Shear Reinforcement in Deep Slabs

Transcription

1 i'h Technical Reprt SL Nvember 1994 US Army Crps f Engineers Waterways Experiment Statin Shear Reinfrcement in Deep Slabs by Stanley C. Wdsn If AW CTE JßM $ fe =:# ' i tc Apprved Fr Public Release; Distributin Is Unlimited i tiii^-^'- Prepared fr Headquarters, U.S. Army Crps f Engineers

2 \j PRINTED ON RECYCLED PAPER The cntents f this reprt are nt t be used fr advertising, publicatin, r prmtinal purpses. Citatin f trade names des nt cnstitute an fficial endrsement r apprval f the use f such cmmercial prducts.

3 Technical Reprt SL Nvember 1994 Shear Reinfrcement in Deep Slabs by Stanley C. Wdsn U.S. Army Crps f Engineers Waterways Experiment Statin 3909 Halls Ferry Rad Vicksburg, MS Final reprt Apprved fr public release; distributin is unlimited Prepared fr U.S. Army Crps f Engineers Washingtn, DC

4 US Army Crps f Engineers Waterways Experiment Statin HEADQUARTERS BULDMG STRUCTURES LABORATORY FOB NFORMATON CONTACT: PUBLIC AFFAIRS OFFICE U. a ARMY ENGINEER WATERWAYS EXPERIMENT STATION 3909 HALLS FERRY ROAD VCKSBURG, MISSISSIPPI PHONE: (601) MO in Z3 AREA OF RESERVATION. 2.7 iq km Waterways Experiment Statin Catalging-in-Publicatin Data Wdsn, Stanley C. Shear reinfrcement in deep slabs / by Stanley C. Wdsn ; prepared fr U.S. Army Crps f Engineers. 136 p.: ill.; 28 cm. (Technical reprt; SL-94-24) Includes bibligraphic references. 1. Cncrete slabs Design and cnstructin. 2. Reinfrced cncrete Design and cnstructin. 3. Shear (Mechanics) I. United States. Army. Crps f Engineers. II. U.S. Army Engineer Waterways Experiment Statin. III. Structures Labratry (U.S.) IV. Title. V. Series: Technical reprt (U.S. Army Engineer Waterways Experiment Statin); SL TA7 W34 n.sl-94-24

5 Cntents Preface IV Cnversin Factrs, Nn-SI t SI Units f Measurement. 1: Intrductin. Backgrund. Objective... Apprach : Experimental Descriptin 3 General : 3 Cnstructin Details 3 Instrumentatin 5 Experimental Prcedure 6 3: Results and Discussin 7 General 7 Instrumentatin Data 7 Discussin 7 Structural Damage and General Respnse 7 Ultimate Resistance and Respnse Limits 10 4: Cnclusins 14 References. 15 Appendix A: Recrded Data Al Accesin Fr NTIS CRA&i DTIC TAB Unannunced Justificatin D Dist Availability Cdes Avail and/r Spt m in

6 Preface The research reprted herein was spnsred by Headquarters, U.S. Army Crps f Engineers, under Prject Wrk Unit AT40-HS-008, entitled "Mechanics f Structural Elements Used in Hardened Cnstructin." The wrk was cnducted at the U.S. Army Engineer Waterways Experiment Statin (WES) under the general supervisin f Messrs. Bryant Mather, Directr, Structures Labratry (SL), James T. Ballard, Assistant Directr, SL, and Dr. Reed L. Msher, Chief, Structural Mechanics Divisin (SMD), SL. Dr. Stanley C. Wdsn, SMD, perfrmed the study and prepared this reprt. During publicatin f this reprt, the Directr f WES was Dr. Rbert W. Whalin. Cmmander was COL Bruce K. Hward, EN. The cntents f this reprt are nt t be used fr advertising, publicatin r prmtinal purpses. Citatin f trade names des nt cnstitute an fficial endrsement r apprval f the use f such cmmercial prducts. IV

7 Cnversin Factrs, Nn-SI t SI Units f Measurement Nn-SI units f measurement used in this reprt can be cnverted t SI units as fllws: Multiply By T Obtain j I degrees (angle) radians D feet metres inches 25.4 millimetres kips (frce) per square inch megapascals punds (frce) newtns punds (frce) per square inch megapascals I

8 1: Intrductin Backgrund A cnsiderable amunt f data is available in the literature regarding the behavir f nrmally-prprtinal slabs, thse with span-t-effective-depth (L/d) ratis greater than apprximately 8 and perhaps as lw as 5 r 6. Wdsn (1993) presented ne f the mst cmprehensive cllectins f data n staticallyand dynamically-tested slabs. The data base was used in the develpment f the Engineer Technical Letter (ETL) (Department f the Army, 1990), "Respnse Limits and Shear Design fr Cnventinal Weapns Resistant Slabs,". In brief, the criteria given in the ETL fr restrained slabs allw design supprt rtatins f 12 and 20 degrees fr anticipated damage levels categrized as "mderate" and "heavy", respectively. The mderate damage level is described as that recmmended fr the prtectin f persnnel and sensitive equipment. Significant cncrete scabbing and reinfrcement rapture have nt ccurred at this level. The dust and debris envirnment n the prtected side f the slab is mderate; hwever, the allwable slab mtins are large. Heavy damage means that the slab is at incipient failure. Under this damage level, significant reinfrcement rupture has ccurred, and nly cncrete rubble remains suspended ver much f the slab. The heavy damage level is recmmended fr cases in which significant cncrete scabbing can be tlerated, such as fr the prtectin f water tanks and stred gds and ther insensitive equipment. The ETL sets frth sme design cnditins that must be satisfied in cnjunctin with applying its respnse limits. These limitatins reflect an aggressive apprach, yet maintain apprpriate cnservatism based n available data. The scaled range must exceed 0.5 ft/lb 1/3 and the span-t-effective-depth (L/d) rati f the slab must exceed 5. Principal reinfrcement spacing is t be minimized and shall never exceed the effective depth (d) f the slab. Stirrup reinfrcement is required, regardless f cmputed shear stress, t prvide adequate cncrete cnfinement and principal steel restraint in the large-deflectin regin. Stirrups are required alng each principal bar at maximum spacing f ne-half the effective depth (d/2) when the scaled range is less than 2.0 ft/lb and at a maximum spacing equal t the effective depth at larger scaled ranges. All stirrup reinfrcement is t prvide a minimum f 50 psi shear stress capacity. The ETL, develped t supplement Technical Manual (TM) (Department f the Army, 1986), is the mst recently published design dcument n the subject. It claims n applicability t slabs having span-t-effective-depth (L/d) ratis less than 5. In additin, due t a lack f data and understanding, the ETL sets frth strict shear reinfrcement requirements fr laterally-restrained slabs with L/d values less than 8, a value n the lw end f the range fr nrmally-prprtined slabs. Thus, guidance fr shear design and respnse

9 limits f deep slabs used in prtective structures is lacking, particularly fr structures t resist the effects f cnventinal weapns. Althugh there is a lack f guidance fr designing efficient deep slabs, deep slabs are very cmmn as rfs and walls f prtective structures. There is sme cncern that designers might inapprpriately apply nrmally-prprtined-slab thery t deep slabs. Objective The verall bjective was t gain a basic understanding f the behavir f deep slabs with reinfrcing details typical f prtective cnstructin. A specific bjective was t cmpare the effects f stirrups and lacing bars n the behavir f deep slabs. The intent was t btain data that will help fill in gaps in design guidance fr slabs used in prtective cnstructin. Apprach Thirteen ne-way reinfrced cncrete slabs were statically laded at the U. S. Army Engineer Waterways Experiment Statin (WES) in March thrugh April, Previus studies (Wdsn, 1993) emphasized that the primary parameters that affect the large-deflectin behavir f a ne-way slab include: supprt cnditins, quantity and spacing f principal reinfrcement, quantity and spacing f shear reinfrcement, span-t-effective-depth (L/d) rati, and scaled range (fr blast lads). The slabs in this study were designed with cnsideratin f the rle f these primary parameters.

