ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
Name: _________________________________
EXAM FOUR (100 POINTS)
Closed book, closed notes. Calculator and writing supplies allowed. 50 Minute Time Limit
Some Moments of Inertia Formulae
Given:
M/EI = 1/
 = -y/
=My/I
 = E
1.
(15 points). Determine the magnitude of the concentrated end-moment M, acting on the beam shown.
Given: A strain-gage is located on the bottom of the beam, reporting a tensile strain of be  = 0.001 in/in.
The modulus of elasticity E = 1500 ksi. The cross-section is 12”x12”, as shown
2.
(50 points) If the maximum magnitude of normal stress due to the applied uniformly-distributed load w on the steel
plate is 21.67 ksi, determine w.
Given: 10”x10” wooden (E=1450 ksi) cross-section with ½”x10” steel plates (E=29000 ksi) that are securely glued
to the top and bottom of the wood. A is a pinned support. B is a roller support.
ES230 Strength of Materials
3.
Hour Exam 4
Compilation of Past Exams
(5 points) If the beam cross-section below is subjected to bending about its x-axis, will there be greater bending
normal stress magnitude (absolute value) on the top or on the bottom of the beam?
ES230 Strength of Materials
1.
Hour Exam 4
Compilation of Past Exams
(15 points). Determine the magnitude of the concentrated end-moment M, acting on the beam shown.
Given: A strain-gage is located on the bottom of the beam, reporting a tensile strain of be  = 0.001 in/in.
The modulus of elasticity E = 1500 ksi. The cross-section is 12”x12”, as shown
ES230 Strength of Materials
2.
Hour Exam 4
Compilation of Past Exams
(50 points) If the maximum magnitude of normal stress due to the applied uniformly-distributed load w on the steel
plate is 21.67 ksi, determine w.
Given: 10”x10” wooden (E=1450 ksi) cross-section with ½”x10” steel plates (E=29000 ksi) that are securely glued
to the top and bottom of the wood. A is a pinned support. B is a roller support.
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
3.
(5 points) If the beam cross-section below is subjected to bending about its x-axis, will there be greater bending
normal stress magnitude (absolute value) on the top or on the bottom of the beam?
1.
(10 points). Determine the modulus of elasticity E for the beam shown.
Given: A commercial test setup is used to physically measure the modulus of elasticity of the wooden beam by
subjecting it to end-moments of 432 kip-in, while measuring the extreme-fiber strain. For this beam, the extremefiber strain has been found to be  = 0.001 in/in.
M = 432 kip-in
M = 432 kip-in
Strain-gage measures
 = 0.001 in/in
12” x 12” Cross-Section
Beam Cross Section
2.
(50 points) Determine the resultant force acting on the top steel plate due to bending stresses at the cross-section that
is subjected to maximum moment magnitude (absolute value) and specify the location of this cross-section with
respect to point A.
Given: 10”x10” wooden (E=1450 ksi) cross-section with ½”x10” steel plates (E=29000 ksi) that are securely glued
to the top and bottom of the wood. A is a pinned support. B is a roller support.
Bonus (5 points): Determine the maximum shear stress in the glue.
0.5 kip/ft
½”x10” Steel
10”x10” Wood
A
B
10 ft.
2 ft.
½”x10” Steel
Beam Cross
Section
ES230 Strength of Materials
3.
Hour Exam 4
Compilation of Past Exams
(35 points) Assuming a square cross-section, determine the minimum dimension b so that the flexural stress in the
wood does not exceed 1.2 ksi. Given: 24-ft simple span with 0.2 kip/ft uniformly-distributed load.
0.2kip/ft
b
A
B
24 ft.
b
Beam Cross
Section
1.
(10 points). Determine the modulus of elasticity E for the beam shown.
Given: A commercial test setup is used to physically measure the modulus of elasticity of the wooden beam by
subjecting it to end-moments of 432 kip-in, while measuring the extreme-fiber strain. For this beam, the extremefiber strain has been found to be  = 0.001 in/in.
ES230 Strength of Materials
2.
Hour Exam 4
Compilation of Past Exams
(50 points) Determine the resultant force acting on the top steel plate due to bending stresses at the cross-section that
is subjected to maximum moment magnitude (absolute value) and specify the location of this cross-section with
respect to point A.
Given: 10”x10” wooden (E=1450 ksi) cross-section with ½”x10” steel plates (E=29000 ksi) that are securely glued
to the top and bottom of the wood. A is a pinned support. B is a roller support.
Bonus (5 points): Determine the maximum shear stress in the glue.
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
3.
