Text

Evaluation of Effect on Structural Strength of Cracks in Walls of Diesel Generator Bldg
	ML20041C141
Person / Time
Site:	Midland
Issue date:	02/11/1982
From:	Sozen M; AMERICAN CONCRETE INSTITUTE, BECHTEL GROUP, INC., ILLINOIS, UNIV. OF, URBANA, IL
To:	;
Shared Package
ML20041C139	List: ML20041C138; ML20041C141;
References
	NUDOCS 8202260258
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{{#Wiki_filter:{- - o o ENCLOSURE EVALUATION OF THE EFFECT ON STRUCTURAL STRENGTH OF CRACKS IN THE WALLS OF THv DIESEL GENERATOR BUILDING MIDLAND PLANI vi41TS 1 AND 2 MIDLAND, MICHICAN A Report to BECHTEL ASSOCIATES PROFESSIONAL CORPORATION Ann Arbor, Michigan by i Mete A. Sozen 503 W. Michigan Urbana, IL 61801 11 February 1982 8202260258 B20216 PDR ADOCK 05000329 A PDR j

v.. ( e 'o - CONTENTS ....... :.......................... - 1

SUMMARY

. INTRODUCTION. 3'- 4 DIESEL GENERATOR BUILDING WALL STRESSES CAUSED BY TEMPORARY SUPPORT FROM THE DUCT BANKS.....-... 6 .:.1. 10 RESIDUAL STRESSES.' EFFECT OF EXISTING. CRACKS ON WALL STRENGTH. 14 FIGURES ATTACHMENTS 1. Crack Development in Reinforced Concrete 2. Effect of Existing. Cracks on Strength of Reinforced Concrete l Members 3. Cracks in Concrete Walls 4. Evaluation of. Cracking in Diesel Generator Building at Midland ' Plant by W. G. Corley.and A. E. Fiorato l l l l l l ~ l l l. i l I 1. [- u..

e. t 1

SUMMARY

This is a study of 'the _ eff ect on strength of the cracks on the walls of the Diesel Generator Building, a box-like reinforced concrete structure with overall dimensions of approximately 70

155 by 50 ft high.

The exterior walls are 30-in. thick. Three 18-in. thick interior walls with their longitudinal axes in the short plan dimension of the building divide the building into four cells of approximately equal size (Fig. 1 and 2.). In addition to typical volume-change cracking, some of the interior walls and the east exterior wall have been observed to contain systematic crack patterns (Fig. 6) near the locations of the du.ct banks (Fig. 4). The duct banks had provided unintended temporary supports for the walls in construction because of settlement of the fill on which the building is founded. Stress conditions in an interior wall during an intermediate construction stage are analyzed. _ Residual crack widths and patterns are evaluated. Background information on cracking and, strength of reinforced concrete structures is'provided in Attachments 1 and 2. The study concludes ' that : (1) At an intermediate construction stage, with the footing resting on the duct bank, normal horizontal tensile stresses in the walls would have caused the cracks near the duct banks, if those cracks had not occurred earlier in fresh concrete.

.e= ~ D' s ~ 2 (20 Residual tensile" stresses in wall reinforcement.are;likely to 'be less than 30-ksiian'd certainlyzin the linearly elasticarange_of the- ~ " Grade 60' reinforcement. (3) ;Th'erenis no evidence to indicate that the strength of the building is;1ess-than tb.at assumed in-its design. ~It!should be emphasized that the function of the Diesel Generator. .Buil' ding is:we'll within the range of the experience which supports th'e theory and practice o'f re'inforced concre'te building construction. The' existence-of discontinuities in.the concrete is a condition anticipated by ordinary. methods of design for reinforced concrete st'ructures. A crack inca concrete wall o'r beam is not-comparable to a discontinuityLin, - for~ example, a steel plate girder. Continuity'in tension of' reinforced . concrete structures is effected not by the concrete but by the reinforcing bars.- Therefore, there is no need to reanalyze'the building using a model to reflect the effects of ter. ile discontinuities implied by the: cracks.: e

'V -6 3 . INTRODUCTION The walls of the reinforced concrete structure to house the ~ emergency' diesel generators for the Midland Power Plant Units 1 and 2 have been observed to have developed cracks ranging in width up to a recorded maximum of 0.028 in. The' object of this report is to study the widths and arrangement of the cracks to determine the conditions leading-to cracking and the possible consequences of'the' existing cracks on the- ~ strength of the structure. This report was' written at the request'of Bechtel Associates Professional Corporation, Ann Arbor, Michigan. In addition to a visit. to inspect the Diesel Generator Building, the writer had access to -information provided'in the following Bechtel documents: ~ (1) Crack mapping sheet,1, February 1980. (2) Drawing showing cracks surveyed in July 1981. (3) Drawing SKC-616 showing progress of concrete casting for the Diesel Generator Building. ..(4) Drawings C-1001 through C-1039 showing concrete outlines and. reinforcement details. (5): Response to NRC Question 14, containing a figure showing crack-patterns in the walls of the Diesel Generator Building ~(dated 24 April'1979). -(6) ' Response to NRC Question 28, containing a figure. differentiating cradks surveyed d2 ring December 1978 and cracks surveyed after September 1979 (dated February 1980).

.- s i ~4 (7) Response to NRC Question 40. DIESEL-GENERATOR ~ BUILDING .The Diesel Generator Building is a stiff box-like structure' cover-ing an area of approximately 70 x.155 ft. .Its plan and sections ~are shown in Fig. 1 and 2. Exterior walls are 30-in. thick. The interior-space is divided into four cells of approximately equal size by three 18-in. thick interior walls running north-south. All interior and exterior walls are suoported by continuous strip footings (10 by 2Lft 6 in. in cross section). The walls rise-from an elevation of 628 (bottom-of footing) to 680 (top of roof slab). The long exterior walls on north and south sides ofLthe building have various openings as in'dicated in Fig. 1. The design compressive strength for-the' concrete in the walls was-4000 psi. Uniformly spaced wall reinforcement is-provided by Grade 60 No. 7 (interior wall) and No. 8 (exterior wall) bars at 12 in, each way near each face of wall. The uniform reinforcenent ratios in both th'e horizontal and. vertical directions are 0.56% for the interior and 0.44% for the exterior walls. Because it houses the generators to provide power in an emergency, the-Diesel Generator Building is classified as being in Seismic Category I. The building must maintain its integrity if subjected to an -earthquake motion having an intensity equal to that of the motions postulated for the " safe shutdown earthquake (SSE)." It must also resist ' forces and missiles generated by tornados. The building is founded on plant fill. Casting of the concrete structure was started in October 1977. Because the observed settlement

