DESIGN OF REINFORCED CONCRETE BEAMS WITH WEB OPENINGS

1. INTRODUCTION

In the construction of modern buildings, a network of pipes and ducts is necessary to accommodate essential services like water supply, sewage, air-conditioning, electricity, telephone, and computer network. Usually, these pipes and ducts are placed underneath the beam soffit and, for aesthetic reasons, are covered by a suspended ceiling, thus creating a dead space. Passing these ducts through transverse openings in the floor beams leads to a reduction in the dead space and results in a more compact design. For small buildings, the savings thus achieved may not be significant, but for multistory buildings, any saving in story height multiplied by the number of stories can represent a substantial saving in total height, length of air-conditioning and electrical ducts, plumbing risers, walls and partition surfaces, and overall load on the foundation.
It is obvious that inclusion of openings in beams alters the simple beam behavior to a more complex one. Due to abrupt changes in the sectional configuration, opening corners are subject to high stress concentration that may lead to cracking unacceptable from aesthetic and durability viewpoints. The reduced stiffness of the beam may also give rise to excessive deflection under service load and result in a considerable redistribution of internal forces and moments in a
continuous beam. Unless special reinforcement is provided in sufficient quantity with proper
detailing, the strength and serviceability of such a beam may be seriously affected.
In his extensive experimental study, Prentzas (1968) considered openings of circular, rectangular, diamond, triangular, trapezoidal and even irregular shapes. However, circular and rectangular openings are the most common ones in practice. When the size of opening is concerned, many researchers use the terms small and large without any definition or clear-cut demarcation line. From a survey of available literature, it has been noted (Mansur and Tan, 1999) that the essence of such classification lies in the structural response of the beam. When the opening is small enough to maintain the beam-type behavior or, in other words, if the usual beam theory applies, then the opening may be termed as small opening. In contrast, large openings are
those that prevent beam-type behavior to develop. Thus, beams with small and large openings need separate treatments in design.
In this paper, beams containing small and large openings are treated separately. Based on the research work reported in the literature, an attempt has been made to give a comprehensive treatment of openings under bending and shear, addressing the major issues concerning structural design. It has been shown that the design of beams with large openings can be further simplified by maintaining its rationality and upholding construction economy.

2. BEAMS WITH SMALL OPENINGS

Openings that are circular, square, or nearly square in shape may be considered as small openings provided that the depth (or diameter) of the opening is in a realistic proportion to the beam size, say, about less than 40% of the overall beam depth. In such a case, beam action may be assumed to prevail. Therefore, analysis and design of a beam with small openings may follow the similar course of action as that of a solid beam. The provision of openings, however, produces discontinuities or disturbances in the normal flow of stresses, thus leading to stress concentration and early cracking around the opening region. Similar to any discontinuity, special reinforcement, enclosing the opening close to its periphery, should therefore be provided in sufficient quantity to control crack widths and prevent possible premature failure of the beam.

2.1 Pure Bending

In the case of pure bending, placement of an opening completely within the tension zone does not change the load-carrying mechanism of the beam because concrete there would have cracked anyway in flexure at ultimate. Mansur and Tan, (1999) have illustrated this through worked out examples, supported by test evidence. Thus, the ultimate moment capacity a beam is not affected by the presence of an opening as long as the minimum depth of the compression chord, hc, is greater than or equal to the depth of ultimate compressive stress block, that is, when

in which As = area of tensile reinforcement; fy = yield strength of tensile reinforcement;

fc′ =

cylinder compressive strength of concrete; b = width of the compression zone. However, due to reduced moment of inertia at a section through the opening, cracks will initiate at an earlier stage of loading. In spite of this, the effects on maximum crack widths and deflection under service load have been found to be only marginal, and may safely be disregarded in design.

2.2 Combined Bending and Shear

In a beam, shear is always associated with bending moment, except for the section at inflection point. When a small opening is introduced in a region subjected to predominant shear and the opening is enclosed by reinforcement, as shown by solid lines in Fig. 1, test data reported by Hanson (1969), Somes and Corley (1974), Salam (1977), and Weng (1998) indicate that the beam may fail in two distinctly different modes. The first type is typical of the failure commonly observed in solid beams except that the failure plane passes through the center of the opening (Fig. 1a). In the second type, formation of two independent diagonal cracks, one in each member bridging the two solid beam segments, leads to the failure (Fig. 1b). Labeled respectively as beam-type failure and frame-type failure (Mansur,1998), these modes of failure require separate treatment.

