where:
tw,min is the smaller web thickness above/below the opening
fy is the yield strength of the steel
This buckling resistance is compared to the horizontal shear force, Vwp,Ed ,
acting in the web-post. The upper bound shear resistance is given by
χwp = 1/√3 = 0.577, which corresponds to pure shear resistance of the webpost
rather than buckling.
For rectangular openings, a further check should be made on the inplane
moment acting at the top or bottom of the web-post due to the
effects of horizontal shear, which may control for narrow web-posts. For a
symmetric section, this moment is given by 0.5VEd h, which should not
wp,oexceed the in-plane bending resistance of the web-post, which is taken as
tmin s2 fy /(6γ).
w,o
M1
Relaxation for adjacent elongated openings or circular and elongated
openings
The maximum buckling length for web-post buckling between circular or
circular and elongated openings of the same height may be taken as:
ℓw ≤ 0.7ho
This leads to an upper bound nondimensional slenderness of the webpost
given by:
wp
Relaxation for adjacent circular and rectangular openings
For adjacent circular and rectangular openings, or openings of different
lengths, it is proposed that the transition between closely spaced and
widely spaced openings is taken as the average of the two opening
lengths. For adjacent circular and rectangular openings, this corresponds to
a transition at an edge-to-edge spacing of
so = 0.5(ℓo + ho). It is proposed that the minimum edge-to-edge spacing is
0.25(ℓo + ho) for the case of adjacent rectangular and circular openings. The
upper bound nondimensional slenderness of the web-post is taken as the
average of the two openings.
Contact: Prof Mark Lawson
Tel: 01344 636555
Email: advisory@steel-sci.com
AD 419:
Composite beams with
different positions of web
openings
SCI publication P355 is widely used to design beams with large web
openings. It is adopted in the development of software to design hot rolled
and fabricated steel sections with openings of various shapes and sizes.
The purpose of this Advisory Desk note is to address some common
practical problems related to adjacent openings of different heights and
positions.
1. Unequal adjacent opening heights
In P355 and in the AD 418, the buckling length of the web post for buckling
between closely spaced openings on the same horizontal axis is given by:
ℓw = 0.7(ho
ℓw = 0.5(ho
where:
ho is the opening height (or average height, as defined below)
so is the edge-to-edge distance between the openings
For unequal adjacent opening heights, it is proposed that the average
height of the openings, ho,eff , may be used to determine the slenderness for
web post buckling with a lower limit of 0.75 of the larger opening height.
This corresponds to the smaller opening height being taken as not less than
half the larger opening height. Therefore, the effective opening height, ho,eff
replaces ho in the above equations and is taken as:
28 NSC
2.4ho
tw1
(6)
2 + so
2)0.5 ≤ ho for rectangular openings (1)
2 + so
2)0.5 ≤ 0.7ho for circular or elongated openings (2)
Technical Digest 2018
ho,eff = 0.5 (ho,1 + ho,2) ≥ 0.75 ho,1 (3)
where:
ho,1 is the height of the larger opening
ho,2 is the height of the smaller opening
2. Different eccentricities of adjacent openings
The eccentricity of the opening, eo , is defined as positive when the centre
line of the opening is above the centre line of the beam and negative when
it is below. For the checks on web-post buckling, the effective opening
height in the above equations for web-post buckling should include the
worst case of the difference in eccentricities, which is as follows:
ho,eff = 0.5 (ho,1 + ho,2) + | eo,1 – eo,2 | ≥ 0.75 ho,1 + | eo,1 – eo,2 | (4)
where:
| eo,1 – eo,2 | is taken as its absolute value, in which eo,1 and eo2 can have
different signs depending on the position of adjacent openings relative to
the centre line of the beam and the heights of the adjacent openings are
defined as above.
The use of the absolute value of | eo,1 – eo,2 | is the worst case for checking
web-post buckling. A more precise treatment that takes account of the
buckling length is given below.
3. More precise treatment of eccentricities or unequal adjacent
opening heights
For unequal adjacent opening heights and positions, the buckling length
should be calculated from the dimension, ℓ which is the diagonal distance
from the low edge of the opening in the High Shear Side (HSS) to the high
edge of the opening at the Low Shear Side (LSS). Various cases are shown in
Figure 1. The buckling length for web-post buckling is taken as:
For circular or elongated openings: ℓw = 0.5ℓ
For rectangular openings: ℓw= 0.7ℓ
For adjacent circular and rectangular openings: ℓw = 0.6ℓ
Circular openings Rectangular openings
Low Shear Side (LSS) High Shear Side (HSS) Low Shear Side (LSS) High Shear Side (HSS)
Low Shear Side (LSS) High Shear Side (HSS)
Low Shear Side (LSS) High Shear Side (HSS)
Figure 1:
Treatment of the diagonal distance for web-post buckling between adjacent openings
The dimension ℓ should be calculated by taking h2 ≥ 0.5h1 to be
o,o,consistent with the limit in equation (4).
For adjacent rectangular openings, it is also necessary to check the
in plane bending resistance of the web-post due to the horizontal force
acting at the mid height of the beam. The position of the critical section
will depend on the relative position of the openings in the beam depth. For
simplicity, the in plane moment in the case of symmetric steel sections is
determined from:
MEd = 0.5 (0.5(h1 + h) + e1 + e2 ) VEd
wp,o,o,2o,o,wp,where:
VEd is the horizontal shear force acting at the mid height of the beam
wp,This moment should not exceed the elastic bending resistance of the web
post which is given by:
MEd = tw s2 fy /(6γ)
wp,o
M0where:
Low Shear Side (LSS) High Shear Side (HSS)
Low Shear Side (LSS) High Shear Side (HSS)
e02
e01
Advisory Desk
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