Struc lecture
•Download as PPT, PDF•
3 likes•2,345 views
The document discusses statically determinate arches and their analysis using analytical methods. It provides examples of calculating reactions, bending moments, normal forces, and shear forces at different points along three-hinged parabolic and circular arches given their equations. Calculations are shown for determining these values at various points along the arches using equations of equilibrium and geometry.
Report
Share
Report
Share
Recommended
Geometry unit 12.5
The document discusses circles in the coordinate plane. It provides examples of writing the equation of a circle given its center and radius or given two points it passes through. It also gives examples of graphing circles given their equations by identifying the center and radius. Additionally, it presents an example of using three points and their perpendicular bisectors to find the center of a circle passing through those three points, and applies this to solving a problem about finding the location of a structure.
12.6 Dimensional Change
Predict and calculate how changing one or more dimensions of a shape affects the perimeter, area, or volume of the shape.
Copier correction du devoir_de_synthèse_de_topographie
1. This document contains the steps to solve two topography exercises.
2. The first exercise involves determining angles, distances, and areas of triangles between stations A, B, C, and D using trigonometric relationships and angle measurements.
3. The second exercise calculates the horizontal distance between station S and a building using zenith angle measurements and the distance measured on a staff. It then determines the height of the building.
5.13.3 Geometric Probability and Changing Dimensions
Students will
* Calculate geometric probabilities
* Use geometric probability to predict results in real-world situations
* Predict the effects of changing dimensions on the perimeter/circumference and area of a figure.
Lesson 12 centroid of an area
Here are the steps to find the centroid of each given plane region:
1. Region bounded by y = 10x - x^2, x-axis, x = 2, x = 5:
- Set up the integral to find the area A: ∫2^5 (10x - x^2) dx
- Evaluate the integral: A = 96
- Set up the integrals to find the x- and y-moments: ∫2^5 x(10x - x^2) dx and ∫2^5 (10x - x^2)x dx
- Evaluate the integrals: Mx = 192, My = 960
- Use the formulas for centroid: C
Sheet 1 electromagnetics
The document contains 11 multi-part math problems involving vector calculus concepts like divergence, flux, and curl. It provides the problems, calculations, and answers for finding things like the angle between two vectors, components of a vector field, and evaluating vector expressions at given points and over surfaces using theorems like divergence and Stokes' theorem.
Module 4 circular functions
This module teaches about circular functions and their graphical representations. Students will learn to define and calculate the six trigonometric functions of an acute angle in standard position. Specifically, the module will:
1) Describe the properties of sine and cosine functions
2) Teach how to draw the graphs of sine and cosine functions
3) Define the six trigonometric functions of an angle given its terminal point is not on the unit circle
4) Calculate trigonometric function values given certain conditions
Statistics Formulas ppt
The document provides formulas and explanations for various statistical concepts related to measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, standard deviation), skewness, index numbers, time series analysis, and regression analysis. Key formulas include those for individual series, discrete series, and continuous series means and standard deviations. Methods for calculating index numbers, regression coefficients, and time series equations are also summarized.
Recommended
Geometry unit 12.5
The document discusses circles in the coordinate plane. It provides examples of writing the equation of a circle given its center and radius or given two points it passes through. It also gives examples of graphing circles given their equations by identifying the center and radius. Additionally, it presents an example of using three points and their perpendicular bisectors to find the center of a circle passing through those three points, and applies this to solving a problem about finding the location of a structure.
12.6 Dimensional Change
Predict and calculate how changing one or more dimensions of a shape affects the perimeter, area, or volume of the shape.
Copier correction du devoir_de_synthèse_de_topographie
1. This document contains the steps to solve two topography exercises.
2. The first exercise involves determining angles, distances, and areas of triangles between stations A, B, C, and D using trigonometric relationships and angle measurements.
3. The second exercise calculates the horizontal distance between station S and a building using zenith angle measurements and the distance measured on a staff. It then determines the height of the building.
5.13.3 Geometric Probability and Changing Dimensions
Students will
* Calculate geometric probabilities
* Use geometric probability to predict results in real-world situations
* Predict the effects of changing dimensions on the perimeter/circumference and area of a figure.
Lesson 12 centroid of an area
Here are the steps to find the centroid of each given plane region:
1. Region bounded by y = 10x - x^2, x-axis, x = 2, x = 5:
- Set up the integral to find the area A: ∫2^5 (10x - x^2) dx
- Evaluate the integral: A = 96
- Set up the integrals to find the x- and y-moments: ∫2^5 x(10x - x^2) dx and ∫2^5 (10x - x^2)x dx
- Evaluate the integrals: Mx = 192, My = 960
- Use the formulas for centroid: C
Sheet 1 electromagnetics
The document contains 11 multi-part math problems involving vector calculus concepts like divergence, flux, and curl. It provides the problems, calculations, and answers for finding things like the angle between two vectors, components of a vector field, and evaluating vector expressions at given points and over surfaces using theorems like divergence and Stokes' theorem.
Module 4 circular functions
This module teaches about circular functions and their graphical representations. Students will learn to define and calculate the six trigonometric functions of an acute angle in standard position. Specifically, the module will:
1) Describe the properties of sine and cosine functions
2) Teach how to draw the graphs of sine and cosine functions
3) Define the six trigonometric functions of an angle given its terminal point is not on the unit circle
4) Calculate trigonometric function values given certain conditions
Statistics Formulas ppt
The document provides formulas and explanations for various statistical concepts related to measures of central tendency (mean, median, mode), measures of dispersion (range, quartile deviation, standard deviation), skewness, index numbers, time series analysis, and regression analysis. Key formulas include those for individual series, discrete series, and continuous series means and standard deviations. Methods for calculating index numbers, regression coefficients, and time series equations are also summarized.