8. e. ._ o d '5- 'of the(building exceeded theLestimated amount, construction was halted during August?1978. vat the time ~the construction was stopped, walls had- 'been. completed to"an elevation.offapproximately 662. TDistributionfof ~ th'e-settlement observations made indicated a slight " tilt"'of the build'ing.the southwest corner settling perceptibly more;than the .northeasticorner..It was reported that theDfill was settling awayTfrom the' building under the' footing of the east wall.- These-phenomena. ~ suggested that the duct banks (Fig.'3 and 4) had'made contact with the-footings.of the. interior walls and the east wall. In November 1978'the duct' banks were separated from the-footings.. Changes in settlement'are illustrated schematically in Fig. 5.. Construct' ion was resumed in December 1978. To ameliorate future settlementaof the fi11,- .a surcharge-(approximately 20 ft of sand) was placed to' cover the' construction site.' The structure was completed'in April 1979. Surcharge was removed'in' August:1979. Figure 6 shows the cracks observed inlDe.cember 1978 on the surfaces of.the north-south walls up to anLelevation of 664. 'A. cursory review-of- ~ j the: crack patterns suggests their' compatibility with the s'ettlement= history of the' structure.. Cracks on the west wall, which did not have a. duct ~ r bank'below it, are of the type clearly: attributable to: ordinary volume-change effects of the' concrete. On the other. hand walls with. duct. banks. ~ t. beneath them have some cracks which imply a' systematic stress pattern attributable to a' support'placed near~the. position of the duct banks. i The cracks-obsec.ed in the center wall provided the strongest indication I of the pressence of such-a support. The cracks shown in Fig. 6 are 9

d-0 6; those which were measured to-have widths of at-least 0.01 in. Maximum-crack width measured.was reported to be 0.028'in. After the duct banks were separated from the footings there was observed a general reduction in width of the larger cracks near the~ duct banks. Cracks on the north and south walls of.the Diesel Generator Building were generally smaller in width. Their distribution. indicates that they were caused primaril'y by' volume-change tendencies of the concrete. ~ WALL STRESSES CAUSED BY TEMPORARY SUPPORT FROM THE DUCT BANKS A schematic representation of the center wall is'shown in Fig. 7. Soil reaction on the footings is represented by a series of springs. The effect of the duct bank, after it comes into contact with the bottom of the wall footing, is interpreted as.a reaction provided by a.very stiff spring. Consider a particular stage during the construction of the wall. Concreting of portions A'and B has been completed, in that order, within ~ Approximately 'wo weeks later, after the concrcte-t a few days of each other. in portions A and B has hardened, lifts C and D are placed in succession.. Because of the eccentricity of the-reaction provided by the duct bank,'the-building is likely to tilt to the south as it settles. A limiting conditon is one'in which the-portion of the wall north of the duct spring is-lifted off the springs representing soil reaction. Load-dependent stresses in the wall corresponding to this limiting condition may be estimated from -an analysis of the stresses in a linearly clastic model of the " cantilevered" portion of the wall shown in Fig. 8.

m i 7 The elevation and'section shown in Fig. 8 represent the hardened concrete 'in portion -of the center w.11 up to elevation 650 (Fig. 7). It is assumed that the-reaction of the duct bank may be concentrated as a-line load at a point 22 ft'from the inside face of the north wall, as shown in the lower left-hand corner of the wall elevation. The horizontal links represent the restraint of the rest of the wall to the south ~of the support. The pressure of 12.5 psi on the upper surface of the wall represents the effect of the fresh concrete in lift C (Fig. 7). The edge load represents part of the weight of the north wall. When included in the analysis, it was applied along the vertical edge uniformly except for a heavier concentration at the top to represent the weight of fresh concrete above that level. 6 Young's modulus of the concrete was assumed to be 4

10 p,g, Poisson's ratio was taken as zero.

Density of reinforced concrete was set at 150 lb/ cubic ft. Internal stresses were analyzed for two conditions: (a) for zero edge load and (b) for a nominal distributed edge load of 200,000 lb. In both cases self-weight and pressure on top surface were included. Horizon *.a1 stresses calculated on a vertical plane one foot away t 'from the left face of the wall segment (fixed edge) considered are-plotted in~ Fig. 9 for both solutions. The tendency of both tensile stress distributions to increase near the effective neutral axis is due the " bursting" stresses caused by the concentrated reaction at the bottom flange.

e 6' 8 The reason for showing two stress distributions in Fig. 9 is to emphasize the indeterminacy of the. actual loading conditions on the wall. The edge' load could be considerably higher than that. assumed. The range of the calculated tensile' stresses" suggests that stressesLof a-magnitude-to cause cracks in-the hardened concrete would have existed in the wall i in the vicinity of the duct-bank at'a time'when the concrete'in lifts C and' D (Fig. 7 ) was. f resh. ~ It is important to note that the analysis above demonstrates.that cracking would have occurred'after casting of lifts C and D but it does not preclude the appearance of cracks to accommodate' settlement deformations before that stage in construction. In reference to Fig. 7, it will be appreciated that stress-related cracking depends on res'istances and stiffnesses (strength and stiffness of the concrete as well'as the 'stiffnesses of the duct banks and'the supporting soil)'which are all, time-dependent. Complex as these combinations are, they are further complicated by' construction' events. To reconstruct the stress / strength interaction. loading to cracking of the concrete is virtually impossible ~but also unnecessary. If no cracks had formed before the construction stage considered, calculations indicate that cracks would have-formed-then and consistently.with the observations of settlements and crack patterns. 'In relation to the observed phenomena, it is of intecost to investigate the progress of a crack.in the wall once it'is initiated. Figure 10 shows the' reinforcement in the wall segment considered 'above. The relationship between crack height and resisting moment was - determined assuming a direct tensilestrengthof4/f[forthe4000 psi

