Introduction- Muller Breslau principle , Arches i.e. Two hinged, fixed hinged arches and Stiffening Girder.
Explanation of procedure for all methods.
Illustrate some examples to understand the concept better
The document provides information about the course CV 725 Pile Foundations, including the instructor Dr. Babloo Chaudhary, course contents which cover various topics related to pile foundations, educational qualifications and experience of the instructor, intended learning outcomes, reference books, and timetable and evaluation plan.
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Module 1 Behaviour of RC beams in Shear and TorsionVVIETCIVIL
This document summarizes key concepts related to shear and torsion behavior in reinforced concrete beams. It discusses modes of cracking in shear, shear failure modes, critical sections for shear design, the influence of axial forces and longitudinal reinforcement on shear strength, and shear transfer mechanisms. The key points covered include web shear cracking, flexure-shear cracking, diagonal tension failure, shear-compression and shear-tension failures, and the four mechanisms that contribute to shear transfer: aggregate interlock, dowel action, stirrups, and the interaction between axial compression and shear strength.
Circular slabs are commonly used as roofs or floors with a circular plan, such as water tanks. They experience bending stresses in two perpendicular directions - radially and circumferentially. Reinforcement is provided as a mesh of bars with equal cross-sectional area in both directions. Near the edges, additional radial and circumferential reinforcement may be needed if edge stresses are significant. Circular slabs are analyzed based on elastic theory, and deflect into a saucer shape under uniform loads, developing tensile and compressive stresses on the convex and concave surfaces respectively. Reinforcement must be provided in both radial and circumferential directions near the convex surface.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document discusses the design of continuous beams. It notes that continuous beams must be designed to resist hogging moments at supports in addition to sagging moments in spans. An example three-span continuous beam is then designed. The beam has a total factored load of 80.57 kN/m and 6.1m spans. Elastic analysis finds maximum moments of 239.94 kN.m in end spans and -299.80 kN.m at interior supports. The beam is designed with a depth of 530mm and reinforcement is checked for bending, shear, development length, and deflection requirements.
Principle of Virtual Work in structural analysisMahdi Damghani
The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.
The document provides information about the course CV 725 Pile Foundations, including the instructor Dr. Babloo Chaudhary, course contents which cover various topics related to pile foundations, educational qualifications and experience of the instructor, intended learning outcomes, reference books, and timetable and evaluation plan.
Geotechnical Engineering-II [Lec #19: General Bearing Capacity Equation]Muhammad Irfan
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
Module 1 Behaviour of RC beams in Shear and TorsionVVIETCIVIL
This document summarizes key concepts related to shear and torsion behavior in reinforced concrete beams. It discusses modes of cracking in shear, shear failure modes, critical sections for shear design, the influence of axial forces and longitudinal reinforcement on shear strength, and shear transfer mechanisms. The key points covered include web shear cracking, flexure-shear cracking, diagonal tension failure, shear-compression and shear-tension failures, and the four mechanisms that contribute to shear transfer: aggregate interlock, dowel action, stirrups, and the interaction between axial compression and shear strength.
Circular slabs are commonly used as roofs or floors with a circular plan, such as water tanks. They experience bending stresses in two perpendicular directions - radially and circumferentially. Reinforcement is provided as a mesh of bars with equal cross-sectional area in both directions. Near the edges, additional radial and circumferential reinforcement may be needed if edge stresses are significant. Circular slabs are analyzed based on elastic theory, and deflect into a saucer shape under uniform loads, developing tensile and compressive stresses on the convex and concave surfaces respectively. Reinforcement must be provided in both radial and circumferential directions near the convex surface.
This document describes the design of a pile cap by a group of civil engineering students. It defines a pile cap as a concrete mat that rests on piles driven into soft ground to provide a stable foundation. It then provides two examples of pile cap design, showing dimensions, load calculations, reinforcement requirements and construction details. The document concludes that a pile cap distributes a building's load to piles to form a stable foundation on unstable soil. It acknowledges the guidance of professors in completing this project.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This document discusses the design of continuous beams. It notes that continuous beams must be designed to resist hogging moments at supports in addition to sagging moments in spans. An example three-span continuous beam is then designed. The beam has a total factored load of 80.57 kN/m and 6.1m spans. Elastic analysis finds maximum moments of 239.94 kN.m in end spans and -299.80 kN.m at interior supports. The beam is designed with a depth of 530mm and reinforcement is checked for bending, shear, development length, and deflection requirements.
Principle of Virtual Work in structural analysisMahdi Damghani
The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.
This document will help you learn an introductory part and some detailed information on Shallow Foundations. As I am presenting this document to you I wish you all a Happy learning arena. It is highly recommended for students taking a bachelor degree in Civil Engineering, also it is a good document for students who are doing final touches for their examinations.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
Piles are deep foundations used to transfer structural loads through weak soil layers to stronger soil strata below. There are different types of piles based on function (load bearing, non-load bearing), material (concrete, timber, steel), and installation method (driven, cast-in-place). Load bearing piles can be end bearing piles that rest on a hard layer or friction piles that transfer load through side friction. Factors like soil conditions, water table, and cost determine the suitable pile type for a given foundation. Load capacity is estimated through testing, soil parameters, or dynamic/static formulas.
Stiffness method of structural analysisKaran Patel
This method is a powerful tool for analyzing indeterminate structures. One of its advantages over the flexibility method is that it is conducive to computer programming.
Stiffness method the unknowns are the joint displacements in the structure, which are automatically specified.
This document contains lecture notes on matrix methods of structural analysis. It discusses three methods for solving systems of linear equations that arise in structural analysis problems - Gauss elimination method, Gauss-Jordan method, and Gauss-Seidel iterative method. For each method, an example problem is provided and solved step-by-step to illustrate the application of the method.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document provides an outline for a presentation on the moment distribution method for structural analysis. It includes:
- An introduction to the moment distribution method and its use for analyzing statically indeterminate beams and frames.
- Definitions of important terms used in the method like stiffness, carry over factor, and distribution factor.
- Sign conventions for support moments, member rotations, and sinking of supports.
- Expressions for fixed end moments under different load cases including centric loading, eccentric loading, uniform loads, support rotations, and sinking of supports.
- Examples of applying the method to a simply supported beam and fixed supported beam with sinking support.
