- The document is a report submitted by Tausif Alam analyzing a truss system during a 4-week summer training program at Reliance Infrastructure.
- It includes an introduction to truss systems, different types of trusses, assumptions in truss analysis, terminology, and methods of truss analysis including the method of joints and method of sections.
- Sample calculations are shown to analyze a truss using the method of joints by writing equilibrium equations at each joint to solve for member forces.
IRJET- VLSI Architecture for Montgomery Modular MultiplicationIRJET Journal
The document discusses several VLSI architectures for Montgomery modular multiplication (MM) algorithms used in public key cryptography. It compares the performance of four MM multiplier designs: Radix-2 Montgomery, SCS-based Montgomery, FCS-based Montgomery, and a modified SCS-based Montgomery. The modified SCS design aims to reduce critical path delay while maintaining low hardware complexity. It was implemented on an FPGA and achieved a delay of 3.59ns, power of 20.36mW, and frequency of 278MHz, showing improvements over the other designs.
C L A S S I C A L M E C H A N I C S J N T U M O D E L P A P E R{Wwwguest3f9c6b
This document contains two sets of questions for a Classical Mechanics exam for engineering students. Set 1 contains 8 questions related to topics like forces, moments of inertia, centroids, and kinematics. Set 2 contains similar questions, involving calculating forces in trusses, centroids, moments of inertia, overtaking problems, and spring/mass systems. The questions involve applying concepts of classical mechanics to solve physics problems regarding structures, forces, motion, springs, and vibrations.
Determination of exact shortest paths based on mechanical analogies doi 10.1...Gokhan ALTINTAS
This brief presentation includes visual explanations of sample solutions using the method detailed in Altintas [1]. The solutions in this presentation were made using the FEM method, and the same results can be easily achieved using Rigid Body Dynamics (RBD) based solvers. It is not the numerical methods to be understood in this study, but the mechanical approach to be used in solving the problem. For this reason, it should not be forgotten that numerical methods are only tools, and the solution techniques to be used are not limited to FEM and RBD based techniques.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document contains solutions to practice problems about direction cosines and direction ratios of lines in three-dimensional space. It begins with five questions about finding the direction cosines of lines given information about their angles with the coordinate axes. Subsequent questions involve determining whether lines are parallel, perpendicular or collinear based on their direction ratios. The document also covers finding equations of lines in vector and Cartesian forms.
The document describes a summer training project report on soil and concrete testing conducted at a site in New Delhi. It provides details of various tests performed on soil samples collected from the site, including sieve analysis, mechanical analysis, liquid limit, plastic limit, shrinkage limit, consolidation, permeability and specific gravity tests. It also describes some basic cement tests conducted like fineness, setting time, soundness and consistency tests. The trainees gained hands-on experience of actual field and lab procedures under expert guidance during their 6-week summer training project.
The document discusses the classification of structures based on stability and statical determinacy. It defines different types of supports and condition equations. A structure is stable and determinate if it has 3 reaction components that are neither parallel nor concurrent. It is stable but indeterminate if it has more than 3 non-parallel/concurrent reactions. Several examples of structures are classified. Structures with less than 3 reactions or with concurrent reactions are unstable. Closed panels require 3 internal condition equations to be stable internally.
IRJET- VLSI Architecture for Montgomery Modular MultiplicationIRJET Journal
The document discusses several VLSI architectures for Montgomery modular multiplication (MM) algorithms used in public key cryptography. It compares the performance of four MM multiplier designs: Radix-2 Montgomery, SCS-based Montgomery, FCS-based Montgomery, and a modified SCS-based Montgomery. The modified SCS design aims to reduce critical path delay while maintaining low hardware complexity. It was implemented on an FPGA and achieved a delay of 3.59ns, power of 20.36mW, and frequency of 278MHz, showing improvements over the other designs.
C L A S S I C A L M E C H A N I C S J N T U M O D E L P A P E R{Wwwguest3f9c6b
This document contains two sets of questions for a Classical Mechanics exam for engineering students. Set 1 contains 8 questions related to topics like forces, moments of inertia, centroids, and kinematics. Set 2 contains similar questions, involving calculating forces in trusses, centroids, moments of inertia, overtaking problems, and spring/mass systems. The questions involve applying concepts of classical mechanics to solve physics problems regarding structures, forces, motion, springs, and vibrations.
Determination of exact shortest paths based on mechanical analogies doi 10.1...Gokhan ALTINTAS
This brief presentation includes visual explanations of sample solutions using the method detailed in Altintas [1]. The solutions in this presentation were made using the FEM method, and the same results can be easily achieved using Rigid Body Dynamics (RBD) based solvers. It is not the numerical methods to be understood in this study, but the mechanical approach to be used in solving the problem. For this reason, it should not be forgotten that numerical methods are only tools, and the solution techniques to be used are not limited to FEM and RBD based techniques.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document contains solutions to practice problems about direction cosines and direction ratios of lines in three-dimensional space. It begins with five questions about finding the direction cosines of lines given information about their angles with the coordinate axes. Subsequent questions involve determining whether lines are parallel, perpendicular or collinear based on their direction ratios. The document also covers finding equations of lines in vector and Cartesian forms.
The document describes a summer training project report on soil and concrete testing conducted at a site in New Delhi. It provides details of various tests performed on soil samples collected from the site, including sieve analysis, mechanical analysis, liquid limit, plastic limit, shrinkage limit, consolidation, permeability and specific gravity tests. It also describes some basic cement tests conducted like fineness, setting time, soundness and consistency tests. The trainees gained hands-on experience of actual field and lab procedures under expert guidance during their 6-week summer training project.
The document discusses the classification of structures based on stability and statical determinacy. It defines different types of supports and condition equations. A structure is stable and determinate if it has 3 reaction components that are neither parallel nor concurrent. It is stable but indeterminate if it has more than 3 non-parallel/concurrent reactions. Several examples of structures are classified. Structures with less than 3 reactions or with concurrent reactions are unstable. Closed panels require 3 internal condition equations to be stable internally.
This document describes the direct stiffness method (DSM) for analyzing truss structures using finite elements. It introduces a simple three-member plane truss example to illustrate the basic steps of the DSM. These include breaking down the structure into individual members, computing the member stiffness equations, and then assembling the member stiffnesses into a global stiffness matrix relating the overall structural displacements and forces. The document outlines the idealization of the truss as a pin-jointed system and defines the key terms used in DSM including members, joints, forces, displacements, and the global stiffness matrix.
1. A plane frame structure was modeled in GSA Suite software and analyzed under full factored loading. Bending moment diagrams were generated which identified maximum and minimum bending moments.
2. Hand calculations were shown to determine the global stiffness matrix partitions for the frame based on its degrees of freedom. The local stiffness matrix for a member was transformed to the global matrix.
