•Download as DOCX, PDF•

7 likes•1,343 views

This chapter discusses beams and support reactions. It defines statically determinate beams and describes the following topics: types of beam supports including simple, pin/hinged, roller, and fixed supports; types of beams such as simply supported, cantilever, overhang, and continuous beams; types of loading including concentrated/point loads and distributed loads such as uniform, uniformly varying, and non-uniform loads; and the procedure to find support reactions of statically determinate beams using equilibrium conditions. It also discusses compound beams and the concept of virtual work.

Report

Share

Report

Share

simply supported beams

The document discusses calculating shear force, bending moment, and deflection distributions over the length of a beam subjected to various transverse loads. It summarizes that the beam material is linear-elastic and isotropic, with all loads acting laterally in the same plane as potential deflections. Deflections are assumed to be small compared to the beam length. Equilibrium equations are applied to relate the loading to shear force, bending moment, slope, and deflection. Examples of simply supported beams with single or multiple loads are provided, showing the relationships between the different mechanical properties.

Influence line diagram for model arch bridge

The Lupu Bridge in Shanghai, China is a steel box section tied arch bridge with a main span of 550m, making it the largest arch bridge in the world when it was completed. A tied arch bridge design was used because the ground conditions on either side of the river were unsuitable for the large forces from a normal arch bridge. The bridge was analyzed using structural analysis software to determine member forces and deformations under load. The bridge is an impressive engineering feat that helped advance Chinese bridge engineering.

what is beam ? types of beam shapes etc

The document summarizes the different types of beams. It discusses 9 types of beams classified based on their support: simply supported, fixed, over hanging, double overhanging, continuous, cantilever, and trussed. A simply supported beam is supported at the ends and free to rotate with no moment resistance. A fixed beam is supported at both ends and restrained from rotating. A cantilever beam is fixed at only one end and projects from that end.

11. kinetics of particles work energy method

The document provides information about work, kinetic energy, work energy principle, and conservation of energy. It defines key terms like work, kinetic energy, spring force, weight force, friction force, power, and efficiency. It explains:
- Work is the product of force and displacement in the direction of force. Work by various forces can be used to solve kinetics problems.
- Kinetic energy is the energy of motion and is defined as one-half mass times velocity squared.
- The work energy principle states that the total work done by forces on an object equals its change in kinetic energy.
- For conservative forces acting on a particle, the mechanical energy (sum of kinetic and potential energy) is

Instructor's Solutions Design of Concrete Structures – Arthur H. Nilson – 15t...

Instructor's Solutions Design of Concrete Structures – Arthur H. Nilson – 15th Edition
Solution Chapter 1 to Chapter 9

Parallel axis theorem and their use on Moment Of Inertia

you can learn how to use parallel axis theorem to calculate the moment of inertia about centroidal axis and its transfer rule.

Stress at a point

This document discusses different types of forces and stresses. It defines surface forces as forces distributed over a body's surface, like hydrostatic pressure, and body forces as forces distributed throughout a body's volume, like gravitational force. It also defines stress as a measure of force per unit area within a body, and explains that stress can be broken down into normal and shear components based on their orientation relative to the plane they act on.

1 introduction - Mechanics of Materials - 4th - Beer

This document provides an overview of the concepts of stress that will be covered in Chapter 1 of the textbook "Mechanics of Materials". It begins with the objectives of studying mechanics of materials and defining stress and deformation. It then reviews concepts from statics like free body diagrams and force equilibrium. It introduces the different types of stresses - normal stress, shear stress, bearing stress - and provides examples of how to calculate each. It discusses stress under general load conditions and the state of stress. The goal is to analyze and design structures to determine stresses and ensure safety under loads.

simply supported beams

The document discusses calculating shear force, bending moment, and deflection distributions over the length of a beam subjected to various transverse loads. It summarizes that the beam material is linear-elastic and isotropic, with all loads acting laterally in the same plane as potential deflections. Deflections are assumed to be small compared to the beam length. Equilibrium equations are applied to relate the loading to shear force, bending moment, slope, and deflection. Examples of simply supported beams with single or multiple loads are provided, showing the relationships between the different mechanical properties.

Influence line diagram for model arch bridge

The Lupu Bridge in Shanghai, China is a steel box section tied arch bridge with a main span of 550m, making it the largest arch bridge in the world when it was completed. A tied arch bridge design was used because the ground conditions on either side of the river were unsuitable for the large forces from a normal arch bridge. The bridge was analyzed using structural analysis software to determine member forces and deformations under load. The bridge is an impressive engineering feat that helped advance Chinese bridge engineering.

what is beam ? types of beam shapes etc

The document summarizes the different types of beams. It discusses 9 types of beams classified based on their support: simply supported, fixed, over hanging, double overhanging, continuous, cantilever, and trussed. A simply supported beam is supported at the ends and free to rotate with no moment resistance. A fixed beam is supported at both ends and restrained from rotating. A cantilever beam is fixed at only one end and projects from that end.

11. kinetics of particles work energy method

The document provides information about work, kinetic energy, work energy principle, and conservation of energy. It defines key terms like work, kinetic energy, spring force, weight force, friction force, power, and efficiency. It explains:
- Work is the product of force and displacement in the direction of force. Work by various forces can be used to solve kinetics problems.
- Kinetic energy is the energy of motion and is defined as one-half mass times velocity squared.
- The work energy principle states that the total work done by forces on an object equals its change in kinetic energy.
- For conservative forces acting on a particle, the mechanical energy (sum of kinetic and potential energy) is

Instructor's Solutions Design of Concrete Structures – Arthur H. Nilson – 15t...

Instructor's Solutions Design of Concrete Structures – Arthur H. Nilson – 15th Edition
Solution Chapter 1 to Chapter 9

Parallel axis theorem and their use on Moment Of Inertia

you can learn how to use parallel axis theorem to calculate the moment of inertia about centroidal axis and its transfer rule.

Stress at a point

This document discusses different types of forces and stresses. It defines surface forces as forces distributed over a body's surface, like hydrostatic pressure, and body forces as forces distributed throughout a body's volume, like gravitational force. It also defines stress as a measure of force per unit area within a body, and explains that stress can be broken down into normal and shear components based on their orientation relative to the plane they act on.

1 introduction - Mechanics of Materials - 4th - Beer

This document provides an overview of the concepts of stress that will be covered in Chapter 1 of the textbook "Mechanics of Materials". It begins with the objectives of studying mechanics of materials and defining stress and deformation. It then reviews concepts from statics like free body diagrams and force equilibrium. It introduces the different types of stresses - normal stress, shear stress, bearing stress - and provides examples of how to calculate each. It discusses stress under general load conditions and the state of stress. The goal is to analyze and design structures to determine stresses and ensure safety under loads.

Cantilever Beam

This study investigates the vibration characteristics of a cantilever beam made of linear elastic material with homogeneous and isotropic material properties. Static and modal analyses are performed to determine the stress, strain, deformation, natural frequencies, and mode shapes of the cantilever beam while it is being designed. The cantilever beam is modeled and analyzed in ANSYS to compare the stress and natural frequency for different materials with the same cross-sectional properties. The results show the deflection, stresses, and natural frequencies of the cantilever beam made of different materials.

Design methods for torsional buckling of steel structures

The document discusses methods for designing steel structures to resist torsional buckling. It summarizes clauses from Eurocode 3 that provide equations for calculating the elastic critical buckling moment and determining the reduction factor used to calculate the design bending strength. It also presents simplified equations that can be used to calculate the elastic critical buckling moment for common steel beam sections. Additional guidance is provided for calculating the critical buckling moment for non-symmetric sections and when bending occurs about the major axis.

CENTROID AND CENTRE OF GRAVITY SPP.pptx

Centroid, Centre of gravity, center of mass,
CG of Line element,
CG of 2D elements,
Solved Numerical;
Practice problem CG;
CG Solved Problems;
Equations of CG for integration method.

Trusses - engineeing mechanics

this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.

Beam (tumpuan)

mekanika kekuatan bahan

Shear and Bending Moment in Beams

This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.

STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

1. The document defines various terms related to strength of materials including stress, strain, elastic limit, Hooke's law, shear stress, Poisson's ratio, Young's modulus, modulus of rigidity, factor of safety, strain energy, and bulk modulus.
2. It also defines terms related to beams such as types of beams, shear force, bending moment, bending stress, pure bending, neutral axis, and section modulus.
3. Terms related to torsion, springs, and deflection of beams are also defined. These include torsion equation, polar modulus, torsional rigidity, types of springs, spring rate, and methods to determine slope and deflection in beams.