1 o 9 concrete. Yield stress of'all reinforcement was assumed to be 60,000 psi. Calculations were made with the bottom edge of the wall in compression. The calculated relationship is plotted in Fig. 11. It illustrates two inherent features of crack development in a reinforced section subjected to flexure. It is noted that after cracking occurs'at a moment of approximately 8,500 kip-feet.there is a drop in resistance. Theoretically, the crack would penetrate almost to the flange (the footing) before the section redevelops a moment of comparable magnitude. Even though the wall is adequately reinforced (p = 0.0056), the reinforcement is distributed over its height rather than being concentrated-near the extreme fiber in tension. Consequently, the flexural crack penetrates deeply into the section before sufficient reinforcement force is mobilized to compensate for the loss of the tensile strength of the concrete. It may also be noted.from Fig._11 that after the crack penetrates about 12 ft into the section, the slope of the curve becomes positive. Its progress'is controlled after a penetration of approximately 17 ft. Equilibrium of internal forces and-external effects is re-established. The exten_t of the cracks observed especially in the center wall is quite consistent with the expected behavior'of reinforced concrete sections subjected to flexure. It should, however, be remembered that the walls-of the Diesel Generator Building are not likely to be subjected to

e . V 10-flexural stresses of this magnitude in their normal function because the ' duct. banks have been" separated ~from the footings and because.the buiiding is now complete. The overall depth of the section is now over-50 ft rather than 22.ft as considered in the calculations. RESIDUAL STRESSES Figure 10 shows the trajectories of the cracks recorded in' July 1981 on east face of the center wall. Cracks shown are those having widths of' O.01 in. or larger. East face of the center wall was' chosen for study because'it had more and wider cracks than the other walls. The maximum crack width at the' time of the July 1981 survey was -reported to be'O.02 in..This is less than the maximum of 0.028'in. observed earlier.. The reduction in wid'th is consistent with the. result of the calculations in the previous section which supported the_ observation that' bending stresses caused by the temporary concentrated support contributed to crack formation. Separation of. the duct banks from the footings would cause the wall cracks in the vicinity of the. duct banks to reduce in size. On the other hand, these cracks would.not be expected. to close-completely because the concrete surfaces bounding the cracks are not likely to fit perfectly ar.d because the foundation profile is not likely to have returned to precisely the shape ~it had before opening of the cracks. It should also be remembered that crack-width measurements made at different times may differ. In addition to the natural scatter in

In a CTL1 survey made in February 1982 (Attachment 4) a maximum width of 0.025 in, was recorded on the center wall.

= 11' observation, changes in temperature and humidity may' affect the size of the cracks within a short period of time. The small variation in maximum c? served crack width from 0.028 to 0.02 in. is consistent with what- ~ would be anticipated,~given the history of the building. An estimate of the residual stress in the wall reinforcement may be obtained from the~ residual crack widths. A brief perspective of the information on the relationship between tensile reinforcement stress and crack width is provided in Attachment 1. Crack width estimates or measurements are used typically to make judgments about serviceability -and/cr durability of a reinforced concrete structure. For that task, the role of the crack-width estimate as an index value is relevant and useful. But the relationships which yield an estimate 'of the crack width as a function of steel stress, concrete cover and other variables are not typically used in reverse; to determine stress from width measure-ments. Used for that purpose, they may help provide informatio:. as to whether and to what extent yielding may have occurred at a given location. Any quantitative inference made on that basis must be treated as a very rough measure. It was stated in.the previous section that the cracks related to the support from the duct bank could have occurred before concrete in sportions A and B (Fig. 7) hardened. In the following' discussion, it will-be assumed that cracks occurred in mature concrete and within a short period of time, thus leading to upper-bound estimates of residual stress in the reinforcement. 4 h a w v-v v-

o

.12 The. simp.1 cst and most direct method for estimating steel stress from crack-width data is to use-the data simply as a measure of bar extension. Crack widths were measured at two levels on the east face of the center wall (Fig.12). Widths measured ~at the upper 1evel (elevation ~ of approximately 645) are seen-to add to a larger sum than those in the lower level. Considerirg the sum of crack widths at'the outer level between two 0.02-in._ cracks' indicated by the letter B and assuming that the one crack not measured'at that level had a width'of 0.01 in. as measured at the lower level, the total extension is.found to be approximately 1/8 in. 'The length, L, over which this extension is ~ g assumed to have taken' place is approximately 150 in. T'he corresponding strain, c,,'is approximately 0.008 and the related steel stress 3 f =c

E

=-(.125/150)

29
10 s

s s = 24 ksi Considering the reliability of the crack width measurements and the' probability of the very small cracks in this area not being reported, the plausible conclusion from this attempt is that the residual stress would be in the range 20 to 30 ksi'if the crack occurred-in mature concrete. The strong inference is that the reinforcement-is in the linear (clastic) range of response. To obtain another perspective of the residual steel stresses in relation to crack widths, it is instructive to attempt a calculation of

q a a . c J 13 - + the crack width using a predic'or expression of. thel type described-in 4. The conditions in.Jer which ' stress-related cracking 'is . assumed to have occurred in.the walls of.the Diesel Cen'erator' Building are not typical of conditions in' beams. Therefore,~ the:pred'ictor-expression chosen is one developed by Holmberg:and Lindgren (Attachment

3) from data obtained using wall elements in direct' tension.

Using.the metre as a' unit of length, Holmberg and Lindgren give the mean crack spacing, i o f, for a. wall (with all bars having the same diameter) as i ^ 0.055 + 0.144 (A,/d ) & = b where-is'the " effective" concrete area around the bar A = e d bar diameter = b .t. Holmberg and Lindgren tested wall segments with centrally 11ocated-reinforcement in a specimen thickness representing twice the cover of the bars in the wall. ~ Adopting. their approach, -for= bars ' spaced at 12 in. with the distance from center of bar to near face of wa11' assumed to be. - 2.5 in.... 2 2 A'.=112

5 = 60 in = 0.039 m i

e re'sulting in 0.055l+ (0.144f*. 039/0.022) ='O.31:m (approx. one ft) L = r" s y-4-. +re g ...m,+ q-q n p, m -c.- ,-9 e c y , g .--iy s3 +w m .M

n,.. m - 3 a u-S,n. w3r .s . E s ./Y g y N t 14 ,\\ A

1 +:

g. To obtain in estimage of the cha'cActeristic crack spacing, Holinberg - 5 and Lindgren multiply the mean calculated ci'sck width bycl.'4. To obtain. y. g f. .the corresponding maximum crackt width,amaghiIlcationfactor(basedon 6 s'. + 4 statistical data. on crack ' width disi rEbu,tiord of 1.7. is used. For the,. ~ t walls of the Diesel Generator BuiIdingthe manimum calculated crack width 3 g 4 for a stress of 20sksi would.be. N / q './ \\., .ss u s w = 1.7 *zl.4

