EI M M 0 dx. EI M x C dx. EIy M x C x C

Size: px
Start display at page:

Download "EI M M 0 dx. EI M x C dx. EIy M x C x C"

Transcription

1 PROE 9. For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, (c) the slope at the free end. (a) Elastic curve: : K d d d, : [, ] ( ) ( ) (b) at : d (c) at : ( ) d ( ) ( ) PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 7

2 w PROE 9. For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam, (b) the deflection at the free end, (c) the slope at the free end. J : ( w) w (a) Elastic curve. d w d w 6 d, : w w 6 6 d w w 6 6 w w 6 [, ] w w 6 w w 6 w ( ) (b) at. w w 8 w 8 d (c) at. d w 6 w 6 PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 75

3 w PROE 9.7 / For the beam and loading shown, determine (a) the equation of the elastic curve for portion of the beam, (b) the deflection at midspan, (c) the slope at. (a) Elastic curve. Reactions: : R w w 6 R w 8 oundar conditions: [, ] [, ] For portion onl, ( ) J w : w ( ) 8 w w 8 6 d w w 8 6 d w w 6 w w 8 5 [, ]: [, ]: w w 8 w 8 w d w 6 8 (b) at w 5w w 56 d (c) at. d w w 6 8 w PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 79

4 P P PROE 9.67 For the cantilever beam and loading shown, determine the slope and deflection at the free end. / / oading I: P downward at. ase of ppendi D applied to portion. remains straight. ( P)( /) ( P)( /) 8 5 oading II: P downward at. ase of ppendi D. superposition,, 5 PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 75

5 kip kip/ft. in. PROE 9.75 ft ft. in. For the cantilever beam and loading shown, determine the 6 slope and deflection at end. Use E 9 psi. Units: Forces in kips; lengths in ft. oading I: oncentrated load at. ase of ppendi D. ()(5).5 ()(5).667 oading II: Uniforml distributed load over portion. ase of ppendi D applied to portion. Portion remains straight. superposition, Data: Slope at. Deflection at. w ()() w ()() a () E 9 psi = 9 ksi I (.)(.).667 in (9 )(.667) 9. kip in 8 kip ft rad ft. in. 8 PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted 8

6 P P PROE 9.8 D E For the uniform beam shown, determine the reaction at each of the three supports. / / / / eam is indeterminate to first degree. onsider R to be the redundant reaction, and replace the loading b loadings I, II, and III. oading I: ase of ppendi D. ( ) I R ( ) 8 6 R oading II: ase 5 of ppendi D. ( ) II I Pb [ 6 ( ) {( ) b }] P( /) 8 oading III: ase 5 of ppendi D. ( ) II II ( ) II Superposition and constraint: ( ) ( ) ( ) I II III R R Statics: 6 F E : R( ) P ( 6 P P) : R R 7 P P P P R E 6 R E 6 P 7 P P PROPRIETRY TERI. opright 5 cgraw-hill Education. This is proprietar material solel for authorized instructor use. Not authorized for sale or distribution in an manner. This document ma not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 9

PROBLEM 5.1. wl x. M ( Lx x )

PROBLEM 5.1. wl x. M ( Lx x ) w PROE 5.1 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. SOUTION Reactions: 0: 0 0: 0 Free bod diagram

More information

This procedure covers the determination of the moment of inertia about the neutral axis.

This 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 information

= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200

= 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 information

PROBLEM 3.3 ( )(45 10 ) T 5.17 kn m. A c c. 2 J c, (2)( ) 2 ( ) mm ( )

PROBLEM 3.3 ( )(45 10 ) T 5.17 kn m. A c c. 2 J c, (2)( ) 2 ( ) mm ( ) 0 mm PROEM..4 m 45 mm (a) Determine the torque that causes a maximum shearing stress of 45 MPa in the hollow cylindrical steel shaft shown. Determine the maximum shearing stress caused by the same torque