3. Further analysis of the bending moment diagrams identified the locations of zero bending moments. For linear members, graphs were plotted and linear equations solved. Members with parabolic bending followed a quadratic equation to find two zero points.
This document provides an introduction to beams and beam mechanics. It discusses different types of beams and supports, how to calculate beam reactions and internal forces like shear force and bending moment, shear force and bending moment diagrams, theories of bending and deflection, and methods for analyzing statically determinate beams including the direct method, moment area method, and Macaulay's method. The key objectives are determining the internal forces in beams, establishing procedures to calculate shear force and bending moment, and analyzing beam deflection.
Trusses are structures composed of individual structural elements called members that form triangular patterns to support loads. Truss analysis assumes members only experience axial forces and joints allow frictionless rotation. There are two main methods for analyzing trusses - the method of joints, which considers force equilibrium at each joint, and the method of sections, which cuts the truss into parts to analyze member forces. For a truss to be stable and determinate, the number of members and reactions must equal the number of joints based on the equation m + R = 2j, where m is members, R is reactions, and j is joints.
This document discusses the direct stiffness method (DSM) for analyzing a simple plane truss structure using finite elements. It begins by introducing the example truss, which has 3 members and 3 joints. It then covers idealizing the truss as a pin-jointed assembly, defining the joint forces and displacements, developing the master stiffness equations relating forces and displacements, and an overview of the breakdown steps to compute member stiffness equations from geometry and material properties.
Approximate Analysis of Statically Indeteminate Structures.pdfAshrafZaman33
This document discusses approximate analysis methods for statically indeterminate structures like trusses and frames. It introduces the concept of making a structure statically determinate by assuming certain members carry zero force, then analyzing the simplified structure. Two common assumptions are mentioned: (1) slender diagonals cannot carry compression, and (2) diagonals share the panel load equally between tension and compression. Examples show how to apply these methods to trusses. The document also discusses analyzing building frames by assuming points of inflection act as pins, then using superposition to account for multiple load cases.
This document provides tutorials on mechanical principles and engineering structures. It focuses on tutorial 2 which covers reaction forces in pin-jointed framed structures. It defines pin joints and how they allow rotation. It distinguishes between struts, which are members in compression, and ties, which are in tension. It introduces Bow's notation for solving forces in framed structures by drawing force polygons at each joint. Worked examples demonstrate how to apply this method to determine the forces and whether each member is a strut or tie. Further practice problems are provided for the student to solve pin-jointed frames.
The document discusses the direct stiffness method for analyzing truss structures. This method treats each individual truss element as a structure and develops the element stiffness matrix. Transformation matrices are used to relate element deformations to structure deformations. The total structure stiffness matrix is obtained by assembling the individual element stiffness matrices based on how the elements are connected at joints in the structure. This direct stiffness method forms the basis for computer programs to analyze truss structures.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
Direct Stifness Method- Trusses updated.pptxRanaKami4
The document discusses the direct stiffness method for analyzing trusses.
[1] The direct stiffness method treats each individual truss element as a structure and calculates the element stiffness matrix using the element's local coordinate system. The total structure stiffness matrix is obtained by superimposing the stiffness matrices of all elements.
[2] To transform between the local and global coordinate systems, a deformation transformation matrix [T] is derived. This matrix relates the element deformations in the local system to the structure deformations in the global system.
[3] The structure stiffness matrix of each element [K]m is obtained by transforming the element stiffness matrix [k]m from the local to the global system using [
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 discusses truss structures and their analysis. It defines trusses and describes common types of trusses like simple, compound, and complex trusses. It explains how trusses are modeled as ideal structures where members only experience axial forces. Two methods for analyzing trusses are presented: the method of joints, which uses equilibrium at the joints, and the method of sections, which uses equilibrium of cutting sections. Concepts like determinacy, stability, and redundant members are covered. Truss analysis allows determining member forces and whether a truss is determinate or indeterminate.
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.
1) The document discusses adding suspended cantilever parts to existing reinforced concrete residential buildings in Iraq to create outdoor gardens and improve living conditions.
2) A preliminary analytical model of a 5-story building was developed with 10m long suspended concrete beams strengthened by steel strands.
3) Initial analysis found large negative bending moments in the suspended beams, but inserting hinge supports at the beam ends solved this issue. The final analysis found stresses and deformations within acceptable limits.
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.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A study of r.c.c. beam column connection subjected to monotonic loadingeSAT Journals
Abstract
Beam and column where intersects is called as joint or Connection. The different types of joints are classified as corner joint, exterior
joint, interior joint etc. on beam column joint applying quasi-static loading .i. e. monotonic loading on cantilever end of the beam and
study of various parameters as to be find out on corner and exterior beam column joint i.e. maximum stress, minimum stress,
displacement and variation in stiffness of beam column joint can be analyzed in Ansys software ( Non-Linear FEM Software) The
various research studies focused on corner and exterior beam column joints and their behavior, support conditions of beam-column
joints. Some recent experimental studies, however, addressed beam-column joints of substandard RC frames with weak columns, poor
anchorage of longitudinal beam bars and insufficient transverse reinforcement. the behavior of exterior beam column joint is different
than the corner beam column joint.
Keywords: beam, column, corner, exterior, joint, monotonic load, quasi-static, varying stiffness
A study of r.c.c. beam column connection subjected to monotonic loadingeSAT Journals
Abstract
Beam and column where intersects is called as joint or Connection. The different types of joints are classified as corner joint, exterior
joint, interior joint etc. on beam column joint applying quasi-static loading .i. e. monotonic loading on cantilever end of the beam and
study of various parameters as to be find out on corner and exterior beam column joint i.e. maximum stress, minimum stress,
displacement and variation in stiffness of beam column joint can be analyzed in Ansys software ( Non-Linear FEM Software) The
various research studies focused on corner and exterior beam column joints and their behavior, support conditions of beam-column
joints. Some recent experimental studies, however, addressed beam-column joints of substandard RC frames with weak columns, poor
anchorage of longitudinal beam bars and insufficient transverse reinforcement. the behavior of exterior beam column joint is different
than the corner beam column joint.
Keywords: beam, column, corner, exterior, joint, monotonic load, quasi-static, varying stiffness.
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 describes the direct stiffness method (DSM) for analyzing truss structures using finite elements. It introduces a simple three-member plane truss example to illustrate the basic steps of the DSM. These include breaking down the structure into individual members, computing the member stiffness equations, and then assembling the member stiffnesses into a global stiffness matrix relating the overall structural displacements and forces. The document outlines the idealization of the truss as a pin-jointed system and defines the key terms used in DSM including members, joints, forces, displacements, and the global stiffness matrix.
1. A plane frame structure was modeled in GSA Suite software and analyzed under full factored loading. Bending moment diagrams were generated which identified maximum and minimum bending moments.
2. Hand calculations were shown to determine the global stiffness matrix partitions for the frame based on its degrees of freedom. The local stiffness matrix for a member was transformed to the global matrix.
