Civil Engineering Reference
In-Depth Information
Figure 6.6
Equivalent temperature parameters: (a) actual member of a plane frame; (b)
conjugate beam subjected to rise of temperature producing the same forces at
ends A and B as in the actual beam.
T
O
T
1/A
0
0
0
l
/(6I)
5
l
/(6I)
0
−
A
r1
A
r2
A
r3
1
E
c
α
′
1
=
1/I
(6.9)
T
′
2
−
1/I
where
A
and
I
is the cross-sectiona
l
are
a
and its second moment about cen-
troidal axis;
l
is length of member;
E
c
(
≡
E
c
(
t
k
,
t
j
) ) is the age-adjusted modul
u
s
and
α
is an arbitrary thermal expansion coe
cient. The same values of
E
c
and
α
used in Equation (6.9) must be entered as input in Computer run 2. The
fi
′
2
can be expressed (by an
equation similar to Equation (6.9) ) in terms of the
ctitious temperature parameters
T
0
,
T
′
1
and
T
xed-end forces at end
B
instead of end
A
, to give the same result. The subdivision of members into
two parts should not be done in Computer run 1. Also the subdivision is not
necessary in Computer run 2, when the structure is a plane or a space truss. In
this case, the input in Computer run 2 is a uniform rise of temperature,
T
0
;
where
fi
A
r
(
t
k
,
t
j
)
T
O
=
(6.10)
α
E
c
(
t
k
,
t
j
)
A
where
A
r
(
t
k
,
t
j
) is an axial force at the
fi
rst-end of the member (given by
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