More information

Lecture 8: Flexibility Method. Example

Lecture 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 information

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method

Module 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method Module 2 Analysis of Statically Indeterminate Structures by the Matrix Force Method Lesson 8 The Force Method of Analysis: Beams Instructional Objectives After reading this chapter the student will be

More information

Statically Indeterminate Beams

Statically Indeterminate Beams Deflection Part Staticall Indeterminate eams We can use the same method that we used for deflection to analze staticall indeterminate beams lessed are the who can laugh at themselves for the shall never

More information

Supplement: Statically Indeterminate Frames

Supplement: 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 information

Deflection of Beams. Equation of the Elastic Curve. Boundary Conditions

Deflection of Beams. Equation of the Elastic Curve. Boundary Conditions Deflection of Beams Equation of the Elastic Curve The governing second order differential equation for the elastic curve of a beam deflection is EI d d = where EI is the fleural rigidit, is the bending

More information

ANSWERS September 2014

ANSWERS 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 information

Software Verification

Software 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 information

8.3 Shear and Bending-Moment Diagrams Constructed by Areas

8.3 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 information

Structural Analysis III Compatibility of Displacements & Principle of Superposition

Structural 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 information

Experimental Lab. Principles of Superposition

Experimental Lab. Principles of Superposition Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you

More information

Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.

Purpose 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 information

6.5 Cables: Concentrated Loads

6.5 Cables: Concentrated Loads 6.5 ables: oncentrated Loads 6.5 ables: oncentrated Loads Procedures and Strategies, page 1 of 3 Procedures and Strategies for Solving Problems Involving ables With oncentrated Loads 1. Pass sections through

More information

PROBLEM 7.37 SOLUTION

PROBLEM 7.37 SOLUTION PROLEM 7.37 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the maimum absolute values of the shear and bending moment. Free bod: Entire beam Σ M = 0: E(6

More information

Method of Virtual Work Frame Deflection Example Steven Vukazich San Jose State University

Method of Virtual Work Frame Deflection Example Steven Vukazich San Jose State University Method of Virtual Work Frame Deflection xample Steven Vukazich San Jose State University Frame Deflection xample 9 k k D 4 ft θ " # The statically determinate frame from our previous internal force diagram

More information

Chapter 7: Internal Forces

Chapter 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 information

ME 323 Examination #2 April 11, 2018

ME 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 information

Name (Print) ME Mechanics of Materials Exam # 2 Date: March 29, 2017 Time: 8:00 10:00 PM - Location: WTHR 200

Name (Print) ME Mechanics of Materials Exam # 2 Date: March 29, 2017 Time: 8:00 10:00 PM - Location: WTHR 200 Name (Print) (Last) (First) Instructions: ME 323 - Mechanics of Materials Exam # 2 Date: Time: 8:00 10:00 PM - Location: WTHR 200 Circle your lecturer s name and your class meeting time. Koslowski Zhao

More information

3 A y 0.090

3 A y 0.090 ROBLM.1 5.0 in. 5 8 in. diameter A standard tension test is used to determine the properties of an experimental plastic. The test specimen is a 5 -in.-diameter rod and it is subjected to an 800-lb tensile

More information

Chapter 3. Load and Stress Analysis. Lecture Slides

Chapter 3. Load and Stress Analysis. Lecture Slides Lecture Slides Chapter 3 Load and Stress Analysis 2015 by McGraw Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner.

More information

Deflections. Deflections. Deflections. Deflections. Deflections. Deflections. dx dm V. dx EI. dx EI dx M. dv w

Deflections. 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 information

5. What is the moment of inertia about the x - x axis of the rectangular beam shown?

5. 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 information

Chapter 8 Supplement: Deflection in Beams Double Integration Method

Chapter 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 information

CHAPTER 7 DEFLECTIONS OF BEAMS

CHAPTER 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 information

lb ( psi)( in ) (29 10 psi)(5.9641in ) E (29 10 psi)( ) psi

lb ( psi)( in ) (29 10 psi)(5.9641in ) E (29 10 psi)( ) psi P POBLM 2.5.5 ft 18 in. 1 The.5-ft concrete pot i reinforced with ix teel bar, each with a 1 -in. diameter. 8 Knowing that 2 10 pi and c =.2 10 pi, determine the normal tree in the teel and in the concrete

More information

, and M A , R B. , and then draw the shear-force and bending-moment diagrams, labeling all critical ordinates. Solution 10.