3. Further analysis of the bending moment diagrams identified the locations of zero bending moments. For linear members, graphs were plotted and linear equations solved. Members with parabolic bending followed a quadratic equation to find two zero points.
This document provides an introduction to beams and beam mechanics. It discusses different types of beams and supports, how to calculate beam reactions and internal forces like shear force and bending moment, shear force and bending moment diagrams, theories of bending and deflection, and methods for analyzing statically determinate beams including the direct method, moment area method, and Macaulay's method. The key objectives are determining the internal forces in beams, establishing procedures to calculate shear force and bending moment, and analyzing beam deflection.
Trusses are structures composed of individual structural elements called members that form triangular patterns to support loads. Truss analysis assumes members only experience axial forces and joints allow frictionless rotation. There are two main methods for analyzing trusses - the method of joints, which considers force equilibrium at each joint, and the method of sections, which cuts the truss into parts to analyze member forces. For a truss to be stable and determinate, the number of members and reactions must equal the number of joints based on the equation m + R = 2j, where m is members, R is reactions, and j is joints.
This document discusses the direct stiffness method (DSM) for analyzing a simple plane truss structure using finite elements. It begins by introducing the example truss, which has 3 members and 3 joints. It then covers idealizing the truss as a pin-jointed assembly, defining the joint forces and displacements, developing the master stiffness equations relating forces and displacements, and an overview of the breakdown steps to compute member stiffness equations from geometry and material properties.
Approximate Analysis of Statically Indeteminate Structures.pdfAshrafZaman33
This document discusses approximate analysis methods for statically indeterminate structures like trusses and frames. It introduces the concept of making a structure statically determinate by assuming certain members carry zero force, then analyzing the simplified structure. Two common assumptions are mentioned: (1) slender diagonals cannot carry compression, and (2) diagonals share the panel load equally between tension and compression. Examples show how to apply these methods to trusses. The document also discusses analyzing building frames by assuming points of inflection act as pins, then using superposition to account for multiple load cases.
This document provides tutorials on mechanical principles and engineering structures. It focuses on tutorial 2 which covers reaction forces in pin-jointed framed structures. It defines pin joints and how they allow rotation. It distinguishes between struts, which are members in compression, and ties, which are in tension. It introduces Bow's notation for solving forces in framed structures by drawing force polygons at each joint. Worked examples demonstrate how to apply this method to determine the forces and whether each member is a strut or tie. Further practice problems are provided for the student to solve pin-jointed frames.
The document discusses the direct stiffness method for analyzing truss structures. This method treats each individual truss element as a structure and develops the element stiffness matrix. Transformation matrices are used to relate element deformations to structure deformations. The total structure stiffness matrix is obtained by assembling the individual element stiffness matrices based on how the elements are connected at joints in the structure. This direct stiffness method forms the basis for computer programs to analyze truss structures.
This document discusses structural analysis methods for statically indeterminate structures. It defines key terms like degree of static indeterminacy, internal and external redundancy, and methods for analyzing indeterminate structures. Specific methods discussed include the flexibility matrix method, consistent deformation method, and unit load method. Examples of statically indeterminate beams and frames are also provided.
Direct Stifness Method- Trusses updated.pptxRanaKami4
The document discusses the direct stiffness method for analyzing trusses.
[1] The direct stiffness method treats each individual truss element as a structure and calculates the element stiffness matrix using the element's local coordinate system. The total structure stiffness matrix is obtained by superimposing the stiffness matrices of all elements.
[2] To transform between the local and global coordinate systems, a deformation transformation matrix [T] is derived. This matrix relates the element deformations in the local system to the structure deformations in the global system.
[3] The structure stiffness matrix of each element [K]m is obtained by transforming the element stiffness matrix [k]m from the local to the global system using [
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 discusses truss structures and their analysis. It defines trusses and describes common types of trusses like simple, compound, and complex trusses. It explains how trusses are modeled as ideal structures where members only experience axial forces. Two methods for analyzing trusses are presented: the method of joints, which uses equilibrium at the joints, and the method of sections, which uses equilibrium of cutting sections. Concepts like determinacy, stability, and redundant members are covered. Truss analysis allows determining member forces and whether a truss is determinate or indeterminate.
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.
1) The document discusses adding suspended cantilever parts to existing reinforced concrete residential buildings in Iraq to create outdoor gardens and improve living conditions.
2) A preliminary analytical model of a 5-story building was developed with 10m long suspended concrete beams strengthened by steel strands.
3) Initial analysis found large negative bending moments in the suspended beams, but inserting hinge supports at the beam ends solved this issue. The final analysis found stresses and deformations within acceptable limits.
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.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
A study of r.c.c. beam column connection subjected to monotonic loadingeSAT Journals
Abstract
Beam and column where intersects is called as joint or Connection. The different types of joints are classified as corner joint, exterior
joint, interior joint etc. on beam column joint applying quasi-static loading .i. e. monotonic loading on cantilever end of the beam and
study of various parameters as to be find out on corner and exterior beam column joint i.e. maximum stress, minimum stress,
displacement and variation in stiffness of beam column joint can be analyzed in Ansys software ( Non-Linear FEM Software) The
various research studies focused on corner and exterior beam column joints and their behavior, support conditions of beam-column
joints. Some recent experimental studies, however, addressed beam-column joints of substandard RC frames with weak columns, poor
anchorage of longitudinal beam bars and insufficient transverse reinforcement. the behavior of exterior beam column joint is different
than the corner beam column joint.
Keywords: beam, column, corner, exterior, joint, monotonic load, quasi-static, varying stiffness
A study of r.c.c. beam column connection subjected to monotonic loadingeSAT Journals
Abstract
Beam and column where intersects is called as joint or Connection. The different types of joints are classified as corner joint, exterior
joint, interior joint etc. on beam column joint applying quasi-static loading .i. e. monotonic loading on cantilever end of the beam and
study of various parameters as to be find out on corner and exterior beam column joint i.e. maximum stress, minimum stress,
displacement and variation in stiffness of beam column joint can be analyzed in Ansys software ( Non-Linear FEM Software) The
various research studies focused on corner and exterior beam column joints and their behavior, support conditions of beam-column
joints. Some recent experimental studies, however, addressed beam-column joints of substandard RC frames with weak columns, poor
anchorage of longitudinal beam bars and insufficient transverse reinforcement. the behavior of exterior beam column joint is different
than the corner beam column joint.
Keywords: beam, column, corner, exterior, joint, monotonic load, quasi-static, varying stiffness.
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.
1. SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENT FOR
FOUR WEEKS SUMMER TRAINING
At
RELIANCE INFRASTRUCTURE
(From JUNE 16, 2010 to JULY 16, 2010)
ANALYSIS OF TRUSS SYSTEM, BY PREPARING EXCEL
PROGRAMMING SHEET AND VERIFYING THE DESIGN
EXCEL SHEET BY STAAD ANALYSIS
SUBMITTED BY: -
TAUSIF ALAM
0809700426
B.Tech, 2nd
Year
DEPARTMENT OF CIVIL ENGINEERING
GALGOTIA’S COLLEGE OF ENGG. & TECH.