Similar to the traditional shear design approach, it may be assumed in both the cases that the nominal shear resistance, Vn is provided partly by the concrete, Vc, and partly by the shear reinforcement crossing the failure plane, Vs. That is,

Vn = Vc +Vs

(2)
Design for bending may be carried out independently in the usual manner and combined with shear design solutions.

2.2.1. Beam-type failure

In designing for beam-type failure, a 45o inclined failure plane, similar to a solid beam may be assumed, the plane being traversed through the center of the opening (Fig. 2). Following the simplified approach of the ACI Code (1995), the shear resistance Vc provided by the concrete may be estimated (Mansur, 1998) by considering the net concrete area available as

n which bw = web width; d = effective depth; and do = diameter of opening.
For the contribution of the shear reinforcement, Vs, reference may be made to Fig. 2. It may

be seen that the stirrups available to resist shear across the failure plane are those by the sides of the opening within a distance (dv − do), where dv is the distance between the top and bottom

longitudinal rebars, and do is the diameter (or depth) of opening, as shown. Thus,

in which Av = area of vertical legs of stirrups per spacing s; fyv = yield strength of stirrups.

Knowing the values of Vc and Vs, the required amount of web reinforcement to carry the factored shear through the center of the opening may be calculated in the usual way. This
amount should be contained within a distance (dv − do) ⁄ 2, or preferably be lumped together on
either side of the opening. Other restrictions applicable to the usual shear design procedure of
solid beams must also be strictly adhered to.

2.2.2 Frame-type failure

Frame-type failure occurs due to the formation of two independent diagonal cracks, one on each of the chord members above and below the opening, as shown in Fig. 1(b). It appears that each member behaves independently similar to the members in a framed structure. Therefore, each chord member requires independent treatment, as suggested by Mansur (1998).
In order to design reinforcement for this mode of failure, let us consider the free-body diagram at beam opening, as shown in Fig. 3. Clearly, the applied factored moment, Mu, at the center of the opening from the global action is resisted by the usual bending mechanism, that is, by the couple formed by the compressive and tensile stress resultants, Nu, in the members above and below the opening. These stress resultants may be obtained by

 

 

subject to the restrictions imposed by Eq. (1). In this equation, d = the effective depth of the beam, a = depth of equivalent rectangular stress block, and the subscripts t and b denote the top and bottom cross members of the opening, respectively.

  The applied shear, Vu, may be distributed between the two members in proportion to their cross-sectional areas (Nasser et al., 1967). Thus,

Knowing the factored shear and axial forces, each member can be independently designed for shear by following the same procedure as for conventional solid beams with axial compression for the top chord and axial tension for the bottom chord.

2.2.3 Reinforcement details

Consideration of beam-type failure will require long stirrups to be placed on either side of the opening, while that of the frame-type failure will need short stirrups above and below the opening. For anchorage of short stirrups, nominal bars must be placed at each corner, if none is available from the design of solid segments. This will ensure adequate strength. For effective crack control, nominal bars should also be placed diagonally on either side. The resulting arrangement of reinforcement around the opening is shown in Fig. 4.
Under usual circumstances, introduction of a small opening with proper detailing of reinforcement does not seriously affect the service load deflection. However, in case any doubt one can follow the procedure described in Art. 3.2.3 for beams with large openings to calculate the service load deflections and check them against the permissible values.

