PROBLEM 16.40
A glue laminated column of 3–m effective length is to be made
from boards of 24 × 100–mm cross section. Knowing that for the
grade of wood used,
11 GPa=E
and the adjusted allowable
stress for compression parallel to the grain is
9 MPa,
σ
=
C
determine the number of boards that must be used to support the
centric load shown when (a)
34 kN,P=
(b)
17 kN.=P
consent of McGraw–Hill Education.
SOLUTION Continued
Let
1/
2
CE C
uc
σσ
+
=
and
/.
σσ
=
CE C
vc
Then
2
P
C u uv=−−
6
all
9 10
CP P
CC
σσ
= = ×
n u v
P
C
all
(MPa)
σ
2
(m )A
all (kN)
P
3 0.71904 0.36330 0.32697 2.9477
3
7.2 10−
×
21.19
4
0.84619
0.58128
0.47910
4.3119
3
9.6 10−
×
41.39
5n≥
0.87092
0.63072
0.51345
4.6210
3
2.4 10
−
×n
11.09 n
(a)
34kN: Use 4 boards.P=
(b)
17kN: Use 3 boards.P=
PROBLEM 16.41
For a rod made of the aluminum alloy 2014–T6, select the smallest square cross section that
may be used if the rod is to carry a 55-kip centric load.
PROBLEM 16.42
An aluminum tube of 90–mm outer diameter is to carry a centric load of
120 kN. Knowing that the stock of tubes available for use are made of alloy
2014-T6 and with wall thicknesses in increments of 3 mm from 6 mm to
15 mm, determine the lightest tube that can be used.
PROBLEM 16.43
A centric load P must be supported by the steel bar AB. Using allowable stress
design, determine the smallest dimension d of the cross section that can be used
when
(a)
108 kN,P=
(b)
166 kN.P=
Use
250 MPa
Y
σ
=
and
200 GPa.E=
PROBLEM 16.44
A column of 4.5–m effective length must carry a centric load of 900 kN. Knowing that
345 MPa
σ
=
Y
and
200 GPa,=E
use allowable stress design to select the wide–flange shape of 250–mm nominal depth that
should be used.
PROBLEM 16.45
A column of 22.5–ft effective length must carry a centric load of 288 kips. Using allowable stress design, select
the wide-flange shape of 14-in. nominal depth that should be used. Use
50 ksi
s
=
Y
and
6
29 10 psi.= ×E
consent of McGraw–Hill Education.
PROBLEM 16.46
A square steel tube having the cross section shown is used as a column of 26–ft
effective length to carry a centric load of 65 kips. Knowing that the tubes available
for use are made with wall thicknesses ranging from
1
4
in.
to
3
4
in. in increments of
1
16
in., use allowable stress design to determine the lightest tube that can be used.
6
SOLUTION Continued
Try
2
3in. 0.375 in. 5.25 in. 8.4375 in
8i
t bA= = = =
44 4
2
cr 2
1[(6) (5.25) ] 44.6924 in
12
2.3015 in.
312 135.564 > 133.68
2.3015
0.877 13.659 ksi
( /)
p
s
=−=
= =
= =
= =
e
e
I
I
rA
L
r
E
Lr
cr
all (13.659)(8.4375) 69.0 kips > 65 kips
1.67 1.67
A
P
s
= = =
Use 3/8 in.t=
consent of McGraw–Hill Education.
PROBLEM 16.40
A glue laminated column of 3–m effective length is to be made
from boards of 24 × 100–mm cross section. Knowing that for the
grade of wood used,
11 GPa=E
and the adjusted allowable
stress for compression parallel to the grain is
9 MPa,
σ
=
C
determine the number of boards that must be used to support the
centric load shown when (a)
34 kN,P=
(b)
17 kN.=P
consent of McGraw–Hill Education.
SOLUTION Continued
Let
1/
2
CE C
uc
σσ
+
=
and
/.
σσ
=
CE C
vc
Then
2
P
C u uv=−−
6
all
9 10
CP P
CC
σσ
= = ×
n u v
P
C
all
(MPa)
σ
2
(m )A
all (kN)
P
3 0.71904 0.36330 0.32697 2.9477
3
7.2 10−
×
21.19
4
0.84619
0.58128
0.47910
4.3119
3
9.6 10−
×
41.39
5n≥
0.87092
0.63072
0.51345
4.6210
3
2.4 10
−
×n
11.09 n
(a)
34kN: Use 4 boards.P=
(b)
17kN: Use 3 boards.P=
PROBLEM 16.41
For a rod made of the aluminum alloy 2014–T6, select the smallest square cross section that
may be used if the rod is to carry a 55-kip centric load.
PROBLEM 16.42
An aluminum tube of 90–mm outer diameter is to carry a centric load of
120 kN. Knowing that the stock of tubes available for use are made of alloy
2014-T6 and with wall thicknesses in increments of 3 mm from 6 mm to
15 mm, determine the lightest tube that can be used.
PROBLEM 16.43
A centric load P must be supported by the steel bar AB. Using allowable stress
design, determine the smallest dimension d of the cross section that can be used
when
(a)
108 kN,P=
(b)
166 kN.P=
Use
250 MPa
Y
σ
=
and
200 GPa.E=
PROBLEM 16.44
A column of 4.5–m effective length must carry a centric load of 900 kN. Knowing that
345 MPa
σ
=
Y
and
200 GPa,=E
use allowable stress design to select the wide–flange shape of 250–mm nominal depth that
should be used.
PROBLEM 16.45
A column of 22.5–ft effective length must carry a centric load of 288 kips. Using allowable stress design, select
the wide-flange shape of 14-in. nominal depth that should be used. Use
50 ksi
s
=
Y
and
6
29 10 psi.= ×E
consent of McGraw–Hill Education.
PROBLEM 16.46
A square steel tube having the cross section shown is used as a column of 26–ft
effective length to carry a centric load of 65 kips. Knowing that the tubes available
for use are made with wall thicknesses ranging from
1
4
in.
to
3
4
in. in increments of
1
16
in., use allowable stress design to determine the lightest tube that can be used.
6
SOLUTION Continued
Try
2
3in. 0.375 in. 5.25 in. 8.4375 in
8i
t bA= = = =
44 4
2
cr 2
1[(6) (5.25) ] 44.6924 in
12
2.3015 in.
312 135.564 > 133.68
2.3015
0.877 13.659 ksi
( /)
p
s
=−=
= =
= =
= =
e
e
I
I
rA
L
r
E
Lr
cr
all (13.659)(8.4375) 69.0 kips > 65 kips
1.67 1.67
A
P
s
= = =
Use 3/8 in.t=
consent of McGraw–Hill Education.