GREATER NOIDA
1
3. I here by certify that ‘ TAUSIF ALAM ’ROLL No. 0809700426of GALGOTIA’S
COLLEGE OF ENGG.& TECNOLOGY, Greater Noida has undergone one
month of training from June 16 to July 17 at Reliance Infrastructure Ltd to
fulfill the requirements for the award of degree of B.Tech (Civil Engineering).
He worked on the analysis of Structure (Truss Analysis) during the training
under my supervision. During his tenure with us we found him sincere and
hard working. I wish him great success in the future.
DATE:
Signature of the Student
Signature
(Mr. C.M Sarvaiya)
Head, In-house engineering department,
Reliance Infrastructure Ltd; Noida
(Seal of Organization)
3
4. ACKNOWLEDGEMENT
I would like to express a deep sense of gratitude and thanks profusely to Mr.
C.M Sarvaiya (Head, In house engineering department, Reliance Infrastructure)
without the wise counsel and able guidance, it would have been impossible to
complete the report in this manner.
The help rendered by Rupesh Anand (Design Engineer, In House Engineering
Department) and P. Ramakanth (Design Engineer, In House Engineering
Department) and all other member for intellectual support throughout the
course of his work is greatly acknowledged.
Finally, I am indebted to all whosoever have contributed in this report work and
friendly stay at RELIANCE INFRASTRUCTURE.
TAUSIF ALAM
080970042
B.Tech 2nd
year
Department of civil engineering
Gagotia’s College of Engg.& Technology
INTRODUCTION
4
5. Reliance Infrastructure Limited, incorporated in 1929, is a fully integrated
utility engaged in the generation, transmission and distribution of electricity. It
ranks among India’s top listed private companies on all major financial
parameters, including assets, sales, profits and market capitalization.
It is India’s foremost private sector utility with aggregate estimated revenues
of Rs 9,500 crore (US$2.1 billion) and total assets of Rs 10,700 crores
(US$2.4 billion).
Reliance Infrastructure Limited distributes more than 21 billion units of
electricity to over 25 million consumers I Mumbai, Delhi, Orissa and Goa,
across an its power stations located in Maharashtra, Andhra Pradesh, Kerala,
Karnataka and Goa.
The company is currently pursuing several gas, coal, wind and hydro-based
power generation projects in Maharashtra, Uttar Pradesh, arunachal Pradesh
and Uttaranchal with aggregates capacity of over 12,500 MW. These projects
are at various stages of development.
Reliance Infrastructure Limited is vigorously participating in emerging
opportunities in the areas of trading and transmission of power. It is also
engaged in a portfolio of services in the power sector in engineering,
procurement and construction (EPC) through regional offices in India.
5
6. CONTENTS
TOPIC Page no.
1. Introduction to Truss 7
2. Truss
2.1 Plane Truss 7
2.2 Space Truss 9
2.2.1 Equilibrium and Stability Equation 9
3. Types of Truss
3.1 Perfect Truss 10
3.2 Imperfect Truss 10
3.3 Deficient Truss 10
3.4 Redundant Truss 11
4. Assumption made in classical Truss Analysis 12
5. Terminology
5.1 Nature of forces in the member 13
6. Determinate, Indeterminate and Unstable Truss
6.1 Determinate Truss 14
6.2 Indeterminate Truss 14
6.3 Unstable Truss 14
6.4 Unknown Reaction Component at
6.4.1 Roller Support 14
6.4.2 Hinged Support 14
6.4.3 Fixed Support 14
7. Method of Analysis
7.1 Method of Joints 15
7.2 Method of Section (Method of Moments) 15
8. Analysis of truss systems in STAAD.PRO 29
9. Results and conclusions 30
6
7. 1. INTRODUCTION TO TRUSS
1.1) A truss is an articulated structure composed of straight members
arranged and connected in such a way that they transmit primarily axial
forces. If all the members lie in one plane it is called a plane truss. A three
dimensional truss is called a space truss.
2. TRUSS
2.1) Plane Truss: - The basic form of truss is a triangle formed by three
members joined together at their common ends forming three joints. Another
two member connected to two of the joints form a stable system of two
triangles.
a) I f whole structure is built up in this way it must be internally rigid. Such a
truss if supported suitably will be stable.
b) The truss has to be supported in general by three reaction components, all
of which neither parallel nor concurrent such a truss is called simple truss.
Various types of trusses are shown in Fig 1 a, b and c. These are stable and
statically determinate.
(a)
JOINT
MEMBER
SUPPORTS
7
8. (b)
(c)
Fig (1)
(2.2) SPACE TRUSS
The basic element of space truss which is just rigid is a tetrahedron with four
joints space truss is shown in figure 2.
Fig (2)
8
9. (2.2.1) EQUILIBRIUM AND STABILITY EQUATION
The equilibrium of an entire space truss or Section of a space truss is
described by the sir scalar equation given below:-
∑Fx = 0 ∑Mx = 0
∑Fy = 0 ∑My = 0
∑Fz = 0 ∑Mz = 0
Or in vector from
Fr = 0 Mr = 0
Fr and Mr represent three – dimensional force and moment Vector.
3. Type of Truss:-
I) Perfect Truss
II) Imperfect Truss
- Deficient Truss
- Redundant Truss.
(3.1) Perfect Truss:-
A truss which has got just sufficient number of members to resist load without
undergoing appreciable deformation in shape is called Perfect Truss. The
number of members in a perfect truss may also be expressed by the relation:
m = 2j-3
Where,
m = number of members,
j = number of joints
Perfect truss is shown in fig (3) a and b.
9
10. (b)
(a) (b)
FIG. 3
3.2) Imperfect truss: - It is a truss in which the no. of members is more or less
than (2j-3). The imperfect truss may be further classified into following two
types.
1. DEFICIENT TRUSS
2. REDUDANT TRUSS
Imperfect truss does not satisfy the equation m=2j-3
(3.3) Deficient Truss:-
A truss which has got less number of members than that required for a perfect
truss. Deficient truss is shown in fig (4)
Fig. (4)
(3.4) Redundant Truss: -
A truss which has got more number of members than that required for a
perfect frame or truss. A redundant truss is a statically indeterminate since the
forces in the member can not be determined using equation of equilibrium
alone.
Each extra member adds one degree of indeterminacy.
Redundant truss is shown in figure (5).
10
11. Fig (5)
4. Assumptions made in classical truss analysis.
Every member of truss is straight.
Each end of the member is connected to a joint by a frictionless pin on
the longitudinal centroidal axis of the member.
The self weighs of the members of a truss are taken to be negligible
compared with the applied loads.
