7.8 For the simply supported beam subjected to the
loading shown,
(a) Derive equations for the shear force V and the
bending moment M for any location in the beam.
(Place the origin at point A.)
(b) Plot the shear-force and bending-moment
diagrams for the

5
7 For a beam of rectangular cross section (b x h), show that the max bending
stress, M(Ymax/Izz), is the section moment times 6/(bh2). If a stiffener (b x h2)
is bonded to the top surface, the max stress must decrease (for the same
moment) since h is no

2.
(a) For the case of plane stress, use Hookes law to show that the equations for computing
principal strain directions are identical to the equations for computing principal stress
directions, thereby confirming that for isotropic materials, principal s

7. Draw Mohrs circle for the plane stress state:
X = -150psi, Y = 650 psi, XY = -300 psi
(a) Show the point on the circle for the plane of X , X ,
XY (where theta =0).
(b) Show the point on the circle where =90 degrees.
(c) Show the points of max and min

6. Show that the X, Y, Z face areas of a tetrahedron are related to the normal face area by
direction cosines l = Cos(X), m = Cos(Y ) and n = Cos(Z ) through:
A-x = An Cos(X ), A-y = An Cos (Y ) and A-z = An Cos(Z )
Y
Y
n
X
Area A-z
Area A-x
X
Area An
Z
z

1. Consider the stress field
(a) Show that the stresses satisfy the plane stress differential eqns. of equilibrium.
(b) Sketch the boundary stresses on all boundary surfaces of the rectangle.
(c) What are the resultant forces and moments on the x=L surfac

AME 324a
Fall 2012
HW#13 Part 2
1. Calculate the maximum shear stresses for Problem 5.5-
10.
Show on sketches where along the beam and where on the
cross section of the beam these maximum shear stresses are
l

P113 The compound solid steel rod shown in
Figure P11314 is subjected to a tensile force P.
AssumeE= 29,000 ksi, d1 = 0.50 in., L1 =18 in., d;
= 0.815 in. L2 = 27 in., and P = 5.5 kips.
Determine:
(a) the elastic strain energy in rod ABC.
(1) the correspo

Moments of composite areas
First moments
Qx = ydA,
A
C t id
Centroid
x=
Qy
A
y=
,
Qy = xdA,
A
Qx
,
A
When th
Wh
the area possesses th
the axis
i off symmetry,
t th
the centroid
t id iis llocated
t d on th
thatt axis,
i as th
the
first moment about an axis

Stress-Strain Relationships III
1
Example 3 (previous lecture)
Problem Statement: A circle of diameter d = 9
in. is scribed on an unstressed aluminum plate
of thickness t = 3/4 in. Forces acting in the
plane of the plate later cause normal stresses
x = 12

Torsion (cont)
Torsion(cont)
Chapter3
StressConcentrations(Section3.5)
Fig. 3.26 Coupling of
shafts using (a) bolted
fl
flange,
(b) slot
l t for
f
keyway.
The
Th derivation
d i ti off the
th torsion
t i formula,
f
l
max =
Tc
J
assumed a circular shaft w

Pure Bending
Chapter 4
Pure Bendingg
Pure Bending: Prismatic members
subjected to equal and opposite
couples
l acting
ti in
i the
th same
longitudinal plane
Fig. 4.2 (a) Free-body
Free body diagram of
the barbell pictured in the chapter
opening photo and

Stress-Strain Relationships II
1
Static Indeterminate Problems
Section 2.2
2
Static Indeterminate Problems
Structures for which internal forces and reactions
cannot be determined from statics alone are said
t be
to
b statically
t ti ll indeterminate.
i d

Stress-Strain Relationships I
Section 2.1
1
Stress & Strain
Suitability of a structure or machine may depend on the deformations in
the structure as well as the stresses induced under loading. Statics
analyses alone are not sufficient.
Considering struc

AME 324A
Mechanical Behavior of Engineering Materials
Fall 2016
Midterm Exam
September 26, 2016
Time: 10:00-10:50 am
Name _
Problem 1 (25 points)
Two solid cylindrical rods AB and BC are welded together at B and loaded as shown.
Determine the magnitude of

Torsion
Chapter 3
Torsion of Circular Shafts
Sections 3.1-3.2
3.1 3.2
2
Torsional Loads on Circular Shafts
Stresses and strains in members of
circular cross-section are subjected
to twisting couples or torques
Turbine exerts torque T on the shaft
Shaft

AME:324A Mechanical Behavior of Engineering Materials
(3 units), Fall 2016
Course Information
Class meeting times & location: M W F 10:00 am 10:50 am
am,
Chemistry, Rm 134
Instructor:
Prof. Olesya Zhupanska
Office: AME N625, Tel: (520) 626-2257
E-mail: oi

Stresses on an Oblique
q Plane under
Axial Loading
Section 1.3
1
Normal and Shear Stresses on an Oblique Plane
Problem Statement:
Find normal and shear stress on an oblique
plane under axial loading
Fig. 1.28 Oblique section through a two-force member.
(a