2.3 Effects of Creating Openings in Existing Beams

It is obvious that transverse openings through beams are a source of potential weakness. When the service systems are preplanned and the sizes and locations of openings required to achieve the necessary layout of pipes and ducts are decided upon well in advance, adequate strength and serviceability may be ensured by following the method described in the preceding section.
However, this is not always the case. While laying the ducts in a newly constructed building, the M&E contractor frequently comes up with the request to drill an opening for the sake of simplifying the arrangement of pipes. When such a request comes, the structural designer finds it difficult to give a decision. Of course, from the owner’s viewpoint, creating an opening may represent some financial savings, but the structural engineer would have to take the risk of jeopardizing the safety and serviceability of the structure.
Another situation arises in an old building where concrete cores are taken for structural assessment of the building. In this case, however, the holes are generally filled in by non- shrink grout. If the structure is to stay, then the question is whether or not such repair is adequate to restore the original level of safety and serviceability of the structure. In a recent study (Mansur et al., 1999), an attempt was made to answer some of these frequently asked questions of the effect of drilling holes in an existing beam.
As part of the study, four prototype T-beams simulating the conditions that exist in the negative moment region of a continuous beam were tested. All beams were 2.9 m long and contained a central stub to represent the continuous support. The cross section consisted of a
400-mm-deep and 200-mm-wide web and, a 100-mm-thick and 700-mm-wide flange. For symmetry, one opening, 150 mm in diameter, was created on each side of the central stub at a distance 525 mm from the face of the central stub, and all beams contained the same amount and arrangement of reinforcement as can be seen in Fig. 5.

The beam, designated S in Table 1, contained no openings. It served as a reference to assess the performance of the remaining beams with openings. Beam O was intended to gage the effects of creating an opening. The openings in beam O-G were filled in with non-shrink grout to simulate field conditions, while beam O-FRP was strengthened by externally bonded carbon fiber reinforced polymer plates in an attempt to restore the original response.

Table 1. Principal results of beam tested by Mansur et al. (1999).

Beam	Cylinder compressive strength, fc′ (MPa)	Load at shear cracking (kN)	At service load*	Pu Pu of beam S (kN)
Beam	Cylinder compressive strength, fc′ (MPa)	Load at shear cracking (kN)	Maximum crack width (mm)	Maxumum deflection (mm)	Pu Pu of beam S (kN)
S	30.8	200	0.27	4.38	1.000
O	29.7	134	>1.00	5.57	0.713
O-G	37.9 37.1	195 215	0.98 0.25	4.91 3.57	0.820 1.003
O-FRP	37.9 37.1	195 215	0.98 0.25	4.91 3.57	0.820 1.003

* Assumed service load = Ultimate load of beam S / 1.7
The cracking patterns of the beams after failure are presented in Fig. 6. It may be seen that beam O, which contained an opening exhibited a cracking pattern remarkably similar to that of the solid beam S. The major diagonal crack, which led to the failure traversed through the center of the opening. Beam O-G, in which the openings were filled with non-shrink grout, behaved in a similar manner except that failure crack bypassed the center of the opening and progressed along the opening periphery, as can be seen in Fig. 6. In contrast, beam O-FRP, which was strengthened by FRP plates, had almost the same behavior as the solid beam except that it had less number of narrower web cracks.

 The maximum width of cracks and midspan deflections of the beams are plotted against the applied load in Figs. 7 and 8, respectively. Table 1 shows the summary of principal test results. Taking the response of the solid beam Sas the required target, it may be seen that creating an opening in existing beams leads to early cracking (Table 1), wider crack widths at all loading stages (Fig. 7), smaller post-cracking stiffness (Fig. 8), and significantly reduces the load carrying capacity of a beam (Table 1 and Fig. 8). This serves as a warning that drilling an opening in an existing beam might seriously affect the safety and serviceability of the structure.

 Filling the opening with non-shrink grout, as was done in beam O-G, results in some improvement over the corresponding beam O without any grout in-fill, but the overall performance was far beyond the target performance of the solid beam S. However, strengthening by externally bonded FRP plates as used in beam O-FRP can completely eliminate the weakness introduced by creating an opening in an already constructed beam.
The results of these beams clearly indicate that drilling an opening near the support region of an existing beam may seriously impair the safety and serviceability of the structure. Also, filling the opening by non-shrink grout is not adequate to restore the original strength and stiffness. The risk may, however, be minimized by limiting the size of opening or drilling the opening without cutting any stirrups. In any case, the designer must carefully analyze and assess the situation. Unless larger than usual factor of safety is incorporated in the original design or suitable measures to strengthen the beam is undertaken, no opening should be created in existing beams.

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