All the load and reactions are applied or transmitted to the joints only.
11
12. The cross-section of the members is uniform i.e.; members are
prismatic.
5. TERMINOLOGY:
(5.1) Nature of forces in members.
The members of truss are subjected to either tensile or compressive forces. A
typical truss ABCDE loaded at joint E is shown in figure .6(a).
The member BC is subjected to compressive force C as shown in fig 6 (b).
Effect of this force on the joint B (or C) is equal and opposite to the force C as
shown in fig 6 (b).
The member AE is subjected to tensile force T. It effect on the Joint A and E
are as shown in fig. 6 (b).
12
A
B C
D
E
13. E D
In the analysis of frame. We work forces on the joints, instead of the forces in
the member as shown in figure 1.6 (c). It may be noted that compressive force
in a member is represented in the in the figure by two arrows going away
from each other and a tensile force by two arrows coming towards each other.
(6).DETERMINATE, INDETERMINATE & UNSTABLE
TRUSS:-
(6.1) A structural system which can analyzed with the use of equation of
statical
Equilibrium only is called as statically determinate structure e.g. trusses with
both end simply supported, one end hinged and other rollers etc.
If m+r -2j =0 then truss is said to be statically determinate.
13
Fig 6(a)
Fig 6(b)
C
T
A
B C
D
E
14. (6.2) A structure which can not be analyzed with the use of equation of
equilibrium only is called statically indeterminate structure.
If m+r-2j > 0 then truss is said to be statically in indeterminate.
Indeterminate structures are also called redundant structure.
(6.3) if m+r-2J<0 then truss is said to be unstable.
(6.4) Unknown reaction component at
a) Roller support ---1
b) Hinged support---2
c) Fixed support------3
7. Methods of Analysis:-
The following to analytical methods for finding out the forces in the members
of a perfect frame, are important from the subject point of view.
7.1 Method of Joints
7.2 Method of section
7.1 Method of Joints
14
2
KN
1 2
15. (a) Space diagram (b) Joint ’1’ (c) Joint
(2)
Fig. 7 (a, b, c)
In this method, each and every joint is treated as a free body in equilibrium as
shown in figure 7 (a), (b), (c) & (d). The unknown forces are then determined
by equilibrium equation viz; ∑v=0 and ∑h-=0.
i.e.; sum of all the vertical forces and horizontal forces is equated to zero.
Note:1.:-The member of the frame may be named either by Bow’s method or
by joints at their ends.
7.1.1. While selecting the joints, for calculation work, care should be taken that
at any instant. The joint should not contain more then two members in which
the forces are unknown.
7.2 Method of section (or Method of Moments)
This method is particularly convenient when the forces in a few members of a
truss are required to be found out. In this method the truss is cut into two
parts and equilibrium equations are written for one of the parts of truss
treating it as a free –body diagram for the purpose. The critical aspect of this
method is the choice of the proper free body diagram for the purpose.
The method of joints is effective if want to calculate forces in all
members of the truss but the method of section is obviously superior if we
seek forces only in certain members. In such case section can be made only
through the selected members, where as the method of joints would require
the analysis of joints from one end of the structure progressively up to
particular member.
15
22. PROCEDURE FOR ANALYSIS
Taking moment about A
MA = VB*a-HBtanθ+Vc*2a-HC*2a*tanθ+VD*3a-
HD*atanθ+VE*4a+VF*a+VG*2a+VH*3a+RE*4a=0
RE*4a=-(VB*a-HB*tanθ+VC*2a-HC*2ª*tanθ+VD*3a-
HD*atanθ+VE*4a+VF*a+VG*2a+VH*3a)
Cancelling a from both side we get,
RE=-(VB/4-HBtanθ/4*2Vc/4-2Hctanθ/4+3VD/4-HDtanθ/4+VE+VF/4+2VA/4+3VH/4)
RE=-(VB/4-HB/4tanθ+VC/2-HC/2tanθ+3/4VD-HD/4tanθ+VE+VF/4+VG/2+3VH/4)
RA=-(∑F-RE)
RA= -(VA+VB+VC+VD+VE+VF+VG+VH-VB/4-HBtanθ/4-VC/2-HCtanθ/2-3VD/4-
HDtanθ/4-VE-VF/4-VG/2-3VH/4)
RA= -(VA-3VB/4-HBtanθ-VC/2-HCtanθ/2-VD/4-HDtanθ-3VF/4-VG/2-VH/4)
CALCULATION OF FORCE IN MEMBERS
At joint (A)
∑Fy=0 gives
-(VA+RA)=PAB*Sinθ
PABsin30 = - (VA-VA+VB*0.75+HB*tanθ*0.25+0.5*VC+HC*tanθ*0.5+VD*0.25+HD*
tanθ
22
27. At joint (E)
ΣFy=0 gives;
PDEsin30 = - (RE+VE)
PDE= - (0.5VB-0.5HBtanθ+VC-HCtanθ+1.5VD-0.5HBtanθ+0.5VF+VG+1.5VH+HE)
8. ANALYSIS OF TRUSS SYSTEMS IN STAAD.PRO
Two truss systems were modeled in STAAD.PRO and are checked for a
particular Loading Pattern. The arrangement and the Output are mentioned in
this report. First the Truss System 1 was analyzed and then Truss system 2,
the output for which has been mentioned as per the order mentioned above.
27
VEPDE
PEH
RE
HE
28. STAAD OUTPUT FOR TRUSS SYSTEM 1
Job Information
Engineer Checked Approved
Name: TAUSIF ALAM RUPESH ANAND
Date: 13-Jul-10
Structure Type TRUSS ANALYSIS
28
ARRANGEMENT OF TRUSS SYSTEM 1
29. Number of Nodes 6 Highest Node 6
Number of Elements 9 Highest Beam 9
Number of Basic Load Cases 1
Number of Combination Load Cases 0
Included in this printout are data for:
All The Whole Structure
Included in this printout are results for load cases:
Type L/C Name
Primary 1 ALL AXIAL FORCES
Nodes
Node
X
(m)
Y
(m)
Z
(m)
1 0.000 0.000 0.000
2 3.000 0.000 0.000
3 6.000 0.000 0.000
4 6.000 3.000 0.000
5 3.000 3.000 0.000
6 0.000 3.000 0.000
Beams
Beam Node A Node B
Length
(m)
Property
β
(degrees)
1 1 2 3.000 1 0
2 2 3 3.000 1 0
3 3 4 3.000 1 0
4 2 5 3.000 1 0
5 1 6 3.000 1 0
6 6 2 4.243 1 0
7 4 2 4.243 1 0
8 4 5 3.000 1 0
9 5 6 3.000 1 0
Section Properties
Prop Section
Area
(in2
)
Iyy
(in4
)
Izz
(in4
)
J
(in4
)
Material
1 ISMB100 2.263 0.985 6.198 0.050 STEEL
29
30. Supports
Node
X
(kip/in)
Y
(kip/in)
Z
(kip/in)
rX
(kip-
ft/deg)
rY
(kip-
ft/deg)
rZ
(kip-
ft/deg)
1 Fixed Fixed Fixed - - -
3 - Fixed - - - -
Releases
There is no data of this type.
