Civil Engineering Reference
In-Depth Information
Curves for other values of
R
are obtained by multiplying the ordinates
of the base curve by
R
. Those for
R
4, 8 and 16 are shown. The
appropriate value of
R
for use in design depends on the environment. The
British Standard gives:
=
R
=
4 for offices,
R
=
8 for workshops,
with the comment that use of double those values 'may result in adverse
comment', which 'may increase significantly' if the magnitudes of vibration
are quadrupled.
Some relaxation is possible if the vibration is not continuous. Wyatt
[36] recommends that a floor subject to a person walking at resonant
frequency once a minute could reasonably be permitted, a response double
the value acceptable for continuous oscillation.
3.9.1
Prediction of fundamental natural frequency
In composite floors that need checking for vibration, damping is sufficiently
low for its influence on natural frequencies to be neglected. For free
elastic vibration of a beam or one-way slab of uniform section, the funda-
mental natural frequency is
f
0
=
K
(
EI
/
mL
4
)
1/2
(3.95)
where
K
=
π
/2 for simple supports and
K
=
3.56 for both ends fixed
against rotation.
Values for other end conditions and multi-span members are given by
Wyatt. The relevant flexural rigidity is
EI
(per unit width, for slabs),
L
is
the span, and
m
the vibrating mass per unit length (beams) or unit area
(slabs). Concrete in slabs should normally be assumed to be uncracked, and
the dynamic modulus of elasticity should be used for concrete, in both
beams and slabs. This modulus,
E
cd
, is typically about 8 kN/mm
2
higher
than the static modulus, for normal-density concrete, and 3 to 6 kN/mm
2
higher, for lightweight-aggregate concretes of dry density not less than
1800 kg/m
3
. For composite beams in sagging bending, approximate allow-
ance for these effects can be made by increasing the value of
I
by 10%.
Unless a more accurate estimate can be made, the mass
m
is usually
taken as the mass of the characteristic permanent load plus 10% of the
characteristic variable load.
A convenient method of calculating
f
0
is to find first the mid-span
deflection,
δ
m
say, caused by the weight of the mass
m
. For simply-
supported members this is
