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This document provides instructions for 4 problems to solve using the consistent deformation method. Problem 1 asks to determine reactions and draw the bending moment diagram for a propped cantilever beam under a load. Problem 2 repeats problem 1 considering different moments of inertia. Problem 3 asks to draw shear force and bending moment diagrams for a fixed beam. Problem 4 analyzes a beam with settled supports using given material properties and area moment of inertia.

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B spline surfeces

B-spline surfaces are constructed using a grid of control points and blending functions. The blending functions are polynomials defined over intervals in each parametric direction. This allows a B-spline surface to be defined by blending between control points. Properties include continuity and local influence of control points. A surface can be subdivided by inserting knots or raising the degree. Rational B-spline surfaces use homogeneous coordinates to represent common surfaces like planes and spheres. NURBS are the basis for CAD standards like IGES.

Surface representation

Bezier surfaces are parametric surfaces used in computer graphics and CAD/CAM. They are based on Bernstein polynomials and control points. A Bezier surface is defined by a grid of control points that determine the shape of the surface. Changing control points modifies the shape globally. B-spline surfaces allow for more local control and ensure continuity between patches. Coons patches interpolate between four boundary curves to generate a smooth surface. Sculptured surfaces are used for complex, free-form shapes and consist of blended parametric surface patches.

Hermit curves & beizer curves

This document discusses Hermite curves and Bezier curves. Hermite curves are defined by two endpoints and the tangent vectors at those endpoints. This provides enough information to define a cubic Hermite spline. Bezier curves use control points and Bernstein polynomials to define the curve. Both curves use parametric equations and have properties like following the shape of control points and containing curves within the convex hull of control points. The document also discusses B-spline curves, which provide automatic continuity, and NURBS curves, which extend B-splines to be rational curves using weights.

Synthetics surfaces unit ii

This document discusses two types of parametric surfaces: Hermite bi-cubic surfaces and Bezier surfaces.
For Hermite bi-cubic surfaces, it describes that they connect four corner data points and eight tangent vectors at the corners, requiring 16 vectors (48 scalars) to determine the coefficients. The parametric equation uses polynomials and parameters u and v between 0 and 1.
For Bezier surfaces, it explains they are defined by a network of control points and basic polynomial functions of the parameters u and v. Key properties include passing through the first and last control points, convex hull containment, and affine invariance when transformations are applied to the control points.

Bezier Curves

A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

Curve modeling bezier curves

This document discusses Bézier curves and their properties. It begins by stating that traditional parametric curves are not very geometric and do not provide intuitive shape control. It then outlines desirable properties for curve design systems, including being intuitive, flexible, easy to use, providing a unified approach for different curve types, and producing invariant curves under transformations. The document proceeds to discuss Bézier, B-spline and NURBS curves which address these properties by allowing users to manipulate control points to modify curve shapes. Key properties of Bézier curves are described, including their basis functions and the fact that moving control points modifies the curve smoothly. Cubic Bézier curves are discussed in detail as a common parametric curve type, and

9 beam deflection

The document discusses various methods for analyzing beam deflection and deformation under loading, including:
1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection.
2) Using the method of superposition to analyze beams subjected to multiple loadings by combining the effects of individual loads.
3) Applying moment-area theorems which relate the bending moment diagram to slope and deflection, allowing deflection calculations for beams with various support conditions.

M2l7

1. The document discusses the force method of analysis for statically indeterminate structures. It begins by introducing the force method and explaining that it involves writing compatibility equations for displacements and rotations, which are then used to calculate redundant forces.
2. The example problem presented involves a propped cantilever beam carrying a uniform load. It demonstrates solving the problem by treating either the reaction at the support or the moment at the fixed end as the redundant force.
3. The key steps of the force method are outlined, which are to identify the redundant forces, calculate displacements due to applied loads and redundant forces using superposition, apply compatibility conditions to determine redundant forces, and then use equilibrium equations to find the

B spline surfeces

B-spline surfaces are constructed using a grid of control points and blending functions. The blending functions are polynomials defined over intervals in each parametric direction. This allows a B-spline surface to be defined by blending between control points. Properties include continuity and local influence of control points. A surface can be subdivided by inserting knots or raising the degree. Rational B-spline surfaces use homogeneous coordinates to represent common surfaces like planes and spheres. NURBS are the basis for CAD standards like IGES.

