8 CHAPTER 8: DESIGN OF ONE-WAY SLABS

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1 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 1 8 CHAPTER 8: DESIGN OF ONE-WAY SLABS 8.1 Itrodctio A slab is strctral elemet whose thickess is small compared to its ow legth ad width. Slabs are sally sed i floor ad roof costrctio. Accordig to the way loads are trasferred to spportig beams ad colms, slabs are classified ito two types; oe-way ad two-way. Oe-way slabs: Whe the ratio of the loger to the shorter side (L/ S) of the slab is at least eqal to.0, it is called oe-way slab, show i Figre 8.1.a. Uder the actio of loads, it is deflected i the short directio oly, i a cylidrical form. Therefore, mai reiforcemet is placed i the shorter directio, while the loger directio is provided with shrikage reiforcemet to limit crackig, as show i Figre 8.1.b. Whe the slab is spported o two sides oly, the load will be trasferred to these sides regardless of its loger spa to shorter spa ratio, ad it will be classified as oe-way slab.

2 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS (a) (b) Figre 8.1: Oe way slab; (a) classificatio; (b) reiforcemet Two-way Slabs: Whe the ratio (L/ S) is less tha.0, it is called two-way slab, show i Figre 8.. Bedig will take place i the two directios i a dish-like form. Accordigly, mai reiforcemet is reqired i the two directios.

3 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 3 Figre 8.: Two way slabs 8. Oe-way Slabs I this sectio, two types will be discssed, oe-way solid slabs ad oe-way ribbed slabs Oe-way Solid Slabs Miimm Thickess To cotrol deflectio, ACI Code specifies miimm thickess vales for oe-way solid slabs, show i Table 8.1. These vales are applicable for ormal loadig coditios ad for slabs ot spportig or attached to partitios or other costrctio likely to be damaged by large deflectios.

4 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 4 Table 8.1: Miimm thickess of oe-way solid slabs Elemet Simply spported Oe ed cotios Both eds cotios Catilever Oe-way solid slabs l/0 l/4 l/8 l/10 where l is the spa legth i the directio of bedig Miimm Cocrete Cover Accordig to ACI Code 7.7.1, the followig miimm cocrete cover is to be provided: a. Cocrete ot exposed to weather or i cotact with grod: Larger tha φ 36 mm bar cm φ 36 mm ad smaller bars cm b. Cocrete exposed to weather or i cotact with grod: φ 19 mm ad larger bars cm φ 16 mm ad smaller bars cm c. Cocrete cast agaist ad permaetly exposed to earth cm Desig Cocept Oe-way solid slabs are desiged as a mber of idepedet 1 m wide strips which spa i the short directio ad spported o crossig beams Maximm Reiforcemet Ratio Oe-way solid slabs are desiged as rectaglar sectios sbjected to shear ad momet. Ths, the maximm reiforcemet ratio correspods to a et stai i the reiforcemet, ε t of Shrikage Reiforcemet Ratio Accordig to ACI Code ad for steels yieldig at f y = 400 kg / cm, the shrikage reiforcemet is take ot less tha of the gross cocrete area, or A shrikage s = b h. where, b = width of strip, ad h = slab thickess.

5 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS Miimm Reiforcemet Ratio Accordig to ACI Code , the miimm flexral reiforcemet is ot to be less tha the shrikage reiforcemet, or A s mi b h Spacig Of Flexral Reiforcemet Bars Based o ACI , flexral reiforcemet is to be spaced ot farther tha three times the slab thickess, or farther apart tha 45 cm, ceter-to-ceter Spacig Of Shrikage Reiforcemet Bars Based o ACI 7.1.., shrikage reiforcemet is to be spaced ot farther tha five times the slab thickess, or farther apart tha 45 cm, ceter-to-ceter Loads Assiged to Slabs (1) Ow weight of slab: The weight of the slab per it area is estimated by mltiplyig the thickess of the slab h by the desity of the reiforced cocrete, or hγ c. () Weight of slab coverig materials: This weight per it area depeds o the type of fiishig which is sally made of - Sad fill with a thickess of abot 5 cm, t/m - Cemet mortar,.5 cm thick t/m - Tilig t/m - A layer of plaster abot cm i thickess t/m (3) Live Load: It depeds o the prpose for which the floor is costrcted. Table 8. shows typical vales sed by the Uiform Bildig Code (UBC).

6 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 6 Table 8.: Miimm live Load vales o slabs Type of Use Uiform Live Load kg/m Residetial Residetial balcoies Compter se 500 Offices 50 Warehoses Light storage Heavy Storage Schools Classrooms 00 Libraries Readig rooms Stack rooms Hospitals 00 Assembly Halls Fixed seatig Movable seatig Garages (cars) 50 Stores Retail 400 wholesale 500 Exit facilities 500 Mafactrig Light Heavy (4) Eqivalet Partitio Weight: This load is sally take as the weight of all walls carried by the slab divided by the floor area ad treated as a dead load rather tha a live load Loads Assiged to Beams The beams are sally desiged to carry the followig loads: - Their ow weights. - Weights of partitios applied directly o them. - Floor loads. The floor loads o beams spportig the slab i the shorter directio may be assmed iformly distribted throghot their spas.

