Centroid
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this is a ppt on centroid,covering centroid of regular figures and there is a example of a composite figure,it has applications,uses of centroid,it is use ful for engineering students,it has 15 slides. by -nishant kumar. nk18052001@gmail.com
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CENTROID
This document discusses the concept of centroid and provides formulas to calculate the centroid of different geometric shapes. It defines centroid as the point within an object where the downward force of gravity appears to act. The centroid allows an object to remain balanced when placed on a pivot at the centroid point. Formulas are given for finding the centroid of triangles, rectangles, circles, semicircles, right circular cones, and composite figures. Real-life applications of centroid calculation in construction and engineering are also mentioned.
Structural analysis (method of sections)
The method of sections can be used to determine member forces in a truss. It involves cutting or sectioning the truss and applying equilibrium equations to the cut parts. For example, a truss can be cut through members to determine the forces in those members by drawing and analyzing the free-body diagram of each cut section. Either the method of joints or method of sections can be used to analyze trusses.
Resultant of forces
This document provides an overview of the content covered in the Basic Civil Engineering course. It discusses the following topics:
1. Mechanics of Rigid Bodies and Mechanics of Deformable Bodies, which make up Parts I and II of the course.
2. Concepts in mechanics of solids including resultant and equilibrium of coplanar forces, centroids, moments of inertia, kinetics principles, stresses and strains.
3. Five textbooks recommended as references for the course.
4. Definitions of terms like particle, force, scalar, vector, and rigid body.
5. Methods for resolving forces into components, obtaining the resultant of coplanar forces, and solving mechanics problems
Bef 2
This document discusses beams supported on an elastic foundation. It begins by introducing the Winkler foundation model and defining short, medium, and long beams based on the parameter βL. It then provides solutions for the deflection, slope, bending moment and shear force of an infinite beam under a point load. The document also discusses beams supported by discrete elastic supports and beams subjected to a distributed load segment. It provides examples calculating deflection, bending stress, and pressure for specific beam problems.
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.
Analysis of statically indeterminate structures
Method of consistent deformations, three moment equation, slope deflection method and moment distribution method
Chapter 3-analysis of statically determinate trusses
The document discusses various types of trusses used in building structures including simple trusses, compound trusses, and complex trusses. It also covers the assumptions made in truss analysis, classifications of trusses based on stability and determinacy, and different methods for analyzing trusses including the method of joints, method of sections, and analyzing zero force members. Several examples are provided to demonstrate how to apply these analysis methods to solve for unknown member forces in various truss configurations.
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.
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CENTROID
This document discusses the concept of centroid and provides formulas to calculate the centroid of different geometric shapes. It defines centroid as the point within an object where the downward force of gravity appears to act. The centroid allows an object to remain balanced when placed on a pivot at the centroid point. Formulas are given for finding the centroid of triangles, rectangles, circles, semicircles, right circular cones, and composite figures. Real-life applications of centroid calculation in construction and engineering are also mentioned.
Structural analysis (method of sections)
The method of sections can be used to determine member forces in a truss. It involves cutting or sectioning the truss and applying equilibrium equations to the cut parts. For example, a truss can be cut through members to determine the forces in those members by drawing and analyzing the free-body diagram of each cut section. Either the method of joints or method of sections can be used to analyze trusses.
Resultant of forces
This document provides an overview of the content covered in the Basic Civil Engineering course. It discusses the following topics:
1. Mechanics of Rigid Bodies and Mechanics of Deformable Bodies, which make up Parts I and II of the course.
2. Concepts in mechanics of solids including resultant and equilibrium of coplanar forces, centroids, moments of inertia, kinetics principles, stresses and strains.
3. Five textbooks recommended as references for the course.
4. Definitions of terms like particle, force, scalar, vector, and rigid body.
5. Methods for resolving forces into components, obtaining the resultant of coplanar forces, and solving mechanics problems
Bef 2
This document discusses beams supported on an elastic foundation. It begins by introducing the Winkler foundation model and defining short, medium, and long beams based on the parameter βL. It then provides solutions for the deflection, slope, bending moment and shear force of an infinite beam under a point load. The document also discusses beams supported by discrete elastic supports and beams subjected to a distributed load segment. It provides examples calculating deflection, bending stress, and pressure for specific beam problems.
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.
