TYPES OF STRUCUTRES. HD in Civil Engineering Page 1-1
|
|
- William Thornton
- 5 years ago
- Views:
Transcription
1 E2027 Structural nalysis I TYPES OF STRUUTRES H in ivil Engineering Page 1-1
2 E2027 Structural nalysis I SUPPORTS Pin or Hinge Support pin or hinge support is represented by the symbol H or H V V Prevented: llowed: Horizontal translation and vertical translation Rotation Roller Support roller support is represented by the symbol or V V Prevented: llowed: Vertical translation Horizontal translation and Rotation H in ivil Engineering Page 1-2
3 E2027 Structural nalysis I Fixed Support fixed support is represented by the symbol M H or H V V M Prevented: llowed: Horizontal translation, Vertical translation and Rotation None H in ivil Engineering Page 1-3
4 E2027 Structural nalysis I EQUILIRIUM OF STRUTURES structure is considered to be in equilibrium if it remains at rest when subjected to a system of forces and moments. If a structure is in equilibrium, then all its members and parts are also in equilibrium. For a structure to be in equilibrium, all the forces and moments (including support reactions) acting on it must balance each other. For a plane structure subjected to forces in its own plane, the conditions for equilibrium can be expressed by the following equations of equilibrium: F x 0, Fy = 0, M z = = 0 The third equation above states that the sum of moments of all forces about any point in the plane of the structure is zero. Equations of ondition Sometimes internal hinges are present within a structure. n internal hinge cannot transmit moment. Therefore the bending moment at a hinge is zero. The condition that the moment is zero at a hinge provides an additional equation for analyzing the structure. Such equations are commonly called equations of condition. (a) (b) (c) H in ivil Engineering Page 1-4
5 E2027 Structural nalysis I eterminate and Indeterminate Structures structure is externally determinate if the support reactions can all be obtained by statics, i.e. No. of Support Reactions = No. of Equations (incl. Equilibrium & onditions) structure which is not determinate is called indeterminate. egree of Statical Indetermincy = No. of Support Reactions No. of Equations FREE-OY IGRMS 1. Free-body diagrams make use of the concept that if a whole structure is in equilibrium, any part of it is also in equilibrium. 2. Free-body diagrams can be constructed for various parts of a structure, and also for the entire structure. 3. When drawing a free-body, it is important to indicate on it all possible forces acting in the given structure at the cuts. 4. Internal forces common to two free-bodies (on opposite sides of the cut ) should be denoted as equal in magnitude but opposite in direction. 5. Free-body iagrams are very useful in finding the support reactions and determining the internal forces in structures. The use of free-body diagram is an important tool in structural analysis and stress analysis. H in ivil Engineering Page 1-5
6 E2027 Structural nalysis I Original Structure P1 P2 P3 1 1 H Free-body diagram of the structure to the left of 1-1 V P1 P2 P3 M H V Free-body diagrams of the individual elements P3 H V P1 P2 V H V H M H V Note the equal but opposite directed representation of the connecting forces at. H in ivil Engineering Page 1-6
7 E2027 Structural nalysis I Original Structure ( three-hinge arch) Free-body iagram for the whole structure P1 P2 P1 a b a b P2 H L L H H V L L V H 1 P1 a H H V b P2 Free-body iagrams of arch segments H H V L 1 V L V H V 1 M 1 H 1 P1 H 1 a V H Free-body iagrams to analyze internal forces at section 1-1 H V V 1 H in ivil Engineering Page 1-7
