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Opening in Slab and BeamBeamMost reinforced concrete members are statically indeterminate becausethey are part of monolithic structure, i.e., in this form of building

construction, slabs are cast monolithically with a beam-and –girder floorframing that carries the floor load to columns. A beam is a flexuremember. It may be of steel, wood or any other structural materials.Reinforced concrete beams are nonhomogeneous in that they are made of two entirely different materials. A flexural member should suffer a axialcompression force less than Ag fc´ !". #he member must be at least !"in wide and its clear span should be least $ times the effecti%e depth andthe width-to-depth ratio should be at least ".&.

Slab'labs are used to furnish a flat and useful surface in reinforced concreteconstruction. It is broad, flat plate, usually hori(ontal, with top andbottom surfaces parallel or nearly so. It may be supported by reinforcedconcrete beams, by masonry or reinforced concrete walls, by structuralsteel members, by directly by columns or continuously by the ground.

'labs in which the deflected surface is predominantly cylindrical is calledone-way slabs spanning in the direction of cur%ature. #his condition ariseswhen slabs are supported on two opposite sides, and those supported onall four sides with the longer span greater than twice the shorter span andalso in cantile%er slabs. In many cases, rectangular slabs are of suchproportions and are supported in such a way that two-way action results.when loaded, such slabs bend into a dished surface i.e., an any point theslab is cur%ed in both principal directions, and since bending moments areproportional to cur%ature, moments also in both directions.

)oncrete slabs may in some cases be carried directly by columns, withoutthe use of beams or girders. 'uch slabs are called flat plates. In somecases, to reduce the stresses due to shear and negati%e bending aroundcolumns, a thic*ened slab region in the %icinity of column and flaredcolumn tops are incorporated. 'uch construction is called flat- slab

construction.Occurrence of OpeningSlabs

In almost all constructions, slab system include openings. #hese may beof substantial si(e, as re+uired by stair-ways and ele%ators shafts, or theymay be of smaller dimensions, li*e those needed to accommodateheating, plumbing, and %entilating risers, floor and roof drains, and accesshatches.

Beams

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13.5.1 pening of any si(e are permitted in slabs if analysis shows thatboth strength and deflection are acceptable.

13.5.2 In lieu of special analysis as re+uired by !&./.! opening may bepro%ided in slab systems without beams only in accordance with thefollowing.

13.5.2.1 pening of any si(e may be located in the area common tointersecting middle strips.

13.5.2.2 In area common to intersecting column strips, not more than! 0 the width of column strip in either span shall be interrupted byopenings.

13.5.2.3 In the area common to one column strip and one middle strip,

opening si(e is limited to ! $ the width of column strip in either span.

Beams

In regions of small shear, as near the middle of a beam span, a hori(ontalpipe slee%e is not serious. 1lsewhere, shear strength must be closelywatched and in many places bending strength as well.

Strip et!od to anal"#e Opening#he strip method was first de%eloped by illerborg, and later 2ood and

Armer analy(ed the method critically and performed test on slabsdesigned by this method. #hey found that a design made by the stripmethod and reinforced exactly according to moments found, was an exactsolution.

#he strip method is the simplest one for slabs on simple supports, butcontinuity can be handled on a basis similar to limit design. #he mostdifficult slabs for this method are slabs supported on columns. or such acase, illerborg de%eloped the ad%anced strip method, using a rectangularelement carrying load in two directions to a support at one corner of theelement.

#he e+uilibrium e+uation for slabs is

All elements of this e+uation, except w, follows the #imoshen*o3snotation.

i.e., Mx and My 4 bending moment about respecti%e directions.

Mxy 4 twisting moment.

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and w 4 load per unit area on slab.illerborg designs the slab to ma*e Mxy unnecessary, that is he assumes

Mxy 4 " and than apportions the load to 56Mx 5x6 and 56My 5y6, usuallyat a particular spot wholly to one or to the other. #his particularapportionment is more of a con%enience than a necessity, howe%er, loadsin a particular area are assign to particular slab strips and continuity of the resulting moments and shear must be carefully maintained. Apparentdiscontinuity in tor+ue or deflection may be disregarded, but adiscontinuity in moment or shear is not permitted. 7oth elastic and plasticanalysis concepts are permissible in e%aluating moments on strips.

