This document discusses basic structural analysis concepts including plane trusses, beams, shear force, bending moment, and their relationships. It describes different types of trusses like Pratt and bowstring trusses, and the methods of joints and sections for truss analysis. Zero force members in trusses are explained. Beams are classified as statically determinate and indeterminate, and methods for determining beam deflections are listed. The relationships between load, shear force, and bending moment diagrams are outlined.
This document provides an overview of trusses and frames for a course on prestressed concrete design. It defines trusses as structures composed of members connected to resist changes in shape. Trusses are made of triangular units and transfer loads through tension and compression forces in their members. The document discusses different types of trusses, including plane and space trusses, and terminology for roof and bridge trusses. It also covers methods for analyzing trusses and frames, including the joint and section methods using free body diagrams. Frames are similar structures that contain members subject to multiple forces.
This document summarizes key concepts from a chapter on analyzing structures. It discusses how to determine the internal and external forces acting on trusses, frames, and machines. The objectives are to calculate the forces carried by various structures and determine if they can withstand these forces. It describes analyzing trusses using the method of joints and method of sections. Frames are introduced as structures with multi-force members. The document also distinguishes between determinate and indeterminate structures, with determinate structures having solvable equilibrium equations and indeterminate structures lacking sufficient equations.
A truss is a structure composed of straight members connected at joints that forms a stable structure. There are three types of trusses: perfect trusses which have just enough members for equilibrium, deficient trusses with fewer members that change shape under load, and redundant trusses with extra members that maintain shape under load. Truss analysis involves applying equilibrium equations to sections or joints of the truss to determine member forces. Trusses are commonly used in roofs, bridges, and other engineering structures.
This document discusses structural analysis of frames and trusses. It defines frames and trusses, and explains that trusses are structures composed of triangular units that distribute loads efficiently. The document then covers various types of trusses including Warren trusses, Howe trusses, and Pratt trusses. It also discusses truss analysis methods and compares trusses to frames. Finally, the document provides examples of roof truss design and types of truss connections.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
The document discusses frames and trusses, which are structures consisting of bars, rods, angles, and channels pinned or fastened together to support loads and transmit them to supports. Trusses contain only two-force members that experience either tension or compression, while frames can contain multi-force members and experience transverse forces as well. Common truss configurations include pinned, gusset plate, and bolted or welded joints. Trusses are analyzed using methods of joints or sections to determine member forces.
1. A truss is a rigid structure composed of straight members connected at joints that is statically determinate.
2. Trusses can be perfect, deficient, or redundant depending on the number of members compared to the number of joints. Perfect trusses have just enough members, deficient trusses have too few, and redundant trusses have excess members.
3. The document discusses the definition of a truss, different types of trusses, assumptions made in truss analysis, analysis methods including the method of joints and method of sections, and includes examples of solving for member forces using these methods.
This document provides an overview of trusses and frames for a course on prestressed concrete design. It defines trusses as structures composed of members connected to resist changes in shape. Trusses are made of triangular units and transfer loads through tension and compression forces in their members. The document discusses different types of trusses, including plane and space trusses, and terminology for roof and bridge trusses. It also covers methods for analyzing trusses and frames, including the joint and section methods using free body diagrams. Frames are similar structures that contain members subject to multiple forces.
This document summarizes key concepts from a chapter on analyzing structures. It discusses how to determine the internal and external forces acting on trusses, frames, and machines. The objectives are to calculate the forces carried by various structures and determine if they can withstand these forces. It describes analyzing trusses using the method of joints and method of sections. Frames are introduced as structures with multi-force members. The document also distinguishes between determinate and indeterminate structures, with determinate structures having solvable equilibrium equations and indeterminate structures lacking sufficient equations.
A truss is a structure composed of straight members connected at joints that forms a stable structure. There are three types of trusses: perfect trusses which have just enough members for equilibrium, deficient trusses with fewer members that change shape under load, and redundant trusses with extra members that maintain shape under load. Truss analysis involves applying equilibrium equations to sections or joints of the truss to determine member forces. Trusses are commonly used in roofs, bridges, and other engineering structures.
This document discusses structural analysis of frames and trusses. It defines frames and trusses, and explains that trusses are structures composed of triangular units that distribute loads efficiently. The document then covers various types of trusses including Warren trusses, Howe trusses, and Pratt trusses. It also discusses truss analysis methods and compares trusses to frames. Finally, the document provides examples of roof truss design and types of truss connections.
Truss is a framework, typically consisting of rafters, posts, and struts, supporting a roof, bridge, or other structure.
a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object"
The document discusses frames and trusses, which are structures consisting of bars, rods, angles, and channels pinned or fastened together to support loads and transmit them to supports. Trusses contain only two-force members that experience either tension or compression, while frames can contain multi-force members and experience transverse forces as well. Common truss configurations include pinned, gusset plate, and bolted or welded joints. Trusses are analyzed using methods of joints or sections to determine member forces.
1. A truss is a rigid structure composed of straight members connected at joints that is statically determinate.
2. Trusses can be perfect, deficient, or redundant depending on the number of members compared to the number of joints. Perfect trusses have just enough members, deficient trusses have too few, and redundant trusses have excess members.
3. The document discusses the definition of a truss, different types of trusses, assumptions made in truss analysis, analysis methods including the method of joints and method of sections, and includes examples of solving for member forces using these methods.
In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object".
