Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Flow Through Orifices, Orifice, Types of Orifice according to Shape Size Edge Discharge, Jet, Venacontracta, Hydraulic Coefficients, Coefficient of Contraction,Coefficient of Velocity, Coefficient of Discharge, Coefficient of Resistance, Hydraulic Coefficients by Experimental Method, Discharge Through a Small rectangular orifice, Discharge Through a Large rectangular orifice, Discharge Through a Fully Drowned orifice, Discharge Through Partially Drowned orifice, Mouthpiece and its types. By Engr. M. Jalal Sarwar
Strength of Materials all formulas in pdf
it subject iosd also klnown as mechanics of Soilid.
in this pdf there are formulas of stress strain springs - closed coil helical spring , open coil helical Springs etc.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Lecture slides on the calculation of the bending stress in case of unsymmetrical bending. The Mohr's circle is used to determine the principal second moments of area.
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Flow Through Orifices, Orifice, Types of Orifice according to Shape Size Edge Discharge, Jet, Venacontracta, Hydraulic Coefficients, Coefficient of Contraction,Coefficient of Velocity, Coefficient of Discharge, Coefficient of Resistance, Hydraulic Coefficients by Experimental Method, Discharge Through a Small rectangular orifice, Discharge Through a Large rectangular orifice, Discharge Through a Fully Drowned orifice, Discharge Through Partially Drowned orifice, Mouthpiece and its types. By Engr. M. Jalal Sarwar
Strength of Materials all formulas in pdf
it subject iosd also klnown as mechanics of Soilid.
in this pdf there are formulas of stress strain springs - closed coil helical spring , open coil helical Springs etc.
This document gives the class notes of Unit-8: Torsion of circular shafts and elastic stability of columns. Subject: Mechanics of materials.
Syllabus contest is as per VTU, Belagavi, India.
Notes Compiled By: Hareesha N Gowda, Assistant Professor, DSCE, Bengaluru-78.
Mechanical Engineering is the Branch of Engineering.The mechanical engineering field requires an understanding of core areas including mechanics, dynamics, thermodynamics, materials science and structural analysis,Fluid Mechanics, Metrology and Instrumentation, Dynamics of Machinery- II, Manufacturing Processes II, Industrial Drafting and Machine Design, Engineering Graphics, Power Plant Engineering. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Ekeeda Provides Online Video Lectures for Mechanical Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Ekeeda Provides Online Video Lectures for Mechanical Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/mechanical-engineering
Civil Engineering is the Branch of Engineering.The Civil engineering field requires an understanding of core areas including Mechanics of Solids, Structural Mechanics - I, Building Construction Materials, Surveying - I, Geology and Geotechnical Engineering, Structural Mechanics, Building Construction, Water Resources and Irrigation, Environmental Engineering, Transportation Engineering, Construction and Project Management. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Civil Engineering is the Branch of Engineering.The Civil engineering field requires an understanding of core areas including Mechanics of Solids, Structural Mechanics - I, Building Construction Materials, Surveying - I, Geology and Geotechnical Engineering, Structural Mechanics, Building Construction, Water Resources and Irrigation, Environmental Engineering, Transportation Engineering, Construction and Project Management. Ekeeda offers Online Mechanical Engineering Courses for all the Subjects as per the Syllabus Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Kinetics of particles impulse momentum methodEkeeda
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
Learn Online Courses of Subject Introduction to Civil Engineering and Engineering Mechanics. Clear the Concepts of Introduction to Civil Engineering and Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/introduction-to-civil-engineering-and-engineering-mechanics
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Coplanar forces res & comp of forces - for mergeEkeeda
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us/l http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Ekeeda Provides Online Engineering Subjects Video Lectures and Tutorials of Mumbai University (MU) Courses. Visit us: https://ekeeda.com/streamdetails/University/Mumbai-University
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
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P
INTRODUCTION
We know everybody is attracted to the centre of the earth by a force of
attraction, known as the weight of the body.
The weight being a force acts through a point known as the centre of gravity
of the body. In Chapter 2 we have emphasised in article 2.2 that the point of
application of the force is one of the necessary data to define a force. Hence
the location of centre of gravity becomes important while dealing with the
weight force.