(35 points) Assuming a square cross-section, determine the minimum dimension b so that the flexural stress in the
wood does not exceed 1.2 ksi. Given: 24-ft simple span with 0.2 kip/ft uniformly-distributed load.
2.
(15 points). The beam cross-section shown is subjected to x-axis bending moment which causes the
extreme top and bottom surfaces to have a normal stress magnitudes of 5 ksi. Determine the resultant
force that acts on the top flange.
8”x 1” Flange
x
8”x 1”
Web
8”x 1” Flange
I-BEAM
CROSSSECTION
x
ES230 Strength of Materials
3.
Hour Exam 4
Compilation of Past Exams
(5 points). The beam cross-section shown is subjected to y-axis bending moment which causes the
extreme left and right surfaces to have a normal stress magnitudes of 5 ksi. Determine the resultant force
that acts on the top flange.
y
8”x 1” Flange
8”x 1”
Web
x
x
8”x 1” Flange
y
I-BEAM
CROSSSECTION
4.
(40 points) Determine the maximum x-axis bending moment (units: kip-inches) that the composite beam shown can
resist if the allowable stress for the wood w =1 ksi and the allowable stress for steel s= 18 ksi.
Given: 12” x 12” wooden beam (Ew=1450 ksi) with ½” x 12” steel plates (Es=29000 ksi) on each side.
x
x
12”x12”
Wood
½” x 12” Steel
BEAM CROSSSECTION
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
1.
Hour Exam 4
Compilation of Past Exams
(10 points). Determine the maximum bending stress in the steel plate that is ¼” thick and 2” wide if it is
bent around a 50” diameter wheel. E=30000 ksi. Assume that the steel remains elastic.
M
M
50”
¼” x 2”
Cross-Section
¼”
Steel Plate
ES230 Strength of Materials
2.
Hour Exam 4
Compilation of Past Exams
(25 points). The composite beam consists of 1”x1” Nylon (E=500 ksi), sandwiched by two ½” x 1”
Aluminum (E=10000 ksi) plates. Under x-axis bending the bottom aluminum plate has a resultant force
in it of 15 kips, due to bending. Determine the maximum bending normal stress in the Nylon. Assume all
materials remain elastic.
½” x 1”
Aluminum
½”
1” x 1”
Nylon
½”
x
x
½”
½” x 1”
Aluminum
½”
1”
3.
(15 points). In a lab experiment, Point B was subjected to a moment of 10 kip-in, while the deflection of
the beam was measured at 1” increments, with the data reported, below. Determine EI of the beam.
Deflected shape
Given: Deflection Data
M = 10 kip-in
A
4.
x
B
10”
(10 points) True or False. If the maximum bending normal stress on the beam for x-axis bending is 18
ksi, then the force on the flange is 75 kips.
1”x5” Flange
1”x4” Web
x
x
1”x5” Flange
5.
(10 points) True or False. If the maximum bending normal stress on the beam for x-axis bending is 12
ksi, then the force on the flange is 50 kips.
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
1”x5” Flange
1”x4” Web
x
x
1”x5” Flange
6.
(40 points). Determine the absolute maximum bending stress in the beam below if P = 1kip.
Given: A is a pinned support. B and D are roller supports (reminder: rollers can resist forces that are directed either
up or down). C is a pinned connection.
P = 1 kip
20”
A
B
D
C
100”
7.
100”
100”
50”
10”
Cross-Section
(40 points). Determine the absolute maximum bending stress in the beam below if P = 1kip.
Given: A is a fixed support. B pinned connection. C is a roller support.
P = 1 kip
A
B
20”
C
200”
100”
50”
10”
Cross-Section
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams
ES230 Strength of Materials
1.
Hour Exam 4
Compilation of Past Exams
(20 points). A composite beam is constructed with 1”x12” steel plates on the top and bottom of a
12”x12” wooden beam, as shown. It is bent about the x-axis with the moments shown, into a radius of
curvature of 100,000 inches. Determine the maximum stress in the steel plate.
Given: Steel E = 30,000 ksi, Wood E = 1,500 ksi

M
 = 100,000 inches
M
1” x 12” Steel
x
12”x12”
Wood
x
1” x 12” Steel
BEAM CROSSSECTION
BEAM SIDE VIEW
ES230 Strength of Materials
2.
Hour Exam 4
Compilation of Past Exams
(30 points). Determine the maximum uniformly distributed load that can be safely applied to the beam below.
Report your answer in units of lbs per inch (lbs/in).
Given: The maximum allowable normal stress in the beam is allow = 1200 psi.
w = ? (lbs/inch)
6 in
50 in
100 in
50 in
4 in
CrossSection
ES230 Strength of Materials
Hour Exam 4
Compilation of Past Exams