Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Select the correct shear and bending—moment diagrams for the beam and loading shown,
and determine the maximum absolute value (a) of the shear, (b) of the bending
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Two shafts, each of 7/8 in. diameter are connected by the gears as shown. Knowing that
G = 11.2 X 106 psi and that the shaft at F is ﬁxed, determine the angle t
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
The electric motor exerts a 550 N'm torque on the aluminum shaft A B C B when it is
rotating at a constant speed. Knowing that G = 26 GPa and that the torques e
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
C 7
A a 5‘ W
B
_> .4— 41 In
12'” / t=1l4
in.
%
Y i
‘ Dan E
6m H“ Eds
J—QJT
The solid spindle A B has a diameter (is = 2.2 in. and is made of steel with an a
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
The brass strip A B has been attached to a ﬁxed support at A and rests on a rough
support at B . Knowing that the coefﬁcient of friction is 0.606 between the stri
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
r3 = 20.13 mm“\
Q = 24.27 men—,er
\‘Q‘flA
‘2:
71.9 mm.(\L
L!
For P = 80 kN, determine the minimum plate thickness
is 120 MPa.
Step 1:
At the hole:
1"A
dA
Step
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
The concrete post (E C = 3.8 X 10 6 psi and a c = 5.3 X 10—6/0F) is reinforced with six
3 _
steel bars, each of Tin. diameter (EC = 29 x 106 psi and a S = 6.5 x 1
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
The aluminum shell is fully bonded to the brass core and the assembly is unstressed at a
temperature of 20°C. It is known that E = 105 GPa and a = 20.9 X 10 _6/°C
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Two cylindrical rods, one of steel and the other of brass, are joined at C and restrained by
rigid supports at A and E . For the loading shown and knowing that E
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Knowing that the couple shown acts in a vertical plane, determine the stress at
(a) point A , (b) point B .
+20 40 204_
1 1H1 1_,
20
'A —A
80
_V
20
Bo 7‘
Dime
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Two vertical forces are applied to a beam of the cross section shown. Determine the
maximum tensile and compressive stresses in portion B C of the beam.
3in.‘3 in
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Determine ( a) the distance a for which the maximum absolute value of the bending
moment in the beam is as small as possible, ( b) the corresponding maximum norma
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Select the correct shear and bending—moment diagrams for the beam and loading shown
and determine the maximum normal stress due to bending.
Step 1:
l4 2m>
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Select the correct shear and bending—moment diagrams for the beam and loading shown
and determine the maximum normal stress due to bending.
18 kips 18 kips 18 kip
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Find maximum normal stress in given beam section a —a .
30 kN 50 kN 50 kN 30 kN
1a : 5 W310 x 60
2.5 m i
< 5 @ 1.0 m = 5 m >
Step 1:
Reactions:
By symme
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Knowing that the clamp shown has been tightened until
stress at point A , (b) the stress at point B , (c) the location of the neutral axis of
section a -a .
Cross
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
A vertical force P of magnitude 17 kips is applied at a point C located on the axis of
symmetry of the cross section of a short column. Knowing that y = 5 in., de
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
A short wooden post supports a 6—kip axial load as shown. Determine the stress at
point A when (1)!) =0, (1) 1) =1.5 in., (c) 1) =3 in.
Step 1:
A : m2: 77:(4)2 :
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
The beam shown is made of a nylon for which the allowable stress is
and 30 MPa in compression. Determine the largest
23 MPa in tension
couple M’ that can be appli
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Knowing that a 0.03—in. gap exists when the temperature is 75
temperature at which the normal stress in the aluminum bar will be equal to
—-1I712in.4>|7 18in.—-—|
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
A rod consisting of two cylindrical portions AB and BC is restrained at both ends. Portion
AB is made of steel (ES = 200 GPa, a S = 11.7 X 10—6/ °C) and portion B
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Members AB and BC are made of steel (E = 29 X 106 psi) with cross—sectional areas of
0.88 in2 and 0.35 in 2, respectively. For the loading shown, determine the el
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
Each of the four vertical links has a 9 X 38— mm uniform rectangular cross section and
15— mm diameter. Determine the maximum value of the
B and I).
each of the f
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
For the Pratt bridge truss and loading shown, determine the average normal stress in
member BE, knowing that the cross—sectional area of that member is 5.55 in 2.
Do not round intermediate calculations. Give your ﬁnal answer(s) to three signiﬁcant
ﬁgures.
In the marine crane shown, link C D is known to have a uniform cross section of
50 X 150 mm. For the loading shown, determine the normal stres
1
Mechanics of Materials and Structural Principles
Introduction
The purpose of this lecture is to lay the groundwork for concepts that will be introduced
throughout the semester. The lecture will focus on the inherent properties that all
materials share a
CHAPTER
6
MECHANICS OF
MATERIALS
Shearing Stresses in
Beams and ThinWalled Members
MECHANICS OF MATERIALS
Introduction
Transverse loading applied to beam results in
normal and shearing stresses in transverse
sections.
Distribution of normal and shearing s
BEAMS: SHEARING STRESS
Slide No. 1
Shearing Stress in Beams
Shear and Bending
Although it has been convenient to restrict
the analysis of beams to pure bending, this
type of loading is rarely encountered in an
actual engineering problem.
It is much comm