, and M A , R B. , and then draw the shear-force and bending-moment diagrams, labeling all critical ordinates. Solution 10. SETIN 0. ethod of Superposition 63 roblem 0.- The propped cantilever beam shown in the figure supports a uniform load of intensity on the left-hand half of the beam. Find the reactions R, R, and, and then

More information

MAHALAKSHMI ENGINEERING COLLEGE

MAHALAKSHMI ENGINEERING COLLEGE CE840-STRENGTH OF TERIS - II PGE 1 HKSHI ENGINEERING COEGE TIRUCHIRPI - 611. QUESTION WITH NSWERS DEPRTENT : CIVI SEESTER: IV SU.CODE/ NE: CE 840 / Strength of aterials -II UNIT INDETERINTE ES 1. Define

More information

FUNDAMENTALS OF STRUCTURAL ANALYSIS

FUNDAMENTALS OF STRUCTURAL ANALYSIS FUNMENTLS OF STRUTURL NLYSIS 5th Edition Kenneth M. Leet, hia-ming Uang, Joel T. Lanning, and nne M. Gilbert SOLUTIONS MNUL HPTER 5: EMS N FRMES 5-1 opright 018 McGraw-Hill Education. ll rights reserved.

More information

MECE 3321: Mechanics of Solids Chapter 6

MECE 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 information

NAME: Given Formulae: Law of Cosines: Law of Sines:

NAME: 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 information

MECHANICS OF MATERIALS

MECHANICS 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 information

Problem d d d B C E D. 0.8d. Additional lecturebook examples 29 ME 323

Problem 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 information

Deflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering

Deflection 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 information

Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications

Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1 of 6 Continuing Education Course #207 What Every Engineer Should Know About Structures Part B Statics Applications 1. As a practical matter, determining design loads on structural members involves several

More information

Indeterminate Analysis Force Method 1

Indeterminate 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 information

Deflection of Flexural Members - Macaulay s Method 3rd Year Structural Engineering

Deflection 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 information

REVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002

REVIEW 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 information

Method of Least Work. Theory of Structures II M Shahid Mehmood Department of Civil Engineering Swedish College of Engineering & Technology, Wah Cantt

Method of Least Work. Theory of Structures II M Shahid Mehmood Department of Civil Engineering Swedish College of Engineering & Technology, Wah Cantt Method of east Work Theor of Structures II M Shahid Mehmood epartment of ivil Engineering Swedish ollege of Engineering & Technolog, Wah antt Method of east Work / astigliano s Second Theorem Staticall

More information

Methods of Analysis. Force or Flexibility Method

Methods of Analysis. Force or Flexibility Method INTRODUCTION: The structural analysis is a mathematical process by which the response of a structure to specified loads is determined. This response is measured by determining the internal forces or stresses

More information

MECHANICS OF MATERIALS

MECHANICS 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 information

Chapter 4 Deflection and Stiffness

Chapter 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 information

MECHANICS OF MATERIALS

MECHANICS 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 information

F = 0 can't be satisfied.

F = 0 can't be satisfied. 11/9/1 Equilibrium of eams 1. asics 1.1. Reactions: Draw D ount number of reactions (R) and number of internal hinges (H). If R < H 3 > unstable beam staticall determinate staticall indeterminate (a) (b)

More information

Solid Mechanics Homework Answers

Solid 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 information

1.1 To observe, evaluate and report on the load deflection relationship of a simply supported beam and a cantilever beam.