Trusses are structures composed of straight members connected at joints. They have three key characteristics: they only experience axial loads, loads are applied only at end points, and members are joined by pins. Trusses are used to support roofs and bridges. To analyze a truss, assumptions are made that loads act only at end points, member weight is ignored, and members experience only axial loads as either tension or compression. The method of joints and method of sections can be used to calculate the internal forces in each member and determine if each member is in tension or compression.
1) A truss is a structure composed of straight members connected at joints that allows the members to only experience axial forces from the connections and any applied loads.
2) Trusses are divided into bridge trusses and roof trusses with various types of each including Pratt, Howe, Warren, and more.
3) Trusses can be analyzed through the method of joints which involves applying equilibrium conditions to each joint sequentially or the method of sections which uses equilibrium on a cut portion of the truss to directly find member forces.
A planar truss is the one whose all members lies in a single plane. If a plane truss does not change its shape when loaded then it is known as Rigid Planar Truss. Copy the link given below and paste it in new browser window to get more information on Planar Truss:- http://www.transtutors.com/homework-help/civil-engineering/planar-truss/
1. The document discusses the analysis of truss structures using the method of joints and method of sections. It defines what a truss is and provides examples of applications of trusses.
2. The method of joints involves applying equilibrium conditions to individual joints, while the method of sections uses equilibrium of isolated sections cut from the truss. Special cases that simplify the analysis are also described.
3. The document presents sample problems and exercises for analyzing trusses using both methods and determining member forces and reactions.
this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.
The document describes Maxwell's diagram, a graphical method for analyzing trusses. It involves drawing force polygons to scale for each joint to determine member forces. The process includes solving for support reactions, drawing a force polygon around the entire truss clockwise, then drawing individual force polygons for each joint with two unknown forces to measure member forces from the diagram. As an example, it provides a sample problem to determine stresses in a Fink truss using this graphical method.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides an overview of analyzing plane trusses through the method of joints and method of sections. It defines what a truss is and describes trusses as being composed of slender members joined at their endpoints that can only experience axial forces. The document then covers the method of joints which involves solving for equilibrium at each joint. It also covers the method of sections which involves cutting the truss and solving for equilibrium of each section. Examples are provided to demonstrate solving for forces in a truss using both methods.
Overall gusset plate due to its advantages in the
design, manufacture, installation, widely used in large span steel
bridge, but for the whole gusset plate of local stress mechanism
few scholars study. With the development of computer
technology, often in practical projects through the finite element
software to simulate, domestic scholars about the boundary
conditions of the simulation is roughly divided into three kinds,
that is, one end of the consolidation, center consolidation and
simply supported at both ends, the principle of selecting the
three boundaries often do not mention, for later users bring
distress, In this paper, through theoretical analysis and finite
element software simulation, illustrates the principle of three
kinds of boundary selection, And according to the viewpoint of
stress nephogram real simulation presents a recommended
boundary conditions which formed at both ends simply
supported constraints.
This document discusses engineering mechanics and frames/trusses. It defines frames as built structures made of members like angles and channels that resist external loads. Trusses are frames where all members form triangles connected by frictionless pins. Frames are classified as determinate or indeterminate based on whether equilibrium equations can analyze them. Trusses are also classified based on the number of members, including perfect, imperfect deficient and redundant frames. The document also covers support conditions, forces in frames, and methods of analyzing frames and trusses.
Lec.1 introduction to the theory of structures. types of structures, loads,Muthanna Abbu
This document provides an introduction to structural analysis and the theory of structures. It defines structural analysis as determining the response of a structure to loads through internal forces and deformations. It classifies skeletal structures and describes the different types of internal forces that can develop in structural members. The document also discusses structural loads, equilibrium, and reactions.
Chapter 3-analysis of statically determinate trussesISET NABEUL
The document discusses various types of trusses used in building structures including simple trusses, compound trusses, and complex trusses. It also covers the assumptions made in truss analysis, classifications of trusses based on stability and determinacy, and different methods for analyzing trusses including the method of joints, method of sections, and analyzing zero force members. Several examples are provided to demonstrate how to apply these analysis methods to solve for unknown member forces in various truss configurations.
1) The document discusses trusses and methods for analyzing truss structures.
2) A truss is a structure composed of slender members joined at endpoints that can support loads. The method of joints is introduced to analyze trusses by applying equilibrium equations at each joint.
3) Zero-force members, which do not experience internal forces, are identified through applying the method of joints and considering the geometry and external loads on the truss. Identifying zero-force members simplifies the analysis.
This document discusses two approximate methods for analyzing building frames subjected to loads: the portal method and cantilever method. The portal method assumes inflection points at midpoints of beams and mid-heights of columns, and that interior columns carry twice the shear of exterior columns. The cantilever method assumes inflection points at beam midpoints and column mid-heights, and that column axial stresses are proportional to their distance from the storey's centroid. Examples demonstrate applying each method to determine member forces in frames.
The document provides information about aircraft structures and structural analysis. It defines primary and secondary aircraft structures, and monocoque and semi-monocoque constructions. It describes the functions of different structural elements like the skin, ribs, spars, and stringers. It discusses simplifications made in structural analysis, including lumping longitudinal members and assuming webs only experience shear stresses. It also covers topics like unsymmetric bending, shear flow, shear centers, and torsion of thin-walled closed sections.