TRUSS ANALYSIS (TERM PAPER REPORT)

This document provides an introduction and overview of truss analysis. It defines a truss and describes the key assumptions made in truss analysis, including that loads act only at joints and member weights are negligible. It then describes the two main methods for truss analysis - the method of joints and method of sections. An example problem is worked through for each method to demonstrate how to determine the forces in each truss member.

A Review of Flight Dynamics and Numerical Analysis of an Unmanned Aerial Vehi...

A brief study of flight dynamics and different types of simulation and analysis are presented here.
Find case studies in my next PPT.- http://www.slideshare.net/HarshadaGurav/flight-dynamics-and-numerical-analysis-of-an-unmanned-aerial-vehicle-uav

Project report on beams

This document provides information about beams used in structural engineering. It defines beams, discusses their structural characteristics like moment of inertia and stresses, and describes different types of beams including simply supported, fixed, cantilever, and trussed beams. It also covers beam design, applications in bridges and cranes, potential failure modes from plastic hinges, buckling or material failure, and methods to prevent failures like lateral restraints.

Design and Analysis of Pre Stressed I Girders by Midas Civil Software

Today the construction of bridges has gained worldwide importance. Bridges are an important feature of all road networks and the use of pre stressed bridges is increasingly popular in the construction of bridges due to their better stability, service friendliness, economy and durability, beauty and appearance of the building. Reinforced concrete construction, steel or steel construction using composite construction. In the case of high spaces, reinforced concrete construction makes no money due to the large space. cross section is used more effectively than cross section of reinforced concrete. Prefabricated concrete is used for long bridges with a length of more than 10 meters. Typically, when bridges are calculated, the superstructure and substructure are analyzed separately. The supernatural structure is usually a grid made of large strips, a shortcut membrane and a desk slab. vertical grid Columns of large girders with anchors. The superstructure is tested according to IRC 62014 and according to IRC 182000 with unimaginable gravity loads and loads of moving vehicles. Reduced stress and deviation rates compared to a straightforward tender profile. Rishabh Singh | A. K. Jha | R. S. Parihar "Design and Analysis of Pre-Stressed I-Girders by Midas Civil Software" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-5 , August 2022, URL: https://www.ijtsrd.com/papers/ijtsrd50694.pdf Paper URL: https://www.ijtsrd.com/engineering/civil-engineering/50694/design-and-analysis-of-prestressed-igirders-by-midas-civil-software/rishabh-singh

Simple pulley & pulley block

This is a special study on simple pulley and pulley block and their Practical Applications.
I,from KUET , Khulna , Bangladesh

Beam ,Loads,Supports , trusses

The document discusses different types of structural elements used in building construction including beams, loads, supports, columns, and trusses. It describes several types of beams such as simply supported beams, continuous beams, overhanging beams, cantilever beams, and fixed beams. It also discusses different types of loads, supports, and how columns and trusses function structurally.

Engineering Mechanics

Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics

Curved Beams

This document discusses curved beams and unsymmetrical bending. It begins by introducing the Winkler-Bach theory for analyzing the bending of initially curved beams where bending occurs in the plane of curvature and the cross section is symmetrical about this plane. The theory obtains the stress-moment-deflection relationship assuming plane sections remain plane after bending, called the Winkler-Bach formula. It then examines bending of an infinitesimal portion of a curved beam, identifying the neutral axis and neutral surface where stress is zero. The linearized strain equation is presented and solved to derive the Winkler-Bach theory. Unsymmetrical bending is then briefly mentioned where loads can be applied in or out of the plane of symmetry for cross-

Ce 382 l5 truss 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.

Simpale stress and simple strain

This document contains lecture notes on mechanics of solids from the Department of Mechanical Engineering at Indus Institute of Technology & Engineering. It defines key concepts such as load, stress, strain, tensile stress and strain, compressive stress and strain, Young's modulus, shear stress and strain, shear modulus, stress-strain diagrams, working stress, and factor of safety. It also discusses thermal stresses, linear and lateral strain, Poisson's ratio, volumetric strain, bulk modulus, composite bars, bars with varying cross-sections, and stress concentration. The document provides examples to illustrate how to calculate stresses, strains, moduli, and other mechanical properties for different loading conditions.

6161103 6.4 the method of sections

The method of sections involves cutting imaginary sections through structural members to isolate forces. Equilibrium equations are applied to the cut section to determine member forces. For a truss example, a section was drawn through three unknown members. The free body diagram of the cut section was drawn and the equations of equilibrium were used to determine the forces in each member as 800 N in tension, 800 N in compression, and 500 N in tension.

Chapter 5 failure theories final

The document summarizes different theories for predicting failure under static loading conditions. It discusses:
1) Failure theories for ductile materials including maximum shear stress, distortion energy, and ductile Coulomb-Mohr theories, which are based on yield.
2) Failure theories for brittle materials including maximum normal stress, brittle Coulomb-Mohr, and modified Mohr theories, which do not exhibit an identifiable yield strength.
3) Details of the maximum shear stress theory and distortion energy (Von Mises) theory for ductile materials. The distortion energy theory predicts failure when the distortion strain energy equals the energy at yield in tension.

Truss & its analysis

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.

M2l10

1. The document discusses analyzing statically indeterminate structures like trusses using the force method.
2. It provides objectives, introduces how to determine a truss's degree of static indeterminacy, and explains how to select redundant reactions and forces.
3. Two examples are presented to demonstrate calculating member forces for indeterminate trusses using compatibility equations that equate displacements due to loads and redundant forces.

Cantilever Beam

This study investigates the vibration characteristics of a cantilever beam made of linear elastic material with homogeneous and isotropic material properties. Static and modal analyses are performed to determine the stress, strain, deformation, natural frequencies, and mode shapes of the cantilever beam while it is being designed. The cantilever beam is modeled and analyzed in ANSYS to compare the stress and natural frequency for different materials with the same cross-sectional properties. The results show the deflection, stresses, and natural frequencies of the cantilever beam made of different materials.

Design methods for torsional buckling of steel structures

The document discusses methods for designing steel structures to resist torsional buckling. It summarizes clauses from Eurocode 3 that provide equations for calculating the elastic critical buckling moment and determining the reduction factor used to calculate the design bending strength. It also presents simplified equations that can be used to calculate the elastic critical buckling moment for common steel beam sections. Additional guidance is provided for calculating the critical buckling moment for non-symmetric sections and when bending occurs about the major axis.

CENTROID AND CENTRE OF GRAVITY SPP.pptx

Centroid, Centre of gravity, center of mass,
CG of Line element,
CG of 2D elements,
Solved Numerical;
Practice problem CG;
CG Solved Problems;
Equations of CG for integration method.

Trusses - engineeing mechanics

this PPT includes Definition
Classification Of Truss
Assumption Made In Analysis
Methods Of Analysis
Zero Force Member
procedure for analysis trusses using method of joint, ,procedure of method of section ,
graphical method, SPPU, Savitribai Phule pune university.

Beam (tumpuan)

mekanika kekuatan bahan

Shear and Bending Moment in Beams

This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.

STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

1. The document defines various terms related to strength of materials including stress, strain, elastic limit, Hooke's law, shear stress, Poisson's ratio, Young's modulus, modulus of rigidity, factor of safety, strain energy, and bulk modulus.
2. It also defines terms related to beams such as types of beams, shear force, bending moment, bending stress, pure bending, neutral axis, and section modulus.
3. Terms related to torsion, springs, and deflection of beams are also defined. These include torsion equation, polar modulus, torsional rigidity, types of springs, spring rate, and methods to determine slope and deflection in beams.

TRUSS ANALYSIS (TERM PAPER REPORT)

This document provides an introduction and overview of truss analysis. It defines a truss and describes the key assumptions made in truss analysis, including that loads act only at joints and member weights are negligible. It then describes the two main methods for truss analysis - the method of joints and method of sections. An example problem is worked through for each method to demonstrate how to determine the forces in each truss member.

A Review of Flight Dynamics and Numerical Analysis of an Unmanned Aerial Vehi...

A brief study of flight dynamics and different types of simulation and analysis are presented here.
Find case studies in my next PPT.- http://www.slideshare.net/HarshadaGurav/flight-dynamics-and-numerical-analysis-of-an-unmanned-aerial-vehicle-uav

Project report on beams

This document provides information about beams used in structural engineering. It defines beams, discusses their structural characteristics like moment of inertia and stresses, and describes different types of beams including simply supported, fixed, cantilever, and trussed beams. It also covers beam design, applications in bridges and cranes, potential failure modes from plastic hinges, buckling or material failure, and methods to prevent failures like lateral restraints.