10 2: Experimental Descriptin General The fllwing sectins describe the slabs' cnstructin details, instrumentatin, and the experimental prcedure. Cnstructin Details Table 1 qualitatively presents the characteristics f each slab. Table 2 presents the same characteristics in a quantitative manner, reflecting the practical designs based n available cnstructin materials. All slabs were designed t be laded in a clamped (laterally and rtatinally restrained) cnditin. Each slab had a clear span f 24 inches and a width f 24 inches. Slab thickness varied as fllws: 3 slabs had an verall thickness f 5.5 inches, and 10 slabs had an verall thickness f 8.9 inches. The effective depth f each slab was either apprximately 4.8 r 8.0 inches. The L/d rati f each slab was either 3 r 5. Principal reinfrcement cnsisted f either n. 3 r n. 5 Grade 60 rebar. Stirrups and lacing bars were fabricated frm D2 and D3 defrmed wire in slabs with ratis f 5 and 3, respectively. The defrmed wire was annealed t a yield stress f apprximately 60 ksi. At the time f the experiments, the average cncrete cmpressive strength was apprximately 5900 psi. In general, the experimental prgram was designed t study the behavir f unifrmly-laded deep slabs and, in particular, t cmpare the effects f lacing bars and stirrups n the behavir. It was imprtant that the rati f principal steel spacing t slab effective depth (s/d) was held nearly cnstant amng the slabs. Data frm previus studies indicated that this rati shuld be less than 1.0 in rder t enhance the large-deflectin behavir. The s/d rati was maintained at a value f apprximately 0.5. Three shear reinfrcement spacings were used: 0.17d, 0.3 Id, and 2d (d/2 is the value typically given in design manuals fr blast-resistant structures). Figures 1 thrugh 3 are plan views shwing slab prprtins and the principal steel and temperature steel layuts fr each f the slabs. The temperature (transverse) steel spacing was identical fr all f the slabs, but ne difference in the temperature steel placement ccurred between the laced and nnlaced slabs. The temperature steel is typically placed exterir t the principal steel in laced slabs, but it is placed interir t the principal steel in the slabs having stirrups r n shear reinfrcement.

11 Table 1 Slab Characteristics (Qualitative) Slab large large large small large large small large large large small large large tensin P shear nne large large nne nne nne large large large small large small large Lacing Stirrups Principal Steel Spacjrig^^ 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d 0.5d Shear Steel Spacing^^ 0.31 d 0.31 d 0.17d 0.17d 0.17d 2d 0.17d 2d 0.17d =l L/d Rati Table 2 Slab Characteristics (Quantitative) Slab P tensin P shear Lacing Stirrups Principal Steel Spacing (inches) Shear Steel Spacing (inches) L/d Rati nne. N X N X - N nne - - N nne - - N nne. - N X N X N X N X N X - N X - N. 5 (3) X - N I

12 Figures 4 thrugh 14 are sectinal views cut thrugh the lengths f the slabs. The dashed lacing bar in each figure indicates the cnfiguratin f the lacing bar assciated with the next principal steel bar. The psitins f the lacing bars were alternated t encmpass all temperature steel bars. Hwever, sme temperature steel bars were nt encmpassed by lacing bars in slab n. 12 due t the spacing f the lacing bar bends. The spacings f the lacing bar bends were cntrlled by the shear reinfrcement quantities in crrespnding slabs with stirrups. In slabs with stirrups, the stirrups were spaced alng the principal steel bar at the spacings shwn in Table 2, never directly encmpassing the temperature steel. The slabs were cnstructed in the labratry with much care t ensure quality cnstructin with minimal errr in reinfrcement placement. Figures 15 thrugh 27 are phtgraphs f slabs n. 1 thrugh 13 prir t the placement f cncrete. Figure 28 is a clse-up view f the lacing in slab n. 3, and Figure 29 is the clse-up view f the stirrups in slab n. 7. Instrumentatin Each slab was instrumented fr strain, displacement, and pressure measurements. The data were digitally recrded with a persnal cmputer. Tw displacement transducers were used in each experiment t measure vertical displacement f the slab, ne at ne-quarter span and ne at midspan. The displacement transducers used were Celesc Mdel PT-101, having a wrking range f 10 inches. These transducers measured the displacement f the slab by means f a ptentimeter which detected the extensin and retractin f a cable attached t a spring inside the transducer. Mre specifically, a Celesc Mdel PT-101 transducer cntains a drum that is attached t a linear rtary ptentimeter. When the cable is cmpletely retracted, the ptentimeter is at ne end f its range. As the cable is extended, the drum rtates (thus rtating the ptentimeter) until the cable is at full extensin and the ptentimeter is at the ther end f its range. A DC vltage is applied acrss the ptentimeter, and the utput is taken frm the ptentimeter's wiper. As the cable is retracted and the wiper mves alng the ptentimeter, the utput vltage varies since the ptentimeter acts as a vltage divider. The bdy f each transducer was munted t the flr f the reactin structure, and the cable was attached t a hk that was glued t the slab surface. Retractin f the cables int the transducers' bdies ccurred as the slab deflected and dwnward displacement ccurred at the ne-quarter span and midspan lcatins. Tw single-axis, metal film, inch-lng, 350 hm, strain gage pairs were installed n principal reinfrcement in each slab. Each pair cnsisted f a strain gage n a tp bar and ne n a bttm bar directly belw. One pair was lcated at midspan (ST-1, SB- 1), and ne was lcated at ne-quarter span (ST-2, SB-2). Strain gages were als installed at mid-height n shear steel in the slabs that cntained shear reinfrcement. Strain gages were placed n lacing bars in laced slabs at lcatins alng the length f the slabs similar t the lcatins f stirrups with gages in the crrespnding slabs with stirrups. The gages were

