4.5 A beam of the cross section shown is extruded from aluminum alloy for which σ
y
=
250 MPa and σ
u
=
450 MPa. Using a factor of safety of 3.00, determine the largest couple
that can be applied to the beam when it is bent about the
z
axis.
4.10 Two equal
and opposite couples of magnitude
M
= 25 kN . m are applied to the
channel

shaped beam AB. Observing that the couples cause the beam to bend in a
horizontal plane, determine the stress at
(a)
point C,
(b)
point
D, (c)
point
E..
4.15 Knowing that for t
he extruded beam shown the allowable stress is 120MPa in
tension and 150 MPa in compression, determine the largest couple M that can be applied.
4.20 Knowing that for the beam shown the allowable stress is 12 ksi in tension
and 16 ksi
in compression, d
etermine the largest couple M that can be applied.
4.21 Knowing that
σ
all
=24 ksi
for
the steel strip
AD,
determine
(a)
the largest couple M
that can be applied, (6) the corresponding radius of curvature. Use E=29 X
10
6
psi.
4.39 and 4.40 A steel b
ar
(Es
= 210 GPa) and an aluminum bar
(Ea
= 70 GPa) are bonded
together to form the composite bar shown. Determine the maximum stressing
(a)
the
aluminum, (b) the steel, when the bar is bent about a horizontal axis
with M
=60N.m.
4.49 A concrete beam is
reinforced by three steel rods placed as shown. The modulus of
elasticity is 3 x 10
6
psi for the concrete and 30 x 10
6
psi for the steel Using an allowable
stress os 1350 psi for the concrete and 20 ksi for the steel, determine the largest allowable
posit
ive bending moment in the beam.
4.50 Knowing that the bending moment in the reinforced concrete beam is +150 kip.ft
and that the modulus of elasticity is 3.75 x 10
6
psi for the concrete and 30 x 10
6
psi for
the steel, determine
(a)
the stress in the st
eel,
(b)
the maximum stress in the concrete.
4.57 A steel pipe and an aluminum pipe are securely bonded together to form the
composite beam shown. The modulus of elasticity is 210 GPa for the steel and 70 GPa
for the aluminum. Knowing that the composit
e beam is bent by couple of moment
500N.m. determine the maximum stress
(a)
in the aluminum.
(b)
in the steel.
4.59 The
rectangular beam shown is made of a plastic for which the value of the
modulus of elasticity in tension is one

half of its value in
compression. For a bending
moment M
=600 N .In, determine the maximum
(a)
tensile stress,
(b)
compressive stress.
4.103 The vertical portion of the press shown consists of a rectangular tube of wall
thickness
t
= 10 mm. Knowing that the press has been
tightened on wooden planks being
glued together
until P
= 20kN, determine the stress at
(a)
point
A, (b)
point
B.
4.108 The four forces shown are applied to a rigid plate supported by a solid steel post of
radius
a.
Knowing that
P
= 100kN and
a
= 40 mm
. D
etermine the maximum stress in the
post when
(a)
the force at
D
is removed,
(b)
the forces at C and D are removed.
4.114 Knowing that the clamp shown has been tightened on wooden planks being glued
together until
P
=400 N, determine in section
a

a (a
)
the stress at point
A,(b)
the stress. at
point
D, (c)
the location of the neutral axis.
4.116
In order to provide access to the interior of a hollow square tube of 0.25

in. wall
thickness, the portion
CD
of one side of the tube has been removed. Know
ing that the
loading of the tube is equivalent to two equal and opposite 15

kip forces acting at the
geometric centers
A
and
E
of the ends of the tube, determine
(a)
the maximum stress in
section
a

a, (b)
the stress at point
F. Given:
the centroid of the c
ross section is at C and
I
z
= 4.81 in
4
.
*4.138 and *4.139 The couple M acts in a vertical plane and is applied to a beam oriented
as shown. Determine the stress at point
A.
4.161 Knowing that the allowable stress in the bar is 150 MPa, determine th
e largest
permissible distance
a
from the line of action of the 3

kN force to the vertical plane
containing the center of curvature of the bar.
4.164 For the split ring shown, determine the stress at
(0)
point
A, (b)
point
B.
4.175 For the crane hook shown, determine the largest tensile stress in section
a

a.
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