Basic Load Cases
Number Name
1 AXIAL FORCE
Combination Load Cases
There is no data of this type.
Load Generators
There is no data of this type.
Node Loads : 1 AXIAL FORCE
Node
FX
(kN)
FY
(kN)
FZ
(kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
4 - -25.000 - - - -
-10.000 - - - - -
5 - -15.000 - - - -
6 - -15.000 - - - -
10.000 - - - - -
Node Displacements
Node L/C
X
(mm)
Y
(mm)
Z
(mm)
Resultant
(mm)
rX
(rad)
rY
(rad)
rZ
(rad)
1 1:AXIAL FORCE 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL FORCE 0.000 -0.680 0.000 0.680 0.000 0.000 0.000
3 1:AXIAL FORCE 0.000 0.000 0.000 0.000 0.000 0.000 0.000
4 1:AXIAL FORCE -0.128 -0.334 0.000 0.358 0.000 0.000 0.000
5 1:AXIAL FORCE 0.051 -0.835 0.000 0.836 0.000 0.000 0.000
6 1:AXIAL FORCE 0.231 -0.231 0.000 0.327 0.000 0.000 0.000
30
31. Beam End Forces
Sign convention is as the action of the joint on the beam.
Axial Shear Torsion Bending
Beam Node L/C
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL FORCE 0.000 0.000 0.000 0.000 0.000 0.000
2 2 1:AXIAL FORCE 0.000 0.000 0.000 0.000 0.000 0.000
3 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
3 3 1:AXIAL FORCE 32.500 0.000 0.000 0.000 0.000 0.000
4 1:AXIAL FORCE -32.500 0.000 0.000 0.000 0.000 0.000
4 2 1:AXIAL FORCE 15.000 0.000 0.000 0.000 0.000 0.000
5 1:AXIAL FORCE -15.000 0.000 0.000 0.000 0.000 0.000
5 1 1:AXIAL FORCE 22.500 0.000 0.000 0.000 0.000 0.000
6 1:AXIAL FORCE -22.500 0.000 0.000 0.000 0.000 0.000
6 6 1:AXIAL FORCE -10.607 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL FORCE 10.607 0.000 0.000 0.000 0.000 0.000
7 4 1:AXIAL FORCE -10.607 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL FORCE 10.607 0.000 0.000 0.000 0.000 0.000
8 4 1:AXIAL FORCE 17.500 0.000 0.000 0.000 0.000 0.000
5 1:AXIAL FORCE -17.500 0.000 0.000 0.000 0.000 0.000
9 5 1:AXIAL FORCE 17.500 0.000 0.000 0.000 0.000 0.000
6 1:AXIAL FORCE -17.500 0.000 0.000 0.000 0.000 0.000
Beam End Force Summary
The signs of the forces at end B of each beam have been reversed. For example: this means that the Min Fx entry
gives the largest tension value for an beam.
Axial Shear Torsion Bending
Beam Node L/C
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
Max Fx 3 3 1:AXIAL FORCE 32.500 0.000 0.000 0.000 0.000 0.000
Min Fx 7 4 1:AXIAL FORCE -10.607 0.000 0.000 0.000 0.000 0.000
Max Fy 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Min Fy 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Max Fz 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Min Fz 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Max Mx 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Min Mx 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Max My 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Min My 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Max Mz 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
Min Mz 1 1 1:AXIAL FORCE -0.000 0.000 0.000 0.000 0.000 0.000
31
32. Beam Force Detail Summary
Sign convention as diagrams:- positive above line, negative below line except Fx where positive is compression.
Distance d is given from beam end A.
Axial Shear Torsion Bending
Beam L/C
d
(m)
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
Max Fx 3 1:AXIAL FORCE 0.000 32.500 0.000 0.000 0.000 0.000 0.000
Min Fx 7 1:AXIAL FORCE 0.000 -10.607 0.000 0.000 0.000 0.000 0.000
Max Fy 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Min Fy 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Max Fz 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Min Fz 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Max Mx 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Min Mx 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Max My 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Min My 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Max Mz 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Min Mz 1 1:AXIAL FORCE 0.000 -0.000 0.000 0.000 0.000 0.000 0.000
Beam Maximum Moments
Distances to maxima are given from beam end A.
Beam Node A
Length
(m)
L/C
d
(m)
Max My
(kN-
m)
d
(m)
Max Mz
(kN-
m)
1 1 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
2 2 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
3 3 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
4 2 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
5 1 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
6 6 4.243 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
32
33. Max +ve 0.000 0.000 0.000 0.000
7 4 4.243 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
8 4 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
9 5 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
Beam Maximum Axial Forces
Distances to maxima are given from beam end A.
Beam Node A
Length
(m)
L/C
d
(m)
Max Fx
(kN)
1 1 3.000 1:AXIAL FORCE Max -ve
Max +ve 0.000 -0.000
2 2 3.000 1:AXIAL FORCE Max -ve 0.000 0.000
Max +ve
3 3 3.000 1:AXIAL FORCE Max -ve 0.000 32.500
Max +ve
4 2 3.000 1:AXIAL FORCE Max -ve 0.000 15.000
Max +ve
5 1 3.000 1:AXIAL FORCE Max -ve 0.000 22.500
Max +ve
Beam Node A
Length
(m)
L/C
d
(m)
Max Fz
(kN)
d
(m)
Max Fy
(kN)
1 1 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
2 2 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
3 3 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
4 2 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
5 1 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
6 6 4.243 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
7 4 4.243 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
8 4 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
9 5 3.000 1:AXIAL FORCE Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
33
34. 6 6 4.243 1:AXIAL FORCE Max -ve
Max +ve 0.000 -10.607
7 4 4.243 1:AXIAL FORCE Max -ve
Max +ve 0.000 -10.607
8 4 3.000 1:AXIAL FORCE Max -ve 0.000 17.500
Max +ve
9 5 3.000 1:AXIAL FORCE Max -ve 0.000 17.500
Max +ve
Beam Maximum Forces by Section Property
Axial Shear Torsion Bending
Section
Max Fx
(kN)
Max Fy
(kN)
Max Fz
(kN)
Max Mx
(kN-
m)
Max My
(kN-
m)
Max Mz
(kN-
m)
ISMB100 Max +ve 32.500 0.000 0.000 0.000 0.000 0.000
Max -ve -10.607 0.000 0.000 0.000 0.000 0.000
Beam Combined Axial and Bending Stresses
Beam Combined Axial and Bending Stresses Summary
Max Comp Max Tens
Beam L/C
Length
(m)
Stress
(MPa)
d
(m)
Corner
Stress
(MPa)
d
(m)
Corner
1 1:AXIAL FORCE 3.000 -0.000 0.000 1
2 1:AXIAL FORCE 3.000 0.000 0.000 1
3 1:AXIAL FORCE 3.000 22.260 0.000 1
4 1:AXIAL FORCE 3.000 10.274 0.000 1
5 1:AXIAL FORCE 3.000 15.411 0.000 1
6 1:AXIAL FORCE 4.243 -7.265 0.000 1
7 1:AXIAL FORCE 4.243 -7.265 0.000 1
8 1:AXIAL FORCE 3.000 11.986 0.000 1
9 1:AXIAL FORCE 3.000 11.986 0.000 1
Beam Profile Stress
There is no data of this type.