Structure Design-I ( Analysis of truss by method of joint.)Simran Vats
This document discusses analyzing trusses using the method of joints. It begins by defining what a truss is and explaining the relationship between the number of members and joints. It then outlines the steps to use the method of joints, including drawing FBDs at each joint and applying equilibrium equations. Two example trusses are then analyzed using this method, with the forces in each member calculated and reported in a force table.
This document discusses trusses and their analysis. It covers plane trusses, which are used for structures like house coverings, car parking areas, and bridges. Different methods are presented for analyzing trusses, including the analysis of joint and section methods. Examples are provided to illustrate how trusses can be used in real-life structures. A quiz is also listed to assess understanding of the concepts.
This document discusses methods for analyzing plane trusses, including the method of joints and method of sections. The method of joints is more convenient for simple trusses where all member forces are needed, while the method of sections is better for complex trusses where only a few member forces are required. The method of sections involves dividing the truss into parts with an imaginary cut and using equilibrium equations to solve for unknown member forces. An example of applying the method of sections to a space truss is also provided.
This document discusses the analysis of structures including trusses, frames, and machines. It defines trusses as structures formed from two-force members connected at joints. Trusses can be analyzed using the method of joints or sections. Frames contain multi-force members and may cease to be rigid when detached from supports. Machines are designed to transmit and modify forces and transform input to output forces. Sample problems demonstrate applying equilibrium conditions to determine member forces and reactions.
Lesson 29: Integration by Substition (worksheet)Matthew Leingang
This document provides a worksheet with 12 integration problems to practice integration by substitution. The problems involve both indefinite integrals and definite integrals of functions containing variables like x, z, and α. Students are asked to use appropriate substitutions to evaluate the integrals and obtain the most general antiderivative for indefinite integrals or a number for definite integrals. Some problems require determining the substitution, while others provide it. Trigonometric substitutions or identities may also be needed.
Lesson 24: Areas and Distances, The Definite Integral (slides)Matthew Leingang
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
In engineering, a truss is a structure that "consists of two-force members only, where the members are organized so that the assemblage as a whole behaves as a single object".
Trusses are structures composed of straight members connected at joints. They have three key characteristics: they only experience axial loads, loads are applied only at end points, and members are joined by pins. Trusses are used to support roofs and bridges. To analyze a truss, assumptions are made that loads act only at end points, member weight is ignored, and members experience only axial loads as either tension or compression. The method of joints and method of sections can be used to calculate the internal forces in each member and determine if each member is in tension or compression.
1) A truss is a structure composed of straight members connected at joints that allows the members to only experience axial forces from the connections and any applied loads.
2) Trusses are divided into bridge trusses and roof trusses with various types of each including Pratt, Howe, Warren, and more.
3) Trusses can be analyzed through the method of joints which involves applying equilibrium conditions to each joint sequentially or the method of sections which uses equilibrium on a cut portion of the truss to directly find member forces.
A planar truss is the one whose all members lies in a single plane. If a plane truss does not change its shape when loaded then it is known as Rigid Planar Truss. Copy the link given below and paste it in new browser window to get more information on Planar Truss:- http://www.transtutors.com/homework-help/civil-engineering/planar-truss/
1. The document discusses the analysis of truss structures using the method of joints and method of sections. It defines what a truss is and provides examples of applications of trusses.
2. The method of joints involves applying equilibrium conditions to individual joints, while the method of sections uses equilibrium of isolated sections cut from the truss. Special cases that simplify the analysis are also described.
3. The document presents sample problems and exercises for analyzing trusses using both methods and determining member forces and reactions.
this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.
The document describes Maxwell's diagram, a graphical method for analyzing trusses. It involves drawing force polygons to scale for each joint to determine member forces. The process includes solving for support reactions, drawing a force polygon around the entire truss clockwise, then drawing individual force polygons for each joint with two unknown forces to measure member forces from the diagram. As an example, it provides a sample problem to determine stresses in a Fink truss using this graphical method.
Approximate analysis methods make simplifying assumptions to determine preliminary member forces and dimensions for indeterminate structures. Case 1 assumes diagonals cannot carry compression and shares shear between diagonals. Case 2 allows compression in diagonals. Portal and cantilever methods analyze frames by dividing into substructures at assumed hinge locations, solving each sequentially from top to bottom.
This document provides an overview of analyzing plane trusses through the method of joints and method of sections. It defines what a truss is and describes trusses as being composed of slender members joined at their endpoints that can only experience axial forces. The document then covers the method of joints which involves solving for equilibrium at each joint. It also covers the method of sections which involves cutting the truss and solving for equilibrium of each section. Examples are provided to demonstrate solving for forces in a truss using both methods.
Overall gusset plate due to its advantages in the
design, manufacture, installation, widely used in large span steel
bridge, but for the whole gusset plate of local stress mechanism
few scholars study. With the development of computer
technology, often in practical projects through the finite element
software to simulate, domestic scholars about the boundary
conditions of the simulation is roughly divided into three kinds,
that is, one end of the consolidation, center consolidation and
simply supported at both ends, the principle of selecting the
three boundaries often do not mention, for later users bring
distress, In this paper, through theoretical analysis and finite
element software simulation, illustrates the principle of three
kinds of boundary selection, And according to the viewpoint of
stress nephogram real simulation presents a recommended
boundary conditions which formed at both ends simply
supported constraints.