0.31 * (20 9.*10f)c=

0 5

10~

'm-m 4 3 = 0.02 in.- y;. i This. result, indicates that, on the basis ot the' experimental data 'N the wall conside(red, for concrete s obtained by Holmbe and Lindgren, specified)wo'uldbeexkeNtedtodevelop ./ cover and reinforcement amount amaximumcrackwidthofapproximakely0.02-in..forabarstressof ./. x 5 w$,$ ' s 20 ksi. T-f t The calculations using, heHolberg-Lindgrenexp{e'ssiopconfirmthag 3 y ,v'.h s ,4 a maximum residual crack vid,th of 0.02 in.'in the walls of the Diesel ~ fw. t Generator Building. implies;a' residual reinforcement stressiof less than. 'e s 4 s s' Lj j a 1 -30 ksi, well in.the linear range o,f= response.of the. Grade 60 rcinforcement. y', y i e e ,+ EFFECT OF EX1 STING CRACKS ON WALL STRENGTH p ? 3{3...,. ,\\ g 3 3 Reinforced concrete structures are designe6 and built with the g g y explicit assumption that'/ concrete will crack. Appearance o'f cEacks on ~

i s

i .A structural conponents of a ikinforced concrete building provide no. ccuse N[, i .s q 4' 4 for re-evaluation of the strength oi'jthe / structure un'ipss the..l::eacks Ni ds ( ,g [ \\ l y.i %. p y n x c 4. N g., J y g - g 's

Q r

4 4 f. k. 'g., e A w .y .a

O 4 15 indicate general yielding or are related to imminent failure in shear or bond. Attachment 2 contains a discussion of the strength and behavior of "precracked" reinforced concrete structures, or elements with cracks which occurred before the application of a particular loading program. Field observations and the analysis in this report indicate that cracks in the walls of the Diesel Generator Building were caused generally by ordinary volume change effects and locally..in some of the north-south walls, by tensile stresses resulting from temporary support of the duct banks. Analysis of the stress conditions created by the temporary supports indicates that cracks could have occurred in fresh concrete during the setting of concrete in portions A and B of the center w'all (Fig. 7) or, if it did not occur then, in mature concrete after the casting of lifts C and D. In eithe r' ~ case, the cracks would be related primarily to bending deformation. There is no evidence, visual or analytical, to attribute the cracks to shear or~ bond-failure mechanisms. All available evidence indicates that the residual stresses in the wall reinforcement are well within the '.incar (elastic) range of response of the material. Furthermore,, residual reinforcement stresses associated with the existing cracks are on planes unlikely to be subjected to high normal tensile stresses under postulated design-load _ combinations. The function of the Diesel Cencrator, unlike that of a containment vessel, is within the experience record which has led to the theory and practice of reinforced concrete construction. There is no reasonable Ah Na g i

s ':4. "16 'cause for concern about the consequences of the cracks in question, except for protection of.the-steelJfrom any unusual l aggressive environ- ~ ment. Examples of the behavior of reinforced concrete elements subjected. to axial load, bending, and. shear after having been cracked as a result-of other loading conditions are provided in Attachment'2. Currently, there is no indication that the-strength _of the walls of the DieselLCenerator Building is Eless than that assumed in the ' original ~ design.. Design methods-for' reinforced concrete structures have been based-on'the assumption that concrete does not provide.msistance to normal tensile stresses. The presence'of cracks in the walls of the_ Diesel Generator Building does not represent a condition which would require special procedures for modeling the existing structure. 1, F i 4 ( 4 I: .w,

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N f% I Rs Of,, I o ss ,,0 I, sN s 8 10 Qs Ns E l. 662' ,f i Ilf .650' I ff ' El p + Th A s['C'D'I El. 654 i s s. i i %"l \\) l-El. 628' ij ; l j . / 1 Spring Representing Effect of Duct Bank Springs Representing f:- Soil Reaction Fig.7 Center Wall

t t l l l d l ao L { e } g dE } i s} p

5. }

t 2} h

0. l l

g 0a 1 i f ,} ec 0 5W 6 e Wp h r nt u} 0 or f 5 2 io s t N l 2 sg e 1 a e S vo r et 4 l P Ct n g oi t oP 4 l l n ao g Hi t rc g ea t e nR g e Cd e { f n. ous ns f oA f / i atPb# b'VWMp- / c c c c c c c o c c c c c c cc / tu / t pbVtpb#b t ' pf / ro or Ff S. g i F "6 l n = O 0 1 = y u o i _N u o I_m- _i A y _ o '_ mm

O s e s s s D N 'O O ,, h O ~ J e O h V o o o W o Q. = ~ e n m W c y G O @ WV OO O ,b. N

- J O

.y O zJ g aS, ~ .O o ~ c ax @ end D a r.n. O s 7

== U Q - w g O j* ( .N i i = w= O 6. o, O i I-c N. o-

s.S D

a a - o 03 3 m D 4 e.- g w I wa o a o aw _o .a a

M O

o - O U R T

o ta.

O c-1 l l l l l O O O O O O O ON D O D C D l u u u! 'aso8 Su!;ood woJd acuots!a

I '- 6" a a o o o -2 # 7 Bars (Typ.) o o O o o o.o o o o o _8 o o o o O c o -O l [ o o a _N o o N o o o o o o o o O o o o -O i t o o =n o o o o 4 #6 Bars W 'Q o _i ~~, U NU o o o o 4 #6. Bars t 6 '- 6 " =, / Assumed Eff. Flange Width Fig. 10 Cross Section of Center Wall to Elevation 650.0

i 16,000 C 12,000 I 9 .x Ce 8000 2 oi .6 'm'se E 4000 e 4 I I I OO 5.0 10.0 15.0 20.0 Crack Length (Meas. Down From El.650), f t Fig.11 Calculated Eelat ionship 1;etween l'esisting lionent and Length of Crack (!;easured f rom Elevation 650.0 down toward Wall Footing)

- n... - r. :. 4 2 L I = = El.664'

-:.~ :.'. n v:

s':..s 1 <. ;*, : :..

v.i.c *: a:. i.,:. p.;.:..a :': :.ja,: .4:.* .;. ' ;..-,.:.4.:.*..:. :.!::i:.. :. :. ::... :. : : :. k.:. *. : :: :.. '..... .;:. :... c e. .... ~ - , v.. e. . ::i:.