1. The document discusses stress distribution in soils due to different types of loading, including point loads, line loads, triangular loads, strip loads, rectangular loads, and circular loads.
2. Several methods for estimating stress distribution are presented, including Boussinesq's method, Westergaard's method, and the use of influence factor charts and bulbs of pressure charts.
3. Factors that influence stress distribution include the size and shape of the loading area, load magnitude and type, soil type, depth, and distance from the load. Stress decreases with depth and distance from the load.
This report summarizes a document on laterally loaded piles. It discusses how piles transfer both vertical and lateral loads, with lateral loads coming from sources like wind, waves, earthquakes, and earth pressures. It describes mechanisms of load transfer, including shaft friction, end bearing, and lateral resistance from surrounding soil. When piles are in a group, they interact with each other through overlapping displacement fields. The report also summarizes various methods for analyzing laterally loaded piles and groups of piles, including rigid and finite element methods, as well as p-y curve approaches. It states that p-y curves are the best way to determine lateral load capacity in the field.
This lecture discusses the bearing capacity of foundations. It introduces Terzaghi's bearing capacity theory, which evaluates the ultimate bearing capacity of shallow foundations based on a failure surface geometry. Terzaghi's equation for ultimate bearing capacity is presented. Meyerhof's and Hansen's theories are also introduced, which improved on Terzaghi's theory. Hansen's theory provides a more general bearing capacity equation that can be applied to both shallow and deep foundations. Safety factors are applied to the ultimate bearing capacity to determine allowable bearing capacity for foundation design. Settlement criteria may also control and limit the allowable bearing capacity in some cases.
Part-I: Seismic Analysis/Design of Multi-storied RC Buildings using STAAD.Pro...Rahul Leslie
For novice, please continue from "Modelling Building Frame with STAAD.Pro & ETABS" (http://www.slideshare.net/rahulleslie/modelling-building-frame-with-staadpro-etabs-rahul-leslie).
This is a presentation covering almost all aspects of Seismic analysis & design of Multi-storied RC Structures using the Indian code IS:1893-2016 (New edition), with references to IS:13920-2015 (Code for ductile detailing) & IS:16700-2017 (code for design of tall buildings) where relevant; following for each aspect of the code, (1) The clause/formula (2) It's explanation/theory (3) How it is/can be implemented in the software packages of (i) STAAD.Pro and (ii) ETABS
This is the latest edition of the earlier slides based on IS:1893-2002 which this one supersedes. This is Part-I of a two part series.
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
The document discusses indeterminate structures, the stiffness method, and its application to structural analysis. It defines indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, as they consist of more members and restraints. The stiffness method is useful for automatically solving problems related to beams, frames, and trusses. It defines stiffness as the end moment required to produce a unit rotation at one end of a member with the other end fixed. Key steps in a stiffness analysis include determining the degree of kinematic indeterminacy, applying restraints, calculating member forces, and solving the equilibrium equations in matrix form to obtain displacements.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document describes a student project that aims to prepare design aids in the form of interaction curves for column design. The design aids in SP-16 only provide 12 charts each for rectangular and circular column sections, with d'/D ratios in intervals of 0.05. However, in practice d'/D varies from 0.035 to 0.25. The project will prepare 57 charts each for the column sections, with d'/D ratios in intervals of 0.01, to minimize approximation errors. This will result in preparing a total of 2394 interaction curves covering different grades of steel and p/fck ratios, to aid in more accurate column design and analysis.
This document summarizes stress distribution in soil due to concentrated and uniform loads. It presents Westergaard and Boussinesq equations to calculate vertical stress below a concentrated load. It also discusses the approximate and elastic theory methods to calculate vertical stress below a uniform load on circular and rectangular areas using influence coefficients. Several examples are provided to illustrate calculating vertical stress at different depths and locations below concentrated and uniform loads.
The document discusses various types of loads and pressures that act on underground tunnels, including:
1) Earth/rock pressures and water pressure are the most important potential loads. Live loads from surface traffic can usually be neglected.
2) Dimensions of tunnel sections must account for overburden weight (geostatic pressure) or loosening pressure (weight of loosened rock zone).
3) Lateral pressures, bottom pressures, and rock pressures are discussed. Several theories for estimating vertical and lateral loads are presented, including those by Bierbaumer, Terzaghi, and Tsimbaryevitch.
4) Rock pressures depend on factors like the quality of rock, stresses/strains around the
This presentation summarizes the Muller-Breslau principle for constructing influence lines. The principle states that the deflected shape of a structure under a unit internal load or reaction corresponds to the influence line for that load or reaction. The presentation provides the history of Muller-Breslau, explains the principle using virtual work, and outlines the general procedure for constructing influence lines using conjugate beam analysis and deflected shapes. Examples of influence lines for simply supported and continuous beams are presented.
Slope and Deflection Method ,The Moment Distribution Method ,Strain Energy Me...Aayushi5
This document provides information about the Design of Structure I course taught to 5th semester civil engineering students. It discusses the course objectives, outcomes, syllabus, and various structural analysis methods taught - Slope Deflection Method, Moment Distribution Method, and Strain Energy Method. The document focuses on the Slope Deflection Method, providing the theory, procedure, an example numerical problem, and derivation of slope-deflection equations for a continuous beam with 4 degrees of indeterminacy. It summarizes the steps to analyze a structure using the slope-deflection approach.
Force Force and Displacement Matrix MethodAayushi5
The analysis of a structure by the matrix method may be described by the following steps:
1. Problem statement
2. Selection of released structure
3. Analysis of released structure under loads
4. Analysis of released structure for other causes
5. Analysis of released structure for unit values of redundant
6. Determination of redundants through the superposition equations.
7. Determine the other displacements and actions. The following are the four flexibility matrix equations for calculating redundants member end actions, reactions and joint displacements
where for the released structure
8.All matrices used in the matrix method are summarized in the following tables
This document will help you learn an introductory part and some detailed information on Shallow Foundations. As I am presenting this document to you I wish you all a Happy learning arena. It is highly recommended for students taking a bachelor degree in Civil Engineering, also it is a good document for students who are doing final touches for their examinations.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
Piles are deep foundations used to transfer structural loads through weak soil layers to stronger soil strata below. There are different types of piles based on function (load bearing, non-load bearing), material (concrete, timber, steel), and installation method (driven, cast-in-place). Load bearing piles can be end bearing piles that rest on a hard layer or friction piles that transfer load through side friction. Factors like soil conditions, water table, and cost determine the suitable pile type for a given foundation. Load capacity is estimated through testing, soil parameters, or dynamic/static formulas.
