Problem 15.46
The beam is subjected to a distrubuted load. For the
cross section at x = 0.6 m, determine the average shear
stress (a) at the neutral axis; (b) at y = 0.02 m.
Free Body Diagram:
Solution:
Summing the moments about point B to determine the r
Problem 14.34 The load F = 4650 lb. Draw the
shear force and bending moment diagrams for the beam.
Solution:
Draw the FBD of the beam and determine the reactions at points A
and B.
3
(3 x)(400x2 )dx + By (5 ft)
MA = 0 = (4650 lb)(3 ft)+
0
3
(1200x2 400x3
Problem 15.4 The beam consists of material with
modulus of elasticity E = 14x106 psi and is subjected
to couples M = 150, 000 inlb at its ends. (a) What is
the resulting radius of curvature of the neutral axis? (b)
Determine the maximum tensile stress due
Problem 7.28
troids.
Determine the coordinates of the ceny
20 mm
60 mm
x
30 mm
70 mm
Solution: Let us solve this problem by using symmetry and by
breaking the composite shape into parts.
l1
20 mm
y
A1
20 mm
h1
l1 = 70 mm
h1 = 70 mm
l2 = 70 mm
h2 = 70 mm
A
Problem 10.24 A prismatic bar with length L = 6 m
and a circular cross section with diameter D = 0.02 m
is subjected to 20-kN compressive forces at its ends.
The length and diameter of the deformed bar are measured and determined to be L = 5.940 m and D =
Problem 10.44 In Problem 10.43, the iron will safely Free Body Diagram:
support a tensile stress of 100 ksi and the aluminum will
safely support a compressive stress of 40 ksi. What is
the largest safe value of the gap b?
Solution:
We see from the FBD tha
Problem 10.9 The angle of the system in Prob- Free Body Diagram:
lem 10.8 is 60 . The bars are made of a material that will
safely support a tensile normal stress of 8 ksi. Based on
this criterion, if you want to design the system so that it
will support
Problem 9.8 The prismatic bar has a solid circular Free Body Diagram:
cross section with 30-mm radius. It is suspended from
one end and is loaded only by its own weight. The mass
density of the homogeneous material is 2800 kg/m3 . Determine the average no
Problem 6.4 Determine the axial forces in the members of the truss.
A
0.3 m
2 kN
B
0.4 m
C
1.2 m
0.6 m
Solution: First, solve for the support reactions at B and C, and
then use the method of joints to solve for the forces in the members.
A
0.3 m
BY
B
A
2
Ch 4. Concept of stress
1. Notation of stress components
ij
= normal stress along j-direction
on i surface (in this case i = j)
ij
: shear stress along j direction
on i surface (in this case i j)
z
rewrite using stress tensor
xy
xx
xx xy xz
yy
yx
HW #5
1. A block of aluminum in the form of a rectangular
parallelepiped (see figure) of dimensions a = 125mm, b =
100mm, and c = 75mm is subjected to triaxial stresses x = 75
MPa, y = -35 MPa and z = -10 MPa acting on the x, y and z
max
faces, respecti
Ch 5. Strain and Material Relation
Purpose : Detailed explanation of strain
Hookes low in 3-D
5.1 Strain
normal strain ()
shear strain ( )
Normal strain
L
A
B
x
x
P : Normal load
B
A
u
u+du
P
L
Deformation of a prismatic bar
where = axial deformation
L
HW #3
1. A bar ABC having two different cross-sectional areas is loaded by and
axial force P (see figure). parts AB and BC are circular in cross section
with diameters 50 , and 38mm, respectively. If the normal stress in AB is
40 MPa, what is the normal
HW #4
1. A two-dimensional condition of stress at a point in y 2MPa
y
a loaded structure is shown in Fig. Compute
xy with between 0 180 in 5 increments for
x
= 7 MPa, y
= 2 MPa, and
xy
= 5 MPa. Plot
x
and
x
and
xy versus .
xy 5MPa
x 7MPa
x
2. An el
HW #2
1. Identify the lip plane and the slip step in Fig.(Note) for plastic
deformation by motion of a screw dislocation
2. Cold working a metal by rolling it to a lesser thickness or
hammering it introduces a large number of dislocations into the
crysta
HW #1
1. The following data were collected from a 12 mm diameter
test specimen of magnesium :
F /( / 4)(12 mm) 2 F / 113 .1
( 30) / 30
Load
(N)
0
Gage Length
(mm)
30.0000
Stress Strain
(MPa)
(mm/mm)
0
0.0
5000
30.0296
44.2
0.000987
1000
0
30.0592
88.4