Civil Engineering Reference
In-Depth Information
By analogy with a simple spring-mass system, the fundamental fre-
quency can be defined by
f
0
=
(1/2
π
)(
k
e
/
M
e
)
1/2
(3.104)
where
k
e
is the effective stiffness. The effective mass
M
e
is given approx-
imately by
M
e
=
mSL
/4
From Equation 3.104,
k
e
=
π
2
f
2
mSL
With J from Equation 3.101, Equation 3.102 then gives
a
rms
=
340
C
f
/
(
mSL
ζ
)
(3.105)
with
S
given by Equation 3.103.
From the base curve in Fig. 3.26, for 4
<
f
0
<
8 Hz,
a
rms
=
5
×
10
−3
R
m/s
2
so from Equation 3.105,
R
=
68 000
C
f
/
(
mSL
ζ
)
(3.106)
in kg,m units. This equation is given on p. 28 of Reference 36.
For floors with layouts of the type shown in Fig. 3.1, and that satisfy
the assumptions made above, checking for susceptibility to vibration caused
by pedestrian traffic consists of finding
f
0
from Equation 3.98, and
a
rms
or
R
, as given above, and comparing the result with the target response
curve, as in Fig. 3.26.
Relevant calculations are given in Section 3.11.3.2.
The preceding summary is intended only to provide an introduction to
a versatile design method, and to apply it to a single type of structure.
3.10
Fire resistance of composite beams
Fire design, based on EN 1994-1-2,
Structural fire design
, is introduced in
Section 3.3.7, the whole of which is applicable to composite beams, as
well as to slabs, except Section 3.3.7.5.