Design and Analysis of Pre Stressed I Girders by Midas Civil Software

Today the construction of bridges has gained worldwide importance. Bridges are an important feature of all road networks and the use of pre stressed bridges is increasingly popular in the construction of bridges due to their better stability, service friendliness, economy and durability, beauty and appearance of the building. Reinforced concrete construction, steel or steel construction using composite construction. In the case of high spaces, reinforced concrete construction makes no money due to the large space. cross section is used more effectively than cross section of reinforced concrete. Prefabricated concrete is used for long bridges with a length of more than 10 meters. Typically, when bridges are calculated, the superstructure and substructure are analyzed separately. The supernatural structure is usually a grid made of large strips, a shortcut membrane and a desk slab. vertical grid Columns of large girders with anchors. The superstructure is tested according to IRC 62014 and according to IRC 182000 with unimaginable gravity loads and loads of moving vehicles. Reduced stress and deviation rates compared to a straightforward tender profile. Rishabh Singh | A. K. Jha | R. S. Parihar "Design and Analysis of Pre-Stressed I-Girders by Midas Civil Software" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-5 , August 2022, URL: https://www.ijtsrd.com/papers/ijtsrd50694.pdf Paper URL: https://www.ijtsrd.com/engineering/civil-engineering/50694/design-and-analysis-of-prestressed-igirders-by-midas-civil-software/rishabh-singh

Simple pulley & pulley block

This is a special study on simple pulley and pulley block and their Practical Applications.
I,from KUET , Khulna , Bangladesh

Beam ,Loads,Supports , trusses

The document discusses different types of structural elements used in building construction including beams, loads, supports, columns, and trusses. It describes several types of beams such as simply supported beams, continuous beams, overhanging beams, cantilever beams, and fixed beams. It also discusses different types of loads, supports, and how columns and trusses function structurally.

Engineering Mechanics

Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics

Curved Beams

This document discusses curved beams and unsymmetrical bending. It begins by introducing the Winkler-Bach theory for analyzing the bending of initially curved beams where bending occurs in the plane of curvature and the cross section is symmetrical about this plane. The theory obtains the stress-moment-deflection relationship assuming plane sections remain plane after bending, called the Winkler-Bach formula. It then examines bending of an infinitesimal portion of a curved beam, identifying the neutral axis and neutral surface where stress is zero. The linearized strain equation is presented and solved to derive the Winkler-Bach theory. Unsymmetrical bending is then briefly mentioned where loads can be applied in or out of the plane of symmetry for cross-

Ce 382 l5 truss 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.

Simpale stress and simple strain

This document contains lecture notes on mechanics of solids from the Department of Mechanical Engineering at Indus Institute of Technology & Engineering. It defines key concepts such as load, stress, strain, tensile stress and strain, compressive stress and strain, Young's modulus, shear stress and strain, shear modulus, stress-strain diagrams, working stress, and factor of safety. It also discusses thermal stresses, linear and lateral strain, Poisson's ratio, volumetric strain, bulk modulus, composite bars, bars with varying cross-sections, and stress concentration. The document provides examples to illustrate how to calculate stresses, strains, moduli, and other mechanical properties for different loading conditions.

6161103 6.4 the method of sections

The method of sections involves cutting imaginary sections through structural members to isolate forces. Equilibrium equations are applied to the cut section to determine member forces. For a truss example, a section was drawn through three unknown members. The free body diagram of the cut section was drawn and the equations of equilibrium were used to determine the forces in each member as 800 N in tension, 800 N in compression, and 500 N in tension.

Chapter 5 failure theories final

The document summarizes different theories for predicting failure under static loading conditions. It discusses:
1) Failure theories for ductile materials including maximum shear stress, distortion energy, and ductile Coulomb-Mohr theories, which are based on yield.
2) Failure theories for brittle materials including maximum normal stress, brittle Coulomb-Mohr, and modified Mohr theories, which do not exhibit an identifiable yield strength.
3) Details of the maximum shear stress theory and distortion energy (Von Mises) theory for ductile materials. The distortion energy theory predicts failure when the distortion strain energy equals the energy at yield in tension.

Truss & its analysis

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.

Cantilever Beam

Cantilever Beam

Design methods for torsional buckling of steel structures

Design methods for torsional buckling of steel structures

CENTROID AND CENTRE OF GRAVITY SPP.pptx

CENTROID AND CENTRE OF GRAVITY SPP.pptx

Trusses - engineeing mechanics

Trusses - engineeing mechanics

Beam (tumpuan)

Beam (tumpuan)

Shear and Bending Moment in Beams

Shear and Bending Moment in Beams

STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

STRENGTH OF MATERIALS 2 MARKS (CE6306/CE8395)

TRUSS ANALYSIS (TERM PAPER REPORT)

TRUSS ANALYSIS (TERM PAPER REPORT)

A Review of Flight Dynamics and Numerical Analysis of an Unmanned Aerial Vehi...

A Review of Flight Dynamics and Numerical Analysis of an Unmanned Aerial Vehi...

Project report on beams

Project report on beams

Design and Analysis of Pre Stressed I Girders by Midas Civil Software

Design and Analysis of Pre Stressed I Girders by Midas Civil Software

Simple pulley & pulley block

Simple pulley & pulley block

Beam ,Loads,Supports , trusses

Beam ,Loads,Supports , trusses

Engineering Mechanics

Engineering Mechanics

Curved Beams

Curved Beams

Ce 382 l5 truss structures

Ce 382 l5 truss structures

Simpale stress and simple strain

Simpale stress and simple strain

6161103 6.4 the method of sections

6161103 6.4 the method of sections

Chapter 5 failure theories final

Chapter 5 failure theories final

Truss & its analysis

Truss & its analysis

M2l10

1. The document discusses analyzing statically indeterminate structures like trusses using the force method.
2. It provides objectives, introduces how to determine a truss's degree of static indeterminacy, and explains how to select redundant reactions and forces.
3. Two examples are presented to demonstrate calculating member forces for indeterminate trusses using compatibility equations that equate displacements due to loads and redundant forces.

IL of reaction for determinate structure (08.01.03.106)

1) An influence line shows the variation of internal forces, reactions, or displacements at a point in a structure as a unit load moves across the structure.
2) Influence lines for determinate structures are always piecewise linear. They are generated by releasing the structure at the point of interest and applying a unit displacement or rotation.
3) Influence lines are used to find the critical load positions that cause maximum shear, reaction, or bending moment values so that the structure can be designed accordingly.

[Ths]2012 deter-indeter

The document discusses structural analysis and defines key concepts. It defines structures and provides examples like buildings, bridges, tanks and chimneys. It also defines types of supports for structures like fixed, hinged and roller. Additionally, it discusses statically determinate and indeterminate structures, providing examples of frames, beams and trusses. Indeterminate structures are more complex to analyze but provide advantages like greater load distribution, reduced deflections, and ability to accommodate redundancy, temperature effects and support movements.

Cee 3111-150501215431-conversion-gate01

This document provides information about the Structural Analysis-I course CEE-311. It includes details about the course credit hours, instructor, syllabus topics including truss analysis, influence lines and moving loads. It discusses the evaluation process including class performance, final exam and total weightage. It lists references books. It also defines what a structure is and provides examples. It defines structural analysis as a detailed evaluation to ensure deformations are below allowable limits and structural failure will not occur. It discusses common structural forms like beams, columns, frames, trusses etc. It explains the concepts of stability, determinacy, degree of indeterminacy and conditions for stable, unstable and geometrically unstable structures.

Solving statically determinate structures

This document discusses statically determinate and indeterminate structures. A statically determinate structure can be analyzed using equilibrium equations alone, while an indeterminate structure has more unknowns than equations. A structure is determinate if the number of reactions r equals 3 times the number of parts n, and indeterminate if r is greater than 3n. Examples are given of determinate and indeterminate structures. Indeterminate structures can be made determinate by removing redundant supports or adding hinges. The advantages of indeterminate structures are that they allow for lighter, more rigid designs with increased safety through redundancy.

SA-1 PPT OF CHP 1 (FUNDAMENTALS)

The document provides information about statically determinate and indeterminate structures. It begins with defining a determinate structure as one where the reactions and internal forces can be found using equilibrium equations alone. Simply supported beams are given as an example. An indeterminate structure is then defined as one where the equations of equilibrium are not sufficient to determine all forces. The document further discusses degrees of static indeterminacy and provides examples of determinate and indeterminate structures.

Dissertation report

This document presents the layout and introduction for a dissertation report on analyzing multi-storey partially braced frames subjected to seismic and gravity loads using V-braces. The layout includes sections on introduction, literature review, structural analysis methods, earthquake analysis methods, theoretical formulation, results and discussion, conclusion, and references. The introduction discusses the importance of tall structures and braced frames, noting advantages of braced frames include increased strength, stiffness, and reduced member sizes.