7 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS Approximate Strctral Aalysis ACI Code permits the se of the followig approximate momets ad shears for desig of cotios beams ad oe-way slabs, provided: There are two or more spas. Spas are approximately eqal, with the larger of two adjacet spas ot greater tha the shorter by more tha 0 percet. Ufactored live load, L does ot exceed three times factored dead load, D. Loads are iformly distribted. Members are prismatic (similar momet of iertia alog their legths). For calclatig egative momets, l is take as the average of the adjacet clear spa legths. The ACI Code gives the momets at mid spas ad at faces of spports, as follows. 1. Positive Momet: a. Ed Spas: Whe discotios ed restraied, M = w l / 11 Whe discotios ed is itegral with spport, M = w l / 14 where l is the correspodig clear spa legth b. Iterior Spas: M = w l / 16. Negative Momet: a. Negative momet at exterior face of first iterior spport: Two spas, M = w l / 9 More tha two spas, M = w l / 10 where l is the average of adjacet clear spa legths. b. Negative momet at other faces of iterior spports: M = w l / 11 c. Negative momet at iterior face of exterior spport: Spport is edge beam, M = w l / 4 Spport is a colm, M = w l / 16

8 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 8 3. Shear: a. Shear i ed members at face of first iterior spport: V =.15 w l / 1 b. Shear at face of all other spports: V = w l / where l is the correspodig clear spa legth See Figre 8.3 for shear force ad bedig momet coefficiets. (a) (b) (c) (d) Figre 8.3: (a) Two spas, exterior edge restraied; (b) two spas, spport is spadrel beam; (c) more tha two spas, exterior edge restraied; (d) more tha two spas, spport is spadrel beam; (e) two spas, shearig force diagram Smmary of Oe-way Solid Slab Desig Procedre Oce desig compressive stregth of cocrete ad yield stress of reiforcemet are specified, the ext steps are followed: 1. Select represetative 1 m wide desig strip/strips to spa i the short directio, as show i Figre 8.4.a. (e). Choose a slab thickess to satisfy deflectio cotrol reqiremets. Whe several mbers of slab paels exist, select the largest calclated thickess. 3. Calclate the factored load w by magifyig service dead ad live loads accordig to this eqatio w = 1.0 wd wl. The dead load icldes ow weight of the slab i

9 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 9 additio to the coverig materials it spports. The live load is depedet o the iteded se of the slab. (a) Figre 8.4: (a) Represetative strip ad reiforcemet; (b) strip ad loads 4. Draw the shear force ad bedig momet diagrams for each of the strips as show i Figre 8.4.b. 5. Check adeqacy of slab thickess i terms of resistig shear by satisfyig the followig eqatio: V 0. 53Φ f c b d where V = factored shear force V c = shear force resisted by cocrete aloe Φ = stregth redctio factor for shear is eqal to b = width of strip = 100 cm d = effective depth of slab (b) If the previos eqatio is ot satisfied, go ahead ad elarge the thickess to do so.

10 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS Desig flexral ad shrikage reiforcemet: Flexral reiforcemet ratio is calclated from the followig eqatio: 0.85 f c ρ = 1 fy M Φ b d f c Make sre that the et tesile strai i the reiforcemet, εt does't exceed Compte the area of shrikage reiforcemet, where A = s mi b h. Select appropriate bar mbers ad diameters for both, mai ad secodary reiforcemet. Check reiforcemet spacig, modify yor bar selectio if eeded. 7. Draw a pla of the slab ad represetative cross sectios showig the dimesios ad the selected reiforcemet, as show i Figre 8.4.a ad Figre 8.4.c. Figre 8.4.c: Sectio A-A 8.. Oe-Way Ribbed Slabs Sice resistace of cocrete i tesio is too small compared with that i compressio, cocrete i the tesio zoe may be gathered i reglarly spaced ribs cast moolithically with toppig slab o top of these ribs. Hollow blocks made of lightweight cocrete or other materials are arraged betwee the ribs or the voids betwee ribs are left ot withot ay fillig material. The se of these blocks makes it possible to have smooth ceilig which is ofte reqired for architectral or hygieic cosideratios ad have good sod ad temperatre islatig properties besides redcig the dead load of the slab greatly. Ribbed slab floors are most ecoomical for bildigs sch as hospitals, schools, hotels, ad apartmet costrctio where loads are somewhat small ad the spas are relatively large.

