CVG 2140
Mechanics of Materials I
Winter 2006
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
n
x a dx = x a
n +1
Procedure for anal

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
Space for personal notes
dM
V
dx
y
Qx
A
STUDENT ID _
y A
A
i
i
i
You may include notes in this BOXED area ONLY
You

CVG 2140 Assignment No. 9 (Review)
(Due Date: Tuesday, April 10th, 2012)
(This assignment is not compulsory; if you submit it, you will get bonus points.)
Problem 1. The assembly shown in Fig. 1 is made of A-36 steel and consists of a solid rod 20
mm in d

CVG 2140 Assignment No. 8 (Combined Stresses)
(Due Date: Tuesday, April 3rd, 2012)
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

CVG 2140 Assignment No. 7 (Shear & Torsion)
(Due Date: Tuesday, March 27th, 2012)
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

CVG 2140 Assignment No. 5 (Flexural Stresses)
(Due Date: Tuesday, Feb. 28th, 2012)
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 ma

CVG 2140 Assignment No. 4 (Axial Members)
(Due Date: Tuesday, Feb. 14th, 2012)
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

CVG 2140 Assignment No. 3 (Centroids and Moments of Inertia)
(Due Date: Friday, Feb. 3rd, 2012)
Problem 1. Calculate the position of the centroid of the shape shown in Fig. 1.
Fig. 1
Problem 2. Calculate the moments of inertia Ix, Iy, Jo, Ixy of the secti

CVG 2140 Assignment No. 2 (Shear Force & Bending Moment Diagrams)
(Due Date: Friday, Jan. 27th, 2012)
Problem 1. For the cantilever beam shown in Fig. 1, express the shear force and bending
moment as functions of x, and then draw the shear force and bendi

CVG 2140 Assignment No. 1 (External Reactions)
(Due Date: Tuesday, Jan. 17th, 2012)
Compute the external reactions for the following problems:
(1)
P
A
(2)
B
P
A
B
a
a
b
l
(3)
(4)
Mo
A
B
A
Mo
B
a
a
b
l
(5)
wo
A
B
(6)
C
P
b
Q
A
l
B
a
a
a
b
a
(7)
Q
a
a
B
Q
h