This document discusses engineering mechanics and frames/trusses. It defines frames as built structures made of members like angles and channels that resist external loads. Trusses are frames where all members form triangles connected by frictionless pins. Frames are classified as determinate or indeterminate based on whether equilibrium equations can analyze them. Trusses are also classified based on the number of members, including perfect, imperfect deficient and redundant frames. The document also covers support conditions, forces in frames, and methods of analyzing frames and trusses.
Lec.1 introduction to the theory of structures. types of structures, loads,Muthanna Abbu
This document provides an introduction to structural analysis and the theory of structures. It defines structural analysis as determining the response of a structure to loads through internal forces and deformations. It classifies skeletal structures and describes the different types of internal forces that can develop in structural members. The document also discusses structural loads, equilibrium, and reactions.
Chapter 3-analysis of statically determinate trussesISET NABEUL
The document discusses various types of trusses used in building structures including simple trusses, compound trusses, and complex trusses. It also covers the assumptions made in truss analysis, classifications of trusses based on stability and determinacy, and different methods for analyzing trusses including the method of joints, method of sections, and analyzing zero force members. Several examples are provided to demonstrate how to apply these analysis methods to solve for unknown member forces in various truss configurations.
1) The document discusses trusses and methods for analyzing truss structures.
2) A truss is a structure composed of slender members joined at endpoints that can support loads. The method of joints is introduced to analyze trusses by applying equilibrium equations at each joint.
3) Zero-force members, which do not experience internal forces, are identified through applying the method of joints and considering the geometry and external loads on the truss. Identifying zero-force members simplifies the analysis.
This document discusses two approximate methods for analyzing building frames subjected to loads: the portal method and cantilever method. The portal method assumes inflection points at midpoints of beams and mid-heights of columns, and that interior columns carry twice the shear of exterior columns. The cantilever method assumes inflection points at beam midpoints and column mid-heights, and that column axial stresses are proportional to their distance from the storey's centroid. Examples demonstrate applying each method to determine member forces in frames.
The document provides information about aircraft structures and structural analysis. It defines primary and secondary aircraft structures, and monocoque and semi-monocoque constructions. It describes the functions of different structural elements like the skin, ribs, spars, and stringers. It discusses simplifications made in structural analysis, including lumping longitudinal members and assuming webs only experience shear stresses. It also covers topics like unsymmetric bending, shear flow, shear centers, and torsion of thin-walled closed sections.
Structure Design-I ( Analysis of truss by method of joint.)Simran Vats
This document discusses analyzing trusses using the method of joints. It begins by defining what a truss is and explaining the relationship between the number of members and joints. It then outlines the steps to use the method of joints, including drawing FBDs at each joint and applying equilibrium equations. Two example trusses are then analyzed using this method, with the forces in each member calculated and reported in a force table.
This document discusses trusses and their analysis. It covers plane trusses, which are used for structures like house coverings, car parking areas, and bridges. Different methods are presented for analyzing trusses, including the analysis of joint and section methods. Examples are provided to illustrate how trusses can be used in real-life structures. A quiz is also listed to assess understanding of the concepts.
This document discusses methods for analyzing plane trusses, including the method of joints and method of sections. The method of joints is more convenient for simple trusses where all member forces are needed, while the method of sections is better for complex trusses where only a few member forces are required. The method of sections involves dividing the truss into parts with an imaginary cut and using equilibrium equations to solve for unknown member forces. An example of applying the method of sections to a space truss is also provided.
This document discusses the analysis of structures including trusses, frames, and machines. It defines trusses as structures formed from two-force members connected at joints. Trusses can be analyzed using the method of joints or sections. Frames contain multi-force members and may cease to be rigid when detached from supports. Machines are designed to transmit and modify forces and transform input to output forces. Sample problems demonstrate applying equilibrium conditions to determine member forces and reactions.
Lesson 29: Integration by Substition (worksheet)Matthew Leingang
This document provides a worksheet with 12 integration problems to practice integration by substitution. The problems involve both indefinite integrals and definite integrals of functions containing variables like x, z, and α. Students are asked to use appropriate substitutions to evaluate the integrals and obtain the most general antiderivative for indefinite integrals or a number for definite integrals. Some problems require determining the substitution, while others provide it. Trigonometric substitutions or identities may also be needed.
Lesson 24: Areas and Distances, The Definite Integral (slides)Matthew Leingang
We can define the area of a curved region by a process similar to that by which we determined the slope of a curve: approximation by what we know and a limit.
Integration by substitution is the chain rule in reverse.
NOTE: the final location is section specific. Section 1 (morning) is in SILV 703, Section 11 (afternoon) is in CANT 200
Adaptable Engineering: 3D Printing and AgileEvan Leybourn
Agile has been very successful in the software industry, where the cost of change is relatively low; creating an environment for adaptable teams, projects and products. Meanwhile, in other industries, engineering in particular, traditional development approaches hold sway due to the significantly higher cost involved in product change. For an Agile engineering approach to be successful, the cost of change – both in people and fabrication – needs to be reduced. This is where 3D printing technologies come in.
This interactive session will examine many of the issues faced when applying Agile to physical-engineering product development. It will show how 3D printing technologies can decrease the iterative design cycle time, reduce the barrier to entry, and support the creation of highly complex products or prototypes through modular development.
Participate in the real-time development and printing of a product using agile approaches and get a basic understanding of how to use 3D modelling and printing tools. Discover how 3D printing can, and is, being used to develop engineering products.