13 placed n the shear reinfrcement assciated with the center principal steel bars. Figures 30 thrugh 35 shw the lcatins f the strain gages n the shear reinfrcement in the slabs. Tw Kulite Mdel HKM-S375, 500-psi-range pressure gages (PI and P2) were munted in the bnnet f the test chamber in rder t measure the water pressure applied t the slab. Experimental Prcedure The 6-ft diameter static test chamber was used t slwly lad the slabs with water pressure. Huff (1969) presented a detailed descriptin f the test device. Preparatins fr the experiments began with the reactin structure being placed inside the test chamber and surrunded with cmpacted sand. In general, the reactin structure cnsisted f a steel/cncrete bx withut atp. Blts fr clamping the slabs prtruded upward frm the tw sides. The reactin structure had a remvable dr t allw access t the space beneath the slab specimen, particularly fr instrumentatin requirements. Placement f a 36- by 24-inch slab in the reactin structure allwed 6 inches f the slab at each end t be clamped by a steel plate that was blted int psitin, thereby leaving a 24- by 24-inch ne-way restrained slab t be laded with unifrm pressure. After a slab was placed n the reactin structure, the wire leads frm the instrumentatin gages and transducers were cnnected. After placing the remvable dr int psitin, the sand backfill was cmpleted n the dr side f the reactin structure. A 1/8-inch-thick fiber-reinfrced neprene rubber membrane and a 1/8-inch-thick unreinfrced neprene rubber membrane were placed ver the slab as shwn in Figure 36, and 1/2- by 6- by 24-inch steel plates were blted int psitin at each supprt. Prir t the blting f the plates, a waterprfing putty was placed between the membrane and the steel plates t seal gaps arund the blts in rder t prevent a lss f water pressure during the experiment. The chamber's lid was lwered int psitin (Figure 37), and the chamber was rlled inside the large reactin structure. A time f apprximately 18 minutes was required t fill the bnnet indicated when the bnnet had been filled. At that time, the waterline valve was again clsed t allw clsing f the relief plug. The waterline valve was nce again pened slwly, inducing a slwly increasing lad t the slab's surface as the lid f the chamber was pushed upward and against the large reactin structure (shwn in the backgrund f Figure 37). A gasline-pwered pump was cnnected t the waterline t facilitate water pressure lading since the cmmercial line pressure was nt great enugh t reach ultimate resistance f the slab in any f the experiments. Mnitring f the pressure gages and deflectin gages indicated the behavir f the slab during the experiment and enabled this authr t make decisin fr experiment terminatin by clsing the waterline valve. The lading was cntrlled at a slwly changing rate, resulting in a lad applicatin time f several minutes. Fllwing experiment terminatin, measurements and phtgraphs f the slab were taken after remval f the neprene membrane. Finally, the damaged slab was remved and the reactin structure was prepared fr anther slab.

14 3: Results and Discussin General In this chapter, the data are presented in varius frms (i.e., tables and cmpsite plts), and the results f the experiments are evaluated. Psttest phtgraphs shwing the extent f structural damage are included. The implicatins f the results n design criteria are discussed. Instrumentatin Data The electrnically recrded data are presented in the Appendix. All f the strain gage readings and the deflectin gage readings were pltted against the readings f bth f the pressure transducers (P-l and P-2) fr each experiment. Fr the plts presented in the Appendix, the strain and deflectin measurements versus nly ne f the pressure gage's readings are shwn. The tw pressure transducers prvided essentially identical values. In general, the quality f the data was gd. Data were recvered frm all gages, and it appears that all gages functined prperly. Discussin Structural Damage and General Respnse Psttest measurements and inspectin prvided a data check and damage assessment f each slab prir t remval frm the reactin structure. Figures 38 thrugh 50 shw the psttest cnditin f each slab. Except fr slab n. 4, Figures 38 thrugh 50 shw the slab immediately after remval f the neprene membrane. Fr slab n. 4, Figure 41 shws the slab after remval frm the reactin structure. Slab n. 4 was nly slightly damaged and, therefre, culd be safely remved frm the reactin structure prir t phtgraphy. Figure 41 prvides a better view f the side crack pattern than was allwed while the slab remained in the reactin structure. Figure 51 shws the general shape f the midspan lad-deflectin curve. Values f lad and deflectin at pints A thrugh C f Figure 51 are given in Table 3 fr cnvenience in numerical cmparisns. Similarly, Table 4 presents

15 1 Table 3 1 Midspan Lad-Deflectin Summary Slab P* (psi) 8, P B (PSi) 8, Pc (PSi) 6 C Table 4 Quarter-span Lad-Deflectin Summary Slab PA (PSi) 8, P B (PSi) 8, Pc (PSi) 8 C I

16 lad-deflectin values recrded at the quarter-span lcatin fr each slab. Cmparisn f Figures 51 and 52 indicates that the typical experimental laddeflectin curve fr the deep slabs was cnsiderably different frm the general curve fr nrmally-prprtined slabs. Specifically, the deep slabs were suffer up t the ultimate resistance (pint A). Fllwing the attainment f ultimate resistance, the deep slabs incurred a rather sharp transitin, with the remaining respnse being well-characterized by straight lines t pints B and C. Further discussin f maximum deflectins achieved will als prvide insight fr a cmparisn f the deep-slab behavir t that f nrmally-prprtined slabs. Additinally, the cmpsite graphs f the lad-deflectin curves presented in Figures 53 thrugh 59 aid in the evaluatin f the effects f the parameters varied in this experimental series. Fr the slabs with an L/d rati f 5, Figure 53 demnstrates the significance f shear reinfrcement (see Table 1) in that slab n. 1 was nt able t achieve the value f ultimate resistance attained by slabs n. 2 and 3. Lacing bars (slab n. 3) and stirrups (slab n. 2) apparently prvided similar levels f cntributin t the shear strength f the slabs. The experiments n slabs n. 2 and 3 were terminated due t water pressure leaks; thus, they were nt laded t extremely large deflectins. Figure 54 simply indicates the differences in strength due t the L/d values. Nt nly is the strength directly affected by the L/d value, but a thicker slab als requires mre reinfrcement in rder t maintain equivalent values f the principal reinfrcement rati. Figure 55 shws that the replicatin assciated with slabs n. 5 and 6 prvided very similar results. Figure 56 cmpares the effects f stirrups (slab n. 8), lacing (slab n. 13), and n shear reinfrcement (slab n. 6) f the slabs with an L/d f 3. As was shwn in Figure 53 fr the slabs with an L/d f 5, shear reinfrcement did make a significant cntributin t the ultimate resistance and lacing and stirrups were f apprximately equal effectiveness. Slab n. 13 did appear t maintain higher values f resistance ver the full range f lading. Figure 57 indicates that the data are cnsistent in that the smaller amunt f shear reinfrcement (slab n. 10) was less effective than the larger amunt. In all figures cntaining slab n. 10, the data shwn past the ultimate resistance fr slab n. 10 is nt true data since the deflectin transducer cable apparently brke lse frm the slab shrtly after the ultimate resistance was reached. Figure 58 further supprts the previus bservatin that the lacing bars (slab n. 12) and stirrups (slab n. 10) are similarly effective in enhancing ultimate shear resistance. Hwever, in bth Figures 53 and 58, the data indicate that stirrups may be slightly mre effective. As in Figure 57, Figure 59 indicates the cnsiderable difference in effectiveness fr large (slab n. 13) and small (slab n. 12) quantities f shear reinfrcement. Figures 60 thrugh 69 present the psttest deflectin survey data. In these figures, permanent deflectins measured n the tp (lading) surfaces f the slabs are given at numerus lcatins. Additinally the lcatins f majr