Stiffness method of structural analysisKaran Patel
This method is a powerful tool for analyzing indeterminate structures. One of its advantages over the flexibility method is that it is conducive to computer programming.
Stiffness method the unknowns are the joint displacements in the structure, which are automatically specified.
This document contains lecture notes on matrix methods of structural analysis. It discusses three methods for solving systems of linear equations that arise in structural analysis problems - Gauss elimination method, Gauss-Jordan method, and Gauss-Seidel iterative method. For each method, an example problem is provided and solved step-by-step to illustrate the application of the method.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document provides an outline for a presentation on the moment distribution method for structural analysis. It includes:
- An introduction to the moment distribution method and its use for analyzing statically indeterminate beams and frames.
- Definitions of important terms used in the method like stiffness, carry over factor, and distribution factor.
- Sign conventions for support moments, member rotations, and sinking of supports.
- Expressions for fixed end moments under different load cases including centric loading, eccentric loading, uniform loads, support rotations, and sinking of supports.
- Examples of applying the method to a simply supported beam and fixed supported beam with sinking support.
1. The document discusses stress distribution in soils due to different types of loading, including point loads, line loads, triangular loads, strip loads, rectangular loads, and circular loads.
2. Several methods for estimating stress distribution are presented, including Boussinesq's method, Westergaard's method, and the use of influence factor charts and bulbs of pressure charts.
3. Factors that influence stress distribution include the size and shape of the loading area, load magnitude and type, soil type, depth, and distance from the load. Stress decreases with depth and distance from the load.
This report summarizes a document on laterally loaded piles. It discusses how piles transfer both vertical and lateral loads, with lateral loads coming from sources like wind, waves, earthquakes, and earth pressures. It describes mechanisms of load transfer, including shaft friction, end bearing, and lateral resistance from surrounding soil. When piles are in a group, they interact with each other through overlapping displacement fields. The report also summarizes various methods for analyzing laterally loaded piles and groups of piles, including rigid and finite element methods, as well as p-y curve approaches. It states that p-y curves are the best way to determine lateral load capacity in the field.
This lecture discusses the bearing capacity of foundations. It introduces Terzaghi's bearing capacity theory, which evaluates the ultimate bearing capacity of shallow foundations based on a failure surface geometry. Terzaghi's equation for ultimate bearing capacity is presented. Meyerhof's and Hansen's theories are also introduced, which improved on Terzaghi's theory. Hansen's theory provides a more general bearing capacity equation that can be applied to both shallow and deep foundations. Safety factors are applied to the ultimate bearing capacity to determine allowable bearing capacity for foundation design. Settlement criteria may also control and limit the allowable bearing capacity in some cases.
Part-I: Seismic Analysis/Design of Multi-storied RC Buildings using STAAD.Pro...Rahul Leslie
For novice, please continue from "Modelling Building Frame with STAAD.Pro & ETABS" (http://www.slideshare.net/rahulleslie/modelling-building-frame-with-staadpro-etabs-rahul-leslie).
This is a presentation covering almost all aspects of Seismic analysis & design of Multi-storied RC Structures using the Indian code IS:1893-2016 (New edition), with references to IS:13920-2015 (Code for ductile detailing) & IS:16700-2017 (code for design of tall buildings) where relevant; following for each aspect of the code, (1) The clause/formula (2) It's explanation/theory (3) How it is/can be implemented in the software packages of (i) STAAD.Pro and (ii) ETABS
This is the latest edition of the earlier slides based on IS:1893-2002 which this one supersedes. This is Part-I of a two part series.
This document discusses the design of beams. It defines different types of beams like floor beams, girders, lintels, purlins, and rafters. It describes how beams are classified based on their support conditions as simply supported, cantilever, fixed, or continuous beams. Commonly used beam sections include universal beams, compound beams, and composite beams. The document also covers plastic analysis of beams, classification of beam sections, and failure modes of beams.
The document discusses indeterminate structures, the stiffness method, and its application to structural analysis. It defines indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, as they consist of more members and restraints. The stiffness method is useful for automatically solving problems related to beams, frames, and trusses. It defines stiffness as the end moment required to produce a unit rotation at one end of a member with the other end fixed. Key steps in a stiffness analysis include determining the degree of kinematic indeterminacy, applying restraints, calculating member forces, and solving the equilibrium equations in matrix form to obtain displacements.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
The document describes a student project that aims to prepare design aids in the form of interaction curves for column design. The design aids in SP-16 only provide 12 charts each for rectangular and circular column sections, with d'/D ratios in intervals of 0.05. However, in practice d'/D varies from 0.035 to 0.25. The project will prepare 57 charts each for the column sections, with d'/D ratios in intervals of 0.01, to minimize approximation errors. This will result in preparing a total of 2394 interaction curves covering different grades of steel and p/fck ratios, to aid in more accurate column design and analysis.
This document summarizes stress distribution in soil due to concentrated and uniform loads. It presents Westergaard and Boussinesq equations to calculate vertical stress below a concentrated load. It also discusses the approximate and elastic theory methods to calculate vertical stress below a uniform load on circular and rectangular areas using influence coefficients. Several examples are provided to illustrate calculating vertical stress at different depths and locations below concentrated and uniform loads.
The document discusses various types of loads and pressures that act on underground tunnels, including:
1) Earth/rock pressures and water pressure are the most important potential loads. Live loads from surface traffic can usually be neglected.
2) Dimensions of tunnel sections must account for overburden weight (geostatic pressure) or loosening pressure (weight of loosened rock zone).
3) Lateral pressures, bottom pressures, and rock pressures are discussed. Several theories for estimating vertical and lateral loads are presented, including those by Bierbaumer, Terzaghi, and Tsimbaryevitch.
4) Rock pressures depend on factors like the quality of rock, stresses/strains around the
This presentation summarizes the Muller-Breslau principle for constructing influence lines. The principle states that the deflected shape of a structure under a unit internal load or reaction corresponds to the influence line for that load or reaction. The presentation provides the history of Muller-Breslau, explains the principle using virtual work, and outlines the general procedure for constructing influence lines using conjugate beam analysis and deflected shapes. Examples of influence lines for simply supported and continuous beams are presented.