Projectile Motion

The document discusses projectile motion and circular motion. It defines key terms related to projectile motion such as trajectory, angle of projection, horizontal range, time of flight, and velocity of projection. It then derives equations for the trajectory, time of flight, horizontal range, maximum height, and velocity at impact of a projectile. Examples and problems are provided to demonstrate the application of these equations.

Chapter 7

This document discusses different types of beams and beam loadings. It defines beams as members that support loads perpendicular to their longitudinal axis. It describes simply supported beams, cantilever beams, overhanging beams, propped cantilevers, continuous beams, and beams with one end hinged and the other on rollers. The document also discusses concentrated loads, uniformly distributed loads, uniformly varying loads, general loadings, and external moments on beams. It provides examples of how to represent these loads for structural analysis.

ABC Of Project Management

This document provides an overview of project management. It discusses that projects are needed to generate profits for businesses, as profits come from operations which give birth to projects. However, only 34% of projects succeed currently. The document then outlines the basic project life cycle of initiation, planning, execution, controlling, and closing phases. It provides some ABCs of project management, emphasizing always properly defining the project, ensuring stakeholder identification, being aware of constraints and knowledge areas, and cultivating good project management habits and processes within an organization to improve success rates. The overall message is that projects can only succeed by being properly managed to meet defined objectives and baselines.

Equilibrium

This document discusses the topic of equilibrium of rigid bodies. It covers:
- Analytical and graphical conditions for equilibrium of co-planar forces.
- Different types of beam supports like simple, pinned, roller, and fixed supports.
- Free body diagrams and their application in analyzing equilibrium and determining reactions.
- Lami's theorem which states that for three forces in equilibrium, each force is proportional to the sine of the angle between the other two forces.
- Examples of problems involving cylinders, pulleys, beams, and friction on inclined planes.

Chapter no. 6 linear mo

This document discusses linear motion and its related concepts. It defines kinematics as the study of motion without consideration of forces, and kinetics as the study of motion with consideration of forces. It then discusses various types of linear motion including rectilinear motion, motion under gravity, and motion under variable acceleration. Key concepts defined include displacement, velocity, acceleration, uniform motion, and graphical representation of motion using displacement-time and velocity-time curves. Equations of motion are provided for rectilinear motion and motion under gravity with uniform acceleration.

Work power energy

1) This document discusses work, power, and energy. It defines work as the product of force and displacement, and defines the units of work as newton-meters (Nm) or joules (J).
2) Power is defined as the rate of doing work, or the ratio of work to time. The units of power are watts (W).
3) Energy exists in various forms including mechanical, thermal, chemical, light, sound, nuclear, and electrical. Mechanical energy includes potential energy, which depends on position or height, and kinetic energy, which depends on motion or velocity.
4) The work-energy principle states that the work done on an object equals its change in

2. linear kinematics i

1. Linear kinematics describes motion using position, velocity, and acceleration without regard to forces. It includes linear (straight line) and curvilinear (bent line) motion.
2. Angular kinematics describes rotational motion like elbow flexion or spinning.
3. General motion combines translation and rotation, describing most human and sports motions.
4. Key descriptors include position, distance/displacement, speed/velocity, and acceleration. Displacement is the straight-line distance between start and end points while distance is the total path length. Velocity describes speed with direction and acceleration is the rate of change of velocity.

Struc lec. no. 1

The document summarizes key concepts in the theory of structures including:
- Types of loads, reactions, and supports
- Statically determinate beams, frames, arches, and trusses
- Relationship between loads, shear forces, and bending moments
- Concepts of stability, determinacy, and methods of analysis for solving equilibrium and conditional equations
Examples are provided to demonstrate solving for reactions, internal forces, and conditional equations for various statically determinate structures. Factors affecting stability and determinacy are also discussed.

Centre of Gravity

1) The document discusses concepts related to centroid and moment of inertia including: the centroid is the point where the total area of a plane figure is assumed to be concentrated; formulas are provided for finding the centroid of basic shapes; the difference between centroid and center of gravity is explained; properties and methods for finding the centroid are described such as using moments.
2) Formulas are given for moment of inertia including how it is calculated about different axes and the parallel axis theorem.
3) Example problems are provided to demonstrate calculating the centroid and moment of inertia for various shapes.

Solving Statically Indeterminate Structure: Stiffness Method 10.01.03.080

This document discusses stiffness method for analyzing indeterminate structures. It defines stiffness method as the end moment required to produce a unit rotation at one end of a member while fixing the other end. It also defines degree of freedom and degree of kinematic indeterminacy. The steps of stiffness method are outlined, which include determining degree of kinematic indeterminacy, applying restraints, calculating member forces, applying displacements one at a time to write equilibrium equations in matrix form, and solving the equations to obtain displacements and member forces. Stiffness method can be used to analyze beams, frames, and trusses and is suitable for automation in computer programs.

Water Management

This document provides information about water management topics including sources of water, dams, canals, and irrigation methods. It discusses surface and underground water sources like ponds, lakes, rivers, wells, and tube wells. It describes different types of dams such as earth dams, rock-fill dams, gravity dams, and arch dams. Canals are described as the trenches that distribute water from reservoirs for irrigation. Various irrigation methods are outlined including flow irrigation, flood irrigation, storage irrigation, drip irrigation, and spray irrigation. Rainwater harvesting is introduced as a way to conserve water by collecting and filtering rainwater runoff and roof runoff to recharge underground water sources.

Lahaja za kiswahili kwa ujumla

Lahaja za Kiswahili zimekuwa zikichanganya watumiaji wengi na watu wengi wanaojifunza lugha ya Kiswahili, hivyo matini hii imekusudia kuondoa mkanganyiko huo.

Structural sol-week02

Structural sol-week02

M2l10

M2l10

IL of reaction for determinate structure (08.01.03.106)

IL of reaction for determinate structure (08.01.03.106)

[Ths]2012 deter-indeter

[Ths]2012 deter-indeter

Cee 3111-150501215431-conversion-gate01

Cee 3111-150501215431-conversion-gate01

Solving statically determinate structures

Solving statically determinate structures

SA-1 PPT OF CHP 1 (FUNDAMENTALS)

SA-1 PPT OF CHP 1 (FUNDAMENTALS)

Dissertation report

Dissertation report

Projectile Motion

Projectile Motion

Chapter 7

Chapter 7

ABC Of Project Management

ABC Of Project Management

Equilibrium

Equilibrium

Chapter no. 6 linear mo

Chapter no. 6 linear mo

Work power energy

Work power energy

2. linear kinematics i

2. linear kinematics i

Struc lec. no. 1

Struc lec. no. 1

Centre of Gravity

Centre of Gravity

Solving Statically Indeterminate Structure: Stiffness Method 10.01.03.080

Solving Statically Indeterminate Structure: Stiffness Method 10.01.03.080

Water Management

Water Management

Lahaja za kiswahili kwa ujumla

Lahaja za kiswahili kwa ujumla

Beam

This document defines beams and support reactions. It discusses statically determinate beams and explains that support reactions can be determined using equilibrium conditions alone for these beams. The document outlines different types of beam supports including simple, pinned, roller, and fixed supports. It also defines types of beams such as simply supported, cantilever, overhang, and continuous beams. Finally, it discusses determining support reactions for statically determinate beams using equilibrium conditions and introduces the concept of virtual work.

module 3 (Mechanics)

The document provides information about mechanics of solids-I, including:
1) It describes different types of supports like simple supports, roller supports, pin-joint supports, and fixed supports. It also describes different types of loads like concentrated loads, uniformly distributed loads, and uniformly varying loads.
2) It discusses shear force as the unbalanced vertical force on one side of a beam section, and bending moment as the sum of moments about a section.
3) It explains the relationship between loading (w), shear force (F), and bending moment (M) for an element of a beam. The rate of change of shear force is equal to the loading intensity, and the rate of change of bending

Module-4 Notes.pdf

1. Shear force and bending moment diagrams are analytical tools used to determine the shear force and bending moment values at different points along a beam under loading. These diagrams help with structural design and analysis.
2. The document discusses different types of beams, loads, and support conditions. It provides examples of calculating and drawing shear force and bending moment diagrams for beams with various loading scenarios, including cantilever beams with point loads, simply supported beams with point loads, and overhanging beams with uniform loads.
3. Key steps in drawing the diagrams are outlined, such as using consistent scaling, labeling principal values, and showing sign conventions clearly. The variation in shear force and bending moment is also summarized for different load types

2. Modifed Shear Force and Bending Moment Diagrams.pptx

History of group technology, role of G.T in CAD/CAM integration, part families,

Structural analysis and design Basics

This document discusses various topics related to structural analysis and design including:
1. Structural mechanics enables determining forces on members based on loads on the whole structure. Stresses and deformations can then be obtained.
2. Structures can be categorized based on function, form, analysis perspective, and type of loads. Different types of loads include concentrated, distributed, uniform, and varying loads.
3. Key concepts in structural analysis are shear force, bending moment, and deflected shapes. Shear force and bending moment are calculated at cross sections and deflected shapes show beam deformation under loading.

