Steel I-section beam web opening analysis
Clause 4.15 of BS5950 deals with web openings but does not make any specific recommendations as to how the strength of a section with part of the web removed should be determined, referring users of the standard to the CIRIA/SCI paper, 'Design for openings in the webs of composite beams'. This paper includes guidance on checking openings in non-composite beams. In passing, you might note that BS5950-1:2000 was one of the first British Standards to reference a non-BSI publication. Small circular openings that fall within the limits set out in §184.108.40.206 do not need to be checked.
CIRIA/SCI design guidance
When an opening is made through a beam web there is some loss of strength. This will depend on the size and position of the opening. For some openings the residual strength may be adequate so no reinforcement of the section wil be necessary. On the other hand, the loss of strength may be such that the amount of reinforcement required would be impractical. If reinforcement is required, and will not exceed the limits set out below, it will take the form of steel flats (stiffeners) welded horizontally to the web above and below the opening on one or both sides of the web.
A web opening produces an additional (Vierendeel) moment across the length of the opening due to the relative vertical displacement at the ends of the opening. This moment introduces additional shear forces at the opening and there will also be axial forces - compression in the top and tension in the bottom - acting on upper and lower T-shaped web-flange sections. Note that ProSteel does NOT check the effect of the opening(s) on the equivalent slenderness of the beam, and does not calculate the additional deflection due to the reduced Ixx at the opening(s) or the deflection due to shear.
The CIRIA/SCI paper provides two formulae for calculating the additional deflection for beams with two openings symmetrically positioned in the span; with uniform loading or a central point load; and the openings in the middle of the beam depth. These indicate that the additional deflection in these conditions will normally be only slightly greater than the deflection of an unperforated beam. If the deflection of the current section is within 5% of the maximum permissible figure you are advised to use a heavier or deeper section.
Restrictions on size and position of openings
The CIRIA paper provides the following guidance on the size and position of web openings:
Horizontal position: Openings should be positioned not less than twice the beam depth or span/10 from a support and not less than the beam depth from any point load.
Vertical position: The opening should, if possible, be positioned at the mid-height of the beam. Otherwise, the depths of the upper and lower sections should not differ by more than a factor of 2.
Opening size: The opening length and height should not exceed 1.5D and 0.6D respectively in unstiffened sections or 2.0D and 0.7D in stiffened sections (D = o/a beam depth).
Spacing of openings: The distance between adjacent openings should not be less than the beam depth.
The CIRIA/SCI paper suggests that circular openings be treated by assuming a length equal to 0.9 x the radius of the opening, and a depth equal to 1.8 x the radius. All other openings should have radiused corners.
These recommendations are not mandatory but ProSteel will not allow you to enter openings that are larger than recommended. In some cases (e.g. heavy section UC's used as beams) slavish adherence to these recommendations would allow openings to be created that cut away all the beam web. Even if the numbers work this is not advisable At all times please remember that use of ProSteel does not remove the need for sound engineering judgment.
Analysis of the effect of an opening
The effect of the opening on the behaviour of the beam is analysed by considering the tensile and compressive forces due to the applied moment at the side of the opening with the lower bending moment (and thus the higher shear force). The bending moment is translated into equal compressive and tensile stresses which act at the elastic neutral axes of the web-flange sections above and below the opening. The shear force creates a Vierendeel moment across the opening which is resisted by the Vierendeel moment capacity of the sections.
For stiffened openings, this is equal to
2Mpt(1 - To/Fyt) + 2Mpb(1 - To/Fyb)
where Mpt and Mpb = plastic moment capacities of the upper & lower sections
To = axial force in sections
Fyt and Fyb = axial capacities of the sections
For unstiffened compact sections, the terms, To/F yt and To/Fyb in the above are changed to (To/Fyt)² and (To/Fyb)² respectively.
If a web-flange section is not compact (see below), the elastic moment capacity is substituted. The applied shear at the edge of the opening is assumed to be resisted by the upper and lower sections in proportion to the squares of their depths. To allow for the combined shear and compression acting on the upper section, the effective width of the web, te, is assumed to be:
where tw = web thickness,
Vt = shear in upper web and Vtu = ultimate shear in upper web
Since both upper and lower web-flange sections are T-sections, the ultimate shear strength is 0.9 x 0.6 x py x Ao when Ao is the area of the web. (4.2.3f)
To allow for possible yielding effects in unstiffened webs at working loads, the Vierendeel moment capacity is multiplied by a factor of 0.9 as recommended in the CIRIA/SCI paper. The unstiffened web-flange sections are classified as compact, semi-compact, or slender and the moment capacities are calculated accordingly. If stiffeners are added, the sections are considered to be compact unless b/T > 9e (see Table 11 and Figure 5) when the classification is then semi-compact.
The Vierendeel moment across the opening is equal to the shear force x length of opening. Longitudinal stiffeners will be required if this is greater than the moment capacity. If stiffeners are added the web-flange sections will then be classified as compact, and the calculation procedure is repeated.
The CIRIA/SCI paper suggests that the area of the stiffeners should be ignored when calculating the axial capacity of the upper and lower sections and this is the approach adopted by ProSteel. This means that if an unstiffened web-section does not have sufficient axial capacity, its axial capacity is not increased by adding stiffeners. This is particularly important when the opening is positioned near or at the centre of the span where the moment and resulting axial forces are greatest.