ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #2
Solution Set
1. One rst needs to determine the elevation of the centroid of the area. Measuring from
the bottom of the area, as shown below,
160 mm
c1
c
yc1
yc
c2
40 mm
n.a.
200 mm
yc1 = 2

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #8
Solution Set
1. In order to determine the deection and slope of the beam at point A, we need to add
a dummy load PA and a dummy couple MA at A, since they do not already exist.
PA
wx
x/2
A

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #3
Solution Set
1. Consider a beam with the cross section shown below.
(a) Determine the maximum tensile and compressive exural stresses if the bending
moment in the beam is 2000 ft lb.
(b) D

ENGR0145 - Statics and Mechanics of Materials 2 (2071)
Exam #2
50 min., closed book
1. A beam is loaded and supported as shown below. Using any method you like, determine
the reactions at supports A and B.
w
A
B
L
2. A beam is loaded and supported as show

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Homework #10
Solution Set
1. Noting that the angle of orientation for the n-direction is = 30 , it follows from the
plane strain transformation equations that
n = (850) cos2 (30 ) + (300) sin2 (30 ) +

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Exam #2
50 min., closed book
1. A beam is loaded and supported as shown below. Use the beam deflection equation
and singularity functions to determine the deflection of the beam midway between A
and B

Flexure of Beams:
Shearing Stresses
ENGR0145
Learning Objectives
Flexure of Beams: Shearing Stresses
ENGR0145 - Statics and Mechanics of Materials 2
William S. Slaughter
Mechanical Engineering Department
University of Pittsburgh
Shearing Stresses
Theory
E

ENGR0145 - Statics and Mechanics of Materials 2 (04-1)
Final Exam
Answer 5 of the 6 questions
1) Determine the second moment of the shaded area shown below with respect to the horizontal
x-axis through the centroid of the area.
2) Draw complete shear forc

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #1
Solution Set
1. Note that the weight of the 500 kg mass is (500 kg)(9.81 m/s2 ) = 4905 N, let the tensions
in cables A and B be FA and FB , respectively, and consider the free-body diagram

ENGR0145 - Statics and Mechanics of Materials 2 (2161)
Homework #11
Solution Set
1. The axial and hoop stresses in the wall of the pressure vessel are
a =
(180 psi)(24 in)
pr
=
= 720 psi ,
2t
2(3 in)
h = 2a = 1440 psi .
1440 psi
720 psi
30
(a) Using the p

Flexure of Beams:
Second Moments of
Areas
ENGR0145
Flexure of Beams: Second Moments of
Areas
Learning Objectives
Direct Integration
Definition
Examples
ENGR0145 - Statics and Mechanics of Materials 2
Parallel Axis Thm
Derivation
Example
William S. Slaught

Flexure of Beams:
Composite Beams
ENGR0145
Learning Objectives
Flexure of Beams: Composite Beams
ENGR0145 - Statics and Mechanics of Materials 2
William S. Slaughter
Mechanical Engineering Department
University of Pittsburgh
Composite Beams
Transformed Se

Flexure of Beams:
Shear Force and
Bending Moment
Diagrams
ENGR0145
Flexure of Beams: Shear Force and
Bending Moment Diagrams
ENGR0145 - Statics and Mechanics of Materials 2
William S. Slaughter
Mechanical Engineering Department
University of Pittsburgh
Le

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #5
Solution Set
1. Begin with a free-body diagram of the entire beam in order to determine the support
reactions.
15 kN
30 kN
Fy = RA 30 15 = 0
= RA = 45 kN
MA
5m
MA = MA (30)(5) (15)(10) = 0

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #4
Solution Set
1. Method 1: for an all-aluminum transformed section, the ratio of elastic moduli is
n=
45
EMg
=
= 0.6429
EAl
70
and the transformed section, including its neutral axis, is as

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #9
Solution Set
1. Consider the following free-body diagram (note that, if the area of the inclined plane
is dA, then the area of the vertical plane is dA sin 70 and the area of the horizonta

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #6
Solution Set
1. (a) First consider the free-body diagram of the entire beam to determine the support
reactions:
wL
Fy = RA wL = 0
L/2
= RA = wL
B
A
MA = MA (wL)(L/2) = 0
L
MA
= MA =
RA
1
w

ENGR0145 - Statics and Mechanics of Materials 2 (2134)
Homework #7
Solution Set
1. Begin with a free-body diagram of the entire beam and note the boundary conditions:
y
1
wL
2
2
L
3
Boundary Conditions
y |x=0 = 0
y |x=L = 0
x
MB
L
RA
y |x=L = 0
RB
The equ

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Homework #1
Due: 9/7/16
1. A 500 kg mass is supported by steel cables A and B, as shown below. Determine the
minimum diameters required for the two cables if the allowable normal stress in the
cables

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Homework #2
Due: 9/14/16
1. Determine the second moment of the shaded area shown below with respect to the
horizontal axis through the centroid of the area.
160 mm
40 mm
200 mm
40 mm
2. Determine the

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Homework #3
Due: 9/21/16
1. Consider a beam with the cross section shown below.
(a) Determine the maximum tensile and compressive flexural stresses if the bending
moment in the beam is 2000 ft lb.
(b)

ENGR0145 - Statics and Mechanics of Materials 2 (2171)
Homework #1
Solution Set
1. Note that the weight of the 500 kg mass is (500 kg)(9.81 m/s2 ) = 4905 N, let the tensions
in cables A and B be FA and FB , respectively, and consider the free-body diagram

Review of Stress
and Strain
ENGR0145
Learning Objectives
Significant Figures
Review of Stress and Strain
ENGR0145 - Statics and Mechanics of Materials 2
William S. Slaughter
Mechanical Engineering Department
University of Pittsburgh
Axial Loading
Stresses