SFD-BMD.ppt 2 for lecture mechanical engg

lecture mechanical engg

Beams Introduction

This document discusses different types of beams and how to calculate support reactions for various beam configurations. It defines beams as structural members subjected to lateral loads perpendicular to the axis. The main types of beams covered are simply supported, cantilever, overhanging, continuous, and propped cantilever beams. It provides examples of calculating the support reactions of simply supported, cantilever, and continuous beams using free body diagrams and the equations of static equilibrium. The document emphasizes that finding support reactions is the first step in beam analysis and allows determining the internal shear forces and bending moments.

chapter 2 Flexural and Shearing Stresses .pptx

Flexural
and
Shearing Stresses

Engineering Mechanics First Year

This document discusses concepts related to static equilibrium of rigid bodies, including:
- Conditions for static equilibrium are that the net force and net torque on the body are both zero
- Free body diagrams show all forces acting on a body in isolation from its surroundings
- Types of supports include hinges, rollers, fixed supports, and smooth surfaces
- Equilibrium of two-force and three-force bodies follow specific rules
- Lami's theorem relates the magnitudes of three concurrent forces in equilibrium
- An equilibrant force can balance an unbalanced system and bring it into equilibrium

Coplanar forces equilibrium

This document discusses concepts related to static equilibrium of rigid bodies, including:
- Conditions for static equilibrium are that the net force and net moment are both zero
- Free body diagrams show all forces acting on a body in isolation
- Types of supports (fixed, hinge, roller) and the reactions they provide are described
- Concepts like two-force and three-force members, Lami's theorem, and finding equilibrant forces to balance unbalanced systems are explained
- Several example problems are provided to illustrate applying concepts to determine reactions and tensions in static systems

3. coplanar forces equilibrium

Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics

Forces acting on the beam with shear force & bending moment

The document discusses different types of beams and how to analyze the shear forces and bending moments in beams. It defines beams as structural members subjected to lateral loads and describes various types of beams based on their support conditions, including simply supported beams, cantilever beams, and continuous beams. It also covers types of loads beams may experience, such as concentrated loads, distributed loads, and couples. The document then explains how to determine the shear forces and bending moments in beams by using cut sections and equilibrium equations. It provides examples of analyzing shear forces and bending moments in beams with different load conditions.

Chapter 5: Axial Force, Shear, and Bending Moment

1. A beam can experience three internal forces at a section - axial force, shear, and bending moment. Even for planar beams, all three forces may develop.
2. There are three types of supports - roller/link, pin, and fixed. Roller/link supports resist one force, pin supports resist two forces, and fixed supports resist two forces and a moment.
3. Beams can experience different load types - concentrated, uniform distributed, and varying distributed loads. Methods are presented to calculate the shear, axial, and bending effects of these loads on beams.

Unit ii equilibrium of rigid bodies

1. A free body diagram shows the forces and moments acting on an isolated body. A force couple system can replace a single force with an equal force and couple at another point.
2. A couple is a pair of two equal and unlike parallel forces that tends to rotate a body. Varignon's theorem states the sum of the moments of all forces about a point equals the moment of their resultant about that point.
3. Supports include roller, hinged, and fixed. Equations of equilibrium in 2D are the sum of horizontal forces equals zero, the sum of vertical forces equals zero, and the sum of moments equals zero.

Bendingmomentsandshearingforcesinbeams2 100114165451-phpapp01

This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.

B Ending Moments And Shearing Forces In Beams2This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.

B Ending Moments And Shearing Forces In Beams2This document discusses bending moments and shear forces in beams. It defines different types of beams such as simply supported beams, cantilever beams, and beams with overhangs. It also defines types of loads like concentrated loads, distributed loads, and couples. It explains how to calculate the shear force and bending moment at any cross-section of a beam and discusses relationships between loads, shear forces and bending moments. It provides examples of drawing shear force and bending moment diagrams. Finally, it discusses bending stresses in beams and bending of beams made of two materials.

CVE 211- Shear force and bending moments in beams intro..pdf

Shearforce and bending moment . Theory of structures . CVE 211

chapter 3 Ext..pdf

This document discusses transverse loading on beams. It defines different types of beam supports including simple, fixed, overhanging, continuous, and cantilever. It also describes different types of loads acting on beams such as concentrated, uniform, uniformly varying, and moment loads. It provides conventions for determining the sign of shear forces and bending moments on beams. Examples are given to demonstrate calculating shear forces and bending moments at different points on beams subjected to various load configurations.

Beam

Beam

module 3 (Mechanics)

module 3 (Mechanics)

Module-4 Notes.pdf

Module-4 Notes.pdf

2. Modifed Shear Force and Bending Moment Diagrams.pptx

2. Modifed Shear Force and Bending Moment Diagrams.pptx

Structural analysis and design Basics

Structural analysis and design Basics

SFD-BMD.ppt 2 for lecture mechanical engg

SFD-BMD.ppt 2 for lecture mechanical engg

Beams Introduction

Beams Introduction

chapter 2 Flexural and Shearing Stresses .pptx

chapter 2 Flexural and Shearing Stresses .pptx

Engineering Mechanics First Year

Engineering Mechanics First Year

Coplanar forces equilibrium

Coplanar forces equilibrium

3. coplanar forces equilibrium

3. coplanar forces equilibrium

Forces 7

Forces 7

Forces acting on the beam with shear force & bending moment

Forces acting on the beam with shear force & bending moment

Chapter 5: Axial Force, Shear, and Bending Moment

Chapter 5: Axial Force, Shear, and Bending Moment

Unit ii equilibrium of rigid bodies

Unit ii equilibrium of rigid bodies

Bendingmomentsandshearingforcesinbeams2 100114165451-phpapp01

Bendingmomentsandshearingforcesinbeams2 100114165451-phpapp01

B Ending Moments And Shearing Forces In Beams2

B Ending Moments And Shearing Forces In Beams2

B Ending Moments And Shearing Forces In Beams2

B Ending Moments And Shearing Forces In Beams2

CVE 211- Shear force and bending moments in beams intro..pdf

CVE 211- Shear force and bending moments in beams intro..pdf

chapter 3 Ext..pdf

chapter 3 Ext..pdf

Transportation engineering

This document provides an overview of transportation engineering and related topics through a presentation. It begins with an introduction to various modes of transportation including roads, bridges, railways, airports, docks and harbors. It then provides a question bank with sample questions on these topics from previous years. The document concludes by providing detailed answers to some of the sample questions, covering areas like classifications of roads and transportation, structures of roads, and short notes on specific road types.

Chapter wise question papers_bce

This document contains a question bank for the Basic Civil Engineering subject divided into 9 units. Each unit contains 6 questions related to topics within that unit. The questions range from 3-10 marks and cover topics such as sub-branches of civil engineering, surveying, remote sensing, dams, roads, building construction principles, materials, and steel structures. This question bank can be used to prepare for exams on basic civil engineering concepts and their applications.

Design of staircase_practical_example

The document provides design details for staircases on three floors of a building, including dimensions, load calculations, and reinforcement details. Load calculations are performed to determine bending moments and shear forces. Reinforcement area, bar diameter, and spacing are calculated for the waist slabs of each staircase to resist the determined bending moment and satisfy code requirements for minimum steel and shear capacity.

Presentation "Use of coupler Splices for Reinforcement"

This document presents a summary of a presentation on the use of coupler splices for reinforcement. The presentation includes an introduction to coupler splices, a literature review on the topic, details on the experimental procedure used to test coupler splices, a cost analysis comparing coupler splices to lap splices, and conclusions. The experimental results show that coupler splices performed better than lap splices and welded splices in tensile loading tests. A cost analysis also determined that coupler splices provide significant cost savings over lap splices by reducing the amount of reinforcement required. The conclusion is that coupler splices are an effective and economic replacement for lap splices in reinforcement.

Guidelines_for_building_design

This document provides guidelines for the design of reinforced concrete structures in buildings according to the limit state method. It outlines the general process for building design which includes studying architectural drawings and field data, preparing reinforced concrete layouts, analyzing structural frames, and designing columns, beams, slabs, and footings. Computer programs like STAAD and in-house software are used to aid in analysis and design. Designers are advised to be familiar with relevant Indian code provisions and follow the guidelines to independently complete reinforced concrete designs for buildings.