Slope and Deflection Method ,The Moment Distribution Method ,Strain Energy Me...Aayushi5
This document provides information about the Design of Structure I course taught to 5th semester civil engineering students. It discusses the course objectives, outcomes, syllabus, and various structural analysis methods taught - Slope Deflection Method, Moment Distribution Method, and Strain Energy Method. The document focuses on the Slope Deflection Method, providing the theory, procedure, an example numerical problem, and derivation of slope-deflection equations for a continuous beam with 4 degrees of indeterminacy. It summarizes the steps to analyze a structure using the slope-deflection approach.
Force Force and Displacement Matrix MethodAayushi5
The analysis of a structure by the matrix method may be described by the following steps:
1. Problem statement
2. Selection of released structure
3. Analysis of released structure under loads
4. Analysis of released structure for other causes
5. Analysis of released structure for unit values of redundant
6. Determination of redundants through the superposition equations.
7. Determine the other displacements and actions. The following are the four flexibility matrix equations for calculating redundants member end actions, reactions and joint displacements
where for the released structure
8.All matrices used in the matrix method are summarized in the following tables
Suspension bridges tend to be the most expensive to build. A suspension bridge suspends the roadway from huge main cables, which extend from one end of the bridge to the other.
Most of the weight or load of the bridge is transferred by the cables to the anchorage systems. These are imbedded in either solid rock or huge concrete blocks.
Inside the anchorages, the cables are spread over a large area to evenly distribute the load and to prevent the cables from breaking free.
Introduction-Plastic hinge concept-plastic section modulus-shape factor-redistribution of moments-collapse mechanism.
Theorems of plastic analysis - Static/lower bound theorem; Kinematic/upper bound theorem-Plastic analysis of beams and portal frames by equilibrium and mechanism methods.
This document describes CUMBIA, a set of Matlab codes for analyzing reinforced concrete members. CUMBIA can perform monotonic moment-curvature analysis, force-displacement analysis, and axial load-moment interaction analysis. It uses material models for concrete and steel, including default Mander models for confined and unconfined concrete and King/Raynor models for steel. The section analysis iterates to find the neutral axis position for increasing concrete strains. Member response is obtained using a plastic hinge model, calculating displacements from equivalent plastic hinge length and moment-area relationships.
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.
This document outlines the modules for a National Diploma in Industrial Technician for Civil Engineering. The module is on Structural Mechanics and is 60 hours over 2 hours per week. The aims are to develop the ability to analyze statically determinate structures like beams, columns and frameworks using mechanics and mathematics. It also aims to develop an understanding of structural behavior of materials and design factors. The document provides detailed sections and learning objectives on structural behavior, material properties, bending moments, shear forces, bending stresses, columns, beam analysis and framed structures.
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 outlines a project to implement the direct stiffness matrix method for analyzing beam and grid structures. It discusses the objectives of understanding basic matrix analysis principles and applying them to beam and grid structures. For beams, it describes generating the stiffness matrix manually and through coding in MATLAB. For grids, it similarly involves analytical and coded approaches to matrix analysis. The document presents the methodology for each approach and shows sample results of the analyses.
lec3 Direct Stiffness Approach for Beams and Frames.pptShaheerRizwan1
This document outlines the procedure for analyzing beams and frames using the direct stiffness method. It discusses:
1) Dividing the structure into finite elements and defining nodes with degrees of freedom. Forces and deformations are defined at nodes.
2) Calculating the structure stiffness matrix of each element based on its properties.
3) Assembling the overall structure stiffness matrix. Equations are set up relating known/unknown loads and displacements to solve for unknowns.
4) Computing element forces from the determined displacements using appropriate transformation matrices for each element type. Bending moment and shear force diagrams can then be plotted.
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.
Analysis and Design of CIRCULAR SEWERAGE TANK_2023.docxadnan885140
This document provides an overview of the analysis and design of a circular sewerage tank. It discusses the development of a stiffness matrix method to analyze the structural behavior of cylindrical walls subjected to radial pressure. The objective is to determine the internal forces and edge reactions. The analysis involves developing element stiffness and transformation matrices and assembling them into a global stiffness matrix. The matrix equations are then solved to obtain displacements and internal forces for design. The document outlines the theory, literature review, analysis method, computer program, and conclusions for the project on the circular sewerage tank.
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.
This document presents a monolithic bistable mechanism that does not rely on residual stress. It consists of two curved beams clamped at the center.
Analytic and finite element modeling is used to predict and design the bistable behavior. The modeling shows that for a single curved beam to be bistable, its second buckling mode must be constrained. A double curved beam structure satisfies this requirement through mutual cancellation of twisting modes.
Microfabricated double curved beam tests match the analytic predictions well. The design allows tailoring of the bistable behavior without needing residual stress or complex structures.
Analysis and Design of Mid-Rise Building_2023.docxadnan885140
This document provides an overview of a graduation project submitted by Muthena' to the Department of Civil Engineering at the University of Baghdad. The project involves analyzing and designing a mid-rise building using matrix analysis methods. It includes 5 chapters that cover an introduction, literature review, theoretical basis for the matrix analysis method, description of a computer program developed for the analysis, and discussion of results and recommendations. The theory section describes developing the element stiffness matrix [k], transformation matrix [B], and global stiffness matrix [BkBT] which are key to solving the structural analysis problem using the matrix method.
Comparative Study of an Educational Building by Linear Static Analysis and Re...IRJET Journal
This document compares the linear static analysis and response spectrum analysis of a 3-storey educational building located in seismic zone 3 in India. The building was modeled in AutoCAD and analyzed in ETABS. Both analyses found higher displacement, bending moment, axial force, and shear force values from the linear static analysis compared to the response spectrum analysis. Specifically, the bending moment was 88.5% higher, axial force was 0.73% higher, and shear force was 43% higher from the linear static analysis. Therefore, the response spectrum analysis may provide a more accurate representation of the building's response during an earthquake and is recommended over the linear static analysis.