Notes on Equation of Plane
This document provides notes on determining various properties of planes in 3D space, including:
1) The perpendicular distance from a point to a plane using either vector or Cartesian methods.
2) The angle between a plane and line by taking the arcsine of the dot product of their normal vectors.
3) The angle between two planes by taking the arccosine of the dot product of their normal vectors.
Worked examples are provided for calculating distances, angles, and deriving relevant formulas. Revision questions at the end reinforce the content through calculation practice.
Buisness Statistical Formula ppt
This document contains formulas for various statistical measures including mean, median, mode, range, quartiles, mean deviation, standard deviation, correlation, and regression. It provides formulas for calculating these measures using direct, short cut, and step deviation methods for both discrete and continuous data. Formulas are also included for weighted mean, index numbers, skewness, and time series analysis.
5.13.2 Area of Regular Polygons and Composite Shapes
- The document discusses formulas for calculating the areas of regular polygons and composite shapes. It provides formulas for finding the area of a regular polygon, equilateral triangle, and regular hexagon.
- It also explains that to find the area of a composite shape, one divides the shape into simple shapes like triangles, rectangles, trapezoids and circles. The areas of the individual shapes are then calculated and added or subtracted to find the total area.
- Examples are provided to demonstrate using the formulas and dividing composite shapes into simple shapes to calculate their total areas.
Conic sections circles - STEM TEACH
The document discusses determining the equation of a circle given its diameter or radius and center. It provides an example of finding the standard form equation of a circle given the endpoints of its diameter (-3,6) and (3,-2). It also presents a word problem about determining if a point (3,3) lies within a danger zone defined as a circle of radius 4km centered at the origin. It shows solving this graphically and by substituting the point into the standard form equation.
6.14.2 Circle Equations
Determine the center and radius of a circle from its equation.
Write the equation of a circle given its center and radius.
6.2 Unit Circle and Circular Functions
This document discusses the unit circle and circular functions. It begins by explaining how the unit circle is used to define trigonometric function values and determine the measure of an angle based on its coordinates. It then defines the circular functions in terms of the unit circle and provides examples of evaluating circular function values both numerically and exactly. The document concludes by explaining linear and angular speed for a point rotating along a circle.
Module 5 circular functions
This module covers trigonometric equations and identities. Students will learn to:
1. State fundamental trigonometric identities like reciprocal, quotient, and Pythagorean identities.
2. Prove trigonometric identities algebraically by transforming one side into the other.
3. Use sum and difference formulas for sine and cosine to find values of trig functions of angles that are not special angles.
4. Solve simple trigonometric equations.
Worked examples are provided to simplify expressions using identities, prove identities by algebraic manipulation, and apply sum and difference formulas to find trig values of combined angles.
Analytic Geometry
This document provides examples and solutions for solving various types of coordinate geometry problems. It covers changing coordinate equations into standard form, writing equations given a center and radius, finding perpendicular distance between points and lines, and solving systems of linear equations graphically and algebraically. Methods demonstrated include substitution, elimination, and graphing lines to find their point of intersection.
11.3 Distance Midpoint Formulas
This document provides instructions and examples for using the distance and midpoint formulas in coordinate geometry. It explains that the distance formula, which uses Pythagorean theorem, can find the length of a segment on a coordinate plane between two points. The midpoint formula is also explained, which finds the midpoint of a segment by taking the average of the x- and y-coordinates of the two points. Several examples are worked out finding distances and midpoints between points on a coordinate plane.
Chapter 8 circular measure
This document provides information about circular measure including radians, conversion between radians and degrees, length of arc, and area of sectors. It defines a radian as the angle subtended by an arc equal in length to the radius. Formulas are given for converting between radians and degrees, finding the length of an arc given the radian measure of its central angle, and finding the area of a sector given its radian measure and the radius. Several examples demonstrate applying these formulas to solve problems involving radians. Exercises provide additional practice problems for students to work through.
Analytic geometry lecture2
This document discusses key concepts about circles, including:
- The standard equation of a circle is (x - h)2 + (y - k)2 = r2, where (h, k) are the coordinates of the center and r is the radius.
- Given the equation or properties of a circle, one can determine its center and radius or write the equation in standard form.
- Points can lie inside, outside, or on a circle, which can be determined by comparing distances or substituting into the equation.
- A circle and line can intersect in 0, 1, or 2 points, which can be found using algebraic techniques.
- The equation of a circle can be found given 3
Lesson 16 length of an arc
1. This document discusses methods for calculating the length of an arc of a curve and the surface area of revolution. It provides formulas for finding arc length and surface area when curves are defined by rectangular coordinates, parametric equations, or polar coordinates.
2. Several examples are given of applying the formulas to find the arc length of curves and the surface area when graphs are revolved about axes. This includes revolving curves like y=x^3, y=x^2, and xy=2 about the x-axis and y-axis.
3. The key formulas presented are that arc length can be found using an integral of the form ∫√(dx/dy)^2 + 1 dy or
Trigonometric graphs
This document provides a review of trigonometric graphs including how to draw and identify them. It discusses the maximum and minimum values, range, period and number of cycles for sin and cos graphs. It also covers shifting graphs horizontally or vertically and combining trig functions with constants. Examples are provided to illustrate identifying trig graphs from their equations and sketching shifted or combined trig graphs.
Conic sections- Parabola STEM TEACH
The document provides the steps to write the equation of a parabola in standard form given certain information about its properties. It then works through two example problems:
1) Given the equation of a parabola in general form, it rewrites the equation in standard form and determines the vertex, focus, directrix, and axis of symmetry.
2) Given the vertex and directrix of a parabola, it derives the standard form equation that satisfies those conditions.
