R09 - ENGINEERING MECHANICS

I Year B.Tech.

UNIT – I

Introduction to Engineering. Mechanics – Basic Concepts.
Systems of Forces : Coplanar Concurrent Forces – Components in Space – Resultant – Moment of Force
and its Application – Couples and Resultant of Force Systems.

UNIT – II
Equilibrium of Systems of Forces : Free Body Diagrams, Equations of Equilibrium of Coplanar Systems,
Spatial Systems for concurrent forces. Lamis Theorem, Graphical method for the equilibrium of coplanar
forces, Converse of the law of Triangle of forces, converse of the law of polygon of forces condition of
equilibrium.

UNIT – III
Centroid : Centroids of simple figures (from basic principles ) – Centroids of Composite Figures
Centre of Gravity : Centre of gravity of simple body (from basis principles), centre of gravity of composite
bodies, pappus theorem.

UNIT – IV
Area moment of Inertia : Definition – Polar Moment of Inertia, Transfer Theorem, Moments of Inertia of
Composite Figures, Products of Inertia, Transfer Formula for Product of Inertia.
Mass Moment of Inertia : Moment of Inertia of Masses, Transfer Formula for Mass Moments of Inertia,
mass moment of inertia of composite bodies.

UNIT – V
Analysis of perfect frames ( Analytical Method) – Types of Frames – Assumptions for forces in members of a
perfect frame, Method of joints, Method of sections, Force table, Cantilever Trusses, Structures with one end
hinged and the other freely supported on rollers carrying horizontal or inclined loads.

UNIT – VI
Kinematics : Rectilinear and Curvilinear motions – Velocity and Acceleration – Motion of Rigid Body –
Types and their Analysis in Planar Motion.
Kinetics : Analysis as a Particle and Analysis as a Rigid Body in Translation – Central Force Motion –
Equations of Plane Motion – Fixed Axis Rotation – Rolling Bodies.

UNIT – VII
Work – Energy Method : Equations for Translation, Work-Energy Applications to Particle Motion,
Connected System-Fixed Axis Rotation and Plane Motion. Impulse momentum method.

UNIT – VIII
Principle of virtual work: Equilibrium of ideal systems, efficiency of simple machines, stable and unstable
Equilibriums

TEXT BOOKS :
1. Engineering. Mechanics / Timoshenko & Young.
2. Engineering. Mechanics / S.S. Bhavikatti & J.G. Rajasekharappa

REFERENCES :
1. Engineering Mechanics / Fedinand . L. Singer / Harper – Collins.
2. Engineering. Mechanics / Irving. H. Shames Prentice – Hall.
3. Engineering. Mechanics Umesh Regl / Tayal.
4. Engineering. Mechanics / R.V. Kulkarni & R.D. Askhevkar
5. Engineering. Mechanics/Khurmi/S.Chand.
6. Engineering. Mechanics / KL Kumar / Tata McGraw Hill.

R09 - ENGINEERING DRAWING

I Year B.Tech.


UNIT – I
INTRODUCTION TO ENGINEERING DRAWING : Principles of Engineering Graphics and their Significance
– Drawing Instruments and their Use – Conventions in Drawing – Lettering – BIS Conventions. Curves used
in Engineering Practice & their Constructions :
a) Conic Sections including the Rectangular Hyperbola – General method only.
{Ellipse,Parabola,Hyperbola,Rectangular Hyperbola}
b) Cycloid, Epicycloid and Hypocycloid
c) Involute.
d) Scales: Different types of Scales, Plain scales,Diagonal scales,vernier scales, comparative scales, scales of chords.

UNIT – II
DRAWING OF PROJECTIONS OR VIEWS ORTHOGRAPHIC PROJECTION IN FIRST ANGLE
PROJECTION: Principles of Orthographic Projections – Conventions – First and Third Angle, Projections of
Points and Lines inclined to both planes, True lengths, traces.

UNIT – III
PROJECTIONS OF PLANES & SOLIDS: Projections of regular Planes, auxiliary planes and Auxiliary
projection inclined to both planes. Projections of Regular Solids inclined to both planes – Auxiliary Views.

