ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #8
Solution Set
1. One should begin by drawing a free-body diagram for the beam, as shown below. There
are horizontal and vertical reaction forces due to the pin support at A and a vertical
r
ENGR0135 - Statics and Mechanics of Materials 1 (2141)
Homework #9
Solution Set
1. There are different approaches one can take (e.g., one could begin with a free-body
diagram of the entire truss to determine the support reactions at A and F ). In this
cas
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #9
Solution Set
1. There are dierent approaches one can take (e.g., one could begin with a free-body
diagram of the entire truss to determine the support reactions at A and F ). In this
case,
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #3
Due:
1. Tensile tests of structural steel indicate that it fails when the axial tensile strain is
1800 . Determine the maximum change in length that 0.25-in diameter structural
steel rod i
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #9
Due: 11/19 (daytime sections) or 11/27 (evening section)
1. Use the method of joints to determine the force in each member of the truss shown
below. Each member of the truss is 4 m long.
D
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #8
Due: 11/7 (daytime sections) or 11/13 (evening section)
1. A beam is loaded and supported as shown below. Determine the reactions at supports
A and B .
y
7 kN/m
3 kN/m
A
B
2m
x
4m
2. A bea
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #6
Due: 10/17 (daytime sections) or 10/23 (evening section)
1. Replace the 40 lb force exerted on the wrench shown below with an equivalent forcecouple system at the nut A.
5 in
A
40 lb
2. De
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #7
Due: 10/31 (daytime sections) or 11/6 (evening section)
1. Locate the centroid of the shaded area shown below.
y
3 in 2 in 3 in
8 in
3 in
x
2. Locate the centroid of the slender rod shown
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #5
Due: 10/10 (daytime sections) or 10/16 (evening section)
1. Two forces are applied to point C on the truss structure shown below. Determine the
moments of
(a) The 3.5 kN force about points
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #10
Due: 11/28 (daytime sections) or 12/4 (evening section)
1. The coecient of static friction between the block and the incline shown below is 0.30.
Determine
(a) The minimum force P require
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #10
Due: 11/28 (daytime sections) or 12/4 (evening section)
1. The coe cient of static friction between the block and the incline shown below is 0.30.
Determine
(a) The minimum force P requir
ENGR0135 - Statics and Mechanics of Materials 1 (2131)
Homework #2
Due: 9/12(daytime sections) or 9/11(evening section)
1. Four forces act on a particle as shown below. Determine the magnitudes of forces F1
and F2 so that the particle is in equilibrium.
y
6
Thin shells under internal pressure
6.1
Thin cylindrical shell of circular cross-section
A problem in which combined stresses are present is that of a cylindrical shell under internal
pressure. Suppose a long circular shell is subjected to an internal p
3
Shearing stress
3.1
Introduction
In Chapter 1 we made a study of tensile and compressive stresses, which we called direct stresses.
There is another type of stress which plays a vital role in the behaviour of materials, especially
metals.