17 cracks are drawn. The circles shwn in the figures represent the lcatins f the blt hles; thus, a 24-by-36-in slab is shwn in each figure. The clear span fr each slab was 24 inches. Slabs n. 4 and 7 are nt included in the deflectin survey figures since slab n. 4 was nt laded t significant damage and slab n. 7 incurred catastrphic damage. Figures 70 thrugh 80 are artist sketches f the bttm and side psttest views f the slabs. Sketches are nt included fr slabs n. 7 and 11 since they were damaged t heavily fr a meaningful drawing. Figures 60 thrugh 80 are useful fr the reader that wants t carefully evaluate the respnse f the slabs. In this reprt, the figures will nt be discussed in detail, but rather are used t supprt the bservatins and cnclusins drawn frm the instrumentatin data and damage phtgraphs. Examinatin f Figures 60 thrugh 80 indicate that shear behavir generally dminated the respnse f the slabs. This bservatin is als evident frm a cmparisn f the midspan and quarter-span lad-deflectin summaries given in Tables 3 and 4. Since the electrnically-measured deflectins were similar at quarter-span and midspan, it appears that shear behavir dminated the respnse rather than flexure which wuld have prduced a deflectin prfile mre representative f a 3-hinge mechanism. Ultimate Resistance and Respnse Limits Tw cmmnly-used parameters fr describing slab respnse are the midspan-deflectin-t-thickness rati and the equivalent supprt rtatin (defined as the arctan f the qutient f the midspan deflectin divided by nehalf f the clear span). Actually, fr predminantly shear respnse, as is generally the case fr deep slabs, neither f these parameters fully describe the respnse. Hwever, attempts shuld be made t crrelate the allwable respnse f deep slabs with these parameters fr cnsistency in guidance dcuments. Tables 5 and 6 respectively present the midspan deflectin-t-thickness ratis and the equivalent supprt rtatins fr each slab at intervals crrespnding t pints A, B, and C f Figure 51. Table 5 shws that the midspan deflectin-t-slab-thickness rati at ultimate (5 A /t) is cnsiderably small when cmpared t typical values fr nrmally-prprtined slabs. It is well knwn that, fr nrmally-prprtined slabs, this rati has the general value f 0.3 t 0.5. The experiments in this series indicated that the 5 A /t value fr slabs with an L/d rati f 5 (prvided shear reinfrcement is included t prevent premature shear failure) can be expected t be apprximately Similarly, 5 A /t values f 0.03 t 0.05 can be expected fr slabs having an L/d rati f 3. The values given in Table 6 are useful in that they prvide infrmatin t the designer n the equivalent supprt rtatin that shuld be expected at ultimate resistance. Additinally, Table 6 shws that deep slabs can achieve cnsiderably 10

18 1 Table 5 1 Midspan Deflectin/Slab Thickness I I I Slab ^/t 5 B /t 5 c /t I Table 6 Equivalent Supprt Rtatin Slab L/d (degrees) (degrees) (degrees)

19 high values f respnse withut cllapse. Values f equivalent supprt rtatin up t apprximately 16 degrees were sustained. Under slwly applied unifrm lading, a beam r ne-way slab element initially underges elastic deflectin. As lading cntinues, plastic hinges first frm at the supprts and later at midspan. As discussed by Park and Gamble (1980), the ultimate flexural capacity is enhanced in slabs whse edges are restrained against lateral mvement. This plastic thery fr the lad-deflectin behavir f a restrained strip at and after the ultimate resistance is ften referred t as "cmpressive-membrane thery." Full restraint against rtatin and vertical translatin is assumed at the supprts. Partial restraint against lateral displacement is assumed at the supprts as cmpressive membrane actin is dependent f the lateral restraint. As the slab deflects, changes in gemetry cause the slab's edges t tend t mve utward and t react against the stiff bundary elements. The membrane frces enhance the flexural strength f the slab sectins at the yield lines. Fr the slabs in this study, the resistance at pint "A" in Figure 51 crrespnds t the ultimate capacity. Tw relatively difficult-t-define parameters required in the cmputatin f the ultimate flexural resistance due t cmpressive-membrane actin are: (a) the stiffness f the surrund supprting the slab and (b) the midspan deflectin ccurring at ultimate capacity (ften described by the 5 A /t rati). Park and Gamble demnstrated that the surrund stiffness need nt be enrmus t achieve membrane actin similar t that fr an infinitely rigid surrund. Significant membrane actin ccurs when the surrund and the ne-way slab have the same stiffness. Fr slabs with relatively lw values f the rati f slab length t thickness (which applies t the slabs in this study), little increase in membrane actin is achieved by having a surrund much suffer than the slab. As discussed by Park and Gamble, may researchers have attempted t develp methds fr determining 5 A /t. This rati is affected by the relative stiffness f the surrund and slab. It is als affected by whether the slab exhibits ne-way r tw-way actin. A cmputer prgram, cnsistent with the thery as presented by Park and Gamble, was used during this study t cmpute the enhancement due t cmpressive-membrane actin fr the slabs. The thery is based n the equilibrium and defrmatins f a slab strip. Frm an analytical/design viewpint, Table 7 demnstrates the applicatin f cmpressin membrane thery. The W y values in Table 7 crrespnd t yield-line thery, and the W c values crrespnd t cmpressin membrane thery. The W c values were cmputed using the (8 A /t) values supplied in Table 5. Fr mst f the slabs that cntained a "large" amunt f shear reinfrcement, the experimental values and the W c values cmpare rather well. Slabs with n r little shear reinfrcement incurred shear failures prir t attaining the cmpressive membrane resistance values. 12

20 1 Table 7 1 Cmpressive Membrane Slab W y (psl) w 0 (psi) Experimental (psl) P shear t (experimental) I I

21 4: Cnclusins A relatively large amunt f shear reinfrcement is critical fr achieving the ptential ultimate resistance f a deep slab. The experiments indicated that the cntributins frm lacing bars and stirrups are similar. Since deep slabs can achieve relatively high values f resistance, it was difficult t maintain the lading water pressure at large deflectins. Therefre, a thrugh cmparisn f the effects f lacing bars and stirrups at extremely high deflectin levels was nt pssible. The pst-ultimate behavir f the slabs indicates that a substantial amunt f reserve capacity is available in deep slabs with large quantities f principal reinfrcement. Hwever, the series indicated that deep slabs with relatively lw quantities f principal reinfrcement (p=0.0034) are cnsiderably less ductile. Based n this series, the recmmended respnse limit (supprt rtatin) fr deep slabs having a principal steel rati f apprximately 0.01 and adequate shear reinfrcement is apprximately 12 degrees. Fr deep slabs with relatively small quantities f principal steel, the respnse shuld prbably be limited t apprximately 8 degrees fr design purpses. The implicatins f the results are significant in that relatively simple analysis techniques can be successfully emplyed t define the resistance f deep slabs. Cmpressin membrane thery prvides a gd estimate f the ptential ultimate resistance f a deep slab, prvided apprpriate values f 8 A /t are used in the cmputatins. Hwever, the typically-used 8 A /t values f 0.3 t 0.5 are inapprpriate fr deep slabs. The experimentally-determined 5 A /t values were apprximately 0.07 and 0.03 t 0.05 fr the slabs with L/d values f 5 and 3, respectively. Since, these 5 A /t values resulted in slightly high cmpressive membrane resistance values, 5 A /t shuld be increased slightly in rder t decrease the W c values and t prvide cnservative design values. 14

22 References Department f the Army (1986), "Fundamentals f Prtective Design fr Cnventinal Weapns," Technical Manual , Washingtn, D.C. Department f the Army (1990), "Respnse Limits and Shear Design fr Cnventinal Weapns Resistant Slabs," Engineer Technical Letter , Washingtn, D.C. Huff, W. L. (1969), "Test Devices f the Blast Lad Generatr Facility," Miscellaneus Paper N-69-1, U.S. Army Engineer Waterways Experiment Statin, Vicksburg, Mississippi. Park, R. and Gamble, W. L. (1980), Reinfrced Cncrete Slabs, Jhn Wiley and Sns, New Yrk, pp Wdsn, S. C. (1993), "Effects f Shear Reinfrcement n the Large-Deflectin Behavir f Reinfrced Cncrete Slabs," thesis, University f Illinis at Urbana-Champaign. 15