UNIT – IV
SECTIONS AND SECTIONAL VIEWS:- Right Regular Solids – Prism, Cylinder, Pyramid, Cone – Auxiliary views.

DEVELOPMENT AND INTERPENETRATION OF SOLIDS: Development of Surfaces of Right, Regular
Solids – Prisms, Cylinder, Pyramid Cone and their parts. Interpenetration of Right Regular Solids

UNIT – V
INTERSECTION OF SOLIDS:- Intersection of Cylinder Vs Cylinder, Cylinder Vs Prism, Cylinder Vs Cone.

UNIT - VI
ISOMETRIC PROJECTIONS : Principles of Isometric Projection – Isometric Scale – Isometric Views–
Conventions – Isometric Views of Lines, Plane Figures, Simple and Compound Solids – Isometric Projection
of objects having non- isometric lines. Isometric Projection of Spherical Parts.

UNIT –VII
TRANSFORMATION OF PROJECTIONS : Conversion of Isometric Views to Orthographic Views –Conventions.

UNIT – VIII
PERSPECTIVE PROJECTIONS : Perspective View : Points, Lines, Plane Figures and Simple Solids,
Vanishing Point Methods (General Method only).

TEXT BOOKS :
1. Engineering Drawing, N.D. Bhat / Charotar
2. Engineering Drawing and Graphics, Venugopal / New age.
3. Engineering Drawing – Basant Agrawal, TMH

REFERENCES :
1. Engineering drawing – P.J. Shah.S.Chand.
2. Engineering Drawing, Narayana and Kannaiah / Scitech publishers.
3. Engineering Drawing- Johle/Tata Macgraw Hill.
4. Computer Aided Engineering Drawing- Trymbaka Murthy- I.K. International.
5. Engineering Drawing – Grower.
6. Engineering Graphics for Degree – K.C. John.

Rules of Resolution of a Force

Very Important Rules to follow for Mechanics

Nallimilli’s Law1:

If Force is away from the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, the corresponding axis component is always “cos” the opposite axis component is always “sin” using the sign symbols of corresponding quadrant.
Explanation: In above diagram P is in first quadrant, the sign symbols for both components are positive. If an angle makes with X-axis then the resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, if an angle makes with Y-axis then the resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis Px = + Pcosθ, Py= +Psinθ ; If angle with Y-Axis Px = + Psinθ, Py= +Pcosθ

Nallimilli’s Law2:

If Force is towards the origin ( intersection of co – ordinate axis X&Y ) and making an angle with either of the axis, shift the force component into opposite quadrant and away from the intersection of co-ordinate axis, and perfectly shift the angle also with the same axis at the
initial quadrant position then implement law1
Explanation: In above diagram P is in first quadrant & towards origin, shifts P to opposite quadrant i.e. third quadrant, the sign symbols for both components are Negative. If an angle makes with X-axis then shift the angle with same X-axis in opposite quadrant, using law1 resolution component of P corresponding to X-axis is Pcosθ, opposite component is Psinθ related to Y-axis, If an angle makes with Y-axis then shift the angle with same Y-axis in opposite quadrant, using law1 resolution component of P corresponding to Y-axis is Pcosθ, opposite component is Psinθ related to X-axis
If angle with X-Axis in first quadrant after shifting same angle with X-axis in third quadrant
Px = - Pcosθ, Py = -Psinθ
If angle with Y-Axis in first quadrant after shifting same angle with Y-axis in third quadrant
Px = - Psinθ, Py = -Pcosθ
Resolution component of force P Px Py
With X-axis in first quadrant + Pcosθ +Psinθ
With Y-axis in first quadrant +Psinθ + Pcosθ
With X-axis in second quadrant -Pcosθ +Psinθ
With Y-axis in second quadrant -Psinθ + Pcosθ
With X-axis in third quadrant -Pcosθ -Psinθ
With Y-axis in third quadrant -Psinθ -Pcosθ
With X-axis in third quadrant +Pcosθ -Psinθ
With Y-axis in third quadrant +Psinθ -Pcosθ

Foundation of Non Circuit Engineering (Engineering Mechanics)

Before Mechanics

Measurement of angel’s : There are two common systems of measuring angel’s

1.sexagesimal measure : According to this system, divide a right angle 90 into equal parts called degrees. Each degree is divided into sixty equal parts called minutes and each minute is divided into sixty equal parts called seconds. Denoting one degree, one minute and one second by the symbols 1⁰ 1’1”.