Analysis of statically indeterminate structures
Method of consistent deformations, three moment equation, slope deflection method and moment distribution method
Chapter 3-analysis of statically determinate trusses
The document discusses various types of trusses used in building structures including simple trusses, compound trusses, and complex trusses. It also covers the assumptions made in truss analysis, classifications of trusses based on stability and determinacy, and different methods for analyzing trusses including the method of joints, method of sections, and analyzing zero force members. Several examples are provided to demonstrate how to apply these analysis methods to solve for unknown member forces in various truss configurations.
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.
Centroid
The document discusses the concepts of centroid and centre of gravity. It defines centroid as the point where the whole area of a plane figure can be assumed to be concentrated. The centre of gravity is the point where the entire weight of a body acts and can be balanced. The document then provides methods to determine the centroid of common geometric shapes such as rectangles, triangles, semicircles, and composite shapes using the principle of moments. It includes examples of calculating the x- and y-coordinates of the centroid for various geometric problems.
Coplanar Non-concurrent Forces
The document discusses coplanar non-concurrent force systems where multiple forces act in the same plane but at different points. It defines moment as the product of a force and its perpendicular distance from the point of interest. A couple is formed by two equal and opposite forces that rotate a body without translating it. Varignon's principle states that the sum of the moments of individual forces equals the moment of the resultant force about any point. Conditions for equilibrium of coplanar non-concurrent forces on a body are also presented. An example problem finds the resultant and location of a non-concurrent force system.
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Centroids
The document discusses centroids, which are the centers of mass for systems. The centroid of an area is analogous to the center of gravity of a body. To find the centroid, you calculate the first moment of the system, which is the sum of the products of each mass and its distance from the origin. You can find the centroid of multiple points by dividing the first moment about each axis by the total mass of the system. The document provides an example of calculating the centroid of a system with masses located at different coordinate points. It also discusses finding centroids of common geometric shapes.
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This document summarizes key concepts from a chapter on analyzing structures. It discusses how to determine the internal and external forces acting on trusses, frames, and machines. The objectives are to calculate the forces carried by various structures and determine if they can withstand these forces. It describes analyzing trusses using the method of joints and method of sections. Frames are introduced as structures with multi-force members. The document also distinguishes between determinate and indeterminate structures, with determinate structures having solvable equilibrium equations and indeterminate structures lacking sufficient equations.
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The document discusses the differences between centroid and center of gravity. The centroid is defined as a point about which the entire line, area or volume is assumed to be concentrated, and is related to the distribution of length, area and volume. The center of gravity is defined as the point about which the entire weight of an object is assumed to be concentrated, also known as the center of mass, and is related to the distribution of mass. Examples are provided to illustrate the concepts of centroid and center of gravity.
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Centroid
The document discusses the concepts of centroid and centre of gravity. It defines centroid as the point where the whole area of a plane figure can be assumed to be concentrated. The centre of gravity is the point where the entire weight of a body acts and can be balanced. The document then provides methods to determine the centroid of common geometric shapes such as rectangles, triangles, semicircles, and composite shapes using the principle of moments. It includes examples of calculating the x- and y-coordinates of the centroid for various geometric problems.
Coplanar Non-concurrent Forces
The document discusses coplanar non-concurrent force systems where multiple forces act in the same plane but at different points. It defines moment as the product of a force and its perpendicular distance from the point of interest. A couple is formed by two equal and opposite forces that rotate a body without translating it. Varignon's principle states that the sum of the moments of individual forces equals the moment of the resultant force about any point. Conditions for equilibrium of coplanar non-concurrent forces on a body are also presented. An example problem finds the resultant and location of a non-concurrent force system.
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Presentation by:
MEC32/A1 Group 1 4Q 2014
MAGBOJOS, Redentor V.
RIGOR, Lady Krista V.
SALIDO, Lisette S.
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Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
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The document discusses bending stresses in beams. It begins by outlining simplifying assumptions made in deriving the flexure formula to relate bending stresses to bending moments. These assumptions include plane sections remaining plane and perpendicular to the deformed beam axis. The neutral axis is defined as the axis where longitudinal fibers experience no deformation.
The derivation of the flexure formula is shown. Flexural stresses are proportional to the distance from the neutral axis and bending moment. Procedures for determining stresses at given points, as well as maximum stresses, are provided. Sample problems demonstrate applying the flexure formula and finding maximum stresses for different beam cross sections.
