Serviceability limit state - Eurocodes
Serviceability limit state - Eurocodes
Serviceability limit state - Eurocodes
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Vibration – vertical vibrations due to walking<br />
of persons<br />
G. Hanswille<br />
Univ.-Prof. Dr.-Ing.<br />
Institute for Steel and<br />
Composite Structures<br />
University of Wuppertal-Germany<br />
c<br />
F(t)<br />
M gen<br />
w(t)<br />
δ<br />
F n<br />
(t)<br />
m<br />
w(x k<br />
,t)<br />
L/2<br />
k a<br />
F n<br />
(t)<br />
x k<br />
w(t)<br />
L<br />
acceleration<br />
F<br />
w(t) = ka<br />
M<br />
maximum acceleration a, vertical deflection w and<br />
maximum velocity v<br />
a<br />
w<br />
F<br />
(<br />
f L / )<br />
n π<br />
max =<br />
−<br />
E<br />
δ v<br />
a<br />
s<br />
max = ka<br />
1−<br />
e<br />
(2 π f<br />
Mgen<br />
δ<br />
a<br />
vmax<br />
=<br />
2 π f<br />
f E<br />
F n<br />
δ<br />
v s<br />
k a<br />
M gen<br />
n<br />
gen<br />
π<br />
δ<br />
sin (2 π f<br />
E<br />
t)<br />
(<br />
−δ f t<br />
)<br />
1−<br />
e<br />
natural frequency<br />
load component of n-th harmonic<br />
logarithmic damping decrement<br />
forward speed of the person<br />
factor taking into account the different<br />
positions x k<br />
during walking along the beam<br />
generated mass of the system<br />
(single span beam: M gen<br />
=0,5 m L)<br />
E<br />
t =<br />
L<br />
v s<br />
E<br />
E<br />
)<br />
2<br />
65
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