APPENDIX
C
Slopes and Deflections
of Beams
Simply Supported Beam Slopes and Deflections
Beam
v
Slope
P
L
2
umax
L
2
umax
-PL 2
=
16EI
vmax
Elastic Curve
v =
- PL 3
=
48EI
P
u1
u1 =
u2
x
a
u2
b
L
v
- Pab(L + b)
6EIL
Pab(L + a)
=
6EIL
u2
M0
x
u2
x =a
- M0L

12.9 STATICALLY INDETERMINATE BEAMS AND SHAFTSMETHOD OF SUPERPOSITION
12.9
Statically Indeterminate Beams and
ShaftsMethod of Superposition
0 = -vB +
12
P
B
A
L
2
Actual beam
(a)
L
2
The method of superposition has been used previously to solve for the
re

7 24
C H A P T E R 14
ENERGY METHODS
14.2 Elastic Strain Energy for Various
Types of Loading
Using the equations for elastic strain energy developed in the previous
section, we will now formulate the strain energy stored in a member when
it is subjected t

Chapter
8
The offset hanger supporting this ski gondola is subjected to the combined loadings
of axial force and bending moment.
Combined Loadings
CHAPTER OBJECTIVES
This chapter serves as a review of the stress analysis that has been
developed in the pre

2016
Image from the Title Page:
Biocharproject 2011, Tlud biochar stove for sale at Biochar Industries, Viewed 27th May 2014,
<http:/biocharproject.org/charmasters-log/tlud-biochar-stove-sale-biochar-industries/>
48642 Strength of
Engineering
Materials: B

562
C H A P T E R 11
DESIGN
OF
BEAMS
A N D S H A F T S
*11.4
A
P1
B
P2
(a)
z
Az
(P1)z
Ax
T
(P1)x
x
Bz
Shaft Design
Shafts that have circular cross sections are often used in the design of
mechanical equipment and machinery. As a result, they can be subjec

Relationship of Forces and Deformations: (2/8/12 Dr. R. Zhang)
Forces
Relationship
Deformation
F = K
Axial Load (F/P)
( )
Hooks Law
Normal Stress
x
x
E
y
z
x
E
x
E
y
E
z
z
y
E
y
E
Normal Strain
E
E
Shearing Strain
z
E
Shearing Stress
Shear St

Cover Page B
Question one [Stresses under combined loading, transformation of stress] (10
Marks)
Two forces P1 and P2, of magnitude P1=15kN and P2=18kN, are applied as shown
to the end A of bar AB, which is welded to a cylindrical member BD of radius
r=20

Cover type B
University of Technology, Sydney
THIS PAPER MUST NOT BE REMOVED FROM THE EXAM CENTRE.
PLEASE HAND IN WITH ANSWER BOOKS.
Spring Semester 2009
48642 STRENGTH OF ENGINEERING MATERIALS
FINAL EXAM
B. Eng & B.Eng. Dip. Eng. Prac. Courses
All questi