Civil Engineering Reference
In-Depth Information
Equation (7.49) give the values of
σ
i
(temp.) and
σ
o
(temp.) produced by the
temperature rise, i.e.
T
(
α
i
−
α
o
)
E
o
A
i
E
i
A
o
E
o
+
σ
o
(temp
.
)
=
A
i
E
i
(ii)
T
(
α
i
−
α
o
)
A
o
E
o
E
i
A
o
E
o
+
σ
i
(temp
.
)
=
A
i
E
i
In Eq. (ii)
α
o
>α
i
so that
σ
o
(temp.) is a compressive stress while
σ
i
(temp.) is a tensile
stress. Hence
10
−
5
100(1
.
2
−
1
.
85)
×
×
80 000
×
300
×
200 000
σ
o
(temp
.
)
=
108
.
0
×
10
6
28
.
9N
/
mm
2
(i
.
e
.
compression)
=−
10
−
5
100(1
.
2
−
1
.
85)
×
×
2
×
300
×
80 000
×
200 000
σ
i
(temp
.
)
=
10
6
108
.
0
×
57
.
8N
/
mm
2
(i
.
e
.
tension)
=−
Superimposing the sets of stresses, we obtain the final values of stress,
σ
i
and
σ
o
, due
to load and temperature change combined. Hence
127
.
4N
/
mm
2
(compression)
σ
i
=
185
.
2
−
57
.
8
=
103
.
0N
/
mm
2
(compression)
σ
o
=
74
.
1
+
28
.
9
=
The displacements due to the load and temperature change are found using Eqs (7.37)
and (7.51), respectively. Hence
10
3
10
3
100
×
×
4
×
δ
(load)
=
=
3
.
7mm (contraction)
×
10
6
108
.
0
10
3
δ
(temp
.
)
=
4
×
×
100
1
.
85
10
−
5
10
−
5
×
×
2
×
300
×
80 000
+
1
.
2
×
×
300
×
200 000
×
10
6
108
.
0
×
=
6
.
0mm (elongation)
The final displacement of the slab involves an overall elongation of the columns of
6
.
0
−
3
.
7
=
2
.
3mm.
INITIAL STRESSES AND PRESTRESSING
The terms initial stress and prestressing refer to structural situations in which some
or all of the components of a structure are in a state of stress
before
external loads
are applied. In some cases, for example welded connections, this is an unavoidable
by-product of fabrication and unless the whole connection is stress-relieved by suitable
heat treatment the initial stresses are not known with any real accuracy. On the other