34
35. Reactions
Horizontal Vertical Horizontal Moment
Node L/C
FX
(kN)
FY
(kN)
FZ
(kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
3 1:AXIAL FORCE 0.000 32.500 0.000 0.000 0.000 0.000
Reaction Summary
Horizontal Vertical Horizontal Moment
Node L/C
FX
(kN)
FY
(kN)
FZ
(kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
Max FX 3 1:AXIAL FORCE 0.000 32.500 0.000 0.000 0.000 0.000
Min FX 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Max FY 3 1:AXIAL FORCE 0.000 32.500 0.000 0.000 0.000 0.000
Min FY 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Max FZ 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Min FZ 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Max MX 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Min MX 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Max MY 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Min MY 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Max MZ 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Min MZ 1 1:AXIAL FORCE -0.000 22.500 0.000 0.000 0.000 0.000
Reaction Envelope
There is no data of this type - Analysis results are not available
Failed Members
There is no data of this type.
35
37. Job Information
Engineer Checked Approved
Name: TAUSIF ALAM P RAMAKANTH
Date: 16-Jul-10
Structure Type PLANE FRAME
Number of Nodes 8 Highest Node 8
Number of Elements 13 Highest Beam 13
Number of Basic Load Cases 1
Number of Combination Load Cases 0
Included in this printout are data for:
All The Whole Structure
Included in this printout are results for load cases:
Type L/C Name
Primary 1 AXIAL LOADS
37
ARRANGEMENT OF TRUSS SYSTEM 2
38. Nodes
Node
X
(m)
Y
(m)
Z
(m)
1 0.000 0.000 0.000
2 4.000 0.000 0.000
3 10.000 0.000 0.000
4 16.000 0.000 0.000
5 20.000 0.000 0.000
6 4.000 2.000 0.000
7 10.000 5.000 0.000
8 16.000 2.000 0.000
Beams
Beam Node A Node B
Length
(m)
Property
b
(degrees)
1 1 2 4.000 1 0
2 2 3 6.000 1 0
3 3 4 6.000 1 0
4 4 5 4.000 1 0
5 1 6 4.472 1 0
6 6 7 6.708 1 0
7 7 8 6.708 1 0
8 8 5 4.472 1 0
9 4 8 2.000 1 0
10 3 7 5.000 1 0
11 2 6 2.000 1 0
12 6 3 6.325 1 0
13 3 8 6.325 1 0
Section Properties
Prop Section
Area
(cm2
)
Iyy
(cm4
)
Izz
(cm4
)
J
(cm4
)
Material
1 ISMB150 19.000 53.000 725.997 2.866 STEEL
Materials
Mat Name
E
(N/mm2
)
n
Density
(N/mm3
)
a
(1/°K)
3 STEEL 200E 3 0.300 0.000 3.61E -6
4 STAINLESSSTEEL 193E 3 0.300 0.000 5.5E -6
5 ALUMINUM 68.9E 3 0.330 0.000 7.11E -6
6 CONCRETE 21.7E 3 0.170 0.000 3.06E -6
Supports
Node
X
(kN/m)
Y
(kN/m)
Z
(kN/m)
rX
(kN-
m/deg)
rY
(kN-
m/deg)
rZ
(kN-
m/deg)
1 Fixed Fixed Fixed - - -
5 - Fixed - - - -
Releases
There is no data of this type.
38
39. Basic Load Cases
Number Name
1 AXIAL LOADS
Combination Load Cases
There is no data of this type.
Load Generators
There is no data of this type.
Node Displacements
Node L/C
X
(mm)
Y
(mm)
Z
(mm)
Resultant
(mm)
rX
(deg)
rY
(deg)
rZ
(deg)
1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL LOADS 1.537 -12.364 0.000 12.459 0.000 0.000 0.000
3 1:AXIAL LOADS 3.843 -12.378 0.000 12.961 0.000 0.000 0.000
4 1:AXIAL LOADS 5.249 -9.334 0.000 10.709 0.000 0.000 0.000
5 1:AXIAL LOADS 6.186 0.000 0.000 6.186 0.000 0.000 0.000
6 1:AXIAL LOADS 4.937 -12.259 0.000 13.216 0.000 0.000 0.000
7 1:AXIAL LOADS 3.593 -11.733 0.000 12.271 0.000 0.000 0.000
8 1:AXIAL LOADS 2.828 -9.334 0.000 9.753 0.000 0.000 0.000
Node Displacement Summary
Node L/C
X
(mm)
Y
(mm)
Z
(mm)
Resultant
(mm)
rX
(deg)
rY
(deg)
rZ
(deg)
Max X 5 1:AXIAL LOADS 6.186 0.000 0.000 6.186 0.000 0.000 0.000
Min X 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Max Y 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Min Y 3 1:AXIAL LOADS 3.843 -12.378 0.000 12.961 0.000 0.000 0.000
Max Z 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Min Z 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Max rX 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Min rX 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Max rY 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Min rY 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Max rZ 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Min rZ 1 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000 0.000
Max Rst 6 1:AXIAL LOADS 4.937 -12.259 0.000 13.216 0.000 0.000 0.000
Beam End Forces
Sign convention is as the action of the joint on the beam.
