Civil Engineering Reference
In-Depth Information
4.7.5Beam webs in shear
4.7.5.1 Stocky webs
The factored design shear force
V
Ed
on a cross-section must satisfy
V
Ed
≤
V
c
,
Rd
(4.78)
in which
V
c
,
Rd
is the design uniform shear resistance which may be calculated
based on a plastic
(
V
pl
,
Rd
)
or elastic distribution of shear stress.
I-sectionshavedistributionsofshearstressthroughtheirwebsthatareapprox-
imately uniform (Section 5.4.2) and for stocky webs with
h
w
/
t
w
<
72
ε
, the yield
stress in shear
τ
y
=
f
y
/
√
3 is reached before local buckling. Hence EC3 requires
that
V
c
,
Rd
=
V
pl
,
Rd
=
A
v
(
f
y
/
√
3
)
γ
M
0
(4.79)
where
γ
M
0
=
1 and
A
v
is the shear area of the web which is defined in Clause
6.2.6ofEC3.Thisresistanceiscloseto,butmoreconservativethan,theresistance
given in equation 4.28, since the shear area
A
v
is reduced for hot-rolled sections
by including the root radius in its calculation, and because equation 4.79 ignores
theeffectsofstrainhardening.Somesections,suchasamonosymmetricI-section,
have non-uniform distributions of the shear stress
τ
Ed
in their webs. Based on an
elastic stress distribution, the maximum value of
τ
Ed
may be determined as in
Section 5.4.2, and EC3 then requires that
√
τ
Ed
≤
f
y
/
3
γ
M
0
.
(4.80)
Cross-sections for which
h
w
/
t
w
≤
72
ε
are stocky, and the webs of all UB's and
UC's in Grade 275 steel satisfy
h
w
/
t
w
≤
72
ε
.
4.7.5.2 Slender webs
Theshearresistanceofslenderunstiffenedwebsforwhich
h
w
/
t
w
>
72
ε
decreases
rapidly from the value in equation 4.79 as the slenderness
h
w
/
t
w
increases. For
these
V
c
,
Rd
=
V
bw
,
Rd
≤
η
f
yw
/
√
3
γ
M
1
h
w
t
w
(4.81)
where
V
bw
,
Rd
is the design resistance governed by buckling of the web in shear,
f
yw
is the yield strength of the web,
η
is a factor for the shear area that can be
taken as 1.2 for steels up to S460 and 1.0 otherwise, and
γ
M
1
(
=
1
)
is a partial
resistance factor based on buckling. The buckling resistance of the web is given
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