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#he suitability of the method for slabs with opening is a strong point in itsfa%or. #his method ha%e been using for many years by designers,

designing by their 8feel3 for the way the load has most apt to betransferred to the supports. As slabs are normally considerably under-reinforced, it is possible to use certain strips near the opening as smallbeam simply by increasing the local reinforcement. If the opening is solarge that e%en extra slab steel is inade+uate to care for the moment, areal beam is needed around one or more sides of the opening, +uiteprobably spanning to the edge beams. #he assumed 9beam strips: aredrawn as dotted around the opening and the point of inflection assuggested by 2ood and illerborg are added on the slab. #hen differentmoment for different strip is calculated. ;epth can be fixed from loads

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Code Recommendation

13.5.2.& 2here opening in slabs are located at a distance less than !"times the slab thic*ness from a concentrated load or reaction area orwhen opening in slabs are located within column strip, the critical sectionsshall be modified as follows

1' or slabs without shearhead, that part of the perimeter of the criticalsection that is enclosed by straight lines pro?ecting from the centroid of the column, concentrated load or reaction area and tangent to theboundaries of the opening shall be considered ineffecti%e.

2' for slabs with shearheads, the ineffecti%e portion of the perimeter shallbe one-half that defined in

Beams

>arge opening in beams are particularly wea*ening. #hey destroy beamaction and force the reduced section to act such as a Bierendeel truss < a

truss without diagonals=. In such a truss the a%erage bending momento%er the length of the opening is resisted by axial compression one chord

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and tension in the other, with these two forming a couple in the case of pure flexure. 2here shear is present the change in the moment o%er thelength of the opening superimpose a re%ersed bending resistance in eachchord, the total of the four end moments on the chords e+ualing theexternal shear times the length of the opening. ow the shear and thesere%erse moments are shared by the chords depends on the relati%e chordstiffness.

$!ic(ening of edge of opening

In case of larger openings, the edge of the slab around the opening maybe thic*ened to enable them to beha%e li*e trimmer beams for ta*ing upadditional moments and forces. If opening reduce a critical design sectionfor moment, must be maintained by pro%iding extra depth to offset thereduced width.

)unction of Steel

#he steels used around opening tie the free ends of the bars which aretrimmed to form opening. It also ser%e as reinforcement to ma*e theopening stable against deformation or any other types of failure. #his barsta*e care of the loss of steel in a slab on account of forming opening.;iagonal bars pro%ided in corner control the crac*ing that will almostine%itably occur there.

Steel Requirement

Slabs

2ith regard to flexural re+uirements, the total amount of steel re+uiredby calculation must be pro%ided, regardless of opening. Any steelinterrupted by holes should be matched with an e+ui%alent amount of supplementary reinforcement on either sides, proper lapped to transferstress by bond.

If minor crac*ing at the corners of an opening is ob?ectionable, it isalways ad%isable to add one or two diagonal bars at each corner,especially at large openings. 7ars are always desirable around 2indowand door opening in concrete wall slabs, because such reinforcementhelps to ta*e care of shrin*age stresses.

Code Requirement

Slab

13.5.2.1 In case of opening in intersecting middle strips, total amount ofreinforcement re+uired for the panel without opening is maintained.

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13.5.2.2 In case of opening in intersecting column strips, an amount of reinforcement e+ui%alent to that interrupted by an opening shall be addedon the sides of the opening.

13.5.2.3 In case of opening common to one column strip and one middlestrip not more than C the reinforcement in either strip shall beinterrupted by openings. An amount of reinforcement e+ui%alent to thatinterrupted by an opening shall be added on the sides of the opening.

Beam

!!.&.!.& or members with significant axial tension, re+uires all shear tobe resisted by stirrups

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#he arrangement of bars around any but minor opening can constitute areal problem. 7ars running perpendicular to the face of an opening arenot fully effecti%e when simply cut"off at the opening. #his is acceptable if there is a beam at the opening to act as reaction for the slab. If there isno beam it is better to fan the bars out or splay them to go around theopening. If fanning or splaying lea%es too wide an area without steel,extra bars can be placed parallel to the side of the opening, as indicated.