23 , 1 i 24".1 6" D1 Temperature Steel at 1.5 ".e. 24" 6" " (i 2.4".e. Figure 1. Plan View f Slabs N 1, 2, and 3 i - 24" 6" D1 Temperature 1.33" 24» ', N. 3 Principal 4".e. 6" fr slabs 4, 7,11 r N. 5 Principal 4".e. fr slabs 5,6, 8, 9,13 Figure 2 Plan View f Slabs N. 4, 5, 6, 7, 8, 9, 11, and 13 17

24 24' D1 Temperature 1.5 ".e. 24" 6" r N. 5 Principal 4".e. Figure 3. Plan View f Slabs N. 10 and 12 6"- 24 " 6" uuuuuuuuuuuuuu a u~ nnnnnnnnnnnnnna -O Q O- 11/12' 00 N. 3 Principal Steel spaced at 2.4".e. D1 Temperature Steel spaced at 1.5".e. 11/12" Figure 4. Sectinal View Thrugh Length f Slab N. 1 I- 6"- 24" 6" i C E c c_c s z z C C C _ c_s _ :r qq d E - E =2) d c c 11/12" I 00 N. 3 Principal Steel spaced at 2.4".e. D1 Temperature Steel spaced at 1.5".e. 11/12" Figure 5. Sectinal View Thrugh Length f Slab N. 2 18

25 11/12' N. 3 Principal Steel spaced at 2.4".e. D2 Lacing Bars 11/12. D1 Temperature Steel spaced at 1.5".e. Figure 6. Sectinal View Thrugh Length f Slab N. 3 h " 6" (C 3~~ i) 7/8" I vl 00 (5 9gggyQ 5) GO a 00 3 N. 5 Principal Steel spaced at 4.0".e. D1 Temperature Steel spaced at 1.33".e. 7/8" Figure 7. Sectinal View Thrugh Length f Slab N. 4 6" 24"- 6"- (c jj) 7/8" =H _L (f g99gp "^ N. 3 Principal Steel spaced at 4.0".e. D1 Temperature Steel spaced at 1.33".e. 7/8" Figure 8. Sectinal View Thrugh Length f Slabs N. 5 & 6 19

26 . -I c- -JT 24"- T-Z-J-I -! - I 6"-H -l -i ~l -i~t~t~ D _ _._ _ - _ _ _ L.*_ _ _ _I_I_J_J.Jr D3 Stirrups N. 3 P, cipsl M spaced «1.33- ~^JJJ-«*f spaced at 4.0.e. 7/8" CO 7/8" 09 I 5 Figure 9. Sectinal View Thrugh Length f Slab N. 7 6" 24"- i i~c ü_ _ N. 4 Pr ncipal Steel spaced at 4.0".e. c -! _ _ *_ _ _ r *~c 3 "I C -! i_ _S_S_2_S- D3 Stirrups spaced at 1.33".cP_1 ^mp^rature Steel spaced at 1.33".e. =5) 7/8" Nj m* vl GO a t 7/8" a Figure 10. Sectinal View Thrugh Length f Slabs N 8 & 9 6" "h 24"- 7/8" c c c c c T) (? OC OOOC OjtOC c c 5) 03 Stirrups N. 5 Principal Steel spaced at 6".e. D1 Temperature Steel spaced _j «* at >i 4.0" n".e. spaced at 1.5".e. 7/8" Figure 11. Sectinal View Thrugh Length f Slabs N 10 20

27 7/8" N. 3 Principal Steel D1 Temperature Steel spaced at 4.0".e. s P aced at 1-33 " x - D3 Lacing Bars 7/8" Figure 12. Sectinal View Thrugh Length f Slab N. 11 7/8" 1 D3 Lacing Bars N. 5 Principal Steel D1 Temperature Steel spaced at 4.0".e. spaced at 1.5".e. >j 00 _A»J 00 a a T 7/8" Figure 13. Sectinal View Thrugh Length f Slab N. 12 7/8" zdj *J k VI 3 3 N. 5 Principal Steel spaced at 4.0".e. I li 8" D1 Temperature Steel spaced at 1.33".e. D3 Lacing Bars Figure 14. Sectinal View Thrugh Length f Slab N

28 HSHt_ I Mil WEM -,4 Figure 15. Slab N. 1 Prir t Cncrete Placement *fpr-'- Figure 16. Slab N. 2 Prir t Cncrete Placement 22

29 Figure 17. Slab N. 3 Prir t Cncrete Placement Figure 18. Slab N. 4 Prir t Cncrete Placement 23

30 Figure 19. Slab N. 5 Prir t Cncrete Placement Figure 20. Slab N. 6 Prir t Cncrete Placement 24

31 M»TV >. Paw Figure 21. Slab N. 7 Prir t Cncrete Placement M!>1 _y m Figure 22. Slab N. 8 Prir t Cncrete Placement 25

32 Figure 23. Slab N. 9 Prir t Cncrete Placement Figure 24. Slab N. 10 Prir t Cncrete Placement 26

33 Figure 25. Slab N. 11 Prir t Cncrete Placement Figure 26. Slab N. 12 Prir t Cncrete Placement 27

34 ; Figure 27. Slab N. 13 Prir t Cncrete Placement f*' «mw te» H.1 $J;0M.$&* if it «.1 '?'< i/ i- /id' 'S* >1 M W:i' \ M,iJ\d^Sr rf jvr.! ».<>.< «.-«. «' i <«MMr<>.v«i' «i- Mm«!?**»*«j(fH Figure 28. Clse-up View f Lacing in Slab N. 3 28

35 T" t*':*wr-'! s :.7«r ;.,*?» - fc.; NUk. SJu-' *.. "V* *»-. r r' *.7. K-ffiffiÄ."!*..,...JÄNBr.-**^"-'--fcH '"".'."-«lisirt^r Ä*r? '** * *! ****** %jl^rp^" llt'c^" ITT f! WÄ^- 'I I- T^iki-U^MS' 1 Figure 29. Clse-up View f Stirrups in Slab N. 7 29

36 11/16" 1-6" + 11/16" c 24".+. 6" t ul u c uj i c C^TF T SS-I SS2l SS3 SS S3-5 Si-6 d c d d. 4 N. 3 Principal Steel spaced at 2.4".e. D2 stirrups spaced at 1.5".e. D1 Temperature Steel spaced at 1.5".e. Figure 30. Strain Gage Lcatins n Stirrups in Slab N. 2 11/16' h 6" 6" H 1 N. 3 Principal Steel spaced at 2.4".e. D2 Lacing Bars 11/16" D1 Temperature Steel spaced at 1.5".e. Figure 31. Strain Gage Lcatins n Stirrups in Slab N. 3 <T (2= 6" 24" 6" c c c c c c c SS I SS-2 I SS-3 d c d d c c c/ c Z~c~l~l~c~~Z~~c c JS-< c c c c S3-5 SS-6 T D3 Stirrups 7/8" N. 3 Principal Steel spaced at 1.33".e. D1 Temperature Steel spaced at 4.0".e. spaced at 1.33".e. D 3 7/8" I t 8 CO r-. r» 00 Figure 32. Strain Gage Lcatins n Stirrups in Slabs N. 7,,8, 9 30