8 E2027 Structural nalysis I Example 1 eam has a pinned support at and a roller support at. It carries two concentrated loads of 20 kn each and a uniformly distributed load of 4 kn/m over the right hand half as shown. etermine the reactions. 20 kn 20 kn 4 kn/m 3m 1.5m 1.5m 3m Solution: 20 kn 20 kn 4 kn/m H V V 3m 1.5m 1.5m 3m X = 0, H = 0 Take moment about, 20*3 + 20*9 + 4*(4.5)*( /2) V c *6 = 0 V c = kn Y = 0, *4.5 = V + V V = kn, (-ve sign indicates V acts in opposite direction) V = 2.25 kn ( ) H in ivil Engineering Page 1-8
9 E2027 Structural nalysis I Example 2 Find the support reactions for the simple beam shown kn 50 kn 3 4 5m 2.5m 2.5m Solution: kn 40 kn 3 50 kn 30 kn H V V 5m 2.5m 2.5m Resolve the 50 kn inclined external load into horizontal and vertical components as shown. X = 0, H = 30 kn Take moment about, 40*5 + 40*7.5 V *10 = 0 V = 50 kn Y = 0, = V + V V = 30 kn H in ivil Engineering Page 1-9
10 E2027 Structural nalysis I Example 3 etermine the truss reaction forces. 30 kn 30 kn 20 kn 5m 5m 5m 5m 5m Solution: 30 kn 30 kn 20 kn 5m H V V 5m 5m 5m 5m X = 0, H = 20 kn Take moment about, 30* *15 20*2.5 V *20 = 0 V = 35 kn Y = 0, = V + V V = 25 kn H in ivil Engineering Page 1-10
11 E2027 Structural nalysis I Example 4 etermine the support reactions for the frame shown. 20 kn 25 kn m 4m 10 kn E 12 m H in ivil Engineering Page 1-11
12 E2027 Structural nalysis I Solution: 20 kn 20 kn kn 4 4m 4m 10 kn H V V E E 15 kn 12 m Resolve the 25 kn inclined external load into horizontal and vertical components as shown. X = 0, H + 10 = 15 kn H = 5 kn Take moment about, 10*4 + 20*12 15*8 V E *12 = 0 V E = 13.3 kn Y = 0, = V + V E V = 26.7 kn H in ivil Engineering Page 1-12
13 E2027 Structural nalysis I Example 5 Find the reactions for the cantilever beam shown. 6 kn 4 knm 4 kn/m 1.5m 1.5m 1.5m 1.5m Solution: M H V 6 kn 4 kn/m 4 knm 1.5m 1.5m 1.5m 1.5m X = 0, H = 0 kn Y = 0, 6 + 4*1.5/2 = V V = 9 kn Take moment about, 6* *(1.5/2)*(6-1.5*1/3) 4 M = 0 M = 21.5 knm H in ivil Engineering Page 1-13
14 E2027 Structural nalysis I Example 6 etermine the support reactions for the frame shown. 3 kn/m 8 kn/m 3 kn/m 12m 8m H in ivil Engineering Page 1-14
15 E2027 Structural nalysis I Solution: 3 kn/m 5 kn/m 3 kn/m 3 kn/m 12m H V M 8m X = 0, H = 3*12 kn = 36 kn Y = 0, 3*8 + 5*8/2 = V V = 44 kn Take moment about, 3*12*6 + 3*8*4 + 5*(8/2)*(8*2/3) M = 0 M = knm H in ivil Engineering Page 1-15
16 E2027 Structural nalysis I Example 7 etermine the support reactions at the support, and F. Joints and E are internal hinges. 10 kn 4 kn/m E 2.5m 2.5m 2m 2m 4m F Solution: 10 kn 4 kn/m E V V 2.5m 2.5m 2m 2m 4m F M F H F V F H in ivil Engineering Page 1-16
17 E2027 Structural nalysis I reak the beam into three free-body diagrams, namely, E and EF. V 10 kn H V H V V E V E H E H E 4 kn/m M F E F H F V E V F onsider free-body diagram, X = 0, H = 0 kn y symmetry, V = V = 10/2 = 5 kn Remember the internal forces at hinge of and E are equal and opposite. This also applies to hinge E. onsider free-body diagram E, X = 0, H = H E = 0 kn Take moment about E, V *4 = V *2 V = 5*4/2 = 10 kn Y = 0, V + V E = V, V E = 10-5 = 5 kn H in ivil Engineering Page 1-17
18 E2027 Structural nalysis I onsider free-body diagram, EF. X = 0, H E = H F = 0 kn Y = 0, V E + V F = 4*4, V F = 16-5 = 11 kn Take moment about F, V E *4 + M F 4*4*2 = 0 M F = 4*4*2 5*4 = 12 knm H in ivil Engineering Page 1-18
