NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
Scalars, Vectors and Tensors
A scalar is a physical quantity that it represented by a dimensional number at a particular point in space and time. Examples are hydrostatic pressure and temperature.
A vector is a bookkeeping tool to keep track of two pieces
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
11
Rotational Vectors
and Angular Momentum
New Concepts, New Skills
By the end of this chapter you should be
able to
Specify the vector direction of angular
velocity, angular acceleration, and
torque (11.1, 11.2).
Define the vector cross product and
use
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
2.4 Constant Acceleration 21
EXAMPLE 2.3
Motion with Constant Acceleration: Landing a Jetliner
A jetliner touches down at 270 km/h. The plane then decelerates
(i.e., undergoes acceleration directed opposite its velocity) at
4.5 m/s 2 . Whats the minimum r
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
18 Chapter 2 Motion in a Straight Line
Position, x (m)
10
5
0
5
1
2
Time, t (s)
10
Velocity, v (m/s)
1
Acceleration, a (m/s2)
(b)
10
5
0
5
10
15
20
4
Here the position
reaches a maximum, so the
velocity is zero.
(a)
5
0
5
10
15
20
25
3
2
Time, t (s)
4
Pos
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
Exercises and Problems 27
An egg drops from a secondstory window, taking 1.12 s to fall
and reaching 11.0 m/s just before hitting the ground. On contact,
the egg stops completely in 0.131 s. Calculate the average magnitudes of its acceleration while fall
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
39
3.5 Projectile Motion
case solving first for the unknown time and then for the distance. In essence, we
solved two problems in Example 3.4: the first involving vertical motion and the second horizontal motion.
Instead of calculating t numerically in Ex
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
3.2 Velocity and Acceleration Vectors 33
Vector Arithmetic with Unit Vectors
Vector
addition is simple
with unit vectors: Just add the corresponding components. If
!
!
A 5 A x ^ 1 A y ^/ and B 5 Bx ^ 1 By ^/, for example, then their sum is
!
!
A 1 B 5 1A
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
42 Chapter 3 Motion in Two and Three Dimensions
vr1
rr1
u
vr2
rr2
the instantaneous direction of motion. In Fig. 3.21a we focus on two nearby points
!
!
!
!
described by position vectors r1 and r2, where the velocities are v 1 and v 2. Figures 3.21b
!
!
!
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
3
Motion in Two
and Three Dimensions
New Concepts, New Skills
By the end of this chapter you should be
able to
Use vectors to describe position,
velocity, and acceleration in three
dimensions (3.1, 3.2).
Add and subtract vectors, and multiply them by sc
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
36 Chapter 3 Motion in Two and Three Dimensions
Vertical spacing is
the same, showing
that vertical and
horizontal motions
are independent.
FIGURE 3.11 Two marbles, one dropped and
the other projected horizontally.
!
y 5 y0 1 vy0 t 1 12 ay t2. (Remember t
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
24 Chapter 2 Motion in a Straight Line
TIP Multiple Answers
Frequently the mathematics of a problem gives more than one answer. Think about
what each answer means before discarding it! Sometimes an answer isnt consistent
with the physical assumptions of t
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
2.2 Instantaneous Velocity 15
EXAMPLE 2.1
Speed and Velocity: Flying with a Connection
EVALUATE You start in Houston and end up in Kansas City, for a dis
To get a cheap flight from Houston to Kansas Citya distance of
1000 kmyou have to connect in Minneap
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
1
Experimental Stress Analysis
By
Prof. K. Ramesh
Department of Applied Mechanics, IIT Madras.
Course Outline The course covers the basic aspects of experimental stress analysis
that includes exhaustive treatment of the most versatile techniques like phot
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
VESSEL VOLUME
Ellipsoidal head vessel full volume
Volume = ( * D )/ 12 + (* D * L )/ 4
Torispherical head vessel full volume
Volume = (0.1694 * D ) + (* D * L )/ 4
Hemispherical head vessel full volume
Volume = ( * D )/ 6 + (* D * L )/ 4
where,
= 3.141
D
NED University of Engineering & Technology, Karachi
STRESS ANALYSIS
MECHANICAL TE505

Spring 2016
Second Order Linear Equations and the Airy Functions:
Why Special Functions are Really No More Complicated than Most Elementary
Functions
We shall consider here the most important second order ordinary differential equations, namely linear equations.
The