.:; :~.

N: n...

. ~,

s 4;: .

~. . 1- .,a. 4.e*. Measurement Obstructed 'f*. -9. c....... 3 ...s..;... - ..e .. / .g.. i;; . -/..'.'. :

.' r.

20B j 156, 15 20B 10 10 io h2or

. s.

I ?i (Crack Widths in >0 fl e t i is j.. Units of 0.001 it,;h) 'O ( 15 / 10 J:* . O: ' 20, ) 20 4 l /}i lj ' :3 .[

- '^"".. ' '

E I. 63O'- 6" 5

5

" ' ^ *

. 6.,- e a .t:&.,.. ....n ;0-i i

,:..: -::.Y.2.f.

I

.~ J :f. :.. :. a ;

Center Wall - East Face (Looking West) Fig.12 Crack-Width Eeasurement s, July 1981

4 'ATTACIRIENT.1 CRACK DEVELOPMENT IN CONCRETE -Summary This attachment hhs been prepared to_ provide a perspective of. the development-and use of' predictor expressions for crack width. Derivations of the two common-types of predictor expressions ~are-described'and a specific example of each type is used to calculate crack widths for a: test beam. Intro' duction Tensile strength of concrete made with normal weight aggregate is 'approximately a tenth of its comprdssive strength. The low strength ~in ~ tension is not compensated' by a low Young's modulus. Initial modulus of concrete in tension is. comparable to.its modulus in compression. Fu'thermore, the limiting strain in tension is also low, approximately r 0.0002. These properties combine.to make concrete quite susceptible to cracking. Cracking is not necessarily related to stresses generated by loads-or externally imposed deformations. Much of the cracking.in elements having low apparent stress levels is caused by time / temperature dependent: volume changes or by chemical reactions causing local deformations (such as rusting of embedded reinforcement or expansion of aggregates). In general, cracks unrelated to load or imposed deformations are attributable to restraints on dimension change resulting from heating / cooling or expanding / shrinking. y ~ y

e. 1-2 ' Limiting the perspective to phenomena in one dimension only, a qualitative understanding of events leading to a crack as a result of volume change may be obtained with the help of Fig. 1.1. The concrete prism ABCD is assumed to be perfectly insulated on faces'AD.and BC as well as on faces parallel to the. plane of the paper so that there is no loss of heat and moisture on those faces. It is also assumed that there is no external restraint on any face of the prism. At a given time after the concrete is cast, the unreinforced concrete prism ABCD may be expected to assume the shape described by the broken lines. The change in shape is the result of differential shrinkage. (moisture content in regions closer to the free boundary is expected to diminish at a faster rate) or thermal gradient (assumihg in this case an ambient temperature on the free boundary lower than that at longitudinal axis of prism, a typical state during setting of cement). Considering the thin planar element PQRS, it is concluded from the free-body diagram in Fig. 1.lb that restraint forces along RS will result in a tensile force on edge QR. Because it is produced by dimensional changes varying with time, the tensile stress on edge QR varies with time. The effective tensile stress, represented by the broken curve in Fig.1.2, is the result of a complex interaction among variations with time of shrinkage, temperature, stiffness modulus, and creep, the last.two also varying as a. function of the stress level. The solid curve in Fig. 1.2 represents increase in tensile strength with time. Ideally, when the two curves intersect, the crack occurs. a

1. 3 Even ifethe events are limited to the. simple one-dimensional environment considered here, it may be inferred from the figure that exactly when the crack would form would be very dif ficult to predict because of the typical scatter-band widths of the two time functions in Fig. 1.lc.

It should also be noted that,. depending on the relative humidity and temperature on the free boundary, dimensional changes caused by. shrinkage and thermal effects may reverse. It is a statistically established truth that hardened concrete is likely to'contain cracks especially at planes not having sustained compressive stress. Tne mechanism described in reference to Fig.1.1 simply rationalizes in one dimension how cracking can occur without the necessity of stress generated by load or imposed deformation. Relationship Between Crack Width and Reinforcement Stress General concepts used to relate crack width to steel stress in terms of properties of the concrete section refer to the simplified.model in Fig. 1.3: a concrete prism cast around a reinforcing bar. It is assumed-that the crack occurs in mature concrete and as a result of tensile stress in the embedded bar. l If a sufficiently large tensile force is applied at both ends of the i. bar, the prism will crack ideally at equal intervals. The interval (crack l l spacing) is denoted by the notation E. !~ The width of the crack at steel surface can then be calculated using the usual definition of strain. i i l ?

r

1.4

[ (c,y~- c x)Ldx (1), w = g l C- . = crack width w c,j = steel strain.at point'x c =' concrete strain ~at; point'x If c, is. large compared with c , the-variation of c may be cx neglected which also suggests that'the crack width might as well be ' considered at the surface of the concrete, a more convenient location for measuring crack width. If.the variation:of steel stress over t -c is small, the elongation may be written directly in terms of' c,, the ~ y mean steel strain without introducing intolerable error, = c, ' t, (2) wo As it would be expected, there is no controversy about : the use of Eq. 2. However, there are different plausible approaches to organizing the variables in order to obtain the crack interval 1. c-One of the popular approaches to determining i _ from experimental data is very simple.. In essence, it is patterned after the problem of stress trajectories in a " semi-infinite" solid subjected to a r concentrated load on its boundary. Consider the concrete cube in Fig. 1.4 with concentrated colinear - tensile forces applied at both ends of a central steel bar fully bonded to the concrete. The distance from the loaded boundary at which there 4 7,, .a ,s-, ..m

1.5 will be a surf ace crack depends on the dispersion ' rate of the stresses within the cube. From this idealization, the important rariable determining crackLspacing is seen to be the concrete cover,' c. Thus,. Ein evaluating experimental' data, the basic equation may be set up as (3) Ec "'" "' a = constant to -be determined experimentally Another approach to the interpretation of crack-interval observations is illustrated in Fig. 1.5. Figure 1.5a describes idealized conditions immediately before cracking. Bond between steel and concrete transfers the tensile-force at a-varying i rate from the reinforcing bar to the concrete. At a point where the-tensile strength of the concrete section is exceeded, the crack occurs. For the hypothetical example considered, this point has been selected to be at the middle of the prism length. Figure l'5b shows ideally the stress conditions after development'of the first crack. According to the assumrtions made, development of other cracks depends on whether bond is sufficient to transfer the force necessary to crack the section in approximately half the length available for transfer. For a number, m, of bars of equal diameter, d, c nditions leading b to cracking according to this hypothesis may be expressed symbolically-as shown below. Tensile force transferred to concrete by bond over a length t = c tensile force necessary to crack concrete section. . ~. -