Rock mechanics for engineering geology part 1Jyoti Khatiwada
Rock mass classification systems are used to characterize rock masses for engineering design and stability analysis. The key systems discussed include the Rock Mass Rating (RMR) system, Q-system, Slope Mass Rating (SMR), and the New Austrian Tunnelling Method (NATM) classification. These systems aim to identify significant rock mass parameters, divide rock masses into classes of similar quality, and provide guidelines for design and communication between engineers and geologists. The advantages and limitations of each system are reviewed.
This document contains the questions from an engineering mathematics exam with 8 questions divided into 2 parts (A and B). Part A contains 3 multi-part questions on topics related to differential equations, including using Taylor's series, Runge-Kutta method, and Milne's predictor-corrector method to solve initial value problems. Part B contains 5 multi-part questions covering additional topics such as Legendre polynomials, Bessel's differential equation, probability, hypothesis testing, and confidence intervals. The exam tests knowledge of numerical analysis techniques for solving differential equations as well as topics in advanced calculus, probability, and statistics.
This document contains information about an engineering mathematics examination, including five questions covering topics like numerical methods for solving differential equations, complex variables, orthogonal polynomials, and probability. It also provides materials data and stipulations for designing a M35 grade concrete mix according to Indian standards.
The first part of the document outlines five questions on the exam covering numerical methods like Euler's method, Picard's method, Runge-Kutta method, and Milne's predictor-corrector method for solving differential equations. It also includes questions on complex variables, orthogonal polynomials, and probability.
The second part provides test data for materials to be used in designing a concrete mix for M35 grade concrete according to Indian standards, including stipulations
Introduction of system of coplanar forces (engineering mechanics)mashnil Gaddapawar
This document provides an overview of engineering mechanics. It discusses three main classifications of mechanics: mechanics of deformable bodies, mechanics of fluids, and mechanics of rigid bodies. Mechanics of deformable bodies deals with how forces are distributed inside bodies and cause stresses and deformations. Mechanics of fluids concerns liquids and gases and their applications in engineering. Mechanics of rigid bodies examines bodies that do not deform under forces. The document also outlines fundamental concepts in mechanics like length, time, displacement, velocity, and acceleration. It introduces important mechanical laws developed by Sir Isaac Newton like Newton's three laws of motion and Newton's law of universal gravitation. Other topics covered include units of measurement, force, characteristics and classification of forces, and resolution
The document discusses orthographic projection drawings which are a collection of 2D drawings that accurately represent an object. It describes the six principle views used in orthographic projection including front, right side, top, bottom, left side, and rear views. The document also explains rules for orthographic drawings including choosing a front view and common view combinations. Additionally, it outlines the glass box technique, different line types, steps for creating orthographic projection drawings, and guidelines for spacing views.
Structural analysis involves modeling real structures as simplified representations to analyze how they will respond to various loads. Common structural elements include beams, columns, trusses, arches, cables, frames, and thin surface structures. Structural analysis outputs such as displacements, forces, bending moments, and stresses are used to design structures to safely resist loads.
The document contains instructions and examples for 14 exercises related to orthographic projection. The exercises include identifying views of objects from different angles, matching orthographic drawings to isometric or oblique views, sketching projections of objects, and drawing multi-view orthographic projections of components with dimensions. Solutions or spaces for solutions are provided for each exercise.
Engineering drawings are a graphical means of communicating technical details and specifications without language barriers. They allow engineers to visualize and understand complex objects, structures, machines and their components. Drawings use standardized conventions, symbols and techniques to represent views, dimensions, materials, scales and other technical information precisely. They serve as roadmaps for manufacturing complex products. Manual drafting skills are still important for learning fundamental principles, even as computer-aided design has streamlined the process.
What makes a 10X Engineer a class apart?Sumanth Kolar
10x engineers get shit done, think product, are great at collaboration, have amazing communication skills, lead by example, 10x the whole team, are always learning, keep things simple, act as an owner, are decisive about priorities and finally build to last.
Beam deflections using singularity functionsaabhash
This document discusses using singularity functions to calculate beam deflections. It begins with an example problem of finding the deflection of a simply supported beam with a center load. Singularity functions like the unit step, unit ramp, unit impulse and unit doublet are introduced and used to represent the loading as a function. The loading function is integrated to obtain the shear and moment functions, then integrated again to get the slope and deflection functions. Boundary conditions are applied to determine integration constants, resulting in an equation for the deflection of the beam as a function of position.
Isometric projections for engineering studentsAkshay Darji
The document discusses isometric projections and isometric drawing. It begins by explaining the limitations of orthographic views and how isometric projections show all three dimensions of an object in a single view. It then defines the principles and types of projection, including orthographic, pictorial, axonometric, isometric, dimetric and trimetric. The remainder of the document focuses specifically on isometric projection, defining isometric axes, lines, planes and drawings. It provides examples of how to construct isometric views of various objects from their orthographic projections.
This document discusses stresses in beams and beam deflection. It covers several methods for analyzing bending stresses and deflection in beams, including: [1] the engineering beam theory relating moment, curvature, and stress; [2] double integration and moment area methods for calculating slope and deflection; and [3] Macaulay's method, which simplifies calculations for beams with eccentric loads. Formulas are provided relating bending moment, shear force, curvature, slope, and deflection. Moment-area theorems are also described for relating bending moment to slope and deflection.