In this chapter we will learn to find the centre of gravity of bodies, plane areas
and lines. We will also study the approach using integration method to find
the centre of gravity of figures bounded by curve. Finally we will study the
application of the location of centre of gravity to certain engineering problems.
CENTROIDS AND CENTRE OF GRAVITY DEFINE
Centre of Gravity
It is defined as a point through which the whole weight of the body is
assumed to act. It is a term used for all actual physical bodies of any size,
shape or dimensions e.g. book, cupboard, human beings, dam, car, etc.
Centroid
The significance of centroid is same as center of gravity. It is a term used for
center of gravity of all plane geometrical figures. For example, two dimensional
figures (Areas) like a triangle. Rectangle, circle, and trapezium or for one
dimensional figures (Lines) like circular arc, straight lines, bent up wires, etc.
Centroid and Centre of Gravity
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RELATION FOR CENTRE OF GRAVITY
Consider a body of weight whose centre of gravity is located at G X,Y as
shown. If the body is split in n parts, each part will have its elemental weight
Wi acting through its centre of gravity located at Gi (xi yi). Refer Fig.
The individual weights W1, W2, W3, ……Wi……..Wn form a system of parallel
forces. The resultant weight of the body would then be
1 2 3 i n
i
W = W + W + W ........+W......W
= W
To locate the point of application of the resultant weight force W using
Varignon's theorem (discussed earlier in Chapter 2).
Taking moments about y axis
Moments of individual weights = Moment of the total weight
about y axis about y axis
1 1 2 2 i i n nW × X +W ×X +.... + W × X ......+W × X = W×X
B i iW X = W × X
i i i i
i
W X W X
X = =
W W
……6.1 (a)
Similarly if the moment are taken about x axis
Moments of individual weights = Moment of the total weight
about x axis about x axis
1 1 2 2 i i n nW × +W × +.... + W × ......+W × = W×Y Y Y Y Y
i iW = W ×Y Y
i i i i
i
W W
= =
W W
Y Y
Y
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Using the relations (a) and (b), the centre of gravity G of a body having co-
ordinates X,Y can be located.
Relation for Centroid
We recall that weight = mass × g
= (Density × Volume) × g
= (Density × Area × Thickness) × g
W = ρ × A × t × g
= (ρ × t × g) A
For uniform bodies i.e. of same density and thickness throughout the body,
we get,
i i i i
i i
ρ×t×g A X A X
X = =
ρ×t×g A A
……6.2 (a)
Similarly,
i i i i
i i
ρ×t×g A A
= =
ρ×t×g A A
y y
Y
…….6.2 (b)
Using the relation (a) and (b), the centroid G having co-ordinates X,Y of a
Plane area can be located.
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AXIS OF SYMMETRY (A. O. S.)
Axis Of Symmetry is defined as the line which divides the figure into two equal
parts such that each part is a mirror image of the other.
If the geometrical figure whose centroid has to be located is a symmetrical
figure, then the centroid will lie on the axis of symmetry (A.O.S.). If the figure
has more than one axis of symmetry, the centroid will lie on the intersection
of the axis of symmetry. Fig below shows the importance of identifying the
axis of symmetry.
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CENTROIDS OF REGULAR PLANE AREAS
Table shows the centroids of regular plane areas. The co-ordinates X,Y of
the centroid ‘G’ are with respect to the axis shown in the figure.
Sr.No. FIGURE AREA X Y
1 b × d b
2
b
2
2 1
b × h
2
b
3
h
3
3 1
b × h
2
_ h
3
4 2
π r
2
0 4 r
3 r
5 2
π r
4
4r
3r
4 r
3 r
6 2
r α*
#
2 rsin α
3 a
0
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CENTROID OF COMPOSITE AREA
An area made up of number of regular plane areas is known as a Composite
Area.
To locate the centroid of a composite area, adopt the following procedure.