37 <T (2= c SS1 c SS-2 ccac 24" 6" c O O 0 c SS-3 c I ss 4 I 9 c SS-5 D3 Stirrups N. 5 Principal Steel spaced at 6".e. D1 Temperature Steel spaced at 4.0".e. spaced at 1.5".e. 7) 3 7/8" t CO GO *~ rs /8" Figure 33. Strain Gage Lcatins n Stirrups in Slab N. 10 N. 5 Principal Steel D1 Temperature Steel spaced at 4.0".e. spaced at 1.33".e. D3 Lacing Bars Figure 34. Strain Gage Lcatins n Lacing in Slabs N. 11 and 13 N. 5 Principal Steel spaced at 4.0".e. D3 Lacing Bars D1 Temperature Steel spaced at 1.5".e. Figure 35. Strain Gage Lcatins n Lacing in Slab N

38 Figure 36. Membrane Cvering Slab WSiaREK, ^^ ^ S!?l... : r Kt;r :: ;ft*:fessspl iu: \J\! ii&;?:ä^m Figure 37. Test Chamber Ready t Rll Inside Large Reactin Structure 32

39 Figure 38. Psttest View f Slab N. 1 Figure 39. Psttest View f Slab N. 2 33

40 Figure 40. Psttest View f Slab N. 3 Figure 41. Psttest View f Slab N. 4 34

41 np JllllpJIPIk^ ill Figure 42. Psttest View f Slab N. 5 Figure 43. Psttest View f Slab N. 6 35

42 m ü«* p>*. Figure 44. Psttest View f Slab N. 7 F*V* " **: Figure 45. Psttest View f Slab N. 8 36

43 Figure 46. Psttest View f Slab N. 9 Figure 47. Psttest View f Slab N

44 Figure 48. Psttest View f Slab N. 11 Figure 49. Psttest View f Slab N

45 Figure 50. Psttest View f Slab N. 13 CO Deflectin Figure 51. General Lad-Deflectin Curve 39

46 COMPRESSIVE MEMBRANE REGION TRANSITION REGION TENSILE MEMBRANE REGION a < OEF LECTION Figure 52. General Lad-Deflectin Curve fr a Nrmallly-Prprtined Restrained Slab Legend Slabl Slab 2 Slab 3 "04^ Deflectin, inches Figure 53. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 1, 2, and 3 40

47 Legend Slab 1 Slab w 800 n, Deflectin, inches Figure 54. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 1 and 5 "5> Q ; ^. \ I} 800 li 7^\ \\ yy~-'' / \: - Slab 6 -J X >> \ S i 200 / n * I I I I i -.' Deflectin, inches Figure 55. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 5 and 6 41

48 1600 '?' ^ 1400 ir }i 1200 Legend Slab 6 --'- Slab 8 - Slab 13 in a re *i i\ A i i Deflectin, inches Figure 56. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 6, 8, and Legend Slab 8 Slab '35 Q. O 750 n _i Deflectin, inches Figure 57. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 8 and 10 42

49 1400 Legend Slab Deflectin, inches Figure 58. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 12 and p Legend Slab 12 Slab n , Deflectin, inches Figure 59. Cmpsite Midspan Lad-Deflectin Data fr Slabs N. 12 and 13 43

50 CD = CO T- * 1/8 " 1/4 " * 5/8 " g ^ rgl M-9/16"»1-1/2" 1-5/8" 1-3/4" 1-3/4 " «1-13/16" «> 1-7/8"»1-11/16" «1-13/16" «1-7/8 " 1-9/16" «1-11/16" i M-9/16" M-9/16" «1-7/16" * M1/16\ 7/R " '314" ' 9/16" >1/2" «1/2" «* 3/8 " 5/16" «5/16" «1/4" < i -1/4«* 1/4 «3 O C ) c ) \ Figure 60. Psttest Deflectin Survey fr Slab N. 1 CD c = =, s CD CD CD c ( \ - T"~ ^ X - T- CO CD \ CM 3; V CO c CO ^ *» K = s; 9 I 5 ) r : ^- CD - T- 0 ) r i CO c c T- 5 F^ c i, CD CO CO - CD JN in i 1 5 / c/ = I CO CD CD CO E = CD h- = T ^ ^ ^3 = CD = 00 r- I 0C TT T- c c ^- ~~- CM X 5 1 J? CO m g CO Figure 61. Psttest Deflectin Survey fr Slab N. 2 44

51 CO CD CD " T- T- T- Tf a> f- T - GO in CD T- CO I g 5 JN 5; CO T- r- CO I CO CD g CO \ Figure 62. Psttest Deflectin Survey fr Slab N. 5 CM CM 5 T 25 - CD CD = = t CD = CD TJ- CO T CO in *-» ^ CO 1^ ^- O) r^- ; in i c c c 5 c CM 00 ^ 55 Figure 63. Psttest Deflectin Survey fr Slab N. 6 45

52 CM 1-5/16" 1-3/8" 1-1/2" 1-1/2" 1-7/16" 1-1/16" 5/8".7/16" 9/16" 1-1/2"»2"»2-1/16"»2-1/8"»1-3/4" 1-7/16"»7/16^ ^ 7/16" ^3/4", / 1 = - CD = = CO ~.a\ CM -i -«^- CN1 J^ CO ~^ = ^ ^ ^ ^ in h- rs c D i i i i "J 1 - T- CM CM CM CM v- T "-f < O Figure 64. Psttest Deflectin Survey fr Slab N. 8 CD : : : : : (D (O (D <D OT ^-T-T CO 00 CO jf T- c^i'inccct- c = = = r = = = CDCD = O^^g53;CMCM 5 cp:5i?5cct : '«-c T-.- = CD CD CD = CD CO Ö = 5^^^=lO O^ ^ ^ S CO = ^ ^ ^ " S Figure 65. Psttest Deflectin Survey fr Slab N. 9 46

53 CM CM CM CO in CD «-> CD CO CM m ^ 00 *fr CO 00 CO ^ ^ f^ 1 CM CO i i CM 5 CO CO CO T- u5 CO i Figure 66. Psttest Deflectin Survey fr Slab N. 10 Figure 67. Psttest Deflectin Survey fr Slab N

54 Figure 68. Psttest Deflectin Survey fr Slab N. 12 CD in CO in CM CM CD i- CM 5 = CO I CM T- CD ~~ en c CM CM c 5; c i CM c CO = = : _ = ^ CO CO ~ " CO CO ^-" in ^ CM 5 1 T- T- T- in in "f in a> T ~ T ~ CM CM CM CM V CO Figure 69. Psttest Deflectin Survey fr Slab N

55 a. Bttm View b. Side View Figure 70. Sketch f Damage fr Slab N. 1 49

56 a. Bttm View b. Side View Figure 71. Sketch f Damage fr Slab N. 2 50

57 a. Bttm View ül5^ b. Side View Figure 72. Sketch f Damage fr Slab N. 3 51

58 a. Bttm View b. Side View Figure 73. Sketch f Damage fr Slab N. 4 52

59 ^^^^J; Wnüj$ «II HfJrASi a. Bttm View b. Side View Figure 74. Sketch f Damage fr Slab N. 5 53

