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Stresses due to bending
Lecture -4
Stresses due to bending:
x
Mb y
I NA
A
xy
VQ
b I NA
Q ydA yA
y
y
B
y
b
2
BITS Pilani, Pilani Campus
Ex :
The beam ABC has simple supports at A and B and an
overhang from B to C. The length of
BITS Pilani
Pilani Campus
Stresses due to bending
Lecture -3
Ex 7.2:
Determine the maximum tensile and compressive bending
stresses in T shaped beam due to constant bending
moment and show the distribution of these stresses.
2
BITS Pilani, Pilani Campus
E
BITS Pilani
Pilani Campus
Chapter-9
Stability of equilibrium: Buckling
Jitendra S Rathore
Column:
Slender member design to carry compressive loads
Pcritical
RB
Design of a structure/system
ability of a structure to support a
given load
1. Without excessiv
Calculus of Variations and Finite Elements
Andreas Stahel
November 21, 2012
c Andreas Stahel, 1999
All rights reserved. This work may not be translated or copied in whole or in part without the written permission by
the author, except for brief excerpts i
Lect-8
1
Lect-8
In this lecture.
Cycle components and component
performance
Intake
Compressor/fan
Combustion chamber
Turbine
Nozzle
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-8
Cycle components
Jet engine cycle has
Lect-6
1
Lect-6
In this lecture.
Brayton cycles
Ideal Brayton cycle
Variants of Brayton cycle
Actual/real Brayton cycle
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-6
Brayton cycle
The Brayton cycle was proposed by
Lect-14
1
Lect-14
In this lecture.
Axial flow compressors
Basic operation of axial compressors
Velocity triangles
Work and compression
Design parameters
Flow coefficient
Loading coefficient
Degree of reaction
Diffusion factor
Prof. Bhaskar Roy, Prof.
Lect-10
1
Lect-10
In this lecture.
Real cycle analysis
Turbojet engine
Turbojet with afterburning
Turbofan engine
Turboprop and turboshaft engines
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-10
Real cycle for turbojet
Lect-7
1
Lect-7
In this lecture.
Jet engine cycles for aircraft propulsion
Turbojet engine
Turbojet engine with afterburning
Turbofan and its variants
Turboprop and turboshaft engines
Ramjet engines
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Ae
Lect-39
1
Lect-39
In this lecture.
Components of ramjets and pulsejets
Ramjet combustors
Types of pulsejets: valved and
valveless, Pulse detonation engines
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-39
Ramjet engin
Lect-19
1
Lect-19
In this lecture.
Performance characteristics of
centrifugal compressors
Surging and choking
Tutorial on centrifugal compressors
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-19
Performance characteri
Lecture 25
1
Lect 25
Combustion Parameters
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect 25
Pressure losses
Combustion chamber pressure loss is due to two
causes i) Skin friction, mixing and turbulence, and
ii) The rise
Lecture 26
1
Lect 26
Combustion
Fuel Injectors
Flame Stablization
Combustion Instability
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect 26
Fuel injection
Most commonly used injection system in
aircraft gas turbine engines
Lect-30
1
Lect-30
In this lecture.
Subsonic and supersonic nozzles
Working of these nozzles
Performance parameters for nozzles
Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay
2
Lect-30
Variation of fluid velocity with flow
are
BITS Pilani
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Chapter 7
Stresses due to bending
Stresses due to bending:
Slender member subjected to transverse loading
Axial force
F
A
Shear force
V
A
Twisting moment (Mxx or Mt )
Mtr
Ix
M xz
Bending moment (Mb)
Mxy, Mxz
2
BITS Pila
BITS Pilani
Pilani Campus
Chapter 7
Stresses due to bending (Lecture -2)
Jitendra Rathore
Pure bending : assumptions
1. Plane cross-sections remain
plane & perpendicular to
plane of symmetry
2. Original straight longitudinal
lines
become
arcs
of
concentri
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Torsion
Lecture 2 and 3
Jitendra S Rathore
Overall conclusion:
Longitudinal
lines become
twisted
Circle remain
circular
Radial lines
remain straight
No expansion or contraction of circular cross-section
No lengthening or shorteni
P2.6:
Rotation
+
Translation
Rotation
1
BITS Pilani, Pilani Campus
Assignment 2:
The truss consists of three members each made of steel
(E = 205 GPa) 20 cm and having a cross sectional area of 5 cm2.
Applying the energy method (i.e. Castigliano method) de
BITS Pilani
Pilani Campus
Chapter 3
Points to revise
J S Rathore
Point of contra-flexure:
A point where curvature of beam changes sign.
Occurs at a point on the beam where bending
moment changes sign.
Also known as Point of inflexion.
C
2
BITS Pilani,
ME F211 - MF F211 - ES C 221
Mechanics of Solids
BITS Pilani
Pilani Campus
Jitendra S Rathore, Lecturer
Department of Mechanical Engineering
1
BITS Pilani
Pilani Campus
Fundamental principles of mechanics
Chapter - 1
Q1: Friction
A 7 m long ladder rests a
ME F211 - MF F211 - ES C 221
Mechanics of Solids
BITS Pilani
Pilani Campus
Jitendra S Rathore, Lecturer
Department of Mechanical Engineering
1
BITS Pilani
Pilani Campus
Chapter 2
Introduction to Mechanics of Deformable Bodies
Objectives
Steps to analyze
BITS Pilani
Pilani Campus
Lecture 5
Forces and Moments transmitted by Slender Members
Objectives:
A beam have a variety of loads:
1. point loads
2. Uniformly Distributed Load (UDL)
3. Linearly Varying Distributed Load (LDL)
4. applied moments
Singularity