Civil Engineering Reference
In-Depth Information
material and in some cases depends upon whether the material is subjected to tension
or compression.
A knowledge of the failure stress of a material is essential in structural design where,
generally, a designer wishes to determine a minimum size for a structural member
carrying a given load. For example, for a member fabricated from a given material and
subjected to axial load, we would use Eq. (7.1) either to determine a minimum area of
cross section for a given load or to check the stress level in a given member carrying a
given load.
E
XAMPLE
7.1
A short column has a rectangular cross section with sides in the ratio
1 : 2 (Fig. 7.3). Determine theminimumdimensions of the column section if the column
carries an axial load of 800 kN and the failure stress of the material of the column is
400N/mm
2
.
800 kN
B
2
B
F
IGURE
7.3
Column of Ex. 7.1
From Eq. (7.1) the minimum area of the cross section is given by
10
3
400
P
σ
max
=
800
×
2000mm
2
A
min
=
=
But
2
B
2
2000mm
2
A
min
=
=
from which
B
=
31
.
6mm
Therefore the minimum dimensions of the column cross section are 31.6mm
×
63.2mm. In practice these dimensions would be rounded up to 32mm
64mm or,
if the column were of some standard section, the next section having a cross-sectional
area greater than 2000mm
2
would be chosen. Also the column would not be designed
to the limit of its failure stress but to a working or design stress whichwould incorporate
some safety factor (see Section 8.7).
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