1.1 To observe, evaluate and report on the load deflection relationship of a simply supported beam and a cantilever beam. I. OBJECTIVES 1.1 To observe, evaluate and report on the load deflection relationship of a simply supported beam and a cantilever beam. 1.2 To determine the modulus of elasticity of the beam and what the

More information

RODS: STATICALLY INDETERMINATE MEMBERS

RODS: STATICALLY INDETERMINATE MEMBERS RODS: STTICLLY INDETERMINTE MEMERS Statically Indeterminate ackground In all of the problems discussed so far, it was possible to determine the forces and stresses in the members by utilizing the equations

More information

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

MAAE 2202 A. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work. It is most beneficial to you to write this mock final exam UNDER EXAM CONDITIONS. This means: Complete the exam in 3 hours. Work on your own. Keep your textbook closed. Attempt every question. After the

More information

4.MECHANICAL PROPERTIES OF MATERIALS

4.MECHANICAL PROPERTIES OF MATERIALS 4.MECHANICAL PROPERTIES OF MATERIALS The diagram representing the relation between stress and strain in a given material is an important characteristic of the material. To obtain the stress-strain diagram

More information

Structural Continuity

Structural Continuity Architecture 324 Structures II Structural Continuity Continuity in Beams Deflection Method Slope Method Three-Moment Theorem Millennium Bridge, London Foster and Partners + Arup Photo by Ryan Donaghy University

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 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 information

UNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded

More information

Laith Batarseh. internal forces

Laith Batarseh. internal forces Next Previous 1/8/2016 Chapter seven Laith Batarseh Home End Definitions When a member is subjected to external load, an and/or moment are generated inside this member. The value of the generated internal

More information

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012

Lecture Slides. Chapter 4. Deflection and Stiffness. The McGraw-Hill Companies 2012 Lecture Slides Chapter 4 Deflection and Stiffness The McGraw-Hill Companies 2012 Chapter Outline Force vs Deflection Elasticity property of a material that enables it to regain its original configuration

More information

Beams. 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 Beams Beams are structural members that offer resistance to bending due to applied load 1 Beams Long prismatic members Non-prismatic sections also possible Each cross-section dimension Length of member

More information

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection

Mechanics of Materials II. Chapter III. A review of the fundamental formulation of stress, strain, and deflection Mechanics of Materials II Chapter III A review of the fundamental formulation of stress, strain, and deflection Outline Introduction Assumtions and limitations Axial loading Torsion of circular shafts

More information

1 of 7. Law of Sines: Stress = E = G. Deformation due to Temperature: Δ

1 of 7. Law of Sines: Stress = E = G. Deformation due to Temperature: Δ NME: ES30 STRENGTH OF MTERILS FINL EXM: FRIDY, MY 1 TH 4PM TO 7PM Closed book. Calculator and writing supplies allowed. Protractor and compass allowed. 180 Minute Time Limit GIVEN FORMULE: Law of Cosines:

More information

RODS: THERMAL STRESS AND STRESS CONCENTRATION

RODS: THERMAL STRESS AND STRESS CONCENTRATION RODS: HERML SRESS ND SRESS CONCENRION Example 5 rod of length L, cross-sectional area, and modulus of elasticity E, has been placed inside a tube of the same length L, but of cross-sectional area and modulus

More information

Moment Area Method. 1) Read

Moment Area Method. 1) Read Moment Area Method Lesson Objectives: 1) Identify the formulation and sign conventions associated with the Moment Area method. 2) Derive the Moment Area method theorems using mechanics and mathematics.

More information

MECHANICS OF MATERIALS. Analysis of Beams for Bending

MECHANICS OF MATERIALS. Analysis of Beams for Bending MECHANICS OF MATERIALS Analysis of Beams for Bending By NUR FARHAYU ARIFFIN Faculty of Civil Engineering & Earth Resources Chapter Description Expected Outcomes Define the elastic deformation of an axially

More information

EMA 3702 Mechanics & Materials Science (Mechanics of Materials) Chapter 2 Stress & Strain - Axial Loading

EMA 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 information

The bending moment diagrams for each span due to applied uniformly distributed and concentrated load are shown in Fig.12.4b.