3) Given the height and base width of an arch with a parabolic shape, it illustrates the situation, determines the necessary values, and writes the standard form equation that models the arch's shape.
Introduction to coordinate geometry by pratima nayak
The document discusses distance formula and section formula to find the coordinates of points on a plane. It explains how to find the distance between two given points using the distance formula. It also describes how to find the coordinates of a point C that divides the line segment between points A and B in a given ratio using the section formula. The document provides examples of finding coordinates of circumcenter and incenter of a triangle given its vertices. It concludes with some assignment questions related to these concepts.
Coordinate geometry
The document defines key concepts related to coordinate grids and ordered pairs:
- A coordinate grid uses horizontal and vertical intersecting lines to locate points via distances from the lines.
- The x-axis is horizontal and the y-axis is vertical.
- Ordered pairs use the format (x,y) to give the location of a point by listing the distance from each axis.
- Points can be plotted on a four-quadrant grid by first finding the x value and then the y value, with negative numbers indicating left/below the origin.
Trigonometry: Circular Functions
The document discusses the unit circle and trigonometric functions. It defines the unit circle as having a radius of 1 unit and center at the origin (0,0). The equation of the unit circle is provided as x2 + y2 = 1. Quadrantal angles are defined as angles whose terminal rays lie along one of the axes at 90°, 180°, 270°, and 360°. Trigonometric functions are defined in terms of the x- and y-coordinates on the unit circle. Special right triangles and their properties are also discussed.
Truss examples
1) The documents provide examples of solving for forces in truss members by using free body diagrams and equilibrium equations.
2) The solutions involve drawing FBDs of the trusses or sections of trusses, then writing the ΣF and ΣM equations and solving the systems of equations.
3) The determined forces are then identified as either tension or compression forces in the members.
Circular Functions
1) Circular functions can be defined using the coordinates (x,y) of the terminal point of an arc length on the unit circle, where x=cosθ and y=sinθ.
2) Reference angles are used to determine the exact values of circular functions in different quadrants by relating the angle to the reference angle in Quadrant 1.
3) Examples are provided to demonstrate finding the values of sine, cosine, tangent and other circular functions using reference angles for angles in different quadrants.
GRE - Coordinate Geometry
The document provides information about coordinate geometry and straight lines. It defines key concepts like the Cartesian plane, distance between points, slopes of lines, equations of lines in various forms, and transformations of graphs. It also gives examples of determining the type of triangles based on side lengths and slopes, finding equations of lines satisfying given conditions, and identifying collinear points. Practice problems are included at the end to test the understanding of these geometric and algebraic concepts.
Three.hinged.arch
This document provides instruction on analyzing three-hinged arches. It defines a three-hinged arch as a statically determinate structure with three hinges: two at the supports and one at the crown. The document describes how to determine the reactions of a three-hinged arch under a concentrated load using equations of static equilibrium. It presents an example problem showing how bending moment is reduced in a three-hinged arch compared to a simply supported beam carrying the same load.
Ch1 statics
1) The document discusses statics problems where objects are motionless. It focuses on balancing forces and determining unknown forces.
2) Key forces discussed include tension, normal force, friction, and gravity. Tension and normal forces are explained in more detail.
3) An example problem is worked out involving a block on an inclined plane, finding the normal and friction forces for different angles of inclination.
More Related Content
What's hot
Notes on Equation of Plane
This document provides notes on determining various properties of planes in 3D space, including:
1) The perpendicular distance from a point to a plane using either vector or Cartesian methods.
2) The angle between a plane and line by taking the arcsine of the dot product of their normal vectors.
3) The angle between two planes by taking the arccosine of the dot product of their normal vectors.
Worked examples are provided for calculating distances, angles, and deriving relevant formulas. Revision questions at the end reinforce the content through calculation practice.
Buisness Statistical Formula ppt
This document contains formulas for various statistical measures including mean, median, mode, range, quartiles, mean deviation, standard deviation, correlation, and regression. It provides formulas for calculating these measures using direct, short cut, and step deviation methods for both discrete and continuous data. Formulas are also included for weighted mean, index numbers, skewness, and time series analysis.
5.13.2 Area of Regular Polygons and Composite Shapes
- The document discusses formulas for calculating the areas of regular polygons and composite shapes. It provides formulas for finding the area of a regular polygon, equilateral triangle, and regular hexagon.
- It also explains that to find the area of a composite shape, one divides the shape into simple shapes like triangles, rectangles, trapezoids and circles. The areas of the individual shapes are then calculated and added or subtracted to find the total area.
- Examples are provided to demonstrate using the formulas and dividing composite shapes into simple shapes to calculate their total areas.
Conic sections circles - STEM TEACH
The document discusses determining the equation of a circle given its diameter or radius and center. It provides an example of finding the standard form equation of a circle given the endpoints of its diameter (-3,6) and (3,-2). It also presents a word problem about determining if a point (3,3) lies within a danger zone defined as a circle of radius 4km centered at the origin. It shows solving this graphically and by substituting the point into the standard form equation.
6.14.2 Circle Equations
Determine the center and radius of a circle from its equation.
Write the equation of a circle given its center and radius.
6.2 Unit Circle and Circular Functions
This document discusses the unit circle and circular functions. It begins by explaining how the unit circle is used to define trigonometric function values and determine the measure of an angle based on its coordinates. It then defines the circular functions in terms of the unit circle and provides examples of evaluating circular function values both numerically and exactly. The document concludes by explaining linear and angular speed for a point rotating along a circle.
Module 5 circular functions
This module covers trigonometric equations and identities. Students will learn to:
1. State fundamental trigonometric identities like reciprocal, quotient, and Pythagorean identities.
2. Prove trigonometric identities algebraically by transforming one side into the other.
3. Use sum and difference formulas for sine and cosine to find values of trig functions of angles that are not special angles.