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This document discusses the fundamentals of mechanics of materials including external loads, internal forces, equilibrium, and supports. It defines different types of forces like surface forces from direct contact, and body forces from gravitational effects. Supports prevent movement and develop reactions forces. Equilibrium requires the sum of forces and moments on a body to be zero. Understanding loads, forces, and supports is necessary to analyze how structures deform under stress.
First moment of area
The first moment of area of a lamina is defined as the product of the lamina's area and the perpendicular distance of its center of gravity from a given axis. It is used to determine the center of gravity of an area. To calculate the first moment of area, the area is split into segments, and the area of each segment is multiplied by its distance from the axis and summed. This gives the first moment of area, which provides information about the distribution of the area.
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This document discusses the slope-deflection method for analyzing beams and frames. It provides the theory and equations of the slope-deflection method. Examples are included to demonstrate how to use the method to determine support reactions, member end moments, and draw bending moment and shear force diagrams.
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This document describes the slope deflection method of structural analysis. It assumes joints are rigid and distortions from axial/shear stresses are negligible. It derives the slope deflection equations by considering member end rotations and loads. The method solves for unknown end moments, slopes, and displacements. An example problem calculates support moments in a continuous beam due to settlement of one support, using slope deflection equations and drawing shear/moment diagrams.
Influence lines (structural analysis theories)
1. Influence lines represent the variation of reaction, shear, or moment at a specific point on a structural member as a concentrated load moves along the member. They are useful for analyzing the effects of moving loads.
2. To construct an influence line, a unit load is placed at different points along the member and the reaction, shear, or moment is calculated at the point of interest using statics. The values are plotted to show the influence of the load.
3. Influence lines allow engineers to determine the maximum value of a response (reaction, shear, moment) caused by a moving load and locate where on the structure that maximum occurs.
Centroids
The document discusses centroids, which are the centers of mass for systems. The centroid of an area is analogous to the center of gravity of a body. To find the centroid, you calculate the first moment of the system, which is the sum of the products of each mass and its distance from the origin. You can find the centroid of multiple points by dividing the first moment about each axis by the total mass of the system. The document provides an example of calculating the centroid of a system with masses located at different coordinate points. It also discusses finding centroids of common geometric shapes.
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This document discusses various types of trusses and methods for analyzing truss structures. It begins by describing common types of trusses used in roofs and bridges. It then covers topics such as classifying trusses as simple, compound, or complex, and determining their stability and determinacy. The document introduces analytical methods like the method of joints and method of sections for calculating member forces in statically determinate trusses. It provides examples of applying these methods to solve for unknown member forces.
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The document discusses shear force and bending moment in beams. It defines key terms like shear force, bending moment, and types of loads, supports and beams. It provides examples of different loading conditions and how to calculate and draw the shear force and bending moment diagrams for beams subjected to point loads, uniformly distributed loads, uniformly varying loads, couples and overhanging beams. The diagrams show the variations in shear force and bending moment, including locations of maximum and points of contraflexure where bending moment changes sign.
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This document provides an introduction to the concept of equilibrium in statics. It discusses how to isolate a mechanical system and draw a free body diagram showing all external forces acting on it. For equilibrium in two dimensions, the forces must sum to zero in both the x and y directions. In three dimensions, six equations are required - the forces and moments must sum to zero in the x, y, and z directions as well as around each axis. Examples are given of two-force and three-force members in equilibrium. The document also defines statically determinate and indeterminate bodies.
Method of joints
This document summarizes key concepts from a chapter on analyzing structures. It discusses how to determine the internal and external forces acting on trusses, frames, and machines. The objectives are to calculate the forces carried by various structures and determine if they can withstand these forces. It describes analyzing trusses using the method of joints and method of sections. Frames are introduced as structures with multi-force members. The document also distinguishes between determinate and indeterminate structures, with determinate structures having solvable equilibrium equations and indeterminate structures lacking sufficient equations.
Centroid & Centre of Gravity
The document discusses the differences between centroid and center of gravity. The centroid is defined as a point about which the entire line, area or volume is assumed to be concentrated, and is related to the distribution of length, area and volume. The center of gravity is defined as the point about which the entire weight of an object is assumed to be concentrated, also known as the center of mass, and is related to the distribution of mass. Examples are provided to illustrate the concepts of centroid and center of gravity.
