1
MP2001exam-sem1 04/05, Q1
1. Figure 1(a) shows a rigid link ABCD supported by column G and bar F.
Link ABCD is pin-ended at A and D. The compressive axial stress in
column G is 12 MPa and the tensile strain of the bar F is 300 x 10-6
mm/mm. Neglect the
List of Equations
The symbols in the equations have the usual meaning as described in the course text book
Mechanics of Materials, 5th Edition, McGraw Hill, 2009 by Beer F. P., Johnston E. R. &
Dewolf J. T.
Deformation under axial loading
Generalized Hook
Ch 11 Energy Methods
11.1
11.2
11.3
11.4
11.5
11.9
11.10
Introduction
Strain Energy
Strain Energy Density
Elastic Strain Energy for Normal Stresses
Elastic Strain Energy for Shearing Stresses
Work and Energy under a Single Load
Deflection under a Single L
Chap 10 Columns
10.3 Eulers Formula for Pin-Ended Beams
10.4 Extension of Eulers Formula
1
10.3 Eulers Formula for Pin-Ended Beams
[x = 0, y = 0]
Buckling load of an axially loaded
pin ended member is
P = Pcr =
2 EI
L2
=Eulers Load
()
P
2 E Ar2
2E
=
Ch 9 Deflection of Beams
9.1 Introduction
9.3 Equation of Elastic Curve
9.6 Using Singularity Functions
1
9.1 Introduction
Besides strength (max & max) , must also check for
deformation (max deflection).
From Beam Bending,
1
=
M ( x)
EI
(Moment-curvatur
Example 7.02
(a) Rework Ex 7.01 using
Mohrs circle construction
& find
(b) Principal planes,
(c) Principal stresses,
(d) Max shearing stress and
corresponding normal
stress.
1
Construction of Mohrs circle
x + y (50) + ( 10)
=
= 20 MPa
OC = ave =
2
2
CF
Chapter 6
Shearing Stresses in Beams
and Thin-Walled Members
Introduction
Shearing stresses exist other than normal stresses
Chapter 6- Shearing Stresses in Beams and Thin-Walled Members
2
Introduction
Chapter 6- Shearing Stresses in Beams and Thin-Walled
Chapter
Chapter 5
Analysis and Design
of Beams for Bending
W
P1
P2
C
A
W
P1
C
A
RA
wa
P1
C
A
RA
V
Introduction
Objective - Analysis and design of
and design of
beams
B
Transverse loadings of beams are
classified as concentrated loads or
P2
di
distribute
Chapter 4
Pure Bending
Pure Bending
Barbell
Pure Bending: Prismatic members
subjected to equal and opposite
bj
couples acting in the same
longitudinal plane
Chapter 4 - Pure Bending
2
Other Loading Types
Eccentric Loading: Axial loading which does not
Lo
Chapter
Chapter 3
Torsion
Torsional Loads on Circular Shafts
Interested in stresses and
strains of circular shafts
subjected to twisting
couples or torques
Turbine exerts torque T
on the shaft
the shaft
Shaft transmits the torque
transmits the torque
t
Chapter 2
Stress and Strain
Axial Loading
Stress & Strain: Axial Loading
Chapter 2 is concerned with deformation of a
structural member under axial loading. Later
chapters will deal with torsional and pure
bending loads.
Chapter 2 - Stress and Strain -
MP2001/AE2008 MECHANICS OF MATERIALS
Dr Chou Siaw Meng
Associate Professor
Tel: 67904958 | Office: N3.2-02-71
Email: msmchou@ntu.edu.sg
School of Mechanical and Aerospace Engineering
Nanyang Technological University
Textbook: MECHANICS OF MATERIALS (5th e