Checks for walls and details of concrete structuresJo Gijbels
Structural analysis and design of concrete structures is a challenging task – both because of
the natural complexity of the subject and because of the regulation an engineer has to
comply with to get the project done. The construction process has never been as fast as it is
today, and the pressure on cost-effectiveness of structures is growing with zero tolerance of
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Muller-Breslau’s Principle, Two hinged and Fixed Arches and Stiffening Girders
1. Noida Institute of Engineering and Technology,
Greater Noida
Muller-Breslau’s Principle,
Two hinged and Fixed Arches ,
and
Stiffening Girders
Aayushi
Assistant Professor
Civil Engg. Department
6/5/2022
1
Unit: 2
Aayushi RCE-502, DOS 1 Unit 2
Subject Name : Design of
Structure I
Course Details : B Tech 5th
Sem
2. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 2
Content
Course Objective
Course Outcome
CO-PO & PSO Mapping
Prerequisite & Recap
Muller Breslau Principle
Procedure for Muller Breslau principle
Numerical & Deflected shapes
Arches
Types of arches
Two hinged arches
Numerical on two hinged arches
Syllabus of unit 2
Topic outcome and mapping with PO
3. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 3
Content
You tube Video Links
Daily Quiz
Weekly Assignment
MCQs
Old Question Papers
Expected Questions in University Examination
Summary
References
Stiffening girder
Fixed Arches & numerical
Introduction &Numerical
4. Objective
1
To impart the principles of elastic structural analysis and behavior
of indeterminate structures.
2
To impart knowledge about various methods involved in the
analysis of indeterminate structures...
3
To apply these methods for analyzing the indeterminate structures
to evaluate the response of structures .
4
To enable the student get a feeling of how real-life structures
behave
5
To make the student familiar with latest computational techniques
and software used for structural analysis. .
6/5/2022
Aayushi RCE-502, DOS 1 Unit 2
4
Course Objective
5. Students will be able
CO1 To Identify and analyze the moment distribution in beams and frames by Slope
Deflection Method, Moment Distribution Method and Strain Energy Method.
CO2 To provide adequate learning of indeterminate structures with Muller’s
Principle; Apply & Analyze the concept of influence lines for deciding the
critical forces and sections while designing..
CO3 To learn about suspension bridge, two and three hinged stiffening girders and
their influence line diagram external loading and analyze the same.
CO4 To Identify and analyze forces and displacement matrix for various structural.
CO5 To understand the collapse load in the building and plastic moment formed.
CO6 Apply the concepts of forces and displacements to solve indeterminate structure.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 5
Course Outcome
7. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 7
Prerequisite and Recap
Basics of strength of material
Basics of engineering mechanics
8. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 8
Syllabus of Unit 2
Muller-Breslau’s Principle and its applications
for drawing influence lines for indeterminate
beams, Analysis of two hinged and fixed arches,
Influence line diagrams for maximum bending
moment, Shear force and thrust in two hinge
arches. Analysis of two and three hinged
stiffening girders.
9. 6/5/2022 9
Objective of Unit 2
The Muller-Breslau principle for influence lines for BM
and Shear force in beams and truss.Derivation of the
principle for different types of internal forces.
Aayushi RCE-502, DOS 1 Unit 2
10. The Müller-Breslau principle for influence lines.
Derivation of the principle for different types of internal
forces.
Example of application of this principle.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 10
Topic Objective
11. To Identify the moment distribution in beams and Draw ILD for
different sections.
6/5/2022 11
Topic Outcomes
Once the student has successfully completed this unit, he/she will be able
to:
To analyze different beams and frames.
Apply the concepts of forces and displacements to solve indeterminate
structure.
Aayushi RCE-502, DOS 1 Unit 2
12. 6/5/2022 12
Objective of Topic
Topic-1 Name
The Muller-Breslau principle
Objective of Topic-1:
To Construct influence line diagram (ILD) for BM and
SF in beams and truss.
Aayushi RCE-502, DOS 1 Unit 2
13. 6/5/2022 13
Topic Outcome and mapping with PO
Programme Outcomes (POs)
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
TO1 1 1 1 1 1 1 1 1 1
Outcome of Topic-1:
After the successfully competition of this topic students
will be able to Construct influence line diagram (ILD)
for BM and SF in beams and truss.
Aayushi RCE-502, DOS 1 Unit 2
14. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 14
Prerequisite and Recap
Basic concept of Influence line diagram
Influence line Diagram.
Understanding of bending moment and
shear force .
Understanding of forces.
15. Heinrich Franz Bernhard Müller was born in
Wroclaw (Breslau) on 13 May1851.
In 1875 he opened a civil engineer‘s office in Berlin.
Around this time he decided to add the name of his
hometown to his surname, becoming known as Muller-
Breslau.
In 1883 Muller-Breslau became a lecturer and in 1885 a
professor in civil engineering at the Technische
Hochschule in Hanover.
In 1886, Heinrich Müller-Breslau develop a method for
rapidly constructing the shape of an influence line.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 15
Topic: History
16. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 16
Topic: Muller-Breslau principle
The influence line for a function (reaction, shear, moment) is to the
same scale as the deflected shape of the beam when the beam is acted
on by the function.
To draw the deflected shape properly, the ability of the beam to resist
the applied function must be removed.
17. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 17
Topic: Procedure for Muller-Breslau’s
Step-1:To draw ILD forany support removethat support.
Step-2:Applyunit load at that support.
Step-3: Draw bending moment diagram forthat support.
Step-4:Construct conjugate beam.
Step-5:Find deflection at some specifiedintervals
(fora conjugatebeam, deflection at any point = BM at that point).
Step-6: Divide each deflection by deflection corresponding to the point of
application of unit load.
Step-7: W
eobtain the ordinates forthe influence forthat particular support.
18. Step-8: For other support repeat the same
procedure.
Step-9: For ILD of bending moment,
construct a static equations from the
beam and substitute values at different
interval and you will get ordinates of
ILD for BMD.
Step-10: For shear force diagram
construct static equations and
solve.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 18
Continuous…
19. Consider the following simply supported beam.
Let’s try to find the shape of the influence line for the vertical reaction
at A.
Remove the ability to resist movement in the vertical direction at A by
using a guided roller
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 19
Topic: Numerical
20. Remove the ability to resist movement in the vertical direction at A by
using a guided roller
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 20
Continuous…
21. Consider the following simply supported beam.
Let’s try to find the shape of the influence line for the shear at the mid-
point (point C).