Strength of materials_I

This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.

Presentation_on_Cellwise_Braced_frames

This presentation discusses the seismic response of cellwise concentrically braced frames. It introduces cellwise braced frames as a structural system that provides lateral stability through bracing elements arranged in cells within each bay. The document describes a study that analyzed 5 bay, 12 story reinforced concrete frames with different bracing configurations, including single-cell, two-cell, and three-cell arrangements. The study found that single-cell A-braced frames provided the highest material cost savings of up to 9.59% compared to bare frames. Two-cell and three-cell configurations further improved cost savings but required additional bracing. Overall, the study shows that optimally arranged cellwise braced frames produce a stiff, strong and econom

Study of MORT_&_H

The document provides an overview of the Ministry of Road Transport and Highways (MoRTH) in India. It discusses the ministry's role in formulating policies and regulations related to road transport. It outlines the ministry's history and organizational structure. It also summarizes some of the key specifications issued by MoRTH related to road and bridge construction, including specifications for earthworks, pavement layers, drainage, and other aspects of road projects. The document thus provides a high-level introduction to MoRTH and the specifications it issues for road development and transport in India.

List of various_IRCs_&_sps

The Indian Road Congress (IRC) was established in 1934 on the recommendations of the Jayakar Committee to oversee road development in India. It is the apex body for highway engineers and professionals. IRC has over 16,700 members from both public and private sector organizations involved in roads. It aims to promote standard specifications and best practices for road and bridge construction through various technical committees. It has published over 100 codes of practice and guidelines and oversees research activities through its Highway Research Board.

Analysis of multi storey building frames subjected to gravity and seismic loa...

This document summarizes a study on the seismic response of reinforced concrete frames with varying numbers of bays and storeys. Three frame configurations - 3 bay, 5 bay, and 7 bay with 9 stories each - were modeled and analyzed under gravity and seismic loads. Both prismatic frames and frames with non-prismatic elements like stepped beams and haunches at beam-column joints were considered. The effects of variables like haunch size, beam inertia, and live load patterns on internal forces and storey drift were examined. Key results showed that non-prismatic elements can reduce bending moments and axial forces compared to conventional prismatic frames.

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

This document discusses the seismic response of reinforced concrete concentrically braced frames. It analyzes numerically various bracing patterns for a 5-bay 12-story building, including bare frames, fully braced frames, and partially braced frames with bracing applied at the bay-level or level-wise. Optimum bracing patterns are identified that reduce internal forces in columns and provide economic savings compared to bare frames or fully braced frames. Graphs show variations in axial, shear and bending forces for different bracing patterns, identifying patterns that fall within acceptable ranges. Savings of up to 7.87% are achieved with the optimum bracing patterns.

Use of mechanical_splices_for_reinforcing_steel

The document discusses the use of mechanical splices (couplers) as an alternative to traditional lap splicing for reinforcing steel. It provides details on different types of couplers, including threaded couplers. Experimental testing showed that couplers achieved similar or higher yield and ultimate stresses as compared to normal and welded reinforcing bars. While ductility was slightly reduced, factors like epoxy injection and staggered splicing can improve ductility. A cost analysis found that couplers provide significant cost savings over lap splices due to reduced steel requirements. Therefore, the study concludes that mechanical splices are an effective and economic replacement for lap splices.

Guide lines bridge_design

This document provides guidelines for bridge design in the Public Works Department. It introduces the contents and chapters, which cover aspects of bridge design, components, innovative structures, preparation of bridge projects, and other topics. The guidelines are intended to help engineers understand the department's practices for bridge design. The second edition was revised with new chapters and information to aid both new and experienced engineers.

Seismic response of cellwise braced reinforced concrete frames

The document analyzes the seismic response of reinforced concrete frames with different patterns of reinforced concrete bracing. Numerical models of 5-bay, 12-story reinforced concrete frames were analyzed with different bracing configurations including bare frames, fully braced, partially braced, outrigger braced, and cellwise braced. The responses, including internal forces, displacements, and member sizes, were compared for each configuration. Optimal baywise and levelwise locations for bracing were identified based on producing smaller internal forces within acceptable ranges. Cellwise bracing was explored as a configuration that combines advantages of other patterns while allowing for clear openings.

Chaper wise qpapers_bce

1. The document contains a question bank for the Basic Civil Engineering section covering topics like introduction to civil engineering, surveying, linear measurements, bearing, and leveling.
2. It includes 36 questions on surveying topics like chain surveying, compass surveying, and leveling with multiple parts and variations. Calculations and sketches are required to solve some questions.
3. The leveling questions provide staff readings and require entering data in a standard leveling table, calculating reduced levels using different methods, and applying arithmetic checks.

Basic Loads Cases

The document defines various types of loads that should be considered in structural analysis, including dead loads, live loads, wind loads, and earthquake loads. It provides details on how to apply these loads in both positive and negative directions of the X and Z axes. It also lists load combinations that should be analyzed according to Indian standards, including combinations for limit states of collapse and serviceability. The load combinations include factors for dead, live, wind, and earthquake loads.

Earthquake analysis by Response Spectrum Method

This document provides steps for performing an earthquake analysis using the response spectrum method in STAAD v8i. Key steps include:
1. Generating primary load cases for the X and Z directions using the specified code spectrum
2. Modeling dead and live loads
3. Obtaining support reactions for a load combination of dead + 0.25 live loads
4. Exporting the support reaction values to Excel tables
5. Importing the Excel tables back into STAAD as joint loads to apply the earthquake loads
6. Analyzing the structure with fixed supports instead of pin supports
The overall process applies earthquake loads to the structure using the response spectrum method and obtains the response of the structure under seismic loading

Earthquake analysis by psudeo static method

This document provides instructions for performing an earthquake analysis on a structure using the pseudo-static method in STAAD v8i. The steps include:
1. Defining the seismic parameters by adding a seismic definition and inputting values for the zone, response factor, importance factor, etc. based on IS 1893:2002.
2. Creating earthquake load cases in the X and Z directions and combining them with dead and live loads.
3. Assigning pin supports and obtaining support reactions for analysis.
4. Importing the support reaction values into Excel to create weight tables that are then input back into STAAD.
5. Removing the pin supports and assigning fixed supports at the foundation before running the full analysis

Basic Civil Engineering MCQ

The document contains a 58 question multiple choice test on basic civil engineering. The test covers topics such as surveying, building construction materials and techniques, structures, and other basic civil engineering concepts. The questions assess knowledge of concepts like types of surveying, building components, properties of materials like concrete and masonry, earthquake resistance techniques, and more.

PROBLEMS ON BEARINGS

1. The document provides examples of problems involving bearings observed in closed traverse surveys. It discusses calculating included angles, checking for angular errors, and correcting bearings based on lines assumed to be free from local attraction effects.
2. The first example shows calculations for a traverse with station positions, observed fore and back bearings, differences between bearings, included angles, and corrected bearings and stations free from attraction.
3. Several multi-part problems are presented involving calculating included angles from observed bearings, checking for errors, correcting bearings, and identifying stations free from local attraction for closed traverses. Step-by-step working is demonstrated for one example.

Transportation engineering

Transportation engineering

Chapter wise question papers_bce

Chapter wise question papers_bce

Design of staircase_practical_example

Design of staircase_practical_example

Presentation "Use of coupler Splices for Reinforcement"

Presentation "Use of coupler Splices for Reinforcement"

Guidelines_for_building_design

Guidelines_for_building_design

Strength of materials_I

Strength of materials_I

Presentation_on_Cellwise_Braced_frames

Presentation_on_Cellwise_Braced_frames

Study of MORT_&_H

Study of MORT_&_H

List of various_IRCs_&_sps

List of various_IRCs_&_sps

Analysis of multi storey building frames subjected to gravity and seismic loa...

Analysis of multi storey building frames subjected to gravity and seismic loa...

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Use of mechanical_splices_for_reinforcing_steel

Use of mechanical_splices_for_reinforcing_steel

Guide lines bridge_design

Guide lines bridge_design

Seismic response of cellwise braced reinforced concrete frames

Seismic response of cellwise braced reinforced concrete frames

Chaper wise qpapers_bce

Chaper wise qpapers_bce

Basic Loads Cases

Basic Loads Cases

Earthquake analysis by Response Spectrum Method

Earthquake analysis by Response Spectrum Method

Earthquake analysis by psudeo static method

Earthquake analysis by psudeo static method

Basic Civil Engineering MCQ

Basic Civil Engineering MCQ

PROBLEMS ON BEARINGS

PROBLEMS ON BEARINGS

FULL STACK PROGRAMMING - Both Front End and Back End

This ppt gives details about Full Stack Programming and its basics.

