Civil Engineering Reference
In-Depth Information
v
L
=
286 kN/m
The shear per connector is
P
Ek
=
286
×
0.3/2
=
43 kN
From Equation 3.116, 80% of
P
Rk
is:
0.8
P
Rk
=
0.8
×
1.25
×
42.1
=
42.1 kN
since
1.25, so the alternative condition given in Section 3.7.1 is not
quite satisfied.
The reader may inquire why the shear per stud for a loading of 30
kN/m, 43 kN, is almost the same as the resistance provided, 42 kN per stud
(Equation 3.116), for an ultimate loading of 60.9 kN/m. The reason is that
these calculations for a serviceability limit state do not allow any redistri-
bution of force per stud along a half span. This doubles the maximum
force per stud, in this case. The elastic model with full interaction and the
ultimate-strength model with partial interaction happen to give similar
compressive forces in the slab, for a given bending moment. The force
per stud is then unaltered when the bending moment is halved.
This beam is evidently close to the borderline for deflection due to slip
that underlies the rules in EN 1994-1-1. The effect of slip on deflection is
now estimated, using Equation 3.94 with
k
γ
V
=
=
0.3,
n
/
n
f
=
η
=
0.51, and
δ
c
16.0 mm, as found above.
A load of 12.4 kN/m caused the steel beam to deflect 19.5 mm, so
=
δ
a
,
for the total load on the composite beam, is
δ
a
=
19.5(5.2
+
24.8)/12.4
=
47.2 mm
From Equation 3.94,
δ
=
16[1
+
0.3
×
0.49(47.2/16
−
1)]
=
20.6 mm
Slip thus increases a deflection of 16 mm to over 20 mm, and the total
deflection to 40 mm (span/215).
This exceeds the limit recommended in Section 3.7.2 (span/300), so the
steel beam should either be propped during construction, or be cambered
by an amount at least equivalent to the deflection due to permanent load,
which is
δ
g
=
19.5
+
2.8
=
22 mm