Remove the ability to resist shear at point C
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 21
Continuous…
22. Consider the following simply supported beam.
Let’s try to find the shape of the influence line for the moment at the
mid-point (point C).
Remove the ability to resist moment at C by using a hinge
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 22
Continuous…
23. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 23
Topic: Explanation
The Muller-Breslau principle uses Betti's law of virtual
work to construct influence lines. To illustrate the
method let us consider a structure AB(Figurea).
Let us apply a unit downward force at a distance x from A ,
at point C .
Let us assume that it creates the vertical reactions RA and RB at
supports A and B , respectively (Figure b). Let us call this
condition “System 1.”
In “System 2” (figure c), we have the same structure
with a unit deflection applied in the direction of RA .
Here Δ is the deflection at point C .
25. According to Betti's law, the virtual work done by the
forces in System 1 going through the Corresponding
displacements in System 2 should be equal to the virtual
work done by the forces in System 2 going through the
corresponding displacements in System 1. For these two
systems, we can write:
The right side of this equation is zero, because in System 2
forces can exist only at the supports, corresponding to
which the displacements in System 1 (at supports A and B )
are zero. The negative sign before Δ accounts for the fact that
it acts against the unit load in System 1.
Solving this equation we get: RA= Δ.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 25
Continuous…
(RA)(1) + (1)(- Δ)=0
26. In other words, the reaction at support A due to a unit load
at point C is equal to the displacement at point C when the
structure is subjected to a unit displacement corresponding to
the positive direction of support reaction at A .
Similarly, we can place the unit load at any other point and
obtain the support reaction due to that from System 2.
Thus the deflection pattern in System 2 represents
the influence line for RA.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 26
Continuous…
27. ILD FORSIMPLY SUPPORTED BEAM:
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 27
Topic: Deflected Shape
28. ILD FORTWO SPAN CONTINOUS BEAM:
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 28
Continuous…
29. ILD FOR THREE SPAN CONTINOUS BEAM:
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 29
Continuous…
30. In this section, we looked at main
applications for influence lines.
The first is the use of an influence
line to determine the influence of a
single point load.
The second is the use of an
influence line to determine the
effect of a distributed load or
patterned distributed load.
The last is the use of an influence
line to determine the effect of a
moving pattern of loads.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 30
Summary of Muller- Breslau
31. Compute horizontal reaction in two-hinged arch by the method
of least work
Write strain energy stored in two-hinged arch during
deformation.
Analyse two-hinged arch for external loading.
Compute reactions developed in two hinged arch due to
temperature loading.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 31
Topic Objective
32. To Identify the horizontal thrust and forces in the arches.
6/5/2022 32
Topic Outcomes
Once the student has successfully completed this unit, he/she will be able
to:
To analyze different Arches.
Apply the concepts of forces and displacements to solve indeterminate
structure.
Aayushi RCE-502, DOS 1 Unit 2
33. 6/5/2022 33
Objective of Topic
Topic-2 Name
Arches
Objective of Topic-2:
To analysis the strain energy stored in the two hinged
arch during deformation.
Aayushi RCE-502, DOS 1 Unit 2
34. 6/5/2022 34
Topic Outcome and mapping with PO
Programme Outcomes (POs)
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
TO1 1 1 1 1 1 1 1 1
Outcome of Topic-1:
After the successfully competition of this topic students
will be able to analysis the strain energy stored in the
two hinged arch during deformation.
Aayushi RCE-502, DOS 1 Unit 2
35. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 35
Prerequisite and Recap
Briefing about Arches
Basic of force system
Basic of bending moment and shear
force
36. Arches and arched structures have a wide range of uses in bridges,
arched dams and in industrial, commercial, and recreational
buildings. They represent the primary structural components of
important and expensive structures, many of which are unique.
Current trends in architecture heavily rely on arched building
components due to their strengths and architectural appeal.
Complex structural analysis of arches is related to the analysis of the
arches strength, stability, and vibration. This type of
multidimensional analysis aims at ensuring the proper functionality
of an arch as one of the fundamental structural elements.
6/5/2022
Aayushi RCE-502, DOS 1 Unit 2 36
Topic: Arches
37. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 37
Topic: Types of Arches
a) Hinge less arch
b) two-hinged arch
c) one-hinged arch
d) three-hinged arch
38. 1. Material of the arch obeys Hooke’s law (physically linear
statement)
2. Deflections of the arches are small compared with the span of
the arch (geometrically linear statement). The cases of nonlinear
statement are specifically mentioned.
3. All constraints, which are introduced into the arched structure
are two-sided, i.e., each constraint prevents displacements in two
directions. The case of one-sided constraints is specifically
mentioned.
4. In the case of elastic supports the relationship between
deflection of constraint and corresponding reaction is linear.
5. The load is applied in the longitudinal plane of symmetry of
the arch. The case of out-of-plane loading is specifically
mentioned.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 38
Topic: Assumptions
39. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 39
Topic: Shape of the Arches
• Circular arch :
Ordinate y of any point of the central line of the circular arch is
calculated by the formula
Where:-
x is the abscissa of the same point of the central line of the arch;
R is the radius of curvature of the arch;
f and l are the rise and span of the arch.
41. • Analysis of two-hinged arch
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 41
Topic: Two hinged Arch
42. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 42
Continuous…
The strain energy due to bending
The total strain energy of the arch is given by,
according to the principle of least work ,where H is chosen as
the redundant reaction
46. A semicircular two hinged arch of constant cross section is subjected to
a concentrated load as shown. Calculate reactions of the arch and draw
bending moment diagram.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 46
Topic: Numerical
47. Taking moment of all forces about hinge B leads to,
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 47
Continuous…
48. Now, the horizontal reaction H may be calculated by the following
expression
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 48
Continuous…
49. Now the bending moment at any cross section of the arch when one of
the hinges is replaced by a roller support is given by,
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 49
Continuous…
Integrating the numerator in equation
51. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 51
Continuous…
The value of denominator in equation, after integration is,
Hence, the horizontal thrust at the support is,
Bending moment diagram
Bending moment M at any cross section of the arch is given by,
53. The deflection and the moment at the center of the hinge less arch
are somewhat smaller than that of the two-hinged arch. However,
the hinge less arch has to be designed for support moment.