2. Circular measure : The unit of measurement is called radian . ∏ is an irrational number. Its approximate value is 22/7. Its value correct to 5 decimal places is 3.14159. Sometimes1/∏ value also required & is given by 0.31831.

Relation between degree & radian {1 radian = 180⁰ x 1/∏ = 57⁰17’44.8”}; 1⁰ = ∏ /180 radian

Formulas from Trigonometry:

1. sin²A + cos²A = 1 ; sin²A = 1- cos²A ; cos²A = 1- sin²A

2. 1+tan²A = sec²A ; tan²A = sec²A -1 ; tan²A - sec²A = 1

3. sin(A+B) = sin A . cos B + cos A . sin B

4. sin(A - B) = sin A . cos B - cos A . sin B

5. cos(A+B) = cos A . cos B – sin A . sin B

6. cos(A - B) = cos A . cos B + sin A . sin B

7. sin(A+B) . sin(A - B) = sin²A-sin²B = cos²B- cos²A

8. cos(A+B) . cos(A - B) = cos²A – sin²B = cos²B-sin²A

9. sin2θ = 2 sinθ cosθ = 2tan θ / 1+tan²θ

10. cos2θ = cos²θ – sin²θ =1- tan²θ / 1+tan²θ = 1-2 Sin²θ =2cos²θ -1

Formulas from Differentiation:

1. y = xⁿ, dy/dx = nx^n-1

2. y = e^x, dy/dx = e^x

3. y = log x, dy/dx = 1/x

4. y = a^x, dy/dx = a^x log a

5. y = sinx , dy/dx = cos x

6. y = cosx, dy/dx = - sinx

Scalars & Vectors

Those quantities which have only magnitude and are not related to any direction in space are called scalars. Whereas those which have both magnitude and direction are called vector quantities.

1. Vectors are said to be like vectors when they have the same sense of direction, unlike vectors when they are in opposite direction.

2. When two or more vectors are said to be collinear vectors when they act along the same line of action & parallel vectors when they are in parallel lines

3. Three or more vectors are said to be coplanar when they are parallel to the same plane or lie in the same plane whatever their magnitudes be (**two vectors are always coplanar)

4. Two vectors are said to be equal when they have the same length(magnitude &are parallel having the same sense of direction)are called as equal vectors.

5. If the origin and terminal points of a vector coincide, then it is said to be a zero vector

6. { Unit vector = Force vector / Magnitude of vector}

7. The vectors having the same initial point are call co –initial vectors.

8. A vector drawn parallel to a given vector through a specified point in space is called a localized vector. But if the origin of vectors is not specified the vectors are called free vectors.

Formulas from Vectors

1. a.b = b.a = ab cosθ

if the scalar product is of two vectors is zero, then at least one of the vectors is a zero vector or they are perpendicular.

2. a.(b+c) = a.b + a.c

3. i²=j²=k²=1

4. i.j=j.k=k.i=0

5. a x b ≠ b x a but a x b = - b x a

6. i x i = j x j = k x k =0

7. i x j = k = - j x i ; j x k = i = - k x j; k x i = - i x k

8. if a = a₁i+a₂j+a₃j ; b = b₁i+b₂j+b₃k then a x b is given by

a x b = (a₂b₃ – a₃b₂) i +(a₃b₁-a₁b₃) j + (a₁b₂ – a₂b₁) k

Conversion Equivalents:

Length 1in = 2.540cm ; 1ft =12in =30.48cm

1mile=5280ft=1.609km

Force 1lb= 0.4536kg = 4.448N

Velocity 88fps=60mph=96.54km/hr

Acceleration g = 32.2fps² = 9.81m/s²

Pressure 1atm = 14.7psi=760mmof Hg= 1.013 x 10⁵ N/m2

Volume 1cuft=7.481gallons=28.32litres

Sign Conventions:

	I Quadrant	II Quadrant	III Quadrant	IV Quadrant
X -Axis	+	-	-	+
y-Axis	+	+	-	-

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