|Fig. 16.16 Vierendeel-type action in beam with web openings: (a) overall view, (b) detail of|
These deformations, superimposed on the overall bending effects, lead to increased deﬂection and additional web stresses.
A particular type of web hole is the castellation formed when a UB is cut, turned and rewelded as illustrated in Fig. 16.17. For the normal UK module geometry this leads to a 50% increase in section depth with a regular series of hexagonal holes.
|Fig. 16.17 Castellated beam: (a) basic concept, (b) details of normal UK module geometry|
Other geometries are possible, including a further increase in depth through the use of plates welded between the two halves of the original beam. Some aspects of the design of castellated beams are covered by the provisions of BS 5950, while more detailed guidance is available in a Constrado publication.
Based on research conducted in the USA, a comparatively simple elastic method for the design of beams with web holes, including a fully worked example, is available.
This uses the concept of an analysis for girder stresses and deﬂections that neglects the effects of the holes, coupled with checking against suitably modiﬁed limiting values. The full list of design checks considered in Reference 14 is:
(1) web shear due to overall bending acting on the reduced web area
(2) web shear due to local Vierendeel bending at the hole
(3) primary bending stresses (little effect since overall bending is resisted princi-
pally by the girder ﬂanges)
(4) local bending due to Vierendeel action
(5) local buckling of the tee formed by the compression ﬂange and the web adjoining the web hole
(6) local buckling of the stem of the compression tee due to secondary bending
(7) web crippling under concentrated loads or reactions near a web hole; as a simple guide,Reference 14 suggests that for loads which act at least (d/2) from the edge of a hole this effect may be neglected
(8) shear buckling of the web between holes; as a simple guide, Reference 14 sug- gests that for a clear distance between holes that exceeds the hole length this effect may be neglected
(9) vertical deﬂections; as a rough guide, secondary effects in castellated beams may be expected to add about 30% to the deﬂections calculated for a plain web beam of the same depth (1.5D). Beams with circular holes of diameter (D/2) may be expected to behave similarly, while beams with comparable rectangular holes may be expected to deﬂect rather more.
As an alternative to the use of elastic methods, signiﬁcant progress has been made in recent years in devising limit state approaches based on ultimate strength conditions.A CIRIA/SCI design guide dealing with the topic principally from the point of composite beams is now available. If some of the steps in the 24-point design check of Reference 15 are omitted, the method may be applied to non-composite beams, including composite beams under construction.
The governing condition for a stocky web in the vicinity of a hole is taken as excessive plastic deformation near the opening corners and in the web above and below the opening as illustrated in Fig. 16.18. A conservative estimate of web strength may then be obtained from a moment–shear interaction diagram of the type shown as Fig. 16.19.Values of M0 and V1 in terms of the plastic moment capacity and plastic shear capacity of the unperforated web are given previouly for both plain and reinforced holes; M1 may also be determined in this way. Solution of these equations is tedious, but some rearrangement and simpliﬁcation are possible so that an explicit solution for the required area of reinforcement may be obtained.
However, the whole approach is best programmed for a microcomputer, and a program based on the full method of Reference 15 is available from the SCI.
|Fig. 16.18 Hole-induced failure|
|Fig. 16.19 Moment–shear interaction for a stocky web in the vicinity of a hole|