A hinge less arch (fixed–fixed arch) is a statically redundant
structure having three redundant reactions. In the case of fixed–fixed
arch there are six reaction components; three at each fixed end.
Apart from three equilibrium equations three more equations are
required to calculate bending moment, shear force and horizontal
thrust at any cross section of the arch. These three extra equations
may be set up from the geometry deformation of the arch.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 53
Topic : Fixed Arch
54. • Analysis of Symmetrical Hinge less Arch
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 54
Continuous…
The strain energy due to axial compression and bending
55. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 55
Continuous…
Consider bending moment and the axial force at the crown as the
redundant.
56. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 56
Continuous…
Temperature stresses
The moment at any cross-section of the arch
57. Strain energy stored in the arch
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 57
Continuous…
Solving equations , Mt and Ht and may be calculated
58. A semicircular fixed-fixed arch of constant cross section is subjected to
symmetrical concentrated load as shown .Determine the reactions of
the arch.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 58
Continuous…
59. Since, the arch is symmetrical and the loading is also symmetrical,
Now the strain energy of the arch is given by,
6/5/2022
Aayushi RCE-502, DOS 1
Unit 2
59
Continuous…
The bending moment at any cross section is given by
61. • Since the arch is symmetrical, integration need to be carried out
between limits 0 to π/2 and the result is multiplied by two.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 61
Continuous…
63. Two-hinged arch is the statically
indeterminate structure to degree one.
Usually, the horizontal reaction is
treated as the redundant and is
evaluated by the Kharagpur method
of least work.
Towards this end, the strain energy
stored in the two hinged arch during
deformation is given.
The reactions developed due to
thermal loadings are discussed.
Finally, a few numerical examples are
solved to illustrate the procedure.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 63
Summary of Arches
64. Differentiate between rigid and deformable structures.
Define funicular structure.
State the type stress in a cable.
Analyse cables subjected to uniformly distributed load.
Analyse cables subjected to concentrated loads.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 64
Topic Objective
65. To Identify Forces and BM in girders
6/5/2022 65
Topic Outcomes
Once the student has successfully completed this unit, he/she will be able
to:
To analyze different Girder
Apply the concepts of forces and displacements to solve indeterminate
structure.
Analyze moments to joint rotations and support settlements.
Aayushi RCE-502, DOS 1 Unit 2
66. 6/5/2022 66
Objective of Topic
Topic-3 Name
The Stiffening Girder
Objective of Topic-3:
To Differentiate between rigid and deformable
structures. Analysis of cables subjected to different
loads.
Aayushi RCE-502, DOS 1 Unit 1
67. 6/5/2022 67
Topic Outcome and mapping with PO
Programme Outcomes (POs)
PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12
TO1 1 1 1 1
Outcome of Topic-3:
After the successfully competition of this topic students
will be able to ddifferentiate between rigid and
deformable structures. Analysis of cables subjected to
different loads.
Aayushi RCE-502, DOS 1 Unit 2
68. 6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 68
Prerequisite and Recap
Basic of forces in cables
Diagram of bending moment and
shear stress
69. The stiffening girder transmits the dead weight of the roadway and the
live traffic loads acting on the roadway in the transverse direction of
the bridge to the suspension points of the cables where these loads are
removed by the cables. As a result, horizontal compressive forces are
present in the stiffening girder
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 69
Topic : Stiffening Girder
70. The 3-hinged stiffening girder of a suspension bridge of span 120m
is subjected to two point loads of 240KN and 300KN at distance
25m and 80m from the left end.
a) Find the SF and BM for the girder at a distance of 40m from
the left end. The supporting cable has a central dip of 12m.
b) Find, also the maximum tension in the cable and draw the
BMD for the girder.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 70
Topic : Stiffening Girder
72. 1.To find support reaction:
Considering the stiffening girder as a suspension beam supporting the
given external load system,
ΣMa=0
240∗25+300∗80−VB∗120=0
VB=250KN
ΣFY=0
VA−240−300+250=0
VA=290KN
2.To find H:
Beam moment at C=BMc=290∗60−240∗35
BMc=9000KNm
Beam moment under the 240KN load=(290∗25)=7250KNm
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 72
Continuous…
73. Beam moment under the 300KN load= (250∗40)=1000KNm
Horizontal reaction at each end of the cable,H=Mc/h
H=9000/12=750KN
3.Find equivalent UDL:
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 73
Continuous…
74. Let we/unit= UDL transferred to the cable.
H=We∗l2/8∗h=We∗1202/8∗12=750
We=5KN/m
Each vertical reaction for the cable= V=We∗l2=5∗1202=300KN
Max tension in the cable=Tmax=(V2+H2)1/2
(3002+7502)1/2
Tmax=807.8KN
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 74
Continuous…
75. 4. S.F calculation :
For the girder, S.F at any section = SFx=(Beamshear−Htanθ)
For the cable at any point,tanθ=4h/l2∗(l−2x)
At 40m from the left end,tanθ=4∗12/1202∗(120−2∗40)=21/5=0.1333
Beam shear at 40m from left end =(290−240)=50KN
Actual SF at 40m from the left end =(50−750∗2/15)=−50KN
5.BM calculation:
For the girder, BM at any section,
M=(Beammoment−Hmoment)=Beammoment–Hy
Beam moment at 40m from the left end =(290∗40−240∗15)=8000KNm
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 75
Continuous…
76. At 40m from the left end, for the cable,
y=4h/l2∗x(l−x)=4∗12/1202∗40∗80=32/3m
Actual BM at 40m from left end
=(Beammoment−Hmoment)
=(8000−750∗323)=0
6.Actual BMD for the girder:
Dip of the cable 25m from left end
=4h/l2∗x(l−x)= frac4∗121202∗25∗95=7.92m
Actual BM at 25m from left end
=(Beammoment−Hmoment)=(7250−750∗7.92)
=1310KNm
6/5/2022
Aayushi RCE-502, DOS 1
Unit 2
76
Continuous…
77. Dip of the cable 80m from the left end =4∗12/1202∗80∗40=32/3m
Actual BM at 80m from left end =(1000−750∗32/3)=2000KNm
7.Actual BMD for the stiffening girder
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 77
Continuous…
78. The girder is defined as the
structure in pure tension having
the funicular shape of the load.
