Universit dOttawa
University of Ottawa
Facult de gnie
Faculty of Engineering
Dpartement de
Gnie Civil
Department of
Civil Engineering
CVG 2540: Mcanique des Matriaux I
Midterm Exam / Examen de mi-session
Drs. H. Aoude, R. Flores-Vera, B. Martn-Prez
March/

Universit dOttawa
University of Ottawa
Facult de gnie
Faculty of Engineering
Dpartement de
gnie civil
Department of
Civil Engineering
CVG 2140: Mechanics of Materials I
Midterm Exam / Examen de mi-session
Drs. B. Martn-Prez and W.T. Oh
February/ Fvrier 15

Universit dOttawa
University of Ottawa
Facult de gnie
Faculty of Engineering
Dpartement de
gnie civil
Department of
Civil Engineering
CVG 2140: Mechanics of Materials I
Midterm Exam / Examen de mi-session
Dr. B. Martn-Prez
February/ Fvrier 16, 2011
Time /

CVG2140/2540 - Mechanics of Materials I
Midterm formula sheet
NAME _
Relations Between w, V, M
dV
w( x) ,
dx
Centroid
x
Qy
A
x A ,
A
i
i
i
dM
V
dx
y
Qx yi Ai
A
Ai
STUDENT ID _
Space for personal notes
You may include notes in this BOXED area ONLY
You ma

Universit dOttawa
University of Ottawa
Facult de gnie
Faculty of Engineering
Dpartement de
gniecivil
Department of
Civil Engineering
CVG 2140: Mechanics of Materials I
Midterm Exam / Examen de mi-session
Drs. H. Aoude, R. Flores-Vera, B. Martn-Prez
March/

Universit dOttawa
University of Ottawa
Facult de gnie
Faculty of Engineering
Dpartement de
gnie civil
Department of
Civil Engineering
CVG 2140: Mechanics of Materials I
Midterm Exam / Examen de mi
mi-session
Mr. B. Shadravan / Dr. B. Martn
n-Prez
February

CVG2140 Solutions to Assignment No. 8 (Combined Stresses)
Problem 1. Determine the principal stresses and their directions at the surface point C of the
solid cylinder shown in Fig. 1 (diameter = 50 mm, length = 250 mm) subjected to an axial force
P and t

CVG 2140 Solution to Assignment No. 2 (SFD/BMD/Trusses)
Problem 1. Determine the forces in all members of the truss shown in Fig. 1.
Ay
Dy
Fig. 1
Since the truss has symmetry in geometry, boundary conditions (supports) and loading, only half of
it will be

CVG2140
Mechanics of Materials I
Winter 2015
Construction Rules for Shear-Force and Bending-Moment Diagrams
Equation
Load Diagram w
SFD V
Rule 1: Concentrated loads create discontinuities in the SFD.
BMD M
V Po
Rule 2: The slope of SFD is equal to the int

CVG2140
Mechanics of Materials I
Winter 2015
1. The copper shaft is subjected to the axial loads shown. Determine the displacement of end A with
respect to end D. The diameters of each segment are dAB = 3 in, dBC = 2in, and dCD = 1 in. Take Ecu =
18103 ks

CVG2140
Mechanics of Materials I
Winter 2015
Discontinuity functions
Macaulay functions (n 0)
xa
n
for x a
0
n
x a for x a
n 1
xa
x a dx
n 1
n
C
Singularity functions (n < 0)
xa
n
for x a
0
for x a
x a dx x a
n
n 1
Procedure for analysis
The following

CVG2140
Mechanics of Materials I
Winter 2015
COMBINED LOADING
NORMAL STRESS,
(force per unit area acting perpendicular to cross section)
Source
Distribution over cross section
Formula
P
A
Sign convention
+
Axial force, P
P = axial force
A = cross-section

CVG2140
Mechanics of Materials I
Winter 2015
Truss Joints under Special Loading Conditions
E
B
B
P
P
FAE
FAB FAD
FAB
A
FAB
A
FAC FAE
FAC P
FAD
FAD
D
FAC
D
FAB FAD
FAC
C
C
B
B
FAB FAD
FAB
A
FAB
A
FAC 0
FAB FAD
FAD
D
FAD
FAC
D
C
A
B
FAB
D
FAB 0
FAD 0
FAD
Un

CVG2140
Mechanics of Materials I
Winter 2015
1. The assembly consists of two sections of galvanized steel pipe connected together using a reducing
coupling at B. The smaller pipe has an outer diameter of 0.75 in and an inner diameter of 0.68 in,
whereas t

CVG2140
Mechanics of Materials I
Winter 2015
1. A 1.6-m long cantilever beam supports a concentrated load of 7.2 kN as shown in Fig. 1. The
beam is made of a rectangular timber having a width of 120 mm and a depth of 280 mm.
Calculate the maximum horizont

CVG2140
Mechanics of Materials I
Winter 2015
1. The bar in Fig. 1 has a diameter of 40 mm. If it is subjected to the two force components at
its ends as shown, determine the state of stress at point B and show the results on a
differential volume element