4. Solve simple trigonometric equations.
Worked examples are provided to simplify expressions using identities, prove identities by algebraic manipulation, and apply sum and difference formulas to find trig values of combined angles.
Analytic Geometry
This document provides examples and solutions for solving various types of coordinate geometry problems. It covers changing coordinate equations into standard form, writing equations given a center and radius, finding perpendicular distance between points and lines, and solving systems of linear equations graphically and algebraically. Methods demonstrated include substitution, elimination, and graphing lines to find their point of intersection.
11.3 Distance Midpoint Formulas
This document provides instructions and examples for using the distance and midpoint formulas in coordinate geometry. It explains that the distance formula, which uses Pythagorean theorem, can find the length of a segment on a coordinate plane between two points. The midpoint formula is also explained, which finds the midpoint of a segment by taking the average of the x- and y-coordinates of the two points. Several examples are worked out finding distances and midpoints between points on a coordinate plane.
Chapter 8 circular measure
This document provides information about circular measure including radians, conversion between radians and degrees, length of arc, and area of sectors. It defines a radian as the angle subtended by an arc equal in length to the radius. Formulas are given for converting between radians and degrees, finding the length of an arc given the radian measure of its central angle, and finding the area of a sector given its radian measure and the radius. Several examples demonstrate applying these formulas to solve problems involving radians. Exercises provide additional practice problems for students to work through.
Analytic geometry lecture2
This document discusses key concepts about circles, including:
- The standard equation of a circle is (x - h)2 + (y - k)2 = r2, where (h, k) are the coordinates of the center and r is the radius.
- Given the equation or properties of a circle, one can determine its center and radius or write the equation in standard form.
- Points can lie inside, outside, or on a circle, which can be determined by comparing distances or substituting into the equation.
- A circle and line can intersect in 0, 1, or 2 points, which can be found using algebraic techniques.
- The equation of a circle can be found given 3
Lesson 16 length of an arc
1. This document discusses methods for calculating the length of an arc of a curve and the surface area of revolution. It provides formulas for finding arc length and surface area when curves are defined by rectangular coordinates, parametric equations, or polar coordinates.
2. Several examples are given of applying the formulas to find the arc length of curves and the surface area when graphs are revolved about axes. This includes revolving curves like y=x^3, y=x^2, and xy=2 about the x-axis and y-axis.
3. The key formulas presented are that arc length can be found using an integral of the form ∫√(dx/dy)^2 + 1 dy or
Trigonometric graphs
This document provides a review of trigonometric graphs including how to draw and identify them. It discusses the maximum and minimum values, range, period and number of cycles for sin and cos graphs. It also covers shifting graphs horizontally or vertically and combining trig functions with constants. Examples are provided to illustrate identifying trig graphs from their equations and sketching shifted or combined trig graphs.
Conic sections- Parabola STEM TEACH
The document provides the steps to write the equation of a parabola in standard form given certain information about its properties. It then works through two example problems:
1) Given the equation of a parabola in general form, it rewrites the equation in standard form and determines the vertex, focus, directrix, and axis of symmetry.
2) Given the vertex and directrix of a parabola, it derives the standard form equation that satisfies those conditions.
3) Given the height and base width of an arch with a parabolic shape, it illustrates the situation, determines the necessary values, and writes the standard form equation that models the arch's shape.
Introduction to coordinate geometry by pratima nayak
The document discusses distance formula and section formula to find the coordinates of points on a plane. It explains how to find the distance between two given points using the distance formula. It also describes how to find the coordinates of a point C that divides the line segment between points A and B in a given ratio using the section formula. The document provides examples of finding coordinates of circumcenter and incenter of a triangle given its vertices. It concludes with some assignment questions related to these concepts.
Coordinate geometry
The document defines key concepts related to coordinate grids and ordered pairs:
- A coordinate grid uses horizontal and vertical intersecting lines to locate points via distances from the lines.
- The x-axis is horizontal and the y-axis is vertical.
- Ordered pairs use the format (x,y) to give the location of a point by listing the distance from each axis.
- Points can be plotted on a four-quadrant grid by first finding the x value and then the y value, with negative numbers indicating left/below the origin.
Trigonometry: Circular Functions
The document discusses the unit circle and trigonometric functions. It defines the unit circle as having a radius of 1 unit and center at the origin (0,0). The equation of the unit circle is provided as x2 + y2 = 1. Quadrantal angles are defined as angles whose terminal rays lie along one of the axes at 90°, 180°, 270°, and 360°. Trigonometric functions are defined in terms of the x- and y-coordinates on the unit circle. Special right triangles and their properties are also discussed.
Truss examples
1) The documents provide examples of solving for forces in truss members by using free body diagrams and equilibrium equations.
2) The solutions involve drawing FBDs of the trusses or sections of trusses, then writing the ΣF and ΣM equations and solving the systems of equations.
3) The determined forces are then identified as either tension or compression forces in the members.
Circular Functions
1) Circular functions can be defined using the coordinates (x,y) of the terminal point of an arc length on the unit circle, where x=cosθ and y=sinθ.
2) Reference angles are used to determine the exact values of circular functions in different quadrants by relating the angle to the reference angle in Quadrant 1.
3) Examples are provided to demonstrate finding the values of sine, cosine, tangent and other circular functions using reference angles for angles in different quadrants.
GRE - Coordinate Geometry
The document provides information about coordinate geometry and straight lines. It defines key concepts like the Cartesian plane, distance between points, slopes of lines, equations of lines in various forms, and transformations of graphs. It also gives examples of determining the type of triangles based on side lengths and slopes, finding equations of lines satisfying given conditions, and identifying collinear points. Practice problems are included at the end to test the understanding of these geometric and algebraic concepts.