Surface representation

Bezier surfaces are parametric surfaces used in computer graphics and CAD/CAM. They are based on Bernstein polynomials and control points. A Bezier surface is defined by a grid of control points that determine the shape of the surface. Changing control points modifies the shape globally. B-spline surfaces allow for more local control and ensure continuity between patches. Coons patches interpolate between four boundary curves to generate a smooth surface. Sculptured surfaces are used for complex, free-form shapes and consist of blended parametric surface patches.

Hermit curves & beizer curves

This document discusses Hermite curves and Bezier curves. Hermite curves are defined by two endpoints and the tangent vectors at those endpoints. This provides enough information to define a cubic Hermite spline. Bezier curves use control points and Bernstein polynomials to define the curve. Both curves use parametric equations and have properties like following the shape of control points and containing curves within the convex hull of control points. The document also discusses B-spline curves, which provide automatic continuity, and NURBS curves, which extend B-splines to be rational curves using weights.

Synthetics surfaces unit ii

This document discusses two types of parametric surfaces: Hermite bi-cubic surfaces and Bezier surfaces.
For Hermite bi-cubic surfaces, it describes that they connect four corner data points and eight tangent vectors at the corners, requiring 16 vectors (48 scalars) to determine the coefficients. The parametric equation uses polynomials and parameters u and v between 0 and 1.
For Bezier surfaces, it explains they are defined by a network of control points and basic polynomial functions of the parameters u and v. Key properties include passing through the first and last control points, convex hull containment, and affine invariance when transformations are applied to the control points.

Bezier Curves

A Bézier curve is a parametric curve frequently used in computer graphics and related fields. Generalizations of Bézier curves to higher dimensions are called Bézier surfaces, of which the Bézier triangle is a special case.

Curve modeling bezier curves

This document discusses Bézier curves and their properties. It begins by stating that traditional parametric curves are not very geometric and do not provide intuitive shape control. It then outlines desirable properties for curve design systems, including being intuitive, flexible, easy to use, providing a unified approach for different curve types, and producing invariant curves under transformations. The document proceeds to discuss Bézier, B-spline and NURBS curves which address these properties by allowing users to manipulate control points to modify curve shapes. Key properties of Bézier curves are described, including their basis functions and the fact that moving control points modifies the curve smoothly. Cubic Bézier curves are discussed in detail as a common parametric curve type, and

9 beam deflection

The document discusses various methods for analyzing beam deflection and deformation under loading, including:
1) Deriving the differential equation for the elastic curve of a beam and applying boundary conditions to determine the curve and maximum deflection.
2) Using the method of superposition to analyze beams subjected to multiple loadings by combining the effects of individual loads.
3) Applying moment-area theorems which relate the bending moment diagram to slope and deflection, allowing deflection calculations for beams with various support conditions.

M2l7

1. The document discusses the force method of analysis for statically indeterminate structures. It begins by introducing the force method and explaining that it involves writing compatibility equations for displacements and rotations, which are then used to calculate redundant forces.
2. The example problem presented involves a propped cantilever beam carrying a uniform load. It demonstrates solving the problem by treating either the reaction at the support or the moment at the fixed end as the redundant force.
3. The key steps of the force method are outlined, which are to identify the redundant forces, calculate displacements due to applied loads and redundant forces using superposition, apply compatibility conditions to determine redundant forces, and then use equilibrium equations to find the

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.

Ch 1 structural analysis stiffness method

This document introduces the stiffness method for structural analysis. It begins by discussing degrees of freedom and statical determinacy, explaining how to calculate the number of degrees of freedom and degree of statical indeterminacy for frames. It then introduces the direct stiffness method, using a simple spring system example to demonstrate the basic approach. Key steps include establishing equilibrium equations in matrix form relating applied loads to displacements, and solving these equations to determine member forces and displacements. The chapter concludes by discussing local and global coordinate systems for members and how to establish the member stiffness matrix relating forces and displacements.

Para leer

El documento describe dos experimentos para demostrar la transmisión de energía mecánica a través de oscilaciones resonantes. El primero usa dos péndulos unidos por un resorte débil, donde las oscilaciones de uno se transmiten lentamente al otro. El segundo usa diapasones, donde las vibraciones de uno resonante se transmiten por el aire para hacer vibrar otro de la misma frecuencia. Ambos ilustran cómo la energía puede propagarse a través de medios elásticos sin contacto directo.

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The document is a letter from Fulgence to an unknown recipient. It consists of a repeated phrase "Source: www.almohandiss.com" listed over 200 times with no other words. The summary is that the document is a letter containing over 200 repetitions of the phrase "Source: www.almohandiss.com" without any other context or information provided.