Consider a thi
I
Tension and compression:
direct stresses
1.I
Introduction
The strength of a material, whatever its nature, is defined largely by the internal stresses, or
intensities of force, in the material. A knowledge of these stresses i s essential to the safe des
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #3
Solution Set
1. The diameter of the steel rod is not required for this problem. Since the axial strain
is = /L, where is the change in length and L is the original length, it follows that
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #4
Solution Set
1. Note rst that the cross-sectional areas are
As = (1400 mm2 )(103 m/mm)2 = 1.4 103 m2
Ab = (2100 mm2 )(103 m/mm)2 = 2.1 103 m2
If Ps is the tensile axial force in the steel
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #5
Solution Set
1. (a) The perpendicular distances from line of action of the 3.5 kN force to the points
A and B are the same, dA = dB = 4 m. Thus, the moments of this force about
points A an
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #6
Solution Set
1. The moment of the 40 lb force about point A is
MA = (40 lb)(5 in) = 200 lb in
Thus, the equivalent force-couple system at A is
F = 40 lb ,
C = 200 lb in
as shown below
40 l
15
Plastic bending of mild-steel beams
15.1
Introduction
We have seen that in the bending of a beam the greatest direct stresses occur in the extreme
longitudinal fibres; when these stresses attain the yield-point values, or exceed the limit of
proportion
2
Pin-jointed frames or trusses
2.1
Introduction
In problems of stress analysis we discriminate between two types of structure; in the first, the
forces in the structure can be determined by considering only its statical equilibrium. Such a
structure is s
10
Shearing stresses in beams
10.1
Introduction
We referred earlier to the existence of longitudinal direct stresses in a cantilever with a lateral load
at the free end; on a closer study we found that these stresses are distributed linearly over the cros
23
Matrix methods of structural analvsis
23.1
Introduction
This chapter describes and applies the matrix displacement method to various problems in
structural analysis. The matrix displacement method first appeared in the aircraft industry in the
1940s7,w
9
Longitudinal stresses in beams
9.1
Introduction
We have seen that when a straight beam carries lateral loads the actions over any cross-section of
the beam comprise a bending moment and shearing force; we have also seen how to estimate the
magnitudes of
16
Torsion of circular shafts and
t hin-walled tubes
16.1
Introduction
In Chapter 3 we introduced the concepts of shearing stress and shearing strain; these have an
important application in torsion problems. Such problems arise in shafts transmitting .hea
20
Torsion of non-circular sections
20.1
Introduction
The torsional theory of circular sections (Chapter 16) cannot be applied to the torsion of noncircular sections, as the shear stresses for non-circular sections are no longer circumferential.
Furthermo
25
Structural vibrations
25.1
Introduction
In this chapter, we will commence with discussing the free vibrations of a beam, which will be
analysed by traditional methods. This fundamental approach will then be extended to forced
vibrations and to damped o
21
Thick circular cylinders, discs
and spheres
21.I
Introduction
Thin shell theory is satisfactory when the thickness of the shell divided by its radius is less than
1/30. When the thickness: radius ratio of the shell is greater than this, errors start to
ENGR0135 - Statics and Mechanics of Materials 1 (2151)
Homework #7
Solution Set
1. The shaded area can be divided into component areas in a number of dierent ways.
For example, it could be divided into a large 8 in. 10 in. rectangle with two 3 in. 8 in.
r
ENGR0135: Statics and
Mechanics of Materials 1
Fall 2016
Dr. Guofeng Wang
Office: 538B Benedum Hall
1
Announcement
1.Homework#5 is due today.
2.Homework#6 has been posted on CourseWeb and is due on
Wednesday, Oct. 19th.
3.Report of Design Project #1 is du
ENGR0135: Statics and
Mechanics of Materials 1
Fall 2016
Dr. Guofeng Wang
Office: 538B Benedum Hall
1
Announcement
1.Homework#10 has been posted on CourseWeb and is due on
Wednesday, Nov. 30th.
2
07_01
07_04
07_04
6
Example Problem 7-1. A steel shaft is
u
ENGR0135: Statics and
Mechanics of Materials 1
Fall 2016
Dr. Guofeng Wang
Office: 538B Benedum Hall
1
Announcement
Homework#1 has been posted on CourseWeb
under Course Documents ->Homework and Solution.
It is due on Wednesday, Sep. 7th.
2
3
fig_02_11
fig_
ENGR0135: Statics and
Mechanics of Materials 1
Fall 2016
Dr. Guofeng Wang
Office: 538B Benedum Hall
1
What will I learn in this course (statics
and mechanics of materials)?
2
Why should I learn anything about statics
and mechanics of materials?
3
4
Nanoma
ENGR0135: Statics and
Mechanics of Materials 1
Fall 2016
Dr. Guofeng Wang
Office: 538B Benedum Hall
1
Announcement
1.Report of Design Project #1 is due today.
2.Homework#6 has been posted on CourseWeb and is due on
Wednesday, Oct. 19th.
2
05_44
05_45
05_4