19 E2027 Structural nalysis I Example 8 etermine the support reactions at,, G and H. Joints and F are internal hinges. 120 kn 150 kn E F G 10 kn/m 5m 5m 2m 3m 3m 2m 6m H Solution: Resolve the inclined external load into vertical and horizontal components. 120 kn 120 kn 90 kn 10 kn/m H H E F G V V V G V H 5m 5m 2m 3m 3m 2m 6m H in ivil Engineering Page 1-19
20 E2027 Structural nalysis I reak the beam into three free-body diagrams, namely, EF and FGH. 120 kn 120 kn H V V 90 kn E F H V F F H V 10 kn/m F H F F G H V V V G V H H onsider the free-body FGH first, X = 0, H F = 0 onsider the free-body EF, y symmetry, V = V F = 120/2 = 60 kn X = 0, H = H F +90 = = 90 kn. onsider the free-body, X = 0, H = H, H = 90 kn. Take moment about, 120*5 + 60*12 = V *10, V = 132 kn. Y = 0, V + V = , V = 48 kn. onsider the free-body FGH, Take moment about H, 60*8 + 10*8*4 = V G *6, V G = kn. Y = 0, V G + V H = 10*8 + 60, V H = 6.7 kn. H in ivil Engineering Page 1-20
21 E2027 Structural nalysis I Tutorial 1 (Support Reactions) etermine the support reactions for the following structures. Q1. 10 kn 2 kn/m E 2m 2m 1m 3m is an internal hinge Q2. 30 kn/m is an internal hinge 200 kn 10.4m 1.6m 12 m 6m 6m H in ivil Engineering Page 1-21
22 E2027 Structural nalysis I Q3. 4 kn/m 2 kn 1m 3m 1m 2m Q kn 40 kn/m 3m 3m 6m is an internal hinge Q5. 5 kn/m 5 kn/m 2m 2m 2m H in ivil Engineering Page 1-22
23 E2027 Structural nalysis I Q6. 30 kn 10 kn/m E F 3m 3m G 3m 3m, & F are internal hinges Q7. 20 kn/m 40 kn/m E F is an internal hinge 12 m G 3m 5m 3m 5m H in ivil Engineering Page 1-23
24 E2027 Structural nalysis I Q8. 2 kn/m is an internal hinge 4m 6m E 3 kn/m 3m 3m Q9. 60 kn 30 kn E 6 kn/m & E are internal hinges 5m 3m 3m 3m F H in ivil Engineering Page 1-24
25 E2027 Structural nalysis I Q kn 20 kn E 6 knm is an internal hinge 2 kn/m 4m F 2m 1m 1m H in ivil Engineering Page 1-25
Hong Kong Institute of Vocational Education (Tsing Yi) Higher Diploma in Civil Engineering Structural Mechanics. Chapter 1 PRINCIPLES OF STATICS
PRINCIPLES OF STTICS Statics is the study of how forces act and react on rigid bodies which are at rest or not in motion. This study is the basis for the engineering principles, which guide the design
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 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 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 informationContinuing 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 informationTypes of Structures & Loads
Structure Analysis I Chapter 4 1 Types of Structures & Loads 1Chapter Chapter 4 Internal lloading Developed in Structural Members Internal loading at a specified Point In General The loading for coplanar
More informationQUESTION 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 informationFramed Structures PLANE FRAMES. Objectives:
Framed Structures 2 Objectives: ifferentiate between perfect, imperfect and redundant frames. To compute the member forces in a frame by graphical method. To compute the forces in a truss by method of
More informationChapter 4.1: Shear and Moment Diagram
Chapter 4.1: Shear and Moment Diagram Chapter 5: Stresses in Beams Chapter 6: Classical Methods Beam Types Generally, beams are classified according to how the beam is supported and according to crosssection
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 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 informationIf the number of unknown reaction components are equal to the number of equations, the structure is known as statically determinate.