Orthographic projections provide 2D views of an object that together accurately represent it. Common views are the front, top, and side. Objects are imagined inside a glass box and each face is projected onto a plane. Dimensions are drawn with thin continuous lines and indicate sizes. Drawings include title blocks with title, author, date, scale, and other information.
This document discusses the analysis of statically determinate 2D trusses. It explains that truss analysis is an important topic in structural engineering. The document outlines the assumptions made in truss analysis, including that joints are hinged and cannot resist moments. It describes the key methods of truss analysis - the method of joints and method of sections. These methods involve applying equilibrium equations to individual joints or cutting sections of the truss to determine member forces. The document also discusses different types of trusses and their applications in civil engineering structures.
This document provides an introduction and overview of truss analysis. It defines a truss and describes the key assumptions made in truss analysis, including that loads act only at joints and member weights are negligible. It then describes the two main methods for truss analysis - the method of joints and method of sections. An example problem is worked through for each method to demonstrate how to determine the forces in each truss member.
The document discusses vector structural systems, specifically trusses. It begins with introductions to vectors, trusses, and the evolution of vector structural systems. Trusses are composed of triangles for structural stability. Various truss types are then discussed, along with terminology used in trusses. Trusses work by transferring loads through tension and compression members arranged in triangular patterns. Historical examples of trusses and the theories behind how they function are also summarized.
Truss derives from the Old French word trousse, from around 1200, which means "collection of things bound together". The term truss has often been used to describe any assembly of members such as a cruck frame.
The development of railroads in the 1820s has a particular significance for structural engineers.
Railroads created an urgent need for bridges able to carry heavy moving loads and for new building
Analysis of Truss, There are two major methods of analysis for finding the internal forces in members of a truss; the Method of Joints, which is typically used for the case of creating a truss to handle external loads, and the Method of Sections, which is normally used when dealing modifying the internal members of an existing truss.
This document discusses methods for analyzing the internal forces in different types of structures. It focuses on plane trusses, which are frameworks composed of members joined at their ends to form a rigid structure. The two main methods discussed for analyzing truss forces are the method of joints, which satisfies equilibrium conditions at each joint, and the method of sections, which analyzes equilibrium across a cut section. Key assumptions made in truss analysis are that members only experience two internal forces and connections act as pin joints.
Trusses are structures composed of straight members that form triangles and are designed to carry large loads by distributing forces through tension and compression. Common types of trusses include Warren trusses, which are made of equilateral triangles, and Pratt trusses, which are often used in rail bridges. Trusses are widely used in bridges, buildings, and other structures because their triangular geometry enables them to efficiently carry large loads while using less material than beams.
solving statically indeterminate stucture using stiffnes methodSyed Md Soikot
This document is a presentation on the stiffness method for structural analysis. It was presented by ABU SYED MD. TARIN to the Department of Civil Engineering at Ahsanullah University of Science & Technology on December 4, 2013. The presentation introduces the stiffness method and how it can be used to analyze determinate and indeterminate structures. It also discusses how to apply the stiffness method to analyze trusses, beams, frames and other structural elements.
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1. The document discusses the analysis of truss structures using the method of joints and method of sections. It defines what a truss is, provides examples of applications of trusses, and describes the assumptions made in truss analysis.
2. The method of joints involves applying equilibrium conditions to individual joints, while the method of sections uses equilibrium of isolated sections cut from the truss. Both methods are used to determine the forces in the members of statically determinate trusses.
3. Examples are provided to demonstrate the application of each method. Special cases that allow for quicker solutions are also described. Exercises for practicing truss analysis using the methods are included at the end.
solving statically indeterminate stucture by stiffnes methodSyed Md Soikot
This document is a presentation on the stiffness method for structural analysis. It was presented by ABU SYED MD. TARIN to the Department of Civil Engineering at Ahsanullah University of Science & Technology on December 17, 2013. The presentation introduces the stiffness method and how it can be used to analyze determinate and indeterminate structures. It also discusses how to identify the degrees of freedom and apply restraints to make structures kinematically determinate before using the stiffness method to solve for displacements and internal forces.
The document defines a truss as a rigid structure composed of two force members connected at joints. There are three types of trusses: perfect trusses which have just enough members to remain stable under loading, deficient trusses with too few members, and redundant trusses with excess members. The key assumptions in truss analysis are that members are pin jointed and carry only axial forces, and trusses are loaded at joints. Two common methods to analyze trusses are the method of joints, which determines member forces by analyzing joints individually, and the method of sections, which analyzes equilibrium across a cut through selected members. Several example problems demonstrate applying these analysis methods to various truss configurations.
This document provides an overview of trusses and methods for analyzing statically determinate plane trusses. It defines trusses and plane vs space trusses, and describes their applications. Trusses have pin joints that allow rotation, while frames have rigid joints. The document discusses statical determinacy and stability of trusses. It also covers sign conventions, the method of joints, method of sections, and provides examples applying these analysis methods to solve for member forces in example trusses.
This document discusses the analysis of truss and frame structures using the stiffness method and finite element approach. It provides the derivations of the element stiffness matrices for truss members, beam members, and plane frame members. It expresses the stiffness matrices in both the local and global coordinate systems. The analysis approach can handle arbitrary geometry, loading, material properties and boundary conditions for trusses and frames.
