Shafts under combined torsion and bending
Transmission shafts are
common in machinery and
are subjected to torsion and
bending and shear.
M
F
T
Where is the
critical point of
a transmission
shaft?
F
For slender shafts, stresses
due to shear are negligible
Relevant specifications on wind turbines from
VESTAS website :
Blade
Length 44 m
Operating Data
Max. chord 3.5 m
Rated power 1,800 kW
Weight 6,700 kg
From specifications, we deduce the
aerodynamic forces from
Power=Torque x Angular Vel
Rotor
Rotor diamete
Frequently Asked Questions
CONTENTS
SECTION (G)
SECTION I
SECTION II
SECTION III
SECTION IV
General Questions
Analysis of Stress and Strain
Bending of Beams
Stresses in beams
Deflections of beams
1
SECTION (G)
General Questions
1) What is the weightage of
SESSION 2015-16
LESSON PLAN
ME2113 Part I (6 weeks)
13 Aug
Stresses and Strains
20 Aug
Stresses and Strains
27 Aug
Shear force and Bending Moment
03 Sept
Stresses in Loaded Beams
10 Sep
Stresses in Loaded Beams/Deflection of Beams
17 Sep
Deflection of Bea
Solutions to Tutorial 3
Solution Q1
1(a)
P
Mo
Mo
Mxz
R
Fxy
R
L
x
Vertical equilibrium:
Rotational equilibrium:
RP
M o PL
Multiple-integration Method (starting from the Load Intensity Equation)
d 4v
2
1
1
2
1
EI 4 q x M o x R x P x L PL x P x P x L
dx
d 3v
SESSION 2015-16 Semester 1
ME2113 Mechanics of Materials I (Part 1)
A/P Tay C. J.
Tay Cho Jui
Department of Mechanical Engineering
Applied Mechanics Group
NUS ME Dept Web Page
Office EA-05-13
[email protected]
Tel: 65162557
National University of Singap
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mechanical Engineering
ME2113 Mechanics of Materials I
Tutorial 2
Stresses in Beams
1. A straight strip 5 mm thick and 40 mm wide is bent around a cylindrical wine cask of
5 m diameter and the ends are connec
CHAPTER 3
STRESSES IN LOADED BEAMS
National University of Singapore
STRESSES IN LOADED BEAMS
3.1 PURE BENDING
Consider a straight horizontal beam with a cross-section which
is symmetrical about the vertical axis
this beam experiences a bending moment whic
CHAPTER 2
BENDING OF BEAMS
Examples for the use of beams:
Supporting floors of buildings, bridges
Automotive axles, leaf springs
Airplane wings
20085
BENDING OF BEAMS
Singularity Functions
Singularity Functions can be use to describe the load intensity w(
CHAPTER 4
DEFLECTION OF BEAMS
National University of Singapore
CHAPTER 4
DEFLECTION OF BEAMS
4.1 STATICALLY DETERMINATE BEAMS
4.2 STATICALLY INDETERMINATE BEAMS
AND SUPERPOSITION METHOD
Good News!
Both sections 4.1 & 4.2 are Not examinable!
National Unive
Chapter 3
STRESSES IN LOADED BEAMS
3.1 PURE BENDING
3.1
3.2
Points to note:
it is called the:
note:
3.3
(i)
Strain Due to Bending
For a fibre JK the new length L:
(the change in length of JK)
and the max numerical strain m is given by:
3.4
3.5
3.6
Common
Chapter 4
DEFLECTION OF BEAMS
4.1 STATICALLY DETERMINATE BEAMS
From beam bending theory
d 2V d 2v
EI 2EI M M
dx dx 2
(1)
The deflection v can thus be found by double integration of Eq (1).
This method is known as the Macaulays Method.
Hence
V
1
Mdxdx
EI
Founded 1905
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mechanical Engineering
ME2113
MECHANICS OF
MATERIALS I
Course Lecturer:
A/P CJ TAY
i
Founded 1905
SESSION 2015-16
Semester 1
ME2113 Mechanics of Materials I
Modular Credits: 3
Part I Lecture Note
Chapter 2
BENDING OF BEAMS
Examples for the use of beams:
Supporting floors of buildings, bridges
Automotive axles, leaf springs
Airplane wings, brackets.
The following sections discuss singularity functions and sign
convention commonly used in bending
ME2113-1
DEFLECTION AND BENDING STRESSES IN BEAMS
(EA-02-21)
SEMESTER 3
2016/2017
NATIONAL UNIVERSITY OF SINGAPORE
DEPARTMENT OF MECHANICAL ENGINEERING
1
INTRODUCTION
Beams are one of the commonest components encountered in structures. In most cases, they
ME 2113
MECHANICS OF MATERIALS I
Part II
Vincent Tan
Department of Mechanical Engineering
National University of Singapore
Office : EA-05-06
Email : [email protected]
-no xed consultation time; can drop by oce when hes in
-ask doubts by email, typically