1.6-m'n d 'i [ u dx =,A f-(4)' b .:(t = /2) c

where

-m = number of bars r d = bar diameter b u = bond stress - A = area of concrete-section - f = tensile strength of_ concrete. Introducing the definition of reinforcement ratio as mnd b p= 4A c and assuming that bond stress is uniformly distributed along the length of the bar, 4 d f b t t (5) c p 2u Assuming further that f and u vary similarly with concrete strength, the following equation may be used to evaluate observation of t : d3 (6) t' =8 c p i 4 d s -m-->- ,r-g s--,, z,w----w o.-,wm ,w,, .m w s

. l. 7 Recognizing that the experimental constants a and 8 are dominant and that _both mechanisms described may aff ect the physical phenomenon,. Eq. 3.and 6 may be combined - A~ (7) t=ae+B c _p with the understanding that a and 8 are evaluated-for the. combined form. -Application of Predictor Expressions for Crack Width - To demonstrate the physical significance of _ predictor expressions for crack width, it is instructive to apply, them to a case for which crack-- width data are available. Crack widths measured in the central constant-flexure span of a - girder (G141) measuring 14.75

28-in. deep in section and spanning _30 ft' were reported in Reference 1.1 The dimensions of the girder which was reinforced in tension with three Grade l60 No. 14 bars are shown in Fig. 1.6.

Side cover for the reinforcement was 2-1/4 in. Measured crack width distributions at various steel stresses f rom 10: to 42 ksi are illustrated in Fig.1.7.. Widths shown are those measured at-the level'of the reinforcement.on the sides of girder G141. It is to be noted that the number of cracks increased with steel stress as did the difference between minimum and maximum values..These are typical characteristics of crack-width distributions. They emphasize that a reference to or prediction of a crack width for a _ given structural element should never be' treated as, say, a beam-depth measurement but always as an index to a distribution of measurements.

o 1.8: The arrows':in the~ figure indicate magnitudes'of the sum (mean, plusltwo standard deviations). It is seen that this sum agreed-quite: consistently with the maximum width measured at ' each. stress - level. A predictor expression based on~the approach described'by Eq. 3 is the one used in Reference 1.1. It is reproduced below as Eq. 8. - c_f-s (_ 8) w = r-5 . reference crack width,' defined as the sum of the mean w = - crack width plus two standard deviations -(effectively the maximum crack width), in 0.001 in. c = concrete cover in in, f steel stress in ksi = s i . Applying it to girder G141 with f, = 14.0 ksi and c = 2.25 in... e ~ (2.25

31)/5 = 14
10

-in. w = r The European Concrete Committee (1.2) uses a predictor equation based ~ on Eq. 7. It is reproduced below in its original units. 16 d -7 (1.5 e + b) f

10 (9) w =

s m p, maximum crack width, in cm w = c = concrete cover in cm bar diameter in cm d = b s e,. -.,.

1. 9 -

~ p, percentage of reinforcement in the " tributary" area (area-of concrete having its centroid ' coinciding'with the centroid of the steel area)- f, = steel. stress in newtons /cm Using Eq. 9 for G141, it is first necessary to evaluate p ~ i" e percent: , = [(3

2.25)/(6.2 *.14.75)]
100 p

= 7.4% t Substituting the relevant data in'Eq. 9 for f = 31 ksi - 21000 N/cm, 1: = 2.54

2.25 = 5.7 cm-d = 4.3 cm b

w = [(1.5

5.7) + (16
4.3/714)]
21000 m

= 0.038 cm = 15'* 10~ in. Equations 8 and 9, - based on dif ferent behavioral' models give comparable - c results for-the case considered. Considering that the two predictor expressions have been. calibrated to approximately similar populations of data, it is not surprising that they lead to similar estimates of crack width. It is also noteworthy that both overestimate the measured crack width. There are two main reasons for the overestimate. Both expressions

O. _O 1.10 were calibrated to ignore the variation of steel strain between cracks.- (Steel strain is assumed to be constant even though it. reaches a lower value between cracks.) Expressions derived for general application tend to be conservative even in relation to the observed' extremes and are-likely to overestimate crack' widths by varying margins in'most cases. The important feature of these predictor expressions is that, despite their differences, they emphasize that the quantitative relationship between maximum crack width and steel stress'is not constant and that it depends on other variables. t l

A 1.11 REFERENCES 1.1.: M. A.1Sozen;and W. L. Gamble, " Strength and. Cracking Characteristics .of Beams.with No. 14 and No. 18: Bars," ACI' Journal,;. December-1969, ^ pp. 949-956. 1 1.2. Comite Europeen-du Beton, " International' Recommendations for.the ~ Design and' Construction o'1 Concrete. Structures," Information - ~ ~ Bulletin No. 72,' June 1970, p. ' 46. {. i I h k i. L li t. I' i f ;. t i-i r .e p. .= :,..,i,.. + =,., +, .a..... ..,,,.---,,.,, ~.. -. - --,.--a.-n-,-

i P Q l (b) ~ s-- -R A B PI O \\ Sf R \\ Insulated ) f nsulated i \\ i l f_ (0) I i 1 \\ jl \\ / \\ I / L o-c Fig.l.1 Idealized Representation of Volume Change in Concrete

l l I l l I l l l l d Unit Stress l Change of Strength With -Time / / Crack Occurs / / / / ^ / / / j Local Tensile Stress / / / / $/ # Time Fig.1.2 Variation of Concrete Strength and Internal Tensile Stress with Time 4

A -. 4 s 9 0 8 i 9

3 t

I i, ~ y T? g ' .Y, N y it .i. '*y, 4 k .s A, / 6 4 T t h J ' 4 e ,e g i 4 A g %. 3 t A s. 5 9 s l' E \\ rn 1 .g b e e k \\ l \\ ei .j m_,, ..=. - Uu i w r, 5 o y T W y ) W O ,) M g y \\e w Ci s-m a k i i ~: w k ~_3-- y e } ^ f [. 5-q a h ' f,I Ni t 't 3 4 o '4 ( s 9 W ~h5 0 '4 c 4 h it N s I + k g b ' 4 3 g \\ e 4 [ l L I \\,