What's hot (20)
5.13.2 Area of Regular Polygons and Composite Shapes
5.13.2 Area of Regular Polygons and Composite Shapes
Introduction to coordinate geometry by pratima nayak
Introduction to coordinate geometry by pratima nayak
Viewers also liked
Three.hinged.arch
This document provides instruction on analyzing three-hinged arches. It defines a three-hinged arch as a statically determinate structure with three hinges: two at the supports and one at the crown. The document describes how to determine the reactions of a three-hinged arch under a concentrated load using equations of static equilibrium. It presents an example problem showing how bending moment is reduced in a three-hinged arch compared to a simply supported beam carrying the same load.
Ch1 statics
1) The document discusses statics problems where objects are motionless. It focuses on balancing forces and determining unknown forces.
2) Key forces discussed include tension, normal force, friction, and gravity. Tension and normal forces are explained in more detail.
3) An example problem is worked out involving a block on an inclined plane, finding the normal and friction forces for different angles of inclination.
Ak temperature effect on 2 hinged arch
The document discusses temperature effects and rib shortening effects in arches. Due to temperature changes, arches develop a horizontal thrust without any loading, known as the temperature effect. For circular arches, the horizontal thrust at supports creates a maximum bending moment equal to the thrust multiplied by the radius. For parabolic arches, the maximum bending moment equals the horizontal thrust multiplied by the height. Rib shortening occurs as the arch tries to become deeper under axial thrust, reducing the horizontal thrust. The combined effects of temperature and rib shortening on an arch can be expressed through equations that calculate the net horizontal thrust.
Promotional tools analysis
This document analyzes how promotional tools like posters and magazine covers connect different aspects of promotion and convey a film's narrative. Star names and character images are prominently featured to entice audiences. On the Sherlock Holmes poster, Sherlock is positioned in front to highlight his importance, while other characters are smaller. The villain is separate to mark his role. Text and typography link the poster and magazine cover. Overall, the poster and magazine cover effectively convey personality aspects and narrative elements through positioning of characters and inclusion of star names.
Arches
An arch is a structure that spans an opening and supports weight by resolving forces into compression. Key elements include voussoirs, the wedge-shaped stones that form the arch, and the keystone at the top. Arches fail through crushing, sliding of stones, or uneven settlement. A dome is similar to an inverted arch that resembles half a sphere. Domes channel forces into compression through their curved shape. Common dome types include simple domes formed of one curve and compound domes with additional structures.
Promotional tools
This document provides guidance on creating effective promotional tools and advertisements. It discusses key advertising concepts like goals, benefits and types of advertising. It also lists characteristics of effective promotional tools and provides steps to create advertisements, including coming up with a catchy tagline, using persuasive techniques, knowing the target customer, connecting to customer desires, including relevant details, choosing placement, checking the copy, using bright colors, and keeping it concise. The overall tone is very positive and emphasizes why one product stands out compared to others.
Structural analysis lab
The aim of the experiment is to find the flexural rigidity (EI) of a beam and compare it to the theoretical value. A beam with overhangs is loaded at the free ends and the central deflection is measured for different loads. The flexural rigidity is calculated using the measured deflection and load values and beam properties. This calculated EI is then compared to the theoretical EI calculated using the beam's cross-section dimensions and modulus of elasticity. Observing the beam's deflection under various loads allows determining its flexural rigidity and verifying beam theory calculations.
THEORY 1 : Lectures Notes in Reactions
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.
Frame Structures including sap2000
In support of:
• Building Support Structures, Analysis and Design with SAP2000 Software, 2nd ed., eBook by Wolfgang Schueller, 2015. The SAP2000V15 Examples and Problems SDB files are available on the Computers & Structures, Inc. (CSI) website: http://www.csiamerica.com/go/schueller
• The Design of Building Structures (Vol.1, Vol. 2), rev. ed., PDF eBook by Wolfgang Schueller, 2016, published originally by Prentice Hall, 1996, 868 pages
Determinate structures
The document discusses the analysis of statically determinate structures, including defining idealized structures, explaining the principle of superposition and equations of equilibrium, classifying structures as determinate or indeterminate, and providing examples of determining reactions on beams and frames through applying the equations of equilibrium.
Review of structural analysis
This document provides an overview of structural analysis presented by Hassan Abba Musa. It defines structural analysis as predicting the response of a structure to various loads. Loads are classified as dead loads from the structure's weight and imposed loads like wind and seismic forces. Structural analysis ensures equilibrium, displacement compatibility, and force-displacement relationships. Different structural elements, analysis techniques, and matrix operations are also introduced.
Trusses Frame Machines Analysis
The document discusses analysis methods for trusses, frames, and machines. Trusses consist of two-force members and can be analyzed using the method of joints or method of sections. The method of joints uses particle equilibrium at joints to solve for forces. The method of sections uses rigid body equilibrium to solve for forces by cutting the truss into sections. Frames contain multi-force members and can be analyzed by drawing free body diagrams of individual members and applying equilibrium equations. Machines contain multi-force members and are analyzed similarly to frames.
An introduction to arches
An introduction to Arches:-- It explains the basic understanding about Arches before students start drafting in their drawing sheets. This presentation could be shown to first year B.Architecture students to make them a clear idea about Arches.
THEORY 1 : Lecture notes in arches & cables structures
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.
Viewers also liked (14)
THEORY 1 : Lecture notes in arches & cables structures
THEORY 1 : Lecture notes in arches & cables structures
Similar to Struc lecture
GRADE 10_MATHEMATICS GEOMETRY PERMUTATION.pptx
The document provides information about grade 10 mathematics lessons on geometry, permutations, and combinations. It includes definitions of shapes like trapezoids, parallelograms, triangles, rectangles, circles, and more. It provides example problems using concepts like inscribed angles, arc measurements, and the Pythagorean theorem. It also includes mastery tests and word problems involving secants, tangents, and intersecting chords.