CVG2140
Mechanics of Materials I
Winter 2015
1. The copper shaft is subjected to the axial loads shown. Determine the displacement of end A with
respect to end D. The diameters of each segment are dAB = 3 in, dBC = 2in, and dCD = 1 in. Take Ecu =
18103 ks

CVG2140 Solutions to Assignment No. 7 (Shear & Torsion)
Problem 1. The wood beam shown in Fig. 1 has an allowable shear stress of allow = 7 MPa.
Determine the maximum shear force V that can be applied to the cross section.
Fig. 1
I
200 2003 100 1003
1251

CVG2140 Solutions to Assignment No. 6 (Deflections)
Problem 1. Determine the equations of the elastic curve for the beam illustrated in Fig. 1 using
the x coordinate as shown. Specify the slope at A and the maximum displacement of the shaft. EI
is constan

CVG2140 Solution to Assignment No. 4 (Axial Members)
Problem 1. The A-36 steel rod (E = 200 GPa) is subjected to the loading shown in Fig. 1. If the
cross-sectional area of the rod is 50 mm2, determine the displacement of its end D. Neglect the
size of th

CVG2140 Assignment No. 8 (Combined Stresses)
(Due Date: Tuesday, April 9th, 2013)
Problem 1. Determine the principal stresses and their directions at the surface point C of the
solid cylinder shown in Fig. 1 (diameter = 50 mm, length = 250 mm) subjected t

CVG2140 Solutions to Assignment No. 7 (Shear & Torsion)
Problem 1. The wood beam shown in Fig. 1 has an allowable shear stress of allow = 7 MPa.
Determine the maximum shear force V that can be applied to the cross section.
Fig. 1
I=
200 2003 100 1003
= 12

CVG2140 Solutions to Assignment No. 6 (Deflections)
Problem 1. Determine the equations of the elastic curve for the beam illustrated in Fig. 1 using
the x coordinate as shown. Specify the slope at A and the maximum displacement of the shaft. EI
is constan

CVG2140 Solutions to Assignment No. 4 (Axial Members)
Problem 1. The A-36 steel rod (E = 200 GPa) is subjected to the loading shown in Fig. 1. If the
cross-sectional area of the rod is 50 mm2, determine the displacement of its end D. Neglect the
size of t

CVG2140 Assignment No. 5 (Flexural Stresses)
(Due Date: Tuesday, March 5th, 2013)
Problem 1. A simply supported wood beam AB with span length L = 3.5 m carries a uniform
load of intensity q = 6.4 kN/m (see Fig. 1). Calculate the maximum bending stress max

CVG2140 Assignment No. 6 (Deflections)
(Due Date: Friday, March 15th, 2013)
Problem 1. Determine the equations of the elastic curve for the beam illustrated in Fig. 1 using
the x coordinate as shown. Specify the slope at A and the maximum displacement of

CVG2140 Solutions to Assignment No. 5 (Flexural Stresses)
Problem 1. A simply supported wood beam AB with span length L = 3.5 m carries a uniform
load of intensity q = 6.4 kN/m (see Fig. 1). Calculate the maximum bending stress max due to
the load q if th

CVG2140 Assignment No. 4 (Axial Members)
(Due Date: Wednesday, Feb. 13th, 2013)
Problem 1. The A-36 steel rod (E = 200 GPa) is subjected to the loading shown in Fig. 1. If the
cross-sectional area of the rod is 50 mm2, determine the displacement of its en

CVG 2140
Mechanics of Materials I
Winter 2016
Axially Loaded Members
Lecture 8:
Normal Stress and Strain
Structural components subjected only to tension or compression are known as axially loaded members.
Examples include truss members, engine connecting

CVG 2140
Mechanics of Materials I
Lab 2: Flexural Stresses in Beams
1|Page
2|Page
Abstract
This experiment observed the flexural stresses and strains at various heights of a 2.438m, hollow
aluminum beam with an outer height of 76.2mm, an outer width of 25

CVG 2140
Mechanics of Materials I
Lab 1: Beam Reactions
1|Page
2|Page
Abstract
The purpose of this lab was to observe the reactions on the supports of a simplysupported beam while being subjected to three different loading conditions. The theoretical
valu

CVG 2140
Mechanics of Materials I
Lab 3: Deflection Beams
1|Page
2|Page
Abstract
This experiment observed the deflection of a 1.160m long steel beam under two
separate loading conditions. Under loading case 1 a single point load was in the middle of the
b

CVG 2140 Assignment No. 1 (External Reactions)
(Due Date: Friday, January 22nd, 2016 by 5PM)
Compute the external reactions for the following problems:
1.
A
1 kN/m
3m
2.
2.5 m
B
A
15 kN m
5m
3.
10 kN
A
B
3m
4.
2m
A
B
15 kN m
3m
2m
5.
1.5 m
45
3m
10 kN
A
6