Axial Shear Torsion Bending
Beam Node L/C
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
1 1 1:AXIAL LOADS -146.000 0.000 0.000 0.000 0.000 0.000
2 1:AXIAL LOADS 146.000 0.000 0.000 0.000 0.000 0.000
2 2 1:AXIAL LOADS -146.000 0.000 0.000 0.000 0.000 0.000
3 1:AXIAL LOADS 146.000 0.000 0.000 0.000 0.000 0.000
3 3 1:AXIAL LOADS -89.000 0.000 0.000 0.000 0.000 0.000
4 1:AXIAL LOADS 89.000 0.000 0.000 0.000 0.000 0.000
4 4 1:AXIAL LOADS -89.000 0.000 0.000 0.000 0.000 0.000
39
40. 5 1:AXIAL LOADS 89.000 0.000 0.000 0.000 0.000 0.000
5 1 1:AXIAL LOADS 90.561 0.000 0.000 0.000 0.000 0.000
6 1:AXIAL LOADS -90.561 0.000 0.000 0.000 0.000 0.000
6 6 1:AXIAL LOADS 54.784 0.000 0.000 0.000 0.000 0.000
7 1:AXIAL LOADS -54.784 0.000 0.000 0.000 0.000 0.000
7 7 1:AXIAL LOADS 99.505 0.000 0.000 0.000 0.000 0.000
8 1:AXIAL LOADS -99.505 0.000 0.000 0.000 0.000 0.000
8 8 1:AXIAL LOADS 99.505 0.000 0.000 0.000 0.000 0.000
5 1:AXIAL LOADS -99.505 0.000 0.000 0.000 0.000 0.000
9 4 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000
8 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000
10 3 1:AXIAL LOADS -49.000 0.000 0.000 0.000 0.000 0.000
7 1:AXIAL LOADS 49.000 0.000 0.000 0.000 0.000 0.000
11 2 1:AXIAL LOADS -20.000 0.000 0.000 0.000 0.000 0.000
6 1:AXIAL LOADS 20.000 0.000 0.000 0.000 0.000 0.000
12 6 1:AXIAL LOADS 60.084 0.000 0.000 0.000 0.000 0.000
3 1:AXIAL LOADS -60.084 0.000 0.000 0.000 0.000 0.000
13 3 1:AXIAL LOADS 0.000 0.000 0.000 0.000 0.000 0.000
8 1:AXIAL LOADS -0.000 0.000 0.000 0.000 0.000 0.000
Beam End Force Summary
The signs of the forces at end B of each beam have been reversed. For example: this means that the Min Fx entry
gives the largest tension value for an beam.
Axial Shear
Torsio
n
Bending
Bea
m
Nod
e
L/C
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
Max Fx 8 8
1:AXIAL
LOADS
99.505 0.000 0.000 0.000 0.000 0.000
Min Fx 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Max Fy 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Min Fy 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Max Fz 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Min Fz 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Min Mx 1 1
1:AXIAL
LOADS
-146.000 0.000 0.000 0.000 0.000 0.000
Max
My
1 1
1:AXIAL
LOADS
-146.00 0.000 0.000 0.000 0.000 0.000
Min My 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Min Mz 1 1 1:AXIAL -146.000 0.000 0.000 0.000 0.000 0.000
Beam Force Detail Summary
Sign convention as diagrams:- positive above line, negative below line except Fx where positive is compression.
Distance d is given from beam end A.
Axial Shear Torsion Bending
Beam L/C
d
(m)
Fx
(kN)
Fy
(kN)
Fz
(kN)
Mx
(kN-
m)
My
(kN-
m)
Mz
(kN-
m)
Max 8 1:AXIAL 0.000 99.505 0.000 0.000 0.000 0.000 0.000
Min Fx 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Min Fy 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Min Fz 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Min 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
40
41. Max 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Min 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Max 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Min 1 1:AXIAL 0.000 -146.000 0.000 0.000 0.000 0.000 0.000
Beam Maximum Moments
Distances to maxima are given from beam end A.
Beam Node A
Length
(m)
L/C
d
(m)
Max My
(kN-
m)
d
(m)
Max Mz
(kN-
m)
1 1 4.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
2 2 6.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
3 3 6.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
4 4 4.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
5 1 4.472 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
6 6 6.708 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
7 7 6.708
1:AXIAL
LOADS
Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
8 8 4.472 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
9 4 2.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
10 3 5.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
11 2 2.000 1:AXIAL Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
12 6 6.325
1:AXIAL
LOADS
Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
13 3 6.325
1:AXIAL
LOADS
Max -ve 0.000 0.000 0.000 0.000
Max +ve 0.000 0.000 0.000 0.000
Beam Maximum Axial Forces
Distances to maxima are given from beam end A.
Beam Node A
Length
(m)
L/C
d
(m)
Max Fx
(kN)
1 1 4.000 1:AXIAL LOADS Max -ve
Max +ve 0.000 -146.000
2 2 6.000 1:AXIAL LOADS Max -ve
Max +ve 0.000 -146.000
3 3 6.000 1:AXIAL LOADS Max -ve
Max +ve 0.000 -89.000
4 4 4.000 1:AXIAL LOADS Max -ve
Max +ve 0.000 -89.000
5 1 4.472 1:AXIAL LOADS Max -ve 0.000 90.561
Max +ve
6 6 6.708 1:AXIAL LOADS Max -ve 0.000 54.784
Max +ve
7 7 6.708 1:AXIAL LOADS Max -ve 0.000 99.505
Max +ve
8 8 4.472 1:AXIAL LOADS Max -ve 0.000 99.505
Max +ve
9 4 2.000 1:AXIAL LOADS Max -ve 0.000 0.000
41
45. There is no data of this type.
Reactions
Horizontal Vertical Horizontal Moment
Node L/C FX (kN) FY (kN) FZ (kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
1 1:AXIAL LOADS -65.000 40.500 0.000 0.000 0.000 0.000
5 1:AXIAL LOADS 0.000 44.500 0.000 0.000 0.000 0.000
Reaction Summary
Horizontal Vertical Horizontal Moment
Node L/C
FX
(kN)
FY
(kN)
FZ
(kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
Max FX 5
1:AXIAL
LOADS
0.000 4.500 0.000 0.000 0.000 0.000
Min FX 1
1:AXIAL
LOADS
-65.000 40.500 0.000 0.000 0.000 0.000
Max FY 5 1:AXIAL 0.000 44.500 0.000 0.000 0.000 0.000
Min FY 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Max FZ 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Min FZ 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Max MX 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Min MX 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Max MY 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Min MY 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Max MZ 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Min MZ 1 1:AXIAL -65.000 40.500 0.000 0.000 0.000 0.000
Failed Members
There is no data of this type.
Statics Check Results
L/C
FX
(kN)
FY
(kN)
FZ
(kN)
MX
(kN-
m)
MY
(kN-
m)
MZ
(kN-
m)
1:AXIAL
LOADS
Loads 65.000 -85.000 0.000 0.000 0.000 -890.001
1:AXIAL
LOADS
Reactions -65.000 85.000 0.000 0.000 0.000 890.001
45
46. Difference -0.000 0.000 0.000 0.000 0.000 0.000
9. RESULTS & CONCLUSIONS
Truss system has been understood entirely with its various elements, types,
stability and analysis for an unknown set of forces.
Further, two types of truss system have been analytically analyzed for a set of
unknown forces manually. Also, STAAD Files have been generated for both
the Truss systems comprising modeling, loading, and analysis. The results
46
47. drawn from manual calculation and from STAAD.PRO have been found to be
in compliance.
Furthermore, Standard Excel Program Files have been developed for the two
Truss systems for a set of unknown forces and the results were in
concurrence with the results obtained from the analysis of STAAD.PRO.
47