This document discusses the analysis of structures including trusses, frames, and machines. It defines trusses as structures formed from two-force members connected at joints. Trusses can be analyzed using the method of joints or sections. Frames contain multi-force members and may cease to be rigid when detached from supports. Machines are designed to transmit and modify forces and transform input to output forces. Sample problems demonstrate applying equilibrium conditions to determine member forces and reactions.
This document discusses the analysis of structures including trusses, frames, and machines. It defines trusses as structures formed from two-force members connected at joints. Trusses can be analyzed using the method of joints or sections. Frames contain multi-force members and may cease to be rigid when detached from supports. Machines are designed to transmit and modify forces and transform input to output forces. Sample problems demonstrate applying equilibrium conditions to determine member forces and reactions.
The document discusses structural analysis of simple trusses. It defines a truss as a structure composed of slender members joined at their endpoints. Truss members are commonly wood or metal and are connected by bolted or welded joints. When analyzing trusses, it is assumed that all load is applied at the joints and members are joined by smooth pins. The two main methods for truss analysis are the method of joints and method of sections. The method of joints involves taking a free-body diagram of each joint and using equilibrium equations to determine the forces in each member. Two examples are then given applying this method to determine member forces in specific trusses and whether members are in tension or compression.
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2. Basic Structural Analysis.......................................................................................................... 2
Plane Truss.......................................................................................................................................2
Truss types............................................................................................................................................................2
Pratt truss .............................................................................................................................................................3
Bow string roof truss.............................................................................................................................................3
Difference between truss and frame ................................................................................................3
Perfect truss.....................................................................................................................................4
Imperfect truss......................................................................................................................................................4
Deficient Truss ......................................................................................................................................................4
Analysis of Plane trusses.......................................................................................................... 5
Method of joints ..............................................................................................................................5
Method of Sections..........................................................................................................................6
Zero force members.........................................................................................................................8
Reasons for Zero-force members in a truss system..............................................................................................8
Beams ..................................................................................................................................... 8
Types of beams ................................................................................................................................9
Statically Determinate Beams...............................................................................................................................9
Statically Indeterminate Beams........................................................................................................9
Shear force and bending moment in beams ................................................................................... 10
Shear force and bending moment diagrams ......................................................................................................11
Relationship between load, shear and bending moment................................................................ 12
Basic Structural Analysis
Plane Truss
A plane truss is one where all the members and joints lie within a 2-dimensional plane, while a
space truss has members and joints extending into 3 dimensions.
Truss types
There are two basic types of truss:
3. • The pitched truss, or common truss, is characterized by its triangular shape. It is most
often used for roof construction. Some common trusses are named according to their web
configuration. The chord size and web configuration are determined by span, load and
spacing.
• The parallel chord truss, or flat truss, gets its name from its parallel top and bottom
chords. It is often used for floor construction.
A combination of the two is a truncated truss, used in hip roof construction. A metal plate-
connected wood truss is a roof or floor truss whose wood members are connected with metal
connector plates.
Pratt truss
The Pratt truss was patented in 1844 by two Boston railway engineers; Caleb Pratt and his son
Thomas Willis Pratt. The design uses vertical beams for compression and horizontal beams to
respond to tension. What is remarkable about this style is that it remained popular even as wood
gave way to iron, and even still as iron gave way to steel.
The Southern Pacific Railroad bridge in Tempe, Arizona is a 393 meter (1291 foot) long truss
bridge built in 1912. The structure is composed of nine Pratt truss spans of varying lengths. The
bridge is still in use today.
Bow string roof truss
Named for its distinctive shape, thousands of bow strings were used during World War II for
aircraft hangars and other military buildings.
Difference between truss and frame
Truss structure is designed to support huge loads in comparison to its weight. In a truss, the
joints are of pin type and consists of 2 force members (tensile and compression - axial forces).
Here the the members are free to rotate about the pin.
A frame is a structure in which at least one of its individual member is a multi-force member.
The members of frames are connected rigidly at joints by means of welding and bolting. The
joints can transfer moments in addition to the axial loads.
In a plane frame all the moments are perpendicular to a single plane
Frames can be of 2 types - rigid noncollapsible and nonrigid collapsible frames.
4. Perfect truss
A truss is said to be perfect when the number of members in the truss is just sufficient to prevent
distortion of its shape when loaded with an external load.
A perfect truss has to satisfy the following equation:
where m is the number of members.
Imperfect truss
An imperfect truss is that which does not satisfy the equation, m = 2j – 3. Or in other words, a
truss in which the number of members is more or less than 2j – 3. The imperfect truss may be
further classified into the following two types:
1. deficient truss
2. redundant truss.
Deficient Truss
A deficient truss is an imperfect truss, in which the number of members is less than 2j – 3.
5. Analysis of Plane trusses
Because the forces in each of its two main girders are essentially planar, a truss is usually
modeled as a two-dimensional plane frame. If there are significant out-of-plane forces, the
structure must be modeled as a three-dimensional space. The analysis of trusses often assumes
that loads are applied to joints only and not at intermediate points along the members. The
weight of the members is often insignificant compared to the applied loads and so is often
omitted. If required, half of the weight of each member may be applied to its two end joints.
Provided the members are long and slender, the moments transmitted through the joints are
negligible and they can be treated as "hinges" or 'pin-joints'. Every member of the truss is then in
pure compression or pure tension – shear, bending moment, and other more complex stresses are
all practically zero. This makes trusses easier to analyze. This also makes trusses physically
stronger than other ways of arranging material – because nearly every material can hold a much
larger load in tension and compression than in shear, bending, torsion, or other kinds of force.