11 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 11 There are two mai types of ribbed floors (a) hollow block floors ad (b) molded floors as show i Figre 8.5. Each type of floor cosists of mber of reiforced cocrete ribs spaig i the short directios spportig a thi toppig slab above. The hollow block floor is most sitable for small irreglarly shaped floors as the hollow blocks ca be easily fitted ito the irreglar shapes. O the other had, for large symmetrically spported floors, the molded type of floor is most sitable ad ecoomical. Steel or fiberglass molds ca be sed for temporary formwork. Ribbed slabs ca be sed i oe-way ad two-way edge spported slabs. Either drop or hidde beams ca be sed to spport these slabs depedig o the spa. If the ribs are provided i oe directio oly, the slab is classified as beig oe-way, regardless of the ratio of loger to shorter pael dimesios. (a) (b) Figre 8.5: (a) Hollow block floor; (b) molded floor Key Compoets The Figre 8.6: Key compoets ribbed slab cosists of the followig key compoets, show i Figre 8.6: a. Toppig slab: Accordig to ACI Code , toppig slab thickess is ot to be less tha 1/1 the clear distace betwee ribs, or less tha 5.0 cm. The toppig slab is desiged as a cotios beam spported by the ribs. De to the large mber of spportig ribs, the maximm

12 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 1 bedig momet is take as w l c / 1 where w is the factored load resisted by the toppig slab ad l c is the clear distace betwee ribs. The toppig slab thickess t is evalated by coservatively cosiderig it made of plai cocrete ad sbjected to the maximm momet give above. The modls of rptre f r is give by f r ( t / ) M = f c = or 3 Φ b () t / 1 t = 3 M Φ b f c ( 8.1 ) where t = toppig slab thickess M = factored bedig momet Φ = stregth redctio factor for flexre b = web width Shrikage reiforcemet is provided i the toppig slab i both directios i a mesh form. b. Reglarly spaced ribs: Miimm dimesios: Accordig to ACI Code 8.13., ribs are ot to be less tha 10 cm i width, ad a depth of ot more tha 3.5 times the miimm web width. Clear spacig betwee ribs is ot to exceed 75.0 cm as specified by ACI Code Loads: The load o ribs cosists of dead ad live loads. The dead load icldes ow weight of the slab, weight of the srface fiish, ad eqivalet partitio load. The live load is depedat o the iteded se of the bildig. Directio: I oe-way ribbed slabs ribs may be arraged i ay of the two pricipal directios. Two optios are possible; the first is by providig ribs i the shorter directio as show i Figre 8.7.a, which leads to smaller amots of reiforcemet i the ribs, while large

13 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 13 amots of reiforcemet are reqired i the spportig beams, associated with large deflectios. The secod optio is by providig ribs i the loger directio as show i Figre 8.7.b, which leads to larger amot of reiforcemet i the ribs, while smaller amots of reiforcemet are reqired i the spportig beams associated with smaller deflectios compared to the first optio. (a) (b) Figre 8.7: Arragemet of ribs: (a) ribs are arraged i the shorter directio; (b) ribs are arraged i the loger directio

14 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS 14 The desiger has to make p his mid regardig the optio he prefers. Some desigers opt to r the ribs i a directio that leads to smaller momets ad shears i the spportig beams which meas mch more reiforcemet i the ribs. Other desigers opt to r the ribs i the shorter directio which leads to mch more reiforcemet i the spportig beams. The later optio leads to more ecoomical desig. Shear stregth: Accordig to ACI Code , shear stregth provided by rib cocrete V c may be take 10 % greater tha those for beams. It is permitted to icrease shear stregth sig shear reiforcemet or by wideig the eds of ribs. Althogh shear reiforcemet is ot ofte reqired, it is recommeded to se stirrps per meter r, Flexral stregth: 4 φ 6 mm Ribs are desiged as rectaglar beams i the regios of egative momet at the spports ad as T-shaped beams i the regios of positive momets betwee the spports. Effective flage width b e is take as half the distace betwee ribs, ceter-to-ceter. c. Hollow blocks: Hollow blocks are made of lightweight cocrete or other lightweight materials. They are commercially available i stadard sizes ad shapes. The most commo cocrete hollow block sizes are 40 5 cm i pla ad heights of 14, 17, 0, ad 4 cm Miimm Thickess To cotrol deflectio, ACI Code specifies miimm thickess vales for oe-way ribbed slabs, show i Table 8.3. These vales are applicable for ormal loadig coditios ad for slabs ot spportig or attached to partitios or other costrctio likely to be damaged by large deflectios. Elemet Table 8.3: Miimm thickess of oe-way ribbed slabs Simply spported Oe ed cotios Both eds cotios Catilever Oe-way ribbed slabs l/16 l/18.5 l/1 l/8

15 CHAPTER EIGHT DESIGN OF ONE-WAY SLABS Smmary of Oe-way Ribbed Slab Desig Procedre Oce desig compressive stregth of cocrete ad yield stress of reiforcemet are specified, the ext steps are followed: 1. The directio of ribs is chose.. The overall slab thickess h is determied based o deflectio cotrol reqiremet. Also, thickess of toppig slab t, rib width b, ad hollow block size, if ay, are to be determied based o code reqiremets. 3. The factored load o each of the ribs is compted. 4. The shear force ad bedig momet diagrams sig the load evalated i step 3 are draw. 5. The stregth of web i shear is checked. 6. Desig positive ad egative momet reiforcemet. Clear distace betwee bars is to be checked to garatee a free flow of cocrete. 7. Neat sketches showig arragemet of ribs ad details of the reiforcemet are to be prepared.