An Introduction Introduction As pointed out earlier, there are two distinct methods
More informationMECHANICS OF MATERIALS
Third CHTR Stress MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University and Strain xial oading Contents Stress & Strain: xial oading Normal
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 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 informationFINAL EXAMINATION. (CE130-2 Mechanics of Materials)
UNIVERSITY OF CLIFORNI, ERKELEY FLL SEMESTER 001 FINL EXMINTION (CE130- Mechanics of Materials) Problem 1: (15 points) pinned -bar structure is shown in Figure 1. There is an external force, W = 5000N,
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 11
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Module - 01 Lecture - 11 Last class, what we did is, we looked at a method called superposition
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 information