I i i ,It e C C t a I b 4 e rcn t o C n i se ir o tc e j a r T s s e r i t S 4 1 g iF i / 4 1 I:!I a4:1, \\.4k ,;al, !!4l' ,i'i i(,;J i: i : t 5 1

1

O P Tensile Strength of Concrete Concrete Stress i Steel N N Stress (a) ____.____J ~ ~ (Tensile Strength of Concrete l l Concrete Stress / / Steel N N Stress (b) Fig.1.5 Tensile Stress Distributions l' 1

O P P No.5 Stirrups at 6"(15.2 cm) o I I,,I I l I I I ......,,,,i 111I .....IIl11I I I IIIII I Il lII IIii IIIllIIlll1Il1IIeieIeiIiillIIIl iIll1 11III Ii1i liIII t IIIII e i_1 1 I l l t IIi Iel ll ti ie M Ill t N 1-d l 9' (274.3 cm) 12' (365.8 cm) 9' l (30.5 cm) Stroin Measurement Levels (2.5 cm) I" ' (7.6 cm) 3" e e (IO.2 c m) 4" 1 e e. 28.0" ( l.1 cm) G l4I l @-+ No.14 S -@ ' 3.1,,(7.9 cm) h*

h-~3. l"

_ ge_.,, .g _. 4 3 -- m Crock Measurement W Locations - 14.75" M (37.5 cm) i Fig.l.6 Test Girder G141

O 8 10-c Steel t Stress 5- [ F " * e m 42 ksi 0 1 5 10 15 { IO-2 5-c E m 31ksi o s 1 5 10 15 E 5 f 10 - 2 5-21 ksi O 1 5 10 15 10 - ( Mean + 2 Std. Dev.) 5-7 10 ksi 0 1 5 10 15 Crack Width x 1000, in. 1 Fig.1.7 Measured Crack-Uldth Distribution in Girder G141 at Reinforcement Level

ATTACHMENT 2 EFFECT OF EXISTING CRACKS ON STRENGTH OF REINFORCED CONCRETE MEMBERS Summary Do' existing cracks affect _the strength of a reinforced concrete structure? Attachment 2 was prepared to provide information in answer. to this question. Referring specifically to the size and type of cracks in_the Diesel Generator Building, the concern is whether such cracks would reduce'the strength of the structure below the level of nominal strength assumed in design methods. Examples of basic internal-resistance mechanisms are considered i individually. Cracking.in surrounding concrete certainly does not affect the strength of the reinforcement in tension. Test:results from Richart-and Brown (2.1) and Vecchio (2.4) are invoked to demonstrate that strengths in compression and shear are also insensitive to existing-cracks. Bending resistance may be considered'as being made up of flanges- ~ working in essentially axial compression and tension. Evidence-from the Richart and Brown.(2.1) tests would suffice to conclude that flexural strength would be insensitive to existing cracks. Behavior of a beam subjected.co cyclic loading (2.2).is shown to be consistent'with this conclusion. . Cyclic loading data from a test of a box-like specimen with walls similar to the Diesel Cencrator Building are also discussed with the same V a e w g. m- ~ w g w - ~,

w

2. 2 conclusion: existing cracks of the. type observed in the Diesel Generator Building would not reduce the strength of the building below that assumed in its original design.

It is concluded that overwhelming evidence exists from laboratory experiments and experience with actual buildings to demonstrate that "precracks" of the type considered do not affect significantly-the strength of a concrete structure which has been properly' reinforced for the design load combinations. Introduction P.einforced concrete structures are often cracked before application of a load for which the structure has been proportioned. This note has. been prepared to discuss the influence of such "precracks" on structural strength and behavior.' Widths of cracks envisioned are assumed to be typically less than one quarter of an inch and never of a size that can lead to instability of a compressed reinforcing bar crossing the crack. Initially strength of precracked reinforced concrete members subjected to four simple loading conditions are considered: (1) axial tension, (2) axial compression, (3) bending, and (4) shear. Discuasions of behavior I under these four " pure" loading conditions are followed by a description 'of the behavior of a box-like reinforced concrete specimen subjected to cyclic lateral loading. Axial Tension The condition of axial tension is considered not because it requires l ' discussion but because it represents a fundamental case of loading and

2. 3

- because' it helps illustrate directly the basic premise of design in - reinforced concrete. j. A hypothetical case of a single reinforcing bar embedded along the longitudinal axis-of a prism of concrete is considered in Fig. 2.1. Application of an axial tension on the bar will eventually cause cracking of the concrete at-a numbe'r of s etions as shown. The basic premise of design in_ reinforced concrete is that all normal tensile forces are resisted entirely by reinforcement.- If the element in Fig. 2.1 had been designed to carry a certain axial tensile force, all the force would have been assigned to the reinforcement. Consequently, whether these cracks form as the tensile force is applied or whether they had occurred earlier as a resultLof volhme-change or stress effects is of no consequence to the proper functioning of this structural element. Cracking of the concrete would affect only the_ initial slope of the force-extension relationship. ' Axial Compression ~ It is of interest to cer.6;?ar the strength of the same prism (with existing cracks) subjected to axial compression as shown ideally

in Fig. 2.2.-

The prism is assumed _to be loaded axially through stiff-bearing plates so that the overall deformations in the concrete and the steel are the same. i Given that the existing cracks are not.so wide as to lead to local instability;of the bars or overall instability of the entire element, it can be inferred from a knowledge of the stress-strain properties of

2. 4 the materials involved'that-the. reinforcement at.the cracks will i

eventually:be strained sufficiently to close the cracks. After that event, Llarge compressive stresses will be developed:in the concrete leading-typically to failure initiated by spalling of the' concrete.. Whether this " reseating"' process affects the strength of the concrete or of the reinforced concrete section can best be determined by experiment.. Several-series of tests of reinforced concrete' columns were reported by Richart and Brown'(2.1) in the course of an experimental study which-was to. lead to the fundamental principles of reinforced concrete column. design used today. One of these series, Series 3, was dedicated to the investigation of the effect of sustained loading on column strength. A group of.. tied and spirally' reinforced columns, 5 ft'long by 8-in round (Fig. 2.3), were subjected to a sustained service load for approximately one year. A parallel group of columns were stored for the same periodf without any load. Changes in. steel stress, calculated from measured strains, observed for the loade'd and unloaded columas are illustrated in Fig. 2.4. 'The accumulated strain at the end of the observation period was approximately 0.008 in the loaded columns. "because of the arrangement of the time-loading rigs,.it was-necessary to release the loads'and to remove the columns from the rigs before placing them in the testing machine. This 1 release of load permitted a recovery of the large elastic strains in the steel and resulted in the formation of tension . cracks in the concrete, generally 10 to.12 in. apart. The. columns were tested at once, and strain measurements showed that when the applied load.had-reached the value of the one-year sustained load,.the cracks had closed, and the steel and concrete strains corresponded closely with those measured under'the spring. [ previous. sustained] loading."

