Civil Engineering Reference
In-Depth Information
slip to deflection is 3.2
h
/
L
. The ratio
L
/2
h
for a beam is typically about
20, so that the end slip is less than a tenth of the deflection. This shows
that
shear connection must be very stiff if it is to be effective
.
2.2.2
Full interaction
It is now assumed that the two halves of the beam shown in Fig. 2.2 are
joined together by an infinitely stiff shear connection. The two members
then behave as one. Slip and slip strain are everywhere zero, and it can
be assumed that plane sections remain plane. This situation is known as
full interaction
. Except in design with partial shear connection (Sections
3.5.3 and 3.7.1), all design of composite beams and columns in practice is
based on the assumption that full interaction is achieved.
For the composite beam of breadth
b
and depth 2
h
,
I
2
bh
3
/3, and
elementary theory gives the mid-span bending moment as
wL
2
/8. The
extreme fibre bending stress is
=
My
I
wL
2
3
3
16
wL
bh
2
max
σ
=
=
h
=
(2.7)
8
2
bh
3
2
The vertical shear at section
x
is
V
x
=
w
x
(2.8)
so the shear stress at the neutral axis is
3
2
1
3
4
wx
bh
(2.9)
τ
x
=
wx
=
2
bh
and the maximum shear stress is
3
8
wL
bh
(2.10)
τ
=
The stresses are compared in Figs 2.2(c) and (d) with those for the non-
composite beam. The provision of the shear connection does not change
the maximum shear stress, but the maximum bending stress is halved.
The mid-span deflection is
5
384
wL
EI
4
5
256
wL
Ebh
4
δ
=
=
(2.11)
3
which is one-quarter of the previous deflection (Equation 2.3). Thus the
provision of shear connection increases both the strength and the stiffness of
