Civil Engineering Reference
In-Depth Information
As well as strength, structural members must possess sufficient stiffness, under normal
working loads, to prevent deflections being excessive and thereby damaging adjacent
parts of the structure. Another consideration related to deflection is the appearance of
a structure which can be adversely affected if large deflections cause cracking of pro-
tective and/or decorative coverings. This is particularly critical in reinforced concrete
beams where the concrete in the tension zone of the beam cracks; this does not affect
the strength of the beam since the tensile stresses are withstood by the reinforcement.
However, if deflections are large the crack widths will be proportionately large and
the surface finish and protection afforded by the concrete to the reinforcement would
be impaired.
Codes of Practice limit deflections of beams either by specifying maximum span/depth
ratios or by fixing the maximum deflection in terms of the span. A typical limitation
for a reinforced concrete beam is that the total deflection of the beam should not
exceed span/250. An additional proviso is that the deflection that takes place after the
construction of partitions and finishes should not exceed span/350 or 20mm, whichever
is the lesser. A typical value for a steel beam is span/360.
It is clear that the deflections of beams under normal working loads occur within the
elastic range of the material of the beam no matter whether elastic or ultimate load
theory has been used in their design. Deflections of beams, therefore, are checked
using elastic analysis.
T
ABLE
8.1
Material
Density
Modulus of
Shear
Yield
Ultimate
Poisson's
(kN/m
3
)
elasticity,
modulus,
stress,
stress,
ratio ν
E
(N/mm
2
)
G
(N/mm
2
)
σ
Y
(N/mm
2
)
σ
ult
(N/mm
2
)
Aluminium alloy
27.0
70 000
40 000
290
440
0.33
Brass
82.5
103 000
41 000
103
276
Bronze
87.0
103 000
45 000
138
345
Cast iron
72.3
103 000
41 000
552
0.25
(compression)
138 (tension)
Concrete
22.8
21 400
20.7
0.13
(medium strength)
(compression)
Copper
80.6
117 000
41 000
245
345
Steel (mild)
77.0
200 000
79 000
250
410-550
0.27
Steel
77.0
200 000
79 000
414
690
0.27
(high carbon)
Prestressing wire
200 000
1570
Timber
softwood
7 000
16
hardwood
6.0
12 000
30
Composite
20 000
250
(glass fibre)