GRADE_10_MATHEMATICS_GEOMETRY_PERMUTATIO [Repaired].pptx
The document provides information about grade 10 mathematics lessons on geometry, permutations, and combinations. It includes definitions of shapes like trapezoids, parallelograms, triangles, rectangles, circles, and more. It discusses inscribed angles and their relationship to intercepted arcs. Sample problems are provided to find missing angle measures and segment lengths using properties of circles, secants, tangents, and chords. Worked examples demonstrate using formulas to solve for unknown values in geometric figures.
Straight-Line-Graphs-Final -2.pptx
This document contains 5 math problems involving factorizing expressions, solving equations, evaluating expressions for given values, expanding expressions, and finding the highest common factor. It also provides context on working with straight line graphs, including finding the gradient and y-intercept of a line from its equation, finding the gradient between two points, finding the midpoint and a point that divides a line segment in a given ratio, and finding the x- and y-intercepts of a line.
Capitulo 4, 7ma edición
1. The document provides calculations for determining work done by electric fields on charges moving through various paths. It includes determining incremental work from given electric field expressions and calculating potentials from different charge distributions.
2. Key results include the work done on a 20 μC charge moving in different directions in a given electric field, the potential and potential difference from a uniform spherical charge distribution, and expressing the potential field of an infinite line charge with different references.
3. The final problem calculates the potential at a point from the combined electric fields of a uniform sheet charge, uniform line charge, and point charge, with the potential set to zero at a reference point.
Maths 301 key_sem_1_2007_2008
The document contains the solutions to several calculus problems:
1) Finding the total amount spent in an economy where dollars recirculate at 90% each time.
2) Calculating the speed needed to shoot a basketball into a hoop from a given distance and height.
3) Taking derivatives and integrals to solve optimization problems.
Determine bending moment and share force diagram of beam
This document summarizes the bending moment (BMD) and shear force (SFD) calculations for three beam problems. The first problem involves calculating the SFD and BMD for a beam with various point loads. The second problem does the same for a beam with distributed loads. The third problem again calculates SFD and BMD, determining values at specific points along the beam. All problems show the free body diagrams, mathematical equations used, and tabulated results.
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.
Jawaban soal-latihan1mekanika
1. The document provides solutions to 7 miscellaneous physics problems involving kinematics, dynamics, and rotational motion. The problems involve calculating quantities like angular speeds, forces, and times using principles like conservation of energy, angular momentum, and equations of motion. Complex algebraic and calculus solutions are shown.
2. Key steps involve setting up and solving equations derived from applying relevant physics principles to diagrams of the systems. Calculus techniques like differentiation and numerical integration are used.
3. Emphasis is placed on being able to instantly solve equations of the form f(x)=0 that arise, with references provided to resources on techniques like Newton-Raphson iteration.
V2.0
The document discusses addition and multiplication of matrices. It provides examples of adding two matrices of the same order, as well as multiplying a matrix by a scalar value. Key points include:
- To add matrices, corresponding elements are added if the matrices are the same order
- Multiplying a matrix by a scalar involves multiplying each element of the matrix by the scalar value
- Examples are provided to demonstrate calculating the sum and product of matrices step-by-step
Capitulo 9, 7ma edición
1) A point charge moving through an electric field is shown to follow a parabolic trajectory given by z = -1.5×1010t2 m. At t = 3 μs, its position is found to be P(0.90, 0, -0.135) m.
2) A point charge moving through a uniform magnetic field follows a circular path. The equations of motion are derived and solved, giving the position, velocity, and kinetic energy at t = 3 μs.
3) Forces on current loops and filaments in various magnetic field configurations are calculated.
Solucionario_Diseno_en_Ingenieria_Mecani (1).pdf
The document provides information about calculating mean, variance, and standard deviation from a data set. It includes a table of values for number of cycles (x) and failure cycles (f) for a sample of bearings. It then shows the calculations to find:
1) The mean number of cycles is 122.9 thousand cycles.
2) The variance is 912.9 thousand cycles squared.
3) The standard deviation is 30.3 thousand cycles.
Solucionario_Diseno_en_Ingenieria_Mecani.pdf
The document provides information about calculating mean, variance, and standard deviation from a data set. It includes a table of values for number of cycles (x) and failure cycles (f) for a sample. It then shows the calculations to find:
1) The mean number of cycles is 122.9 thousand cycles
2) The variance is 912.9 thousand cycles squared
3) The standard deviation is 30.3 thousand cycles
The intent is to demonstrate calculating statistics from a data set to characterize the distribution and variability. The example uses cycle life data from a fatigue test to find the central tendency and spread.
Numerical integration
This document discusses numerical integration techniques including the trapezoidal rule, Simpson's 1/3 rule, and Gaussian quadrature. It provides examples of calculating definite integrals using each method. The trapezoidal rule approximates the integral by dividing the region into trapezoids. Simpson's 1/3 rule is more accurate and divides the region into Simpson panels. Gaussian quadrature uses specific abscissas and weights to accurately estimate integrals, such as using one, two, or three points. Examples are provided to demonstrate calculating area under a curve and definite integrals using these numerical integration methods.