3rd International Conference on Artificial Intelligence Advances (AIAD 2024)

3rd International Conference on Artificial Intelligence Advances (AIAD 2024) will act as a major forum for the presentation of innovative ideas, approaches, developments, and research projects in the area advanced Artificial Intelligence. It will also serve to facilitate the exchange of information between researchers and industry professionals to discuss the latest issues and advancement in the research area. Core areas of AI and advanced multi-disciplinary and its applications will be covered during the conferences.

Impartiality as per ISO /IEC 17025:2017 Standard

This document provides basic guidelines for imparitallity requirement of ISO 17025. It defines in detial how it is met and wiudhwdih jdhsjdhwudjwkdbjwkdddddddddddkkkkkkkkkkkkkkkkkkkkkkkwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwioiiiiiiiiiiiii uwwwwwwwwwwwwwwwwhe wiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq gbbbbbbbbbbbbb owdjjjjjjjjjjjjjjjjjjjj widhi owqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq uwdhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhwqiiiiiiiiiiiiiiiiiiiiiiiiiiiiw0pooooojjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjj whhhhhhhhhhh wheeeeeeee wihieiiiiii wihe
e qqqqqqqqqqeuwiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiqw dddddddddd cccccccccccccccv s w c r
cdf cb bicbsad ishd d qwkbdwiur e wetwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww w
dddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffw
uuuuhhhhhhhhhhhhhhhhhhhhhhhhe qiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii iqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ccccccccccccccccccccccccccccccccccc bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbu uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuum
m
m mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm m i
g i dijsd sjdnsjd ndjajsdnnsa adjdnawddddddddddddd uw

Introduction to Artificial Intelligence.

Artificial introduction and applications are described

Call Girls Chennai +91-8824825030 Vip Call Girls Chennai

Call Girls Chennai +91-8824825030 Vip Call Girls Chennai

Digital Twins Computer Networking Paper Presentation.pptx

A Digital Twin in computer networking is a virtual representation of a physical network, used to simulate, analyze, and optimize network performance and reliability. It leverages real-time data to enhance network management, predict issues, and improve decision-making processes.

Sri Guru Hargobind Ji - Bandi Chor Guru.pdf

Sri Guru Hargobind Ji (19 June 1595 - 3 March 1644) is revered as the Sixth Nanak.
• On 25 May 1606 Guru Arjan nominated his son Sri Hargobind Ji as his successor. Shortly
afterwards, Guru Arjan was arrested, tortured and killed by order of the Mogul Emperor
Jahangir.
• Guru Hargobind's succession ceremony took place on 24 June 1606. He was barely
eleven years old when he became 6th Guru.
• As ordered by Guru Arjan Dev Ji, he put on two swords, one indicated his spiritual
authority (PIRI) and the other, his temporal authority (MIRI). He thus for the first time
initiated military tradition in the Sikh faith to resist religious persecution, protect
people’s freedom and independence to practice religion by choice. He transformed
Sikhs to be Saints and Soldier.
• He had a long tenure as Guru, lasting 37 years, 9 months and 3 days

AN INTRODUCTION OF AI & SEARCHING TECHIQUES

Useful for engineering students

Call For Paper -3rd International Conference on Artificial Intelligence Advan...

* Registration is currently open *
Call for Research Papers!!!
Free – Extended Paper will be published as free of cost.
3rd International Conference on Artificial Intelligence Advances (AIAD 2024)
July 13 ~ 14, 2024, Virtual Conference
Webpage URL: https://aiad2024.org/index
Submission Deadline: June 22, 2024
Submission System URL:
https://aiad2024.org/submission/index.php
Contact Us:
Here's where you can reach us : aiad@aiad2024.org (or) aiadconference@yahoo.com
WikiCFP URL: http://wikicfp.com/cfp/servlet/event.showcfp?eventid=180509©ownerid=171656
#artificialintelligence #softcomputing #machinelearning #technology #datascience #python #deeplearning #tech #robotics #innovation #bigdata #coding #iot #computerscience #data #dataanalytics #engineering #robot #datascientist #software #automation #analytics #ml #pythonprogramming #programmer #digitaltransformation #developer #promptengineering #generativeai #genai #chatgpt #artificial #intelligence #datamining #networkscommunications #robotics #callforsubmission #submissionsopen #deadline #opencall #virtual #conference

Ericsson LTE Throughput Troubleshooting Techniques.ppt

Ericsson LTE Throughput Troubleshooting Techniques

FUNDAMENTALS OF MECHANICAL ENGINEERING.pdf

EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES
EMERSON EDUARDO RODRIGUES

Unit -II Spectroscopy - EC I B.Tech.pdf

Chemical engineering and electronics engineering and chemical development of the day of the almighty paw paw paw

comptia-security-sy0-701-exam-objectives-(5-0).pdf

Comptia security+

Determination of Equivalent Circuit parameters and performance characteristic...

Includes the testing of induction motor to draw the circle diagram of induction motor with step wise procedure and calculation for the same. Also explains the working and application of Induction generator

OOPS_Lab_Manual - programs using C++ programming language

This manual contains programs on object oriented programming concepts using C++ language.

Object Oriented Analysis and Design - OOAD

This ppt gives detailed description of Object Oriented Analysis and design.

Introduction to Computer Networks & OSI MODEL.ppt

Introduction to Computer Networks

Open Channel Flow: fluid flow with a free surface

Open Channel Flow: This topic focuses on fluid flow with a free surface, such as in rivers, canals, and drainage ditches. Key concepts include the classification of flow types (steady vs. unsteady, uniform vs. non-uniform), hydraulic radius, flow resistance, Manning's equation, critical flow conditions, and energy and momentum principles. It also covers flow measurement techniques, gradually varied flow analysis, and the design of open channels. Understanding these principles is vital for effective water resource management and engineering applications.

Blood finder application project report (1).pdf

Blood Finder is an emergency time app where a user can search for the blood banks as
well as the registered blood donors around Mumbai. This application also provide an
opportunity for the user of this application to become a registered donor for this user have
to enroll for the donor request from the application itself. If the admin wish to make user
a registered donor, with some of the formalities with the organization it can be done.
Specialization of this application is that the user will not have to register on sign-in for
searching the blood banks and blood donors it can be just done by installing the
application to the mobile.
The purpose of making this application is to save the user’s time for searching blood of
needed blood group during the time of the emergency.
This is an android application developed in Java and XML with the connectivity of
SQLite database. This application will provide most of basic functionality required for an
emergency time application. All the details of Blood banks and Blood donors are stored
in the database i.e. SQLite.
This application allowed the user to get all the information regarding blood banks and
blood donors such as Name, Number, Address, Blood Group, rather than searching it on
the different websites and wasting the precious time. This application is effective and
user friendly.

FULL STACK PROGRAMMING - Both Front End and Back End

FULL STACK PROGRAMMING - Both Front End and Back End

3rd International Conference on Artificial Intelligence Advances (AIAD 2024)

3rd International Conference on Artificial Intelligence Advances (AIAD 2024)

Impartiality as per ISO /IEC 17025:2017 Standard

Impartiality as per ISO /IEC 17025:2017 Standard

Introduction to Artificial Intelligence.

Introduction to Artificial Intelligence.

Call Girls Chennai +91-8824825030 Vip Call Girls Chennai

Call Girls Chennai +91-8824825030 Vip Call Girls Chennai

Digital Twins Computer Networking Paper Presentation.pptx

Digital Twins Computer Networking Paper Presentation.pptx

Sri Guru Hargobind Ji - Bandi Chor Guru.pdf

Sri Guru Hargobind Ji - Bandi Chor Guru.pdf

AN INTRODUCTION OF AI & SEARCHING TECHIQUES

AN INTRODUCTION OF AI & SEARCHING TECHIQUES

Call For Paper -3rd International Conference on Artificial Intelligence Advan...

Call For Paper -3rd International Conference on Artificial Intelligence Advan...

Ericsson LTE Throughput Troubleshooting Techniques.ppt

Ericsson LTE Throughput Troubleshooting Techniques.ppt

UNIT 4 LINEAR INTEGRATED CIRCUITS-DIGITAL ICS

UNIT 4 LINEAR INTEGRATED CIRCUITS-DIGITAL ICS

FUNDAMENTALS OF MECHANICAL ENGINEERING.pdf

FUNDAMENTALS OF MECHANICAL ENGINEERING.pdf

Unit -II Spectroscopy - EC I B.Tech.pdf

Unit -II Spectroscopy - EC I B.Tech.pdf

comptia-security-sy0-701-exam-objectives-(5-0).pdf

comptia-security-sy0-701-exam-objectives-(5-0).pdf

Determination of Equivalent Circuit parameters and performance characteristic...