60 a. Bttm View b. Side View Figure 75. Sketch f Damage fr Slab N. 6 54

61 a. Bttm View b. Side View Figure 76. Sketch f Damage fr Slab N. 8 55

62 a. Bttm View b. Side View Figure 77. Sketch f Damage fr Slab N. 9 56

63 a. Bttm View b. Side View Figure 78. Sketch f Damage fr Slab N

64 a. Bttm View b. Side View Figure 79. Sketch f Damage fr Slab N

65 a. Bttm View b. Side View Figure 80. Sketch f Damage fr Slab N

66 Appendix A: Recrded Data Al

67 TIME (secnds) Slab 1 D-1 (lnch»i) A3

68 SM> "TT60 risr 1A t M D-2 (Inchn) "t ~3i5Ki 300(5 ^W -2ÖO0 SB-1 (mier-lneh/lneh) TTOB O 1ÖÖÖ 5500 A4

69 2600 4Ö0Ö 6000 SB-2 (micr-inch/inch) '%» =Rksr 5000" 4000~ 8T-1 (micr-jnch/lnch) ~600Ö BÖÖB TE*4 A5

70 Slab 1 "TÖ55!50ö 5ö~ BT-2 (mler-faich/inch) Slab 2 "TSr ~T^ Ö~~ TIME (secnds) 300 A6

71 -i r D-1 (Inches) ' S>kö si s*i da IÖ ix~ ~~2. 5~ D-2 (Inches) ' T. IS 5. A7

72 1.E+4 "TE+? SEM SB-1 (mtcr-inch/lnch) 4.6*4 re** ei-n " 1?25 iii TÜBS 1.2E> E*4 1.8E+4 2TE*4 SB-2 (micr-fnch/lnch) A8

73 ^nte ~"SSö 3 SS-1 (micr-lnch/lnch) T Sö 6Ö0 T "iar "Tsiis refer 8S-2 (micr-lnch/lnch) ""Zöö 25ÖET A9

74 Slab 2 _i _]_ TOO ÖÖ30ÖÖ 3500 SS-3 (mlcnmnch/inch) ~B55 555"" 8S-4 (mlcrcmnch/inch) A10

75 -4Ö53K *5ö 555 SS-6 (mlcr-inch/lnch) "5ÖÖ TO5 i205~ 2 fe * * 5ir 4.e*4 ~SM+4 SS-* (micrcmnch/inch) All

76 IS+4 3.E+4 8T-1 (micr-inch/inch) -^sk 5t sfe~ -TTsfei Ü05 - ST-2 (micr-inch/inch) ""2000" Ö0Ö 3500 A12

77 200 TIME (secnds) ~5M ÖW D-1 (Inclws) A13

78 D-2 (inches) SB-1 (micr-inch/inch) A14

79 2.E+4 3.E+4 SB-2 (micr-inch/inch) 5.E SL-1 {micr-inch/inch) Al 5

80 -SOOT" SL-3 (mlcr-lnch/inch) 1.5E+4 "TÖOÖ T *t 1.5E-M SL-2 (micnmnch/inch) Al 6

81 "5ÖÖ iöö SL-4 (micr-inch/inch) Slab 3 SL-fi (mlcr-lncmneh) Al 7

82 "556Ö ^1500" ^BS 07 SL-6 (nlicrhnch/lnch) SEÖ ST-1 (mfcr4nch/lnch) Al 8

83 "löö T$~ ST-2 (micr-lnchflnch) ~55Ö 25Ö 30Ü~ T1ME (secnds) Al 9

84 D-2 (inches) A20

85 ~ SB-1 (mlcr-4nch/tnch) Tl SB-2 (micr-inch/inch) 1.4E+4 1.6E+4 1.8E*4 A21

86 ST-1 (micr4nch/lnch) ST-2 (micr-inch/inch) A22

87 200 TIME (secnds) Slab 5 D-1 (Inches) A23

88 -0.5Ö D-2 (Inches) Sl«b5 SB-1 (Rilcr-inch/lncn) A24

89 SB-2 (micr-inch/inch) Slab 5 T^ ST-1 (mlcr-lnch/lnch) A25

90 T1ME (secnds) A26

91 D-1 (inches) %.JB- A27

92 Slab6 i.e+4 SB-1 (micr-inch/inch) 4000 SB-2 (mfcr-inch/inch) A28

93 1E+4 ST-1 (mlcr-lnch/inch) idffi ÖÖÖ 5ÖW ST-2 (mlcr-inch/inch) 70Ö A29

94 200 TIME (secnds) Slab 7 2 T D-1 (inches) A30

95 0-2 (inches) Slab ~l 35T" 8B-1 (micnmnch/lnch) 6660 A31

96

97 1.E*4 8S-2 (micr^nch/inch) 5.E-M "1E*4 TESI senr 8S-3 (mlcnmnch/inch) A3 3

98 Slab 7 "3&r 400 6Ö0 SS-4 (mlcr-tnch/inch) "1Ö0 15ÖÖ SS-S (mlcr4nch/inch) A34

99 T^n "TE?4" 5S?T" 8S-6 (micr-lnch/lnch) 5.6*4 ~KE+4 " 5?te 1.E+4 "TTE+4" 3I*T" ST-1 (micr-lnch/lnch) 4.E*4 A35

100 Slab 7 l.e*4 ST-2 (micrnnchrtnch) A3 6

101 sis nb iö -Ti * D-1 (Inch») Slab8 sin Tjfe ra 1 D-2 (inches) "23 3- A37

102 -2.M+4 ztiar "TE3 j.e+4 SB-1 (mlcr4nch/vnch) E+4 1.5E+4 SB-2 (mlcr4nch/inch) 2.E-M 2.5E-M A38

103 1.6*4 2.E*4 3.E*4 SS-1 (micr-lnch/inch) 5.E»4 6.E*4 -*&* 3^ SS-2 (micr<mnch/inch) 2.E*4 A3 9

104 1.E+4 2.E+4 3.E+4 SS-3 (mlcr-inchanch) 4.E+4 Slab 8 ^sfe" "555 mö~ SS-4 (micr-inch/inch) A40

105 s -2bö ~Tt5ffl JcT SS-5 (micr-taeh/lnch) i *4 ~Z^T 3.E*4 8S-S (mlcr-incwinch) "6^*4 A41

106 ST-1 (micr4nchfinch) 4.E+4 5.E+4 6 *4 ' 5l SOÖ "TÖ0Ö 55SB 3000 ST-2 (mfcr-inch/inch) "Tööö A4 2

107 Slab 9 A4 3

108 "" D-2 (Inches) Slabs ""555 TOO SB-1 (mlcr-lnch/lnch) A4 4

109 I 1400 Slab 9 ^ * ^^< y» a a. 800 e ~ ?1 i *. I! i Ö e 8B-2 (micr-inch/inch) 1500 _ Slab9 N^ 1000 a. CL 500 h i i E E+4 4.E+4 5.E+4 6.E«4 SS-1 (micr-inch/inch) A4 5

110 1.6*4 2.E+4 3.E+4 SS-2 (micr-ineh/inch) i.b*t3.e+4 SS-3 (micrt>4nch/lnch) A4 6