1 of 6 EQUILIBRIUM OF A RIGID BODY AND ANALYSIS OF ETRUCTURAS II 9.1 reactions in supports and joints of a two-dimensional structure and statically indeterminate reactions: Statically indeterminate structures
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 informationMEE224: Engineering Mechanics Lecture 4
Lecture 4: Structural Analysis Part 1: Trusses So far we have only analysed forces and moments on a single rigid body, i.e. bars. Remember that a structure is a formed by and this lecture will investigate
More informationFramed Structures PLANE FRAMES. Objectives:
Framed Structures 2 Objectives: ifferentiate between perfect, imperfect and redundant frames. To compute the member forces in a frame by graphical method. To compute the forces in a truss by method of
More informationSAB2223 Mechanics of Materials and Structures
S2223 Mechanics of Materials and Structures TOPIC 2 SHER FORCE ND ENDING MOMENT Lecturer: Dr. Shek Poi Ngian TOPIC 2 SHER FORCE ND ENDING MOMENT Shear Force and ending Moment Introduction Types of beams
More informationPin-Jointed Frame Structures (Frameworks)
Pin-Jointed rame Structures (rameworks) 1 Pin Jointed rame Structures (rameworks) A pin-jointed frame is a structure constructed from a number of straight members connected together at their ends by frictionless
More informationChapter 2. Shear Force and Bending Moment. After successfully completing this chapter the students should be able to:
Chapter Shear Force and Bending Moment This chapter begins with a discussion of beam types. It is also important for students to know and understand the reaction from the types of supports holding the
More informationT2. VIERENDEEL STRUCTURES
T2. VIERENDEEL STRUCTURES AND FRAMES 1/11 T2. VIERENDEEL STRUCTURES NOTE: The Picture Window House can be designed using a Vierendeel structure, but now we consider a simpler problem to discuss the calculation
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 information6.5 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 information7 STATICALLY DETERMINATE PLANE TRUSSES
7 STATICALLY DETERMINATE PLANE TRUSSES OBJECTIVES: This chapter starts with the definition of a truss and briefly explains various types of plane truss. The determinancy and stability of a truss also will
More informationModule 1 : Introduction : Review of Basic Concepts in Mechnics Lecture 4 : Static Indeterminacy of Structures
Module 1 : Introduction : Review of Basic Concepts in Mechnics Lecture 4 : Static Indeterminacy of Structures Objectives In this course you will learn the following Review of the concepts of determinate
More informationUnit II Shear and Bending in Beams
Unit II Shear and Bending in Beams Syllabus: Beams and Bending- Types of loads, supports - Shear Force and Bending Moment Diagrams for statically determinate beam with concentrated load, UDL, uniformly
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 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 information== Delft University of Technology == Give on the upper right. Exam STATICS /
== elft University of Technology == Give on the upper right University ourse pplied Mechanics corner of each sheet your NME STUY NUMER and ISIPLINE Exam STTIS 2003.08.26 / 09.00-12.00 The work of a student
More informationNewton s Third Law Newton s Third Law: For each action there is an action and opposite reaction F
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
More informationSTATICALLY INDETERMINATE STRUCTURES
STATICALLY INDETERMINATE STRUCTURES INTRODUCTION Generally the trusses are supported on (i) a hinged support and (ii) a roller support. The reaction components of a hinged support are two (in horizontal
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 informationFRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a
FRAMES AND MACHINES Learning Objectives 1). To evaluate the unknown reactions at the supports and the interaction forces at the connection points of a rigid frame in equilibrium by solving the equations
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 informationMethods 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 informationT4/1 Analysis of a barrel vault simplified calculation
T4. MASONRY STRUCTURES 1/4 T4/1 Analysis of a barrel vault simplified calculation Exercise: Check the given masonry vault for symmetrical loading! ata: q k = 4 kn/m (live load) ρ masonry = 17 kn/m 3 (specific
