Problem 1.73 The upper deck of a football stadium is supported by braces each of which transfers a load P = 160 kips to
the base of a column [see gure part (a)]. A cap plate at the bottom of the brace distributes the load P to four ange plates
(t, = l in
Problem 5.55 Each girder of the lift bridge (see gure) is
180 ft long and simply supported at the ends. The design load
for each girder is a uniform load of intensity 1.6 klfr. The girders
are fabricated by welding three steel plates so as to form an
Is
Normal Stress and Strain
Problem 1.31 A hollow circular post ABC (see gure) supports a load
P1 = 1700 lb acting at the top. A second load P2 is uniformly distributed
around the cap plate at B. The diameters and thicknesses of the upper and
lower parts
Problem 2.21 The Lshaped arm ABCD shown in the gure lies
in a vertical plane and pivots about a horizontal pin at A. The arm
has constant crosssectional area and total weight W.
A vertical spring of stiffness k supports the arm at point B.
(a) Obtain a
Hooke's Law for Plane Stress
When solving the problems for Section 7.5, assume that the material[
is linearly elastic with modulus ofetasticily E and Poisson s ratio v.
Problem 7.51 A rectangular steel plate with thickness 1 = SIB in. is
subjected
Problem 5.31 The shear stresses 1 in a rectangular beam are given by
Eq. (543):
v n?
T = sir 32)
in which V is the shear force, I is the moment of inertia of the crossesectional
area, it is the height of the beam. and yl is the distance from the neutral
Torsional Deformations
Problem 3.21 A copper rod of length L : 18.0 in. is to be
twisted by torques T(see gure) until the angle of rotation between
the ends of the rod is 3.0.
(a) If the allowable shear strain in the copper is 0.0006 rad, what
is the m
Problem 2.48 The xedend bar ABCD consists of three prismatic
segments, as shown in the gure. The end segments have crosssectional
areaA] = 340 mm2 and length L1 = 200 mm. The middle segment has
crossisecn'onal area A2 : 1260 mm2 and length L; : 250 mm. L
Problem 3.39 A circular bar AB with ends fixed against rotation has
a hole extending for half of its length (see gure). The outer diameter of
the bar is d2 = 3.0 in. and the diameter of the hole is 111 = 2.4 in. The
total length of the bar is L = 50 in.
tively, due to the load P (see gure part a).
(see gure part a).
(c) For what value of x is RB = (6/5) RA? (See gure part a.)
(1) Repeat part (a) if the bar is now rotated to a vertical position, load P is
SECTION 2.4 Statically Indeterminate Structures
'
3.49 x 10.86 in
.3 . .
800 lb 1600 lb
Problem 4.31 Calculate the shear force V and bending moment M at a cross
section just to the left of the [GOOlb load acting on the simple beam AH shown A
in the gure.
tso in.+L so in. #40 in.
120 imj
Solution 4.31
:x=l3.5ft
Problem 4525 The simple beam AB Shown in the gure supports a
concentrated load and a segment of uniform load.
(a) Draw the Shearforce and bendingmoment diagrams for this beam.
(b) Find the value of P that will result in zero shear at x = 13.5
Problem 2.5415 Pipe 2 has been inserted snugly into Pipe 1,
but the holes for a connecting pin do not line up: there is a gap s.
The user decides to apply either force P1 to Pipe 1 or force P2 [0
Pipe 2, whichever is smaller. Determine the following using
Problem 7310 A propeller shaft subjected to combined torsion and axial
thrust is designed to resist a shear stress of 57 MPa and a compressive stress of
105 MPa (see gure). '
(a) Determine the principal stresses and show them on a sketch of a properly
or
SECTION 1.3 Normal Stress and Strain 33
Solution 1.36
W= l30kN a = 30 A = 490 mm2 a, =150MPa
PART (a)
Wsin(a)
0', = = 132.7 MPa
PART (b)
a arcsi (UGA 4
. n 2
. [DEX 7 3 .4
Problem 1.47 The data shown in the accompanying table were
obtained from a te
Problem 3.116 Calculate the shear stress 1' and the angle of twist q!) (in
degrees) for a steel tube (G = 76 GPa) having the cross section shown
in the gure. The tube has length L = 1.5 m and is subjected to a torque
T = 10 kN'm.