PART AREA
Ai
CO-ORDINATES Ai.Xi Ai.Yi
Xi Yi
1. RECTANGLE A1 X1 Y1 A1.X1 A1.Y1
2. SEMI-CIRCLE A2 X2 Y2 A2.X2 A2.Y2
3. RT. ANGLE
TRIANGLE
A3 X3 Y3 A3.X3 A3.Y3
iA i iA .X i iA .Y
Table 2
1. Divide the composite area into regular areas as in Fig. (b)
2. Mark the centroids G1, G2, G3, .....on the composite figure as shown in Fig.
(b) and find their co-ordinates w. r. t. the given axis. Let the area of a
regular part be Ai and the co-ordinates be Xi and Yi.
3. Prepare a table as shown (Table 2)
a) Add up the areas of the different parts to get iA
b) Add up the product of area and x co-ordinate of different parts to get
i iA .X
c) Add up the product of area and y co-ordinate of different parts to get
i iA .Y
4. The co-ordinates of the centroid of the composite figure are obtained by
using relations (a) and (b) viz.
i i
i
A .X
X
A
and
i i
i
A .Y
Y
A
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APPLICATION OF CENTRE OF GRAVITY
For solution of certain engineering problems, we require the location of centre
of gravity. For example,
The centre of gravity for vehicles should be at minimum distance from the
ground, so that tipping of the vehicles is avoided while negotiating curves at
high speed.
Also in case of dam, which is a structure built
across a river to store water, the centre of gravity
of the dam should lie within the middle one-third
of the base of the dam. If the C. G. goes beyond
the middle one-third, the dam may loose its
stability. Refer Fig.
Another area where location of C.G. becomes
important is when the load acting on a
structure is distributed as per a given
relation and one is required to find the
resultant load and its location.
For example, refer figure. The water pressure
exerted on the face of the dam varies along
the depth being zero at the water surface and
having a maximum intensity h at the base (where ) is the unit weight of
water). This load diagram is triangular in shape and therefore the resultant
pressure due to water acting on the dam would be the area of the triangle.
Resultant water pressure 21 1 1
P = h × h h
2 2 2
This pressure shall act at the C.G. of the triangle i. e. at h/3 from the base of
the dam.
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Another example is of a simply supported beam (refer Fig.) which has a
distributed load having zero intensity at the ends and variation is as per the
relation y = f(x) along the length of the beam. The resultant load would lie at
the C.G. of the load diagram and value of the resultant load would be the area
under the load diagram.
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EXCERCISE
1. Locate the centroiod coordinates of the given figures and fill them in the
blanks. All dimensions are in cm units.
2. Locate the centroid of the composite figure shown.
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3. Find the centroid coordinates of the plane lamina shown w.r.to O.
4. Determine the centroid of the shaded area shown.
5. Locate the centroid of the shaded area shown in figure.
6. Determine centroid of plane area ABCDE w.r.t. A.
7. Find centroid of the shaded area.
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8. G is the centroid of an equilateral triangle ABC with base BC of side 60 cm.
If GBC is cut from the lamina, find the centroid of the remaining area.
9. Locate the centroid of the section.
10. Determine the co-ordinates of centroid of the shaded portion.
11. Find the centroid of the shaded area shown in figure. Note that OAF is a
quarter part of a circle of radius 750 mm.
12. Determine the co-ordinates of the centroid of the lamina shown with
respect to origin. Note that the circle of diameter 5O mm is cut out from
the plane lamina, with centre at (15O, 25).
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13. Determine the centroid of the shaded portion shown.
14. Find centroid of shaded plane area.
15. Determine the centroid of the shaded area shown.
16. Determine centroid of the plane lamina shown. Shaded portion is removed.
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UNIVERSITY QUESTIONS
1. A thin homogeneous wire of uniform section is
built into a shape as shown in figure. Determine
the position of c.g. of a wire. Take = 30° and r =
15 cm. (5 Marks)
2. Determine forces in all the members of the plane truss as shown in figure.
(10 Marks)
3. Locate the centroid of the shaded area. (8 Marks)
4. Find centroid of the shaded area. (8 Marks)
5. Find Centroid of shaded area. (8 Marks)