The bending moment diagrams for each span due to applied uniformly distributed and concentrated load are shown in Fig.12.4b. From inspection, it is assumed that the support moments at is zero and support moment at, 15 kn.m (negative because it causes compression at bottom at ) needs to be evaluated. pplying three- Hence, only

More information

MECHANICS LAB AM 317 EXP 1 BEAM DEFLECTIONS

MECHANICS LAB AM 317 EXP 1 BEAM DEFLECTIONS MECHANICS AB AM 317 EX 1 BEAM DEFECTIONS I. OBJECTIVES I.1 To observe, evaluate and report on the load-deflection relationship of a simply supported beam and a cantilever beam. I.2 To determine the modulus

More information

Shear Force V: Positive shear tends to rotate the segment clockwise.

Shear 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 information

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3

MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.

More information

Method of elastic line

Method of elastic line Method of elastic line To study the method of elastic line we shall first consider a beam of infinite length with a constant cross section (fig. 5.34). This beam rests on elastic soil and the deflection

More information

Problem 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 1: Calculating deflection by integration uniform load Problem 2: Calculating deflection by integration - triangular load pattern Problem 3: Deflections - by differential equations, concentrated

More information

P.E. Civil Exam Review:

P.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 information

structural analysis Excessive beam deflection can be seen as a mode of failure.

structural 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 information

Assumptions: beam is initially straight, is elastically deformed by the loads, such that the slope and deflection of the elastic curve are

Assumptions: 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 information

A concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0.

A concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0. 2011 earson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 8 1. 3 1. concrete cylinder having a a diameter of of 6.00

More information

Chapter 7: Bending and Shear in Simple Beams

Chapter 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

Design of Reinforced Concrete Beam for Shear

Design of Reinforced Concrete Beam for Shear Lecture 06 Design of Reinforced Concrete Beam for Shear By: Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk Topics Addressed Shear Stresses in Rectangular Beams Diagonal Tension

More information

3 Relation between complete and natural degrees of freedom

3 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 information

Final Exam - Spring

Final Exam - Spring EM121 Final Exam - Spring 2011-2012 Name : Section Number : Record all your answers to the multiple choice problems (1-15) by filling in the appropriate circle. All multiple choice answers will be graded

More information

DEFLECTION CALCULATIONS (from Nilson and Nawy)

DEFLECTION 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 information

FINITE 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) 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 information

3.4 Analysis for lateral loads

3.4 Analysis for lateral loads 3.4 Analysis for lateral loads 3.4.1 Braced frames In this section, simple hand methods for the analysis of statically determinate or certain low-redundant braced structures is reviewed. Member Force Analysis

More information

Module 3. Analysis of Statically Indeterminate Structures by the Displacement Method

Module 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 information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS CHATR Stress MCHANICS OF MATRIALS and Strain Axial Loading Stress & Strain: Axial Loading Suitability of a structure or machine may depend on the deformations in the structure as well as the stresses induced

More information

7.4 The Elementary Beam Theory

7.4 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 information

High Tech High Top Hat Technicians. An Introduction to Solid Mechanics. Is that supposed to bend there?

High Tech High Top Hat Technicians. An Introduction to Solid Mechanics. Is that supposed to bend there? High Tech High Top Hat Technicians An Introduction to Solid Mechanics Or Is that supposed to bend there? Why don't we fall through the floor? The power of any Spring is in the same proportion with the

More information

Shear force and bending moment of beams 2.1 Beams 2.2 Classification of beams 1. Cantilever Beam Built-in encastre' Cantilever

Shear force and bending moment of beams 2.1 Beams 2.2 Classification of beams 1. Cantilever Beam Built-in encastre' Cantilever CHAPTER TWO Shear force and bending moment of beams 2.1 Beams A beam is a structural member resting on supports to carry vertical loads. Beams are generally placed horizontally; the amount and extent of