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This document discusses analysis of statically indeterminate structures using the force method. It begins by introducing statically and kinematically indeterminate structures. It then discusses the degree of static indeterminacy for different types of structures like beams, trusses, frames, and grids. It also discusses the different types of deformations that can occur in these structures. The document then covers the concepts of equilibrium, compatibility, and the force method of analysis using the method of consistent deformation. Several examples are provided to illustrate the calculation of degree of static indeterminacy for beams, trusses and frames. It also discusses kinematic indeterminacy and provides examples of its calculation for different structures.

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This document provides information about the Structural Analysis-II course CEE-317, including the instructor details, syllabus, evaluation process, references, and an overview of exact structural analysis methods like the Moment Distribution Method. The Moment Distribution Method distributes internal forces in an indeterminate structure by satisfying equilibrium equations. It was developed in 1932 by Hardy Cross and is still widely used due to its simplicity. The document also covers structural idealization, sign convention, fixed-end moments, and the basics of stiffness and carryover factors in the Moment Distribution Method.

Slope deflection method

This will be helpful to the various students for understanding the slope deflection method for portal frame.

Calcul Des Structures Portiques Methode Des Deplacements Jexpoz

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Moment distribution method

The moment distribution method can be used to analyze statically indeterminate beams and frames. It involves solving the linear equations obtained in the slope-deflection method through successive approximations. The key aspects of the method are:
1. Stiffness factor is defined as the moment required to produce a unit rotation at a point, and is used to relate moments and rotations.
2. Carry-over factor is the ratio of the moment induced at the far end of a propped cantilever to the moment applied at the near end.
3. Distribution factor is the ratio of a member's stiffness factor to the sum of stiffnesses of members meeting at a joint, and is used to distribute an

solving statically indeterminate structure by slope deflection method

This document provides an overview of a presentation on solving statically indeterminate structures using the slope deflection method. The presentation covers the assumptions, sign convention, fundamental equations, and an example problem of determining support moments in a continuous beam. The slope deflection method represents end moments in terms of deflections. An example problem is worked through to determine the support moments in a continuous beam with three spans by writing member equations from the fundamental equation and applying joint equilibrium equations.

Table of Fixed End Moments Formulas

Fixed end moments are moments that occur at the ends of beams or other structural elements. These moments are caused by external forces or reactions that are applied at or very near the ends of the beam. Fixed end moments directly influence the maximum bending stress that will occur within the beam based on the applied loads and how they are transferred into or out of the ends of the beam.

Correction Examen 2014-2015 RDM

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The document provides equations to determine the elastic curve of beams under different loading and boundary conditions. It gives the equations of the elastic curve in terms of the slope and deflection at points along the beam. The maximum deflection is calculated to be wL4/1823EI between supports A and B for a beam with a constant distributed load w and of length L with both ends fixed.

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Slope deflection method

This document provides an overview of the slope deflection method for analyzing statically indeterminate structures. It describes that the slope deflection method was developed in 1914 and can be used to analyze beams and frames. Key assumptions of the method are that joints are rigid and distortions from axial/shear stresses are neglected. The document outlines the application, sign convention, procedure, slope deflection equations, and provides examples for analyzing beams and frames using this method.

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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.

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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.

Ch 1 structural analysis stiffness method

This document introduces the stiffness method for structural analysis. It begins by discussing degrees of freedom and statical determinacy, explaining how to calculate the number of degrees of freedom and degree of statical indeterminacy for frames. It then introduces the direct stiffness method, using a simple spring system example to demonstrate the basic approach. Key steps include establishing equilibrium equations in matrix form relating applied loads to displacements, and solving these equations to determine member forces and displacements. The chapter concludes by discussing local and global coordinate systems for members and how to establish the member stiffness matrix relating forces and displacements.

Para leer

El documento describe dos experimentos para demostrar la transmisión de energía mecánica a través de oscilaciones resonantes. El primero usa dos péndulos unidos por un resorte débil, donde las oscilaciones de uno se transmiten lentamente al otro. El segundo usa diapasones, donde las vibraciones de uno resonante se transmiten por el aire para hacer vibrar otro de la misma frecuencia. Ambos ilustran cómo la energía puede propagarse a través de medios elásticos sin contacto directo.

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Presentación en la Conferencia Rails 2008 sobre cómo montar una web integrando distintas aplicaciones pequeñas en lugar de desarrollando una aplicación monolítica.

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Présentation finale

Cours rdm 1_2_3

The document is a letter from Fulgence to an unknown recipient. It consists of a repeated phrase "Source: www.almohandiss.com" listed over 200 times with no other words. The summary is that the document is a letter containing over 200 repetitions of the phrase "Source: www.almohandiss.com" without any other context or information provided.

