6.3
A simple truss in which all members have the same axial rigidity
AE
is loaded as shown
in Figure P6.5. Calculate the diameter
d
necessary for
(
a
) The bar
AB.
(
b
) The bar
BC.
Given:
E
= 210 GPa
, S
y
= 250 MPa .
Assumption: Buckling occurs in the plane of the truss. The Euler formula applies.
( a )
Applying the method of joints at A:
Fk
N
AB
C
=
40
(
)
and
)
(
220
C
kN
F
BC
=
.
5
.
2
m
L
AB
=
mm
d
d
A
F
cr
AB
3
.
14
,
)
10
(
250
;
4
)
10
(
40
6
2
3
=
=
=
π
σ
W
e
h
a
v
e
rI
and Euler
’
s formula:
A
d
==
4
cr
E
Lr
d
dm
=
×
2
2
29
2
250 10
109 8
6
210 10
25025
()
(.
.
)
;(
)
,
.
m
m
m
Use, a commercial size of :
d
=
110
diameter
( b )
m
L
BC
875
.
1
=
mm
d
d
A
F
BC
cr
5
.
33
,
)
10
(
250
;
4
)
10
(
220
6
2
3
=
=
=
Euler formula:
cr
E
d
=
×
2
2
2
250 10
82 4
6
210 10
1875 025
.
)
)
,
.
m
U
s
e
83
−
mm
diameter
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View Full Document6.5
A steel pipe of outer diameter
D
and inner diameter
d
is employed as a 2m column
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 Winter '10
 Kim
 Leonhard Euler, Euler's formula, Euler's identity

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