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 informationthree point equilibrium and planar trusses Equilibrium Equilibrium on a Point Equilibrium on a Point
RHITETURL STRUTURES: FORM, EHVIOR, N ESIGN R. NNE NIHOLS SUMMER 2014 lecture three Equilibrium balanced steady resultant of forces on a particle is 0 X point equilibrium and planar trusses http:// nisee.berkeley.edu/godden
More informationGLOBAL EDITION. Structural Analysis. Ninth Edition in SI Units. R. C. Hibbeler
GLOAL EDITION Structural Analysis Ninth Edition in SI Units R. C. Hibbeler STRUCTURAL ANALYSIS NINTH EDITION IN SI UNITS R. C. HIELER SI Conversion by Kai eng Yap oston Columbus Indianapolis New York San
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 informationTHEORY OF STRUCTURE SSC-JE STAFF SELECTION COMMISSION CIVIL ENGINEERING STRUCTURAL ENGINEERING THEORY OF STRUCTURE
Page 1 of 97 SSC-JE STAFF SELECTION COMMISSION CIVIL ENGINEERING STRUCTURAL ENGINEERING 28-B/7, JiaSarai, Near IIT, HauKhas, New elhi-110016. Ph. 011-26514888. www.engineersinstitute.com C O N T E N T
More informationUNIT II SLOPE DEFLECION AND MOMENT DISTRIBUTION 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 informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. APPLICATIONS
More informationLecture 4: PRELIMINARY CONCEPTS OF STRUCTURAL ANALYSIS. Introduction
Introduction In this class we will focus on the structural analysis of framed structures. We will learn about the flexibility method first, and then learn how to use the primary analytical tools associated
More informationMethod 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 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 informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body Solve rigid-body equilibrium problems using the equations
More informationENG202 Statics Lecture 16, Section 7.1
ENG202 Statics Lecture 16, Section 7.1 Internal Forces Developed in Structural Members - Design of any structural member requires an investigation of the loading acting within the member in order to be
More informationThe 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 informationChapter 5: Equilibrium of a Rigid Body
Chapter 5: Equilibrium of a Rigid Body Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of a free-body diagram for a rigid body. To show how to solve
More informationEquilibrium of Rigid Bodies
RCH 331 Note Set 5.1 Su2016abn Equilibrium of Rigid odies Notation: k = spring constant F = name for force vectors, as is P Fx = force component in the x direction Fy = force component in the y direction
More informationSupplement: Statically Indeterminate Trusses and Frames
: Statically Indeterminate Trusses and Frames Approximate Analysis - In this supplement, we consider an approximate method of solving statically indeterminate trusses and frames subjected to lateral loads
More informationEngineering Mechanics: Statics in SI Units, 12e
Engineering Mechanics: Statics in SI Units, 12e 5 Equilibrium of a Rigid Body Chapter Objectives Develop the equations of equilibrium for a rigid body Concept of the free-body diagram for a rigid body
More informationContinuous Beams - Flexibility Method
ontinuous eams - Flexibility Method Qu. Sketch the M diagram for the beam shown in Fig.. Take E = 200kN/mm 2. 50kN 60kN-m = = 0kN/m D I = 60 50 40 x 0 6 mm 4 Fig. 60.0 23.5 D 25.7 6.9 M diagram in kn-m
More informationM.S Comprehensive Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... M.S Comprehensive
More 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 informationPreliminaries: Beam Deflections Virtual Work
Preliminaries: Beam eflections Virtual Work There are several methods available to calculate deformations (displacements and rotations) in beams. They include: Formulating moment equations and then integrating
More informationThe analysis of trusses Mehrdad Negahban (1999)
The analysis of trusses Mehrdad Negahban (1999) A truss: A truss is a structure made of two force members all pin connected to each other. The method of joints: This method uses the free-body-diagram of
More informationEQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO- AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. In-Class
More informationLaith 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 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 informationPh.D. Preliminary Examination Analysis
UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... Ph.D.