Module1 rajesh sir

This document discusses analysis of statically indeterminate structures using the force method. It begins by introducing statically and kinematically indeterminate structures. It then discusses the degree of static indeterminacy for different types of structures like beams, trusses, frames, and grids. It also discusses the different types of deformations that can occur in these structures. The document then covers the concepts of equilibrium, compatibility, and the force method of analysis using the method of consistent deformation. Several examples are provided to illustrate the calculation of degree of static indeterminacy for beams, trusses and frames. It also discusses kinematic indeterminacy and provides examples of its calculation for different structures.

Cee 317 (1)(structural analysis)

This document provides information about the Structural Analysis-II course CEE-317, including the instructor details, syllabus, evaluation process, references, and an overview of exact structural analysis methods like the Moment Distribution Method. The Moment Distribution Method distributes internal forces in an indeterminate structure by satisfying equilibrium equations. It was developed in 1932 by Hardy Cross and is still widely used due to its simplicity. The document also covers structural idealization, sign convention, fixed-end moments, and the basics of stiffness and carryover factors in the Moment Distribution Method.

Slope deflection method

This will be helpful to the various students for understanding the slope deflection method for portal frame.

Calcul Des Structures Portiques Methode Des Deplacements Jexpoz

exposé sur le calcul des portiques

Moment distribution method

The moment distribution method can be used to analyze statically indeterminate beams and frames. It involves solving the linear equations obtained in the slope-deflection method through successive approximations. The key aspects of the method are:
1. Stiffness factor is defined as the moment required to produce a unit rotation at a point, and is used to relate moments and rotations.
2. Carry-over factor is the ratio of the moment induced at the far end of a propped cantilever to the moment applied at the near end.
3. Distribution factor is the ratio of a member's stiffness factor to the sum of stiffnesses of members meeting at a joint, and is used to distribute an

solving statically indeterminate structure by slope deflection method

This document provides an overview of a presentation on solving statically indeterminate structures using the slope deflection method. The presentation covers the assumptions, sign convention, fundamental equations, and an example problem of determining support moments in a continuous beam. The slope deflection method represents end moments in terms of deflections. An example problem is worked through to determine the support moments in a continuous beam with three spans by writing member equations from the fundamental equation and applying joint equilibrium equations.

Table of Fixed End Moments Formulas

Fixed end moments are moments that occur at the ends of beams or other structural elements. These moments are caused by external forces or reactions that are applied at or very near the ends of the beam. Fixed end moments directly influence the maximum bending stress that will occur within the beam based on the applied loads and how they are transferred into or out of the ends of the beam.

Correction Examen 2014-2015 RDM

Correction examen RDM

structural analysis CE engg. solved ex.

The document provides equations to determine the elastic curve of beams under different loading and boundary conditions. It gives the equations of the elastic curve in terms of the slope and deflection at points along the beam. The maximum deflection is calculated to be wL4/1823EI between supports A and B for a beam with a constant distributed load w and of length L with both ends fixed.

Structural Analysis - Virtual Work Method

The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.

Slope deflection method

This document provides an overview of the slope deflection method for analyzing statically indeterminate structures. It describes that the slope deflection method was developed in 1914 and can be used to analyze beams and frames. Key assumptions of the method are that joints are rigid and distortions from axial/shear stresses are neglected. The document outlines the application, sign convention, procedure, slope deflection equations, and provides examples for analyzing beams and frames using this method.

Solving Statically Indeterminate Structure: Stiffness Method 10.01.03.080

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Ch 1 structural analysis stiffness method

Ch 1 structural analysis stiffness method

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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.

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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
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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

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

Dissertation report

Dissertation report

Seismic response of cellwise braced reinforced concrete frames

Seismic response of cellwise braced reinforced concrete frames

Water Management

Water Management

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

- 1. ASSIGNMENT NO. 2 COSISTANTANT DEFORMATION METHOD 1) A propped cantilever AB is loaded as shown in fig. Determine the reactions at A and B. Also draw B.M.D .Use consistent deformation method. 2) Solve the above problem by considering M.I for span AD = I and for span BD = 2 I. 3) Draw S.F.D & B.M.D for fixed beam as shown in fig by method of consistent deformation. 4) Analyze following beam by method of consistent deformation. Support B and C settles by 40mm & 80 mm respectively. Take E = 2 x 105 N/mm2 , I = 3x108 mm4 .