111 -1500 SS-4 (micr-inch/inch) 1.&4 SS-6 (micr-tnch/inch) S.E*4 A4 7

112 te+4 2.E+4 3.E+4 SS-6 (micr-inch/inch) Tea 3E?r- ST-1 (mtcr-4nch/inch) A48

113 t 1.E+4 T&i 3.E+4 ST-2 (micr-inch/inch) 1400 " Slab J I MO L -200(. SO i 100 1S TIME (Mcndt) A4 9

114 Slab 10 S D-1 (InehM) Slab 10 -i i- -i e- D-2 (InehM) A50

115 SB-1 (mlcr-lncmneh) Slab 10 ~x.g*- ~i. T^M ji+j SB-2 (mlcnmnch/lncm <&* si- **GS+4 A51

116 S 500. S?ia * ria 5^" si*r 8S-1 (mlcr^newlbch) -Ten 61*4 Slab 10 S %S6 3ifeür HSB5 SS-2 (mlcre-lbch/lnch) 4000 SÖ00 A52

117 T&B 3555 ^85 ^Söö- 8S-3 (mlcre-lneh/lnch) -500 Stab 10 -&. rass assr " S-4 (mlcre-tnch/lnch) "7555 8ÖÖ A53

118 88-6 (mtere-lnch/inch) Slab 10 ri+i si+4 ST-1 (mler-lnemnch) 5.6*4 A54

119 ^JBB BBSS' ST-2 (miere-inch/lnehl ÖÖÖ iööö 9500 Slab 11 T55!55~ TIME ( endt) A55

120 D-1 (inches) (inch«) A56

121 *3i ~ Ö SB-1 (mlcr-tneh/lneh) EM1.4E+4lTE*4 Slab 11 -^.^ it r&4 siff 3TP4 SB-2 (mlcr-tncmnch) 4.E*4 6.6«A57

122 Stabil *$äa dr- 1.E*4 SU (mler-tnch/lnchl z.&r ri?4 z * st«- SL-2 (mlcr-lnch/lneh) E&T - A58

123 Y.&T sin j&r S&- ~g +i SL-3 (mlera-lneh/lneh) m risr T& si«4 *A "TES SL-4 (mler-tneh/lneh) A59

124 m -rkr "TE5i ässr SL«6 (mler-lnchflnch) 4E+4 5.E*4 d«5^m du ST-1 (mlcm-lneli/lnch) "Jtl 5.E+4 EE+4 A60

125 "SPia i da da da ST-2 (mlei-4nch/lneh) 5.E*4 EE-M Slab12 TIME (««nd«) A61

126 D-1 Onches] 4W~ sk~ u D-2 (InehM) A62

127 2.E-H 3.E+4 8B-1 (mler-lncmnch) Slab12 f.e*3~ "TEM si«r SB-2 (micr-tneh/lnch) 5.E-M A63

128 -5.ST" -xka i. 1.E E+4 SL-1 (mlcr-lnchflnchl 4.E+4 5.E+4 Slab12 1.E+4 ji-m 3.E+4 SL-2 (mlcra-4neh/lnch) 4.E-M A64

129 V&T SL-3 (mlci^neh/inch) ii*t~ "HE+T" 3.E+4 SL-4 (mlcr-lnch/tnch) A65

130 ii*4 "5^3 ährm~ SL-S (mlcn>-4nch/lnch) 4.E»4 5.E-M 6.E*4 Slmb12 i'.s4~ 1^53 21* 4.6*4 SL-«(mlcr-inch/Inch) A66

131 V. M" ST-1 (mlcr-inchftnehl 5.E-M 4000 BÖ6S 80ÖÖ~ ST-2 (mfcrhnch/inch) E»4 1.4E«4 A67

132 -ite~ m~ TIME (secnds) «a* 1.5 D-1 (Inches) A68

133 0. üiö riss ti t. is 1. Ts~ DJ (Inch»») Slab 13 *$. «- r r- -zfe 3.e*4 SB-1 (mlcr-lneh/lnch) A69

134 Slab 13 i±a zi SB-2 (mlcr-lnch/inch) IST- il*t 3.e»4 SL-1 (micr-inch/inch) A70

135 m ii+4 T^4 SEM" SL-2 (micr-inch/inch) ~6l*4 1.E*4 2.E-M 3.E*4 SL-3 (mlcr-lnewlnch) A71

136 SL-4 (mlcr-fncmnch) Slab 13 *& -i sk 10Ö0 SL-5 (mlcr-lnch/lnch) 1500 A72

137 ~3öö SScT ST-2 (mlcr-lnchflnch) E-M A73

138 REPORT DOCUMENTATION PAGE Frm Apprved OMB N Public reprting burden fr this cllectin f infrmatin is estimated t average 1 hur per respnse, including the time fr reviewing instructins, searching existing data surces, gathering and maintaining the data needed, and cmpleting and reviewing the cllectin f infrmatin. Send cmments regarding this burden estimate r any ther aspect f this cllectin f infrmatin, including suggestins fr reducing this burden, t Washingtn Headquarters Services, Directrate fr infrmatin Operatins and Reprts, 1215 Jeffersn Davis Highway. Suite 1204, Arlingtn, VA , and t the Office f Management and Budget, Paperwrk Reductin Prject ( ), Washingtn, DC AGENCY USE ONLY (Leave blank) 2. REPORT DATE Nvember TITLE AND SUBTITLE Shear Reinfrcement in Deep Slabs 3. REPORT TYPE AND DATES COVERED Final reprt 5. FUNDING NUMBERS 6. AUTHOR(S) Stanley C. Wdsn 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Army Engineer Waterways Experiment Statin 3909 Halls Ferry Rad, Vicksburg, MS PERFORMING ORGANIZATION REPORT NUMBER Technical Reprt SL SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army Crps f Engineers Washingtn, DC SPONSORING / MONITORING AGENCY REPORT NUMBER 11. SUPPLEMENTARY NOTES Available frm Natinal Technical Infrmatin Service, 5285 Prt Ryal Rad, Springfield, VA a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Apprved fr public release; distributin is unlimited. 13. ABSTRACT (Maximum 200 wrds) A cnsiderable amunt f data is available in the literature regarding the behavir f nrmally prprtined slabs, thse with span-t-effective-depth (L/d) ratis greater than apprximately 8. Hwever, guidance fr shear design and respnse limits f deep slabs (L/d < 6) used in prtective cnstructin is lacking. Thirteen ne-way reinfrced cncrete deep slabs were statically laded with unifrm water pressure t gain a basic understanding f the behavir f deep slabs with reinfrcing details typical f prtective cnstructin. The pst-ultimate behavir f the slabs indicated that a substantial amunt f reserve capacity is available in deep slabs with large quantities f principal reinfrcement. Based n this series, the recmmended respnse limit fr deep slabs having a principal steel rati near 0.01 and adequate shear reinfrcement is apprximately 12 deg. Fr deep slabs with relatively small quantities f principal steel, the respnse shuld prbably be limited t apprximately 8 deg fr design purpses. 14. SUBJECT TERMS Deep slabs Lacing Respnse limits Shear Stirrups 15. NUMBER OF PAGES PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED 18. SECURITY CLASSIFICATION OF THIS PAGE UNCLASSIFIED 19. SECURITY CLASSIFICATION OF ABSTRACT 20. LIMITATION OF ABSTRACT NSN Standard Frm 298 (Rev 2-89) Prescribed by ANSI Std. Z