More informationModule 6. Approximate Methods for Indeterminate Structural Analysis. Version 2 CE IIT, Kharagpur
Module 6 Approximate Methods for Indeterminate Structural Analysis Lesson 35 Indeterminate Trusses and Industrial rames Instructional Objectives: After reading this chapter the student will be able to
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 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 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 informationEngineering Mechanics Statics
Mechanical Systems Engineering _ 2016 Engineering Mechanics Statics 7. Equilibrium of a Rigid Body Dr. Rami Zakaria Conditions for Rigid-Body Equilibrium Forces on a particle Forces on a rigid body The
More informationSTATICS--AN INVESTIGATION OF FORCES
STTIS--N INVESTIGTION O ORES Two areas of study to investigate forces. Statics where the forces acting on a material are balanced so that the material is either stationary or in uniform motion. or fluid
More information11.1 Virtual Work Procedures and Strategies, page 1 of 2
11.1 Virtual Work 11.1 Virtual Work rocedures and Strategies, page 1 of 2 rocedures and Strategies for Solving roblems Involving Virtual Work 1. Identify a single coordinate, q, that will completely define
More information- Beams are structural member supporting lateral loadings, i.e., these applied perpendicular to the axes.
4. Shear and Moment functions - Beams are structural member supporting lateral loadings, i.e., these applied perpendicular to the aes. - The design of such members requires a detailed knowledge of the
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 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 informationTheory of structure I 2006/2013. Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES
Chapter one DETERMINACY & INDETERMINACY OF STRUCTURES Introduction A structure refers to a system of connected parts used to support a load. Important examples related to civil engineering include buildings,
More informationDeflection 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 informationEQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS
EQUATIONS OF EQUILIBRIUM & TWO-AND THREE-FORCE MEMEBERS Today s Objectives: Students will be able to: a) Apply equations of equilibrium to solve for unknowns, and, b) Recognize two-force members. READING
More informationShear Forces And Bending Moments
Shear Forces And Bending Moments 1 Introduction 2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning is a trademark used herein under license. Fig. 4-1 Examples of beams subjected to
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 1 - FRAMES AND BEAMS
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 1 - FRAMES AND BEAMS TUTORIAL 2 - BEAMS CONTENT Be able to determine the forces acting
More informationASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER /13
ASSOCIATE DEGREE IN ENGINEERING EXAMINATIONS SEMESTER 2 2012/13 COURSE NAME: ENGINEERING MECHANICS - STATICS CODE: ENG 2008 GROUP: AD ENG II DATE: May 2013 TIME: DURATION: 2 HOURS INSTRUCTIONS: 1. This
More informationProcedure for drawing shear force and bending moment diagram:
Procedure for drawing shear force and bending moment diagram: Preamble: The advantage of plotting a variation of shear force F and bending moment M in a beam as a function of x' measured from one end of
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a cross-section of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More 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 informationtechie-touch.blogspot.com DEPARTMENT OF CIVIL ENGINEERING ANNA UNIVERSITY QUESTION BANK CE 2302 STRUCTURAL ANALYSIS-I TWO MARK QUESTIONS UNIT I DEFLECTION OF DETERMINATE STRUCTURES 1. Write any two important
More informationARCH 614 Note Set 5 S2012abn. Moments & Supports
RCH 614 Note Set 5 S2012abn Moments & Supports Notation: = perpenicular istance to a force from a point = name for force vectors or magnitue of a force, as is P, Q, R x = force component in the x irection
More informationUNIT II 1. Sketch qualitatively the influence line for shear at D for the beam [M/J-15]
UNIT II 1. Sketch qualitatively the influence line for shear at D for the beam [M/J-15] 2. Draw the influence line for shear to the left of B for the overhanging beam shown in Fig. Q. No. 4 [M/J-15] 3.
More informationENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3 - SHEAR FORCE AND BENDING MOMENTS IN BEAMS
ENGINEERING COUNCIL DIPLOMA LEVEL MECHANICS OF SOLIDS D209 TUTORIAL 3 - SHEAR FORCE AND BENDING MOMENTS IN BEAMS You should judge your progress by completing the self assessment exercises. On completion
More 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 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 informationEquilibrium of a Rigid Body. Engineering Mechanics: Statics
Equilibrium of a Rigid Body Engineering Mechanics: Statics Chapter Objectives Revising equations of equilibrium of a rigid body in 2D and 3D for the general case. To introduce the concept of the free-body
More informationUNIT-III ARCHES Introduction: Arch: What is an arch? Explain. What is a linear arch?
UNIT-III RCES rches as structural forms Examples of arch structures Types of arches nalysis of three hinged, two hinged and fixed arches, parabolic and circular arches Settlement and temperature effects.
More information5.2 Rigid Bodies and Two-Dimensional Force Systems
5.2 Rigid odies and Two-Dimensional Force Systems 5.2 Rigid odies and Two-Dimensional Force Systems Procedures and Strategies, page 1 of 1 Procedures and Strategies for Solving Problems Involving Equilibrium
More informationLevel 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method
9210-203 Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method You should have the following for this examination one answer book No additional data is attached
More informationStructural Steel Design Project
Job No: Sheet 1 of 6 Rev Worked Example - 1 Made by Date 4-1-000 Checked by PU Date 30-4-000 Analyse the building frame shown in Fig. A using portal method. 15 kn C F I L 4 m 0 kn B E H K 6 m A D G J 4
More informationReg. No. : Question Paper Code : B.Arch. DEGREE EXAMINATION, APRIL/MAY Second Semester AR 6201 MECHANICS OF STRUCTURES I
WK 4 Reg. No. : Question Paper Code : 71387 B.Arch. DEGREE EXAMINATION, APRIL/MAY 2017. Second Semester AR 6201 MECHANICS OF STRUCTURES I (Regulations 2013) Time : Three hours Maximum : 100 marks Answer
More informationChapter Objectives. Copyright 2011 Pearson Education South Asia Pte Ltd
Chapter Objectives To develop the equations of equilibrium for a rigid body. To introduce the concept of the free-body diagram for a rigid body. To show how to solve rigid-body equilibrium problems using
More informationENGR-1100 Introduction to Engineering Analysis. Lecture 13
ENGR-1100 Introduction to Engineering Analysis Lecture 13 EQUILIBRIUM OF A RIGID BODY & FREE-BODY DIAGRAMS Today s Objectives: Students will be able to: a) Identify support reactions, and, b) Draw a free-body
More informationENGINEERING MECHANICS STATIC
Trusses Simple trusses The basic element of a truss is the triangle, three bars joined by pins at their ends, fig. a below, constitutes a rigid frame. The term rigid is used to mean noncollapsible and
More informationENGINEERING MECHANICS SOLUTIONS UNIT-I
LONG QUESTIONS ENGINEERING MECHANICS SOLUTIONS UNIT-I 1. A roller shown in Figure 1 is mass 150 Kg. What force P is necessary to start the roller over the block A? =90+25 =115 = 90+25.377 = 115.377 = 360-(115+115.377)
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 informationCalculating Truss Forces Unit 2 Lesson 2.1 Statics
alculating Truss Forces alculating Truss Forces Principles of Engineering 22 Forces ompression body being squeezed Tension body being stretched Truss truss is composed of slender members joined together
More informationThe centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by
Unit 12 Centroids Page 12-1 The centroid of an area is defined as the point at which (12-2) The distance from the centroid of a given area to a specified axis may be found by (12-5) For the area shown
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 information13.4 Resultants, moments, and torques b z
Homework 13. Chapters 14, 14, 15. Forces, torque and replacement 13.1 Momentsofforcesaboutvariouspoints Consider the following sets of forces. Circle the set(s) in which the following are all equal: ote:
More information