Structural analysis of trusses of any type can readily be carried out using a matrix method such
as the direct stiffness method, the flexibility method or the finite element method.
Method of joints
This method uses the force balance in the x and y directions at each of the joints in the truss
structure.
At A,
At D,
6. At C,
Although we have found the forces in each of the truss elements, it is a good practice to verify
the results by completing the remaining force balances.
At B,
Method of Sections
This method can be used when the truss element forces of only a few members wants to be
known. This method is used by introducing a single straight line cutting through the member
whose force wants to be calculated. However this method has a limit in that the cutting line can
pass through a maximum of only 3 members of the truss structure. This restriction is because this
method uses the force balances in the x and y direction and the moment balance, which gives us
a maximum of 3 equations to find a maximum of 3 unknown truss element forces through which
this cut is made. Let us try to find the forces FAB, FBD and FCD in the above example
8. The truss elements forces in the remaining members can be found by using the above method
with a section passing through the remaining members.
Zero force members
In the field of engineering mechanics, a zero force member refers to a member (a single truss
segment) in a truss which, given a specific load, is at rest: neither in tension, nor in compression.
In a truss a zero force member is often found at pins (any connections within the truss) where no
external load is applied and three or fewer truss members meet. Recognizing basic zero force
members can be accomplished by analyzing the forces acting on an individual pin in a physical
system.
NOTE: If the pin has an external force or moment applied to it, then all of the members attached
to that pin are not zero force members UNLESS the external force acts in a manner that fulfills
one of the rules below:
• If only two members meet in an unloaded joint, both are zero-force members.
• If three members meet in an unloaded joint of which two are in a direct line with one
another, then the third member is a zero-force member.
• If two members meet in a loaded joint and the line of action of the load coincides with
one of the members, the other member is a zero-force member.
Reasons for Zero-force members in a truss system
• These members contribute to the stability of the structure, by providing buckling
prevention for long slender members under compressive forces
• These members can carry loads in the event that variations are introduced in the normal
external loading configuration
Beams
A beam is a bar subject to forces or couples that lie in a plane containing the longitudinal section
of the bar. According to determinacy, a beam may be determinate or indeterminate.
9. Types of beams
Statically Determinate Beams
Statically determinate beams are those beams in which the reactions of the supports may be
determined by the use of the equations of static equilibrium. The beams shown below are
examples of statically determinate beams.
Statically Indeterminate Beams
If the number of reactions exerted upon a beam exceeds the number of equations in static
equilibrium, the beam is said to be statically indeterminate. In order to solve the reactions of the
beam, the static equations must be supplemented by equations based upon the elastic
deformations of the beam.
The degree of indeterminacy is taken as the difference between the umber of reactions to the
number of equations in static equilibrium that can be applied. In the case of the propped beam
shown, there are three reactions R1, R2, and M and only two equations (ΣM = 0 and ΣFv = 0) can
10. be applied, thus the beam is indeterminate to the first degree (3 - 2 = 1).
Shear force and bending moment in beams
The deformation of a beam is usually expressed in terms of its deflection from its original
unloaded position. The deflection is measured from the original neutral surface of the beam to
the neutral surface of the deformed beam. The configuration assumed by the deformed neutral
surface is known as the elastic curve of the beam.
11. Methods of Determining Beam Deflections
Numerous methods are available for the determination of beam deflections. These methods
include:
1. Double-integration method
2. Area-moment method
3. Strain-energy method (Castigliano's Theorem)
4. Conjugate-beam method
5. Method of superposition
Shear force and bending moment diagrams
Consider a simple beam shown of length L that carries a uniform load of w (N/m) throughout its
length and is held in equilibrium by reactions R1 and R2. Assume that the beam is cut at point C
a distance of x from he left support and the portion of the beam to the right of C be removed. The
portion removed must then be replaced by vertical shearing force V together with a couple M to
hold the left portion of the bar in equilibrium under the action of R1 and wx.
12. The couple M is called the resisting moment or moment and the force V is called the resisting
shear or shear. The sign of V and M are taken to be positive if they have the senses indicated
above.
Relationship between load, shear and bending moment
Since this method can easily become unnecessarily complicated with relatively simple problems,
it can be quite helpful to understand different relations between the loading, shear, and moment
diagram. The first of these is the relationship between a distributed load on the loading diagram
and the shear diagram. Since a distributed load varies the shear load according to its magnitude it
can be derived that the slope of the shear diagram is equal to the magnitude of the distributed
load. The relationship between distributed load and shear force magnitude is:
Some direct results of this is that a shear diagram will have a point change in magnitude if a
point load is applied to a member, and a linearly varying shear magnitude as a result of a
constant distributed load. Similarly it can be shown that the slope of the moment diagram at a
given point is equal to the magnitude of the shear diagram at that distance. The relationship
between distributed shear force and bending moment is
13. A direct result of this is that at every point the shear diagram crosses zero the moment diagram
will have a local maximum or minimum. Also if the shear diagram is zero over a length of the
member, the moment diagram will have a constant value over that length. By calculus it can be
shown that a point load will lead to a linearly varying moment diagram, and a constant
distributed load will lead to a quadratic moment diagram.