The procedures to analyse cables
carrying concentrated load and
uniformly distributed loads are
developed.
A few numerical examples are
solved to show the application of
these methods to actual problems.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 78
Summary of Stiffening Girder
79. Youtube/other Video Links
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 79
Youtube Video Links
Topic Links Process
Muller Breslau
Principle
https://www.youtube.com/watch?v
=jAuT2qaIszw&t=732s
Click on
the link
Arches https://www.youtube.com/watch?v
=jAuT2qaIszw&t=732s
Click on
the link
Stiffening Girder https://www.youtube.com/watch?v
=cPgKkWK7q28
Click on
the link
80. Top most part of an arch is called ________
a) Sofit
b) Crown
c) Center
d) Abutment
Which of the following is true in case of stone brick?
a) They are weak in compression and tension
b) They are good in compression and tension
c) They are weak in compression and good in tension
d) They are good in compression but weak in tension
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 80
Daily Quiz
81. Explain Müller Breslau principle. Draw the influence line diagram
for reaction R, for the beam shown in the Fig. Compute the ordinate
at 1 m interval. The flexural rigidity is constant throughout.
Derive the influence line diagram for reactions and bending moment
at any section of a simply supported beam. Using the ILD,
determine the support reactions and find bending moment at 2 m, 4
m and 6 m for a simply supported beam of span 8 m subjected to
three point loads of 10 kN, 15 kN and 5 kN placed at 1 m, 4.5 m and
6.5 m respectively.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 81
Daily Quiz
82. Prove that horizontal thrust developed due to a point load W acting
at crown in a two hinged semicircular arch of radius R' is
independent of its radius. Consider EI as constant.
A two hinged parabolic arch of span 30 m and rise 6 m carries two
point loads, each 60 kN, acting at 22.5 m and 15 m from the right
end respectively. Determine the horizontal thrust and maximum
positive and negative moment in the arch.
A parabolic two hinged arch has a span of 32 meters and a rise of 8
m. A uniformly distributed load of 1 kN/m covers 8.0 m horizontal
length of the left side of the arch. If I = I, sec 0, where 0 is the
inclination of the arch of the section to horizontal, and, I, is the
moment of the inertia of the section at the crown, find out the
horizontal thrust at hinges and bending moment at 8.0 m from the
left hinge.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 82
Daily Quiz
83. What is Indeterminate structure?
What is a Procedure for ILD?
What is difference between Two hinge and Fixed arches?
Define stiffening girder.
List out the assumptions made for Arches.
Define Fixed arches and find out its degree of freedom.
Define types of arches.
Mention the formula for circular Arch.
Define Muller- Breslau Principle.
What is an influence line diagram? Explain its importance in
structural analysis.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 83
Weekly Assignment
84. Draw the schematic diagrams for horizontal thrust, bending moment
at any section, radial shear and normal thrust at any given section
for a typical two-hinged symmetrical parabolic arch.
A two hinged parabolic arch has a span of 30 m and a central rise of
5.0 m . Calculate the maximum positive and negative bending
moment at a section distant 10 m from the left support , due to a
single point load of 10 kN rolling from left to right.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 84
Weekly Assignment
85. Shape of three hinged arch is always :-
a) Hyperbolic
b) Circular
c) Parabolic
d) Can be any arbitrary curve
Internal bending moment generated in a three hinged arch is
always:-
a) 0
b) Infinite
c) Varies
d) Non zero value but remains constant
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 85
MCQ s
86. What is the degree of indeterminacy of a fixed arch?
a) 1
b) 2
c) 3
d) 4
What is the degree of indeterminacy of a two hinged arch?
a) 1
b) 2
c) 3
d) 4
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 86
MCQ s
87. Which of the following is true in case of stone brick?
a) They are weak in compression and tension
b) They are good in compression and tension
c) They are weak in compression and good in tension
d) They are good in compression but weak in tension
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 87
MCQ s
88. Identify the FALSE statement from the following, pertaining to
the methods of structural analysis.
1. Influence lines for stress resultants in beams can be drawn using
Muller Breslau's Principle.
2. The Moment Distribution Method is a force method of analysis, not
a displacement method.
3. The Principle of Virtual Displacements can be used to establish a
condition of equilibrium.
4. The Substitute Frame Method is not applicable to frames subjects
to significant side sway.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 88
MCQ s
100. The 3-hinged stiffening girder of a suspension bridge of span 120m
is subjected to two point loads of 240KN and 300KN at distance
25m and 80m from the left end. Find the SF and BM for the girder
at a distance of 40m from the left end. The supporting cable has a
central dip of 12m. Find, also the maximum tension in the cable and
draw the BMD for the girder.
A semicircular two hinged arch of constant cross section is subjected
to a concentrated load as shown. Calculate reactions of the arch and
draw bending moment diagram.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 100
Expected Questions for University Exam
101. Using Muller Breslau Principle, compute the influence line
ordinates at 2 m intervals for moment at mid span of BC of the
continuous beam ABC shown in Fig.
A two hinged semicircular arch of radius R' carried l a load "W' at a
section the radius vector corresponding to which makes an angle 'a'
with the horizontal. Find the horizontal thrust at each support.
Assume uniform flexural rigidity.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 101
Expected Questions for University Exam
102. Introduction- Muller Breslau principle , Arches i.e. Two
hinged, fixed hinged arches and Stiffening Girder.
Explanation of procedure for all methods.
Illustrate some examples to understand concept better.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 102
Summary
103. Jain, A. K., “Advanced Structural Analysis “, Nem Chand
& Bros., Roorkee.
Hibbeler, R.C., “Structural Analysis”, Pearson Prentice
Hall, Sector - 62, Noida-201309
C. S. Reddy “Structural Analysis”, Tata Mc Graw Hill
Publishing Company Limited,New Delhi.
Timoshenko, S. P. and D. Young, “ Theory of Structures”
, Tata Mc-Graw Hill BookPublishing Company Ltd., New
Delhi.
Dayaratnam, P. “ Analysis of Statically Indeterminate
Structures”, Affiliated East-WestPress.
Wang, C. K. “ Intermediate Structural Analysis”, Mc
Graw-Hill Book PublishingCompany Ltd.
6/5/2022 Aayushi RCE-502, DOS 1 Unit 2 103
References