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 (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 #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 #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 #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 #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 #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 #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
ENGR0135 - Statics and Mechanics of Materials 1 (2134)
Homework #11
Solution Set
1. The free-body diagrams for the block at impending downhill and uphill slip are shown
below on the left and right, respectively.
250 lb
250 lb
y
y
x
P
x
P
30
30
0.3N
0.3N
N
ENGR0135 - Statics and Mechanics of Materials 1 (2134)
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 (2134)
Homework #2
Solution Set
1. Summing forces in the y-direction allows one to determine the magnitude of F2 :
Fy = 1000 sin 60 800 sin 37 F2 sin 45 = 0
=
F2 = 543.8689 N
Then, summing forces in the x-di
ENGR0135 - Statics and Mechanics of Materials 1 (2161)
Homework #1
Solution Set
1. The masses of the two bodies are
500 lb
W1
lb s2
=
= 15.5280 slug
= 15.5280
g
32.2 ft/s2
ft
W2
1500 lb
lb s2
m2 =
=
= 46.5839 slug
= 46.5839
g
32.2 ft/s2
ft
m1 =
Then, the
ENGR0135 - Statics and Mechanics of Materials 1 (2161)
Homework #2
Solution Set
1. Summing forces in the y-direction allows one to determine the magnitude of F2 :
Fy = 1000 sin 60 800 sin 37 F2 sin 45 = 0
=
F2 = 543.8689 N
Then, summing forces in the x-di
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
ENGR0135 - Statics and Mechanics of Materials 1 (2161)
Homework #1
Due: 9/9(daytime sections) or 9/14(evening section)
1. Two spherical bodies weigh 500 lb and 1500 lb at the Earths surface. Determine the
gravitational force of attraction between the sphe
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
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
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
ENGR0135 - Statics and Mechanics of Materials 1 (2161)
Homework #6
Due: 10/21 (daytime sections) or 10/26 (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 (2161)
Homework #2
Due: 9/16(daytime sections) or 9/21(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
ENGR0135 - Statics and Mechanics of Materials 1 (2134)
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
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
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 #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 #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
8
Geometrical properties of cross-sections
8.1
Introduction
The strength of a component of a structure is dependent on the geometricalproperties of its crosssection in addition to its material and other properties. For example, a beam with a large crossse
Design of a Cheap
Thermal Switch
ENGR 0135
Due: 10/9/15
Professor Qing-Ming Wang
Madison Milligan, Josh Haupt, Caroline Collopy
ABSTRACT
The purpose of this design project is to come up with a way to develop a cheaper version of a
currently used thermal s
Exam No.1
Student Name
ENGR0135, Fall 2011
Instructor: Prof. Q.M. Wang
Score:
Problem 1
Determine the magnitude of the resultant force acting on the pin and its direction measured
from the positive x axis.
Exam No.1
ENGR0135, Fall 2011
Instructor: Prof. Q
Design Project 1
Design of a Cheap Thermal Switch
Statics and Mechanics of Materials I
ENGR 0135 Section 1040
October 10, 2014
Derek Nichols
Michael Scandrol
Mark Vavithes
Nichols, Scandrol, Vavithes 1
ABSTRACT
This report will detail our data, calculatio
Exam No.2
Student Name
ENGR0135, Fall 2011
Instructor: Prof. Q.M. Wang
Score:
Problem 1
Determine the moment produced by force F about the diagonal AF of the rectangular block.
Express the result as a Cartesian vector.
Exam No.2
ENGR0135, Fall 2011
Instru
Exam No.3
ENGR0135, Fall 2011
Instructor: Prof. Q.M. Wang
11/14/2011
Student Name:
Score:
Problem 1. (30%)
Determine the area and the centroid
(xc, yc) of the area.
Problem 2. (35%)
A force of 900 N and a couple of 600Nm are applied to the rod AB. The col