Maths 301 key_sem_1_2009_2010
This document contains the solutions to 5 questions related to calculus concepts like integration, derivatives, series approximation, and geometry of curves and surfaces. Some of the key steps include:
- Using integration to find volumes, masses, and centroids
- Finding critical points and classifying extrema
- Approximating a series to evaluate an integral
- Solving a geometric series problem to find an initial height
- Analyzing motion problems using kinematic equations
- Finding equations of planes and tangent lines to surfaces
Struc lec. no.444
The document discusses statically determinate rigid frames. It defines a rigid frame as a structure composed of members connected by rigid joints that do not allow rotation. It explains that for a frame to be stable and determinate, the number of equations must equal the number of unknowns. Several examples are then worked through to demonstrate calculating the reactions and internal forces of determinate frames.
Shi20396 ch05
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
Metrix[1]
The document defines and provides examples of matrices. The key points are:
1. A matrix is a rectangular array of numbers organized in rows and columns. It is denoted by its dimensions, such as a 3x2 matrix having 3 rows and 2 columns.
2. Matrices can be added, subtracted, or multiplied by a scalar. Operations between matrices are defined element-wise.
3. Special types of matrices include row matrices, column matrices, square matrices, and zero matrices. Matrix equality and solving systems of equations using matrices are also introduced.
Assignment chapters 3 to 7
1. This document contains mathematics questions on matrices and determinants ranging from 1 to 6 marks. Questions involve finding determinants, inverses, solving systems of equations using matrices, properties of determinants, and continuity and differentiability.
2. The document is divided into sections on 1, 2, 4 and 6 mark questions related to matrices and determinants as well as questions on continuity and differentiability ranging from 2 to 4 marks.
3. The questions cover a wide range of matrix and calculus concepts and techniques including finding determinants, inverses, solving systems of equations, properties of determinants, continuity, differentiation, mean value theorem, Rolle's theorem and related calculus topics.
Sect5 6
1. The document discusses forced oscillations and resonance through examples of solving differential equations using trial solutions with undetermined coefficients.
2. Trial solutions of various forms like cos(ωt), sin(ωt) are used to find particular solutions, which are combined with the general solution to satisfy initial conditions.
3. Resonance occurs when the frequency of oscillation of the driving force matches the natural frequency of vibration, leading to an amplified response.
Engineering Mechanics
The document summarizes problems involving calculating reaction forces at supports of structures using Lame's theorem and the principles of equilibrium. It provides 10 example problems showing the application of these principles to determine unknown reaction forces and loads. Diagrams accompany each problem showing the free body diagram and relevant forces and dimensions. Step-by-step solutions are provided for each problem applying the equations of equilibrium.
Similar to Struc lecture (20)
GRADE_10_MATHEMATICS_GEOMETRY_PERMUTATIO [Repaired].pptx
GRADE_10_MATHEMATICS_GEOMETRY_PERMUTATIO [Repaired].pptx
Determine bending moment and share force diagram of beam
Determine bending moment and share force diagram of beam
Recently uploaded
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
How to Download & Install Module From the Odoo App Store in Odoo 17
Custom modules offer the flexibility to extend Odoo's capabilities, address unique requirements, and optimize workflows to align seamlessly with your organization's processes. By leveraging custom modules, businesses can unlock greater efficiency, productivity, and innovation, empowering them to stay competitive in today's dynamic market landscape. In this tutorial, we'll guide you step by step on how to easily download and install modules from the Odoo App Store.
Educational Technology in the Health Sciences
Plenary presentation at the NTTC Inter-university Workshop, 18 June 2024, Manila Prince Hotel.
Accounting for Restricted Grants When and How To Record Properly
In this webinar, member learned how to stay in compliance with generally accepted accounting principles (GAAP) for restricted grants.
Bossa N’ Roll Records by Ismael Vazquez.
Bossa N Roll Records presentation by Izzy Vazquez for Music Retail and Distribution class at Full Sail University
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
How to Fix [Errno 98] address already in use
This slide will represent the cause of the error “[Errno 98] address already in use” and the troubleshooting steps to resolve this error in Odoo.
How to Manage Reception Report in Odoo 17
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...Nguyen Thanh Tu Collection
https://app.box.com/s/qspvswamcohjtbvbbhjad04lg65waylfLeveraging Generative AI to Drive Nonprofit Innovation
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
skeleton System.pdf (skeleton system wow)
🔥🔥🔥🔥🔥🔥🔥🔥🔥
إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
💀💀💀💀💀💀💀💀💀💀
تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
🔥🔥🔥🔥🔥🔥🔥🔥🔥
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
Slides from a Capitol Technology University webinar held June 20, 2024. The webinar featured Dr. Donovan Wright, presenting on the Department of Defense Digital Transformation.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"National Information Standards Organization (NISO)
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as discipline
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Physical pharmaceutics notes for B.pharm students
Recently uploaded (20)
How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
CapTechTalks Webinar Slides June 2024 Donovan Wright.pptx
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Jemison, MacLaughlin, and Majumder "Broadening Pathways for Editors and Authors"
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
Geography as a Discipline Chapter 1 __ Class 11 Geography NCERT _ Class Notes...
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Struc lecture
- 1. Theory of Structures(1) Lecture No. 5
- 2. Statically Determinate Arches An arch : is a curved beam supported at its two ends. Most known types are: fixed- two hinged- three hinged. It can be analyzed by either analytical or graphical methods
- 3. Analytical Method Three Hinged Arch 1-The reactions of the arch can be calculated from the three equations of equilibrium and conditional equation at the intermediate hinge. 2- The bending moment at any section determined by calculating the moments of all the forces to the right or to the left of the section. 3- Determining normal and shearing force requires resolving resultant of all forces to the left or to the right of section along the tangent and the normal to it.
- 4. 3-The slope of the tangent can be defined if the equation of all the arch is defined first. 4-The slope of the tangent is equal to the first derivative of the equation. 5-Substitute by the coordinates of the specified point in the first derivative to calculate the slope.