Determination of Equivalent Circuit parameters and performance characteristic...

OOPS_Lab_Manual - programs using C++ programming language

OOPS_Lab_Manual - programs using C++ programming language

Object Oriented Analysis and Design - OOAD

Object Oriented Analysis and Design - OOAD

Introduction to Computer Networks & OSI MODEL.ppt

Introduction to Computer Networks & OSI MODEL.ppt

Open Channel Flow: fluid flow with a free surface

Open Channel Flow: fluid flow with a free surface

Blood finder application project report (1).pdf

Blood finder application project report (1).pdf

- 1. CHAPTER No. 3 BEAMS AND SUPPORT REACTIONS CONTENT OF THE TOPIC: - Definition of statically determinate beam o Types of beam supports o Types of Beams o Type of Loading - Procedure To Find The Support Reactions Of Statically Determinate Beam - Compound beam - Concept of virtual work Definition of Beam: A beam is horizontal or inclined member carrying transverse or inclined loads and supported at ends or anywhere. It is a structural member for the frame or structures of steel or concrete which has one dimension (length) considerably larger than the other two dimensions. If support reactions can be determined by using the conditions of equilibrium only, then the beam is known as statically determinate beam. If support reactions cannot be determined by using the conditions of equilibrium only, then the beam is known as statically indeterminate beam. Definition of span: Centre to centre distance between the two end supports is called span. Types of beam supports: 1) Simple support: It is a theoretical case in which the ends of the beam are simply supported or rested over the supports. The reactions are always vertical as shown in Fig.1 below Fig.1 Simple Support It opposes downward movement but allows rotation and horizontal displacement or movement. Chapter No. 3 Beam Page 1
- 2. 2) Pin or hinged Support: In such case, the ends of the beam are hinged or pinned to the support as shown in Fig.2 below. Fig.2 (A) Hinged Support Fig.2 (B) Hinged Support The reaction may be either vertical or inclined depending upon the type of loading. If the loads are vertical the reaction is vertical as shown in Fig. 2 (A) and when the applied loads are inclined the reaction is inclined as shown in Fig. 2 (B). The main advantage of hinged support is that the beam remains stable i.e. there is only rotational motion round the hinge but no translational motion of the beam i.e. hinged support opposes displacement of beam in any direction but allows rotation. 3) Roller Support: In such cases, the end of the beam is supported on roller as shown in Fig. 3 below. Fig. 3 Roller Support Fig. 4 Fixed Support The reaction is always perpendicular to the surface on which rollers rest or act as shown in Fig. 3. The main advantage of the roller support is that, the support can move easily in the direction of expansion or contraction of the beam due to change in temperature in different seasons. 4) Fixed Support: It is also called as Built-in-supports. It is rigid type of support. The end of the beam is rigidly fixed in the wall as shown in Fig. 4 below. It produces reactions Ra in any direction and a moment Ma as shown in Fig. 4 above. Types of Beams: The types of beam are depends upon the types of supports over which it will rest. Chapter No. 3 Beam Page 2
- 3. 1) Simply Supported Beam: A beam supported or rested freely on the supports at its both ends is known as simply supported beam. Such beam can support load in the direction normal to its axis. The support reactions are always vertical (as shown in the Fig. 5 Ra and Rb). Fig. 5 Simply Supported Beam 2) Cantilever Beam: One end of the cantilever beam is rigidly fixed in the wall as shown in Fig. 6 below. Such supports are known as fixed support (as explained in above). It is a type of rigid support. It produces reactions Ra in any direction and a moment Ma as shown in Fig. 6. Fig. 6 Cantilever Beam 3) Overhang Beam: The beam is supported on hinged support and roller support. The beam has overhang on one end i.e. to the right or left of the beam and on both sides as shown in Fig. 7 below. Fig. 7 (a) Overhang Beam (overhang on both sides) Chapter No. 3 Beam Page 3
- 4. Fig. 7 (b) Overhang Beam (to right) (c) Overhang Beam (to left) 4) Continuous Beam: Such beams are supported at more than two points as shown in Fig.8 below. It is also called as multi-span beam. Fig. 8 Continuous Beam Type of Loading: 1) Concentrated load or Point Load: A Concentrated load or Point Load is one which is considered to act at a point, as shown in Fig.9 below. Following Fig. 9 shows three concentrated forces F1, F2 and F3 acting on a simply supported beam. Fig. 9 Point Loads acting on the beam 2) Distributed loads: There are three types of distributed loads: a) Uniformly distributed Load b) Uniformly varying Load c) Non-Uniformly distributed Load Chapter No. 3 Beam Page 4
- 5. a) Uniformly distributed Load: If a load which is spread over beam in such a manner that rate of loading ‘w’ is uniform along the length (i.e. for each unit length the magnitude of load is uniform) as shown in Fig.10 below. Fig. 10 uniformly distributed Load acting on the beam Note: If ‘w’ N/m is the Uniformly distributed Load on beam AB as shown in Fig. 11 above then the total load say (W=w x l) is acting at the midpoint say c as shown in Fig. 11 below. Fig. 11 Conversion of U.D.L. into Point Load b) Uniformly varying Load A Uniformly varying Load is one which is spread over a beam in such a manner that rate of loading varies from point to point along the length of the beam as shown in Fig. 12 below. Fig.12 Uniformly varying Load acting on the Beam For such loading it is zero at one end i.e. end A and increases uniformly at other end i.e. end B. Chapter No. 3 Beam Page 5
- 6. Note: The equivalent Concentrated or point load for this case is the area of the triangle or average loading intensity multiplied by the length, which is acting at a distance of (2/3) l form A or (1/3) l from B of the support as shown in Fig. 13 below. Fig. 13 Conversion of U.V.L. into Point Load c) Non-Uniformly distributed Load If the load distributed on the beam is such that the load per unit length is not constant, then it is called as Non-Uniformly distributed Load. Different types of loading are shown in the Fig. 14 below Fig. 14 (a) Fig. 14 (b) Procedure To Find The Support Reactions Of Statically Determinate Beam Chapter No. 3 Beam Page 6
- 7. If support reactions can be determined by using the conditions of equilibrium only, then the beam is known as statically determinate beam. If support reactions cannot be determined by using the conditions of equilibrium only, then the beam is known as statically indeterminate beam. 1) Such problems are treated as the problem to be a co-planar, non-con-current equilibrium force system. Following equilibrium conditions are used ΣM = 0, ΣFy = 0, ΣFx = 0 2) When the beam is simply supported, the reactions at the supports are vertically upwards. 3) Taking summation of moments (either at A i.e. ΣMA or either at B i.e. ΣMB) of all given forces about any support, assuming the reaction at the other support as vertically upwards. Equating algebraic sum of these moments to zero i.e. ΣM = 0 and calculate unknown reaction RA or RB and then using equations ΣFy = 0 find the reactions of the other support. 4) When one of the reaction as pinned or hinged and other support is on roller, the reaction at the roller support is always perpendicular to the roller line. Find the reaction at the roller support by taking moment of all the forces about hinge support and equate it to zero. 5) Then using equations ΣFy = 0 and ΣFx = 0 find the reactions at the hinge support. 6) To find the reaction at hinge support in magnitude and direction, use the equation R = √ΣFy 2 + ΣFx2 And ΣFy ΣFx θ = tan -1 ( ) Concept of virtual work: 1) Consider a force (P) is acting on a body which get displaces through a distance (s) due to applied force. Then, Work done = Force X Displacement W = F.s Chapter No. 3 Beam Page 7
- 8. 2) But if the body is in equilibrium, under the action of a system of forces, then the work done is zero. 3) If we assume that the body, which is in equilibrium, undergoes a small imaginary displacement (virtual displacement) some work will be imagined to be done. Such imaginary work is called as virtual work. This concept is useful to find out the unknown forces in the structures. Principle of virtual work: “ If system of forces acting on a body (or a system of bodies) be in equilibrium and the system to be imagined to undergo a small displacement consistent with the geometrical conditions, then the algebraic sum of the virtual works done by all the system is zero”. i.e. mathematically, ΣW = 0 Types of virtual work: 1) Linear virtual work: If a force (F) causes a displacement (virtual displacement) in its direction of line of action, then its virtual work is given as, WV = F x δ Sign convention: Upward forces are considered as positive, while downward forces are considered as negative QUESIONS 1. What are the different types of beam support? Explain the reactions exerted by each type of support.(4 Mks) or 2. What are the different types of supports? Indicate with neat sketch of reactions offered by them. 3. Explain the concept of virtual work? (3 Mks) Chapter No. 3 Beam Page 8