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This document discusses methods for calculating the center of gravity and moment of inertia of objects. It provides the following key points:
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This document presents an analysis of simply supported aluminum and composite plates with uniform loading to determine equivalent plate stack-ups. It describes using thin plate theory and ANSYS models to analyze deflection of aluminum and composite plates under uniform pressure. For the aluminum plate, thin plate equations are used to calculate maximum deflection, which is then validated using ANSYS. Composite plate analysis involves determining material properties, developing equations for composite thin plate theory, and applying failure criteria. The results of the aluminum, composite, and ANSYS models are presented along with error analysis. The conclusions summarize the process and results of the plate analyses.
Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Tra...
The analysis of thin rectangular orthotropic plate with two opposite edges clamped and the other two opposite edges simply supported CSCS , carrying transverse loads was investigated in this study. The Ritz total potential energy functional was used. The minimization of the total potential energy functional produces the expression for the coefficient of deflection. The coefficient of deflection was used to obtain equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable deflection. Also, equation for the maximum lateral load of an orthotropic thin rectangular plate based on allowable stress was developed.Developed stiffness coefficients were substituted in the lateral load equations to obtain the maximum lateral load values for a CSCS plate. Numerical examples using permissible deflection of 10mm and yield strength of 250MPa, plate thickness varying from 5mm to 12.5 mm with 0.5mm intervals were done to determine the maximum lateral loads corresponding to an orthotropic thin rectangular CSCS plate carrying transverse loads when n1 = Ey Ex = 0.7 and n2 = G Ex = 0.41 for aspect ratios b a of 1.0, 1.25 and 1.50. Bertram D. I. | Okere C. E. | Ibearugbulem O. M. | Nwokorobia G. C. "Limit States Solution to CSCS Orthotropic Thin Rectangular Plate Carrying Transverse Loads" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-6 , October 2021, URL: https://www.ijtsrd.com/papers/ijtsrd47566.pdf Paper URL : https://www.ijtsrd.com/engineering/civil-engineering/47566/limit-states-solution-to-cscs-orthotropic-thin-rectangular-plate-carrying-transverse-loads/bertram-d-i
Retaining walls (الجدران الاستنادية)-steel sheet piles - sheet piles wall
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Navier-Stokes Equation of Motion
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Vtu fluid mechanics unit-8 flow past immersed bodies problems
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This document discusses fluid mechanics concepts related to flow past immersed bodies. It provides examples of fluids flowing over stationary bodies or bodies moving through fluids, such as air over buildings or ships moving through water. It then presents 3 problems involving calculating forces on flat plates moving through air at different velocities based on given coefficients of drag and lift. The document concludes by defining key terms in fluid mechanics such as boundary layer thickness, displacement thickness, and drag force. It also presents 4 additional practice problems calculating forces on objects like parachutes in air based on given properties.Reg 162 note dr norizal
Young's modulus is a measure of the stiffness of an elastic material and is defined as the ratio of stress to strain for that material. It can be determined from the slope of a stress-strain curve. Young's modulus may vary depending on the direction of applied force for anisotropic materials. The bulk modulus is a measure of how much a material will compress under pressure and is defined as the ratio of change in pressure to fractional volume change. Moment of inertia is a measure of an object's resistance to bending and is used to calculate stresses and deflections. It can be determined using formulas based on the object's geometry and distance from the centroid axis. Combined stresses from bending and axial loads can be calculated using formulas involving moment of inertia
Unit 6: Bending and shear Stresses in beams
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Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.Similar to Centroid (20)
Kantorovich-Vlasov Method for Simply Supported Rectangular Plates under Unifo...
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Analysis of simply supported aluminum and composite plates with uniform loadi...
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Retaining walls (الجدران الاستنادية)-steel sheet piles - sheet piles wall
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Vtu fluid mechanics unit-8 flow past immersed bodies problems
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Centroid
- 1. BY- NISHANT KUMAR SEC- 3A ROLL NO-25
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- 3. Centroid indicate the centre of mass of a uniform solid. lots of construction applications and engineering applications to design things so that minimal stress and energy is used to stabilize a component.
- 4. Consider a plate of thickness t Weight of any elemental portion be wi acting at point(xi,yi).let W be the total weight of the plate acting at the point (X̅,Y̅) x=∑Wixi/W y=∑Wiyi/W Let Ai be the area of the i th element of the plate of uniform thickness in the plate,and Ɣ be the density of each elemental portion . THEN X=∑Aixi/A Y=∑Aiyi/A
- 7. FROM APEX=2H/3 FROM BASE=H/3
- 8. Y̅=4R/3Π