Mechanics of Materials

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14 January 2011
1
Mechanics of Materials
CIVL 3322 / MECH 3322
Shear Stress in Beams
What is the cross-section
area of the tube shown in
mm
2
?

Shear Stress in Beams I
2
141.37
5
565.5
5
141.4
4
565.49
4
OTHER
9
Matched Acceptable Value: 2, Within
Range: 12
Acceptable Value: 565, Acceptable
Range: {563, 567}
14 January 2011
2
What is the cross-section
area of the tube shown in
mm
2
?
Shear Stress in Beams I
3
What is the radius of a
cylinder with an equivalent
cross-section area in mm

?

Shear Stress in Beams I
4
13.4
11
13.42
8
13.41
2
13.416
2
OTHER
3
Matched Acceptable Value: 0, Within
Range: 24
Acceptable Value: 13, Acceptable
Range: {12.5, 13.5}
14 January 2011
3
What is the radius of a
cylinder with an equivalent
cross-section area in mm

?
Shear Stress in Beams I
5
Shear Stress in Beams I
6
14 January 2011
4
Shear Stress in Beams I
7
Shear Stress in Beams I
8
14 January 2011
5
Shear Stress in Beams I
9
Shear Stress in Beams I
10
14 January 2011
6
Shear Stress in Beams I
11


Excerpts from this work may be reproduced by in
structors for distribution on a not
-
for
-
profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted.
Any other reproduction or translation of this work beyond that
permitted by Sections 1
07 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

9.
1

For the following problems, a beam segment subjected to internal bending moments at sections
A

and
B

is shown along with a sketch of the cross
-
sectional dimensions. For each problem:

(a) Sketch a side view of the beam segment and plot the distributio
n of bending stresses acting at
sections
A

and
B
. Indicate the magnitude of key bending stresses on the sketch.

(b) Determine the resultant forces acting in the
x

direction on the specified area at sections
A

and
B

and
show these resultant forces on the s
ketch.

(c)

Is the specified area in equilibrium with respect to forces acting in the x direction?

If not, determine
the horizontal force required to satisfy equilibrium for the specified area and show the location and
direction of this force on the sketch.


Consider area (1) of the 20
-
in.
-
long beam segment, which is subjected to internal bending moments of
M
A

= 24 kip
-
ft and
M
B

= 28 kip
-
ft
.



Fig. P9.
1
a

Beam segment

Fig. P9.
1
b

Cross
-
sectional dimensions

Solution

Moment of inertia about the
z

axis:

Sha
pe

I
C

d

=
y
i


y

d
²
A

I
C

+
d
²
A


(in.
4
)

(in.)

(in.
4
)

(in.
4
)

left web

864.000

0.000

0.000

864.000

top flange

12.505

10.250

1,287.016

1,299.521

bottom flange

12.505


10.250

1,287.016

1,299.521

right web

864.000

0.000

0.000

864.000

Moment of inertia about the
z

axis (in.
4
) =


4,327.042




Excerpts from this work may be reproduced by in
structors for distribution on a not
-
for
-
profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted.
Any other reproduction or translation of this work beyond that
permitted by Sections 1
07 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.

9.
1

For the following problems, a beam segment subjected to internal bending moments at sections
A

and
B

is shown along with a sketch of the cross
-
sectional dimensions. For each problem:

(a) Sketch a side view of the beam segment and plot the distributio
n of bending stresses acting at
sections
A

and
B
. Indicate the magnitude of key bending stresses on the sketch.

(b) Determine the resultant forces acting in the
x

direction on the specified area at sections
A

and
B

and
show these resultant forces on the s
ketch.

(c)

Is the specified area in equilibrium with respect to forces acting in the x direction?

If not, determine
the horizontal force required to satisfy equilibrium for the specified area and show the location and
direction of this force on the sketch.


Consider area (1) of the 20
-
in.
-
long beam segment, which is subjected to internal bending moments of
M
A

= 24 kip
-
ft and
M
B

= 28 kip
-
ft
.



Fig. P9.
1
a

Beam segment

Fig. P9.
1
b

Cross
-
sectional dimensions

Solution

Moment of inertia about the
z

axis:

Sha
pe

I
C

d

=
y
i


y

d
²
A

I
C

+
d
²
A


(in.
4
)

(in.)

(in.
4
)

(in.
4
)

left web

864.000

0.000

0.000

864.000

top flange

12.505

10.250

1,287.016

1,299.521

bottom flange

12.505


10.250

1,287.016

1,299.521

right web

864.000

0.000

0.000

864.000

Moment of inertia about the
z

axis (in.
4
) =


4,327.042


Problem 8.45
Shear Stress in Beams I
12
14 January 2011
7
Homework
¢

Problem P9.2
¢

Problem P9.3
¢

Problem P9.7
Shear Stress in Beams I
13