SHEAR STRESS
T 10 kNm
Problem 2.77 The truss ABC shown in the figure supports a
horizontal load P1 = 300 lb and a vertical load P2 = 900 lb. Both
bars have crosssectional area A = 2.4 in.2 and are made of steel with
E = 30 x 106 psi.
(a) Determine the strain energy U1 of the
Problem 5.83 Two wood beams, each of rectangular cross
section (3.0 in. X 4.0 in., actual dimensions) are glued together
to form a solid beam of dimensions 6.0 in. X 4.0 in. (see gure).
The beam is simply supported with a span of 8 ft.
(a) What is th
Problem 3.87 A stepped shaft ACE is held against rotation at ends
A and B and subjected to a torque To acting at section C (see gure).
The two segments of the shaft (AC and CB) have diameters dA and d3,
respectively, and polar moments of inertia I PA and
Problem 7.23 The stresses acting on elementA on the web of a train rail are found to be 1 18,500 psi
6500 psi Ension in the horizontal direction and 18,500 psi compression in the vertical direction
(see gure). Also, shear stresses o
Problem 5.117 A hollow wood beam with plywood webs has the E in. E in.
crosssectional dimensions shown in the gure. The plywood is attached _ 3 in _, _
to the anges by means of small nails. Each nail has an allowable load 9
in shear 0f 30 lb.
Fin
Problem 5.42 A copper wire having diameter d = 4 mm is bent into a circle and held
with the ends just touching (see gure).
d = diameter
(a) If the maximum permissible strain in the copper is smax = 0.0024, what is the
shortest length L of wire that can
Problem 11.22 The gure shows an idealized structure consisting
of one or more rigid bars with pinned connections and linearly elastic
springs. Rotational stiffness is denoted 13R, and tmnslational stiffness
is denoted B.
(a) Determine the critical load 1
Problem 6.33 A simple beam that is 18 ft long supports a
uniform load of intensity q. The beam is constructed of two
C 8 X 11.5 sections (channel sections or C shapes) on either Side
of a 4 X 8 (actual dimensions) wood beam (see the cross section
shown i
Problem 8.211 ' A hollow pressurized sphere having radius r = 4.8 in. and
wall thickness 2 = 0.4 in. is lowered into a lake (see gure). The compressed
air in the tank is at a pressure of 24 psi (gage pressure when the tank is out Of
the water).
At what d
Problem 3.43 A stepped shaft ABCD consisting of solid circular
segments is subjected to three torques, as shown in the gure. The
torques have magnitudes 12.5 kin., 9.8 kin., and 9.2 kin. The
length of each segment is 25 in. and the diameters of the seg
Chapter 9
STATISTICAL INFERENCE
FOR A SINGLE SAMPLE:
HYPOTHESIS TESTING
Statistical hypothesis
A statistical hypothesis is a statement about the parameters of one or more
populations
Hypotheses are always statements about the
population, no statements abo
Chapter 8
STATISTICAL INFERENCE
FOR A SINGLE SAMPLE:
ESTIMATION OF PARAMETERS
xx
POINT ESTIMATION
A point estimate of some population parameter is a single numerical value of
a statistic . The statistic is called the point estimator.
^
^
Example
is a poin
Chapter 10
STATISTICAL INFERENCE
FOR TWO SAMPLES
Sampling from two independent populations
Population 2
(2 ,2)
Population 1
(1 ,1)
x
Sample n1
INDEPENDENT
x1,x s1
E( x1  x 2 ) = 1  2
V(
x
1

x
2
) = 12 + 22
n1
n2
Sample n2
x 2, s2
HYPOTHESIS TEST ON DI
Chapter 6
DESCRIPTIVE STATISTICS
(Summarize, describe, or present data)
BASIC METHODS OF COLLECTING DATA
A retrospective study using historical data
It may involve a lot of data, but little useful information
It may be missing data, recording errors
An ob