More information

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy

Stress Analysis Lecture 3 ME 276 Spring Dr./ Ahmed Mohamed Nagib Elmekawy Stress Analysis Lecture 3 ME 276 Spring 2017-2018 Dr./ Ahmed Mohamed Nagib Elmekawy Axial Stress 2 Beam under the action of two tensile forces 3 Beam under the action of two tensile forces 4 Shear Stress

More information

k 21 k 22 k 23 k 24 k 31 k 32 k 33 k 34 k 41 k 42 k 43 k 44

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 information

ME 323 Examination #2

ME 323 Examination #2 ME 33 Eamination # SOUTION Novemer 14, 17 ROEM NO. 1 3 points ma. The cantilever eam D of the ending stiffness is sujected to a concentrated moment M at C. The eam is also supported y a roller at. Using

More information

Chapter 11. Displacement Method of Analysis Slope Deflection Method

Chapter 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 information

Introduction to Structural Member Properties

Introduction 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 information

QUESTION BANK ENGINEERS ACADEMY. Hinge E F A D. Theory of Structures Determinacy Indeterminacy 1

QUESTION BANK ENGINEERS ACADEMY. Hinge E F A D. Theory of Structures Determinacy Indeterminacy 1 Theory of Structures eterminacy Indeterminacy 1 QUSTION NK 1. The static indeterminacy of the structure shown below (a) (b) 6 (c) 9 (d) 12 2. etermine the degree of freedom of the following frame (a) 1

More information

Quizzam Module 1 : Statics

Quizzam 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 information

Axial force-moment interaction in the LARSA hysteretic beam element

Axial force-moment interaction in the LARSA hysteretic beam element Axial force-moment interaction in the LARSA hsteretic beam element This document briefl discusses the modeling of tri-axial interaction (i.e. between axial force and bending moments) in the LARSA beam

More information

Review Lecture. AE1108-II: Aerospace Mechanics of Materials. Dr. Calvin Rans Dr. Sofia Teixeira De Freitas

Review Lecture. AE1108-II: Aerospace Mechanics of Materials. Dr. Calvin Rans Dr. Sofia Teixeira De Freitas Review Lecture AE1108-II: Aerospace Mechanics of Materials Dr. Calvin Rans Dr. Sofia Teixeira De Freitas Aerospace Structures & Materials Faculty of Aerospace Engineering Analysis of an Engineering System

More information

[7] Torsion. [7.1] Torsion. [7.2] Statically Indeterminate Torsion. [7] Torsion Page 1 of 21

[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 information

SIMPLY SUPPORTED STRUCTURAL BEAM STRESS AND DEFLECTION ANAL

SIMPLY SUPPORTED STRUCTURAL BEAM STRESS AND DEFLECTION ANAL 1 of 6 22/03/2016 09:17 HOMEPAGE CALCULATORS EXAMPLES GUIDELINES SIMPLY SUPPORTED STRUCTURAL BEAM STRESS AND DEFLECTION ANAL Following calculator has been developed to find forces, moments, stresses, deflections

More information

MAHALAKSHMI ENGINEERING COLLEGE

MAHALAKSHMI ENGINEERING COLLEGE AHAAKSHI ENGINEERING COEGE TIRUCHIRAPAI - 611. QUESTION WITH ANSWERS DEPARTENT : CIVI SEESTER: V SU.CODE/ NAE: CE 5 / Strength of aterials UNIT INDETERINATE EAS 1. Define statically indeterminate beams.

More information

8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method. 8-5 Conjugate-Beam method

8-5 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 information

March 24, Chapter 4. Deflection and Stiffness. Dr. Mohammad Suliman Abuhaiba, PE

March 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 information

MECHANICS OF MATERIALS Sample Problem 4.2

MECHANICS OF MATERIALS Sample Problem 4.2 Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A cast-iron machine part is acted upon by a kn-m couple.

More information