- 5. Determine the N.F, S.F., and M at points d and e of the three-hinged parabolic arch shown The arch equation is Y= x – 0.025 x 2 Solution Σ Ma= 0 = Yb × 40 – 6 (10 + 20 + 30) Yb = 9 t ↑ Σ Y= 0 = Ya + 9 – 3 × 6 Ya = 9 t ↑ = 0 = 9 × 20 – 6 × 10 – 10 Xa Xa = 12 t -> ΣX = 0 = 12 – Xb Xb = 12 t ←
- 6. A section through point d At x = 5, y = Yd = 5 - 0.025 × 5 2 = 4.375 m. = 1-0.05x=1 – 0.05 * 5 = 0.75 = 0.6 and = 0.8 Σ X = 0 = 12 – X X= 12t ← Σ Y = 0 = 9 – Y Y= 9t ↓ ΣMd = 0 = 12 × 4.375 – 9 × 5 + M M = - 7.5 m.t., i.e M= 7.5m.t. (clockwise) Ɵ1 Ysin Ɵ1 Ycos Ɵ1 Xcos Ɵ1 Xsin Ɵ1
- 7. Ɵ1 Ysin Ɵ1 Ycos Ɵ1 Xcos Ɵ1 Xsin Ɵ1
- 8. At x = 30 y = y e = 30 – 0.025 × 30 2 = 7.5 m . At Point e 180-Ɵ2=153.43 Ɵ2=26.57 = 1 – 0.05 × 30 = = 0.50, = 0.446 = 0.893
- 9. ΣMe = 0 = M + 12 × 7.5 – 9 × 10 M is the bending moment at point e = 0 m.t Ne= - (X cos Ɵ2+ Y sin Ɵ2 ) Ne = - (12 × 0.893 + 9 × 0.446) = - 14.74 t Qe=X sin Ɵ2 - Y cos Ɵ2 Qe = 12 × 0.446 – 9 × 0.893 = - 2.685 t For a section just to the right of e ΣX = 0 = 12 – X X = 12 t -> ΣY = 0 = 9 – Y Y = 9 t ↓ 7.5m Ɵ2 X cos Ɵ2 X sin Ɵ2 Y cos Ɵ2 Y sin Ɵ2
- 10. For a section just to the left of e ΣX = 0 = 12 – X X = 12 t -> ΣY = 0 = 9 – 6 – Y Y= 3 t ↓ Ne= - (X cos Ɵ2+ Y sin Ɵ2 ) Ne = - (12 × 0.893 + 3 × 0.446) = - 12.05t Qe=X sin Ɵ2 - Y cos Ɵ2 Qe = 12 × 0.446 – 3 × 0.893 = 2.673 t Y cos Ɵ2 X sin Ɵ2 Y sin Ɵ2 X cos Ɵ2 Ɵ2
- 11. Example 4.2 : Determine the N.F, S.F., and M at point d of the three-hinged circular arch shown The equation of the arch is Y=ax 2 +bx+c At A x=0 y=0 c=0 At x=8 y=4 4=a(8) 2 + 8b 1=16a+2b (1) A t x=16 y=0 0=a(16) 2 + 16b -b = 16a (2) Substitute from 2 into 1 1=-b+2b b=1 a=-1/16 Y=-x 2 /16 +x
- 12. Example 4.2 : Determine the N.F, S.F., and M at point d of the three-hinged circular arch shown The equation of the arch is Y=-x 2 /16+x ΣMb= 0 = Ya × 16+ 4 ×2 – 6 × 10 - 8 × 4- 2 ×2 Ya = 5.5t ΣY= 0 Yb=10.5t ΣMc= 0 for left part 6 ×2+4 ×2 + 4 Xa - 5.5 ×8 = 0 Xa=6t ΣX= 0 Xb=10t Y a = 5.5t Yb =10.5t Xa = 6t Xb = 10t
- 13. Y=-X 2 /16+X At X=11 Y = 3.44m dy /dx = -X / 8+1 dy/dx= tan( 180- Ɵ) = -0.375 Ɵ=20.56 SinƟ= 0.351 CosƟ = 0.936 A section through point d Ɵ 10.5 t 10t 10t 0.5t 10 cos Ɵ 0.5 sin Ɵ 10 sin Ɵ 0.5 cos Ɵ Ɵ
- 14. Nd= - (10 cos Ɵ+ 0.5 sin Ɵ ) Ne = - (10 ×0.936 + 0.5 × 0.351 ) = - 9.53 t Qd=10 sin Ɵ – 0.5 cos Ɵ Qe = 10 × 0.351 – 0.5 × 0. 936 = + 3.04 t Md + 8 ×1+ 2 ×3+ 10 ×3.44 = 10.5 ×5 Md = 4.1 clockwise Ɵ 10.5 t 10t 10t 0.5t 10 cos Ɵ 0.5 sin Ɵ 10 sin Ɵ 0.5 cos Ɵ 3.44 m 5 m 3 m
- 15. Problem 4.2 : Determine the N.F, S.F., and M at point S of the three-hinged circular arch shown Solution Σ MC= 0 = Yb × 6 – 3.6 Xb-2*6*3=0 YB = 0.6 XB + 6 Σ MA= 0 2.8 XB+14YB = 2*14*7 XB= 10 t YB=12 t S 4.8m
- 16. S 4.8m 10t 8t 60 60 8sin60 8cos60 10cos 60 10sin60 8t 16t 10t 4.8m Σ X= 0 XA=10t Σ Y= 0 YA=16 t Σ MS =MS-16*4+ 10*4.8+ 8*2=0 MS=0 Ns= - (10 sin 60+ 8 cos60 )=-12.66t Qs= 8 sin 60 -10 cos 60 = - 1.93t 4m 60