2.5 Richart and Brown did not report crack widths. The widths may be inferred to be approximately 0.01 in. from.the strains indicated in Fig. 2.4 and the reported crack spacing. No cracks were observed in the columns without load. Measured strengths of the columns with and without sustained loading are compared ~in Table 2.1 reproduced directly from Reference 2.1. The last column in the table indicates the ratios of the observed strengths t of columns with sustained load (which'had cracks) P t the observed-T strengths of comparable columns which had not been previously loaded-(and which'did not have cracks) Pf. The ratio is observed to vary from 0.86 to 1.15 with an overall mean value of 1.0 with a coefficient of-variation of 6.2 percent. Richart and Brown concluded"that, against the-background of expected scatter in such test data, there was no significant difference between the strengths of the.two groups of columns. Bending A simple and practical model to understand the flexural strength mechanism of a reinforced concrete section is provided by analogy-to a structural steel wide-flange section with a thin web.. Resisting moment is generated by a couple formed by tensile and compressive forces in the " flanges" of the section as shonn~ schematically'in Fig. 2.5. The tensile force is provided by the steel and the compressive force by a concrete-steel-composite, quite similar to the idealized element in Fig. 2.2. From this interpretation'of the ficxural-strength mechanism and the information supplied above, it follows that existence of cracks perpendicular to the bars, whatever the cause, would not reduce the flexural strength of the section.-

2.6 The same conclusion may be reached by recognizing that the flexural strength of reinforced concrete sections. reinforced in tension only with typical amounts of reinforcement is_ insensitive to changes in concrete strength. -Influence of the concrete strength on flexural capacity is even less if the section has compression reinforcement. Thus, any-reduction in compressive strength because of local spalling during the reseating of the crack is likely to have negligible effect on flexural strength. A common experimental demonstration of the trends discussed above is provided by response of reinforced concrete beams to load reversals. Consider the measured relationship between force and mid-span deflection of a test beam reported in Reference 2.2. The first loading to over 10 kips would cause a pattern of cracks as shown ideally in Fig. 2.7d. Return to zero load would leave a " residual" crack pattern as shown in Fig. 2.7e. Clearly.the concrete to work in compression when the load ' is increased in the opposite direction is cracked at zero load. Jut it is seen in-Fig. 2.6 that the cracks do not prevent the beam from developing its strength in the opposite direction.

Shear, Vecchio (2.4) reported a series of 30 tescs to investigate the force-deformation properties of reinforced concrete laminac subjected to h-plane forces. The results of this investigation permit a comparison of the strength of reinforced concrete laminae which have been cracked

. 2. 7 before shear loading with.the strengths of laminae which had no visible cracks before loading. (The term " lamina" is used here for a slab to-avoid association with " slab shear strength" which' refers typically to out-of-plane forces.) To approximate the conditions'of a " pure" shear loading, Vecchio used the mechanism shown in Fig.'2.8 to apply reasonably uniform shear forces along the edges ~of a reinforced concrete lamina (Fig. 2.9). measuring 35

35
2-3/A in.

Reinforcement was provided by.two layers of annealed welded wire fabric mats. Twelve specimens, with properties listed in Table 2.2,' failed in shear under'" shear loading" before reinforcement in both directions had yielded. Of this group, only ten with' concrete strength in the. range 2300 to 3100 psi are considered here in order to be able to discuss the results directly, without normalizing.the data to account for changes'in concrete strength.- ~ Measured unit shear strengths of.the specimens loaded'monotonically to failure are plotted using open circles against the product p :f in Fig. 2.10. '(The term p -refers to the lower of the reinforcement ratios in the two orthogonal directions.) One specimen,LPV 26, was-cracked.in biaxial tension before loading in shear. The cracks were'obtained by applying forces equal to 60-percent of the calculated yield' stress of the reinforcement simultaneou'ly s in each direction (of the reinforcement paralle1~to the edges of-the specimen).. Shear forces were applied after release of the tensile forces. As represented in Fig. 2.10 by a. solid circle,7 this specimen developed-a strength comparable to that of the monotonically loaded specimens.

f

2. 8 -

Another specimen, PV_30, was also; initially cracked in biaxial tension in the same manner as PV 26 was cracked. However, PV 30 was increased in 100-psi increments starting from 125 psi. At each stress level, the stress was. cycled ten times.' The maximum shear stress developed by PV 30 is also shown by a solid circle in Fig. 2.10. It is: evident that the strength of PV 30 was not perceptibly affected by existence of initial cracks and by the stress reversals. The observed results can be anticipated har interpreting the response of the lamina in terms of the simple " truss mechanism" illustrated in. Fig.-2.11. The diagonal truss elements operate in a manner similar to the tension and compression elements shown in Fig. 2.1 and 2.2. The stiffness of the lamina would be expected to decrease because of cracks existing before load application, and it does. But given that the "precracks" do not affect strength in cases illustrated in Fig. 2.1 and-2.2, it follows that precracks would not change strength'significantly in the case of a lamina subjected to shear forces. Behavior Under Cyclic Loading of a Reinforced Concrete " Box" The observed behavior of a stubby box-like reinforced concrete structure subjected to lateral-load reversals at the structural engineer-ing laboratory of the University of Tokyo (2.5) is of interest for two reasons: (a) the specimen is a low-rise (stubby) reinforced concrete -box with uniformly reinforced walls similar to the Diesel Generator Building and (b) the loading conditions in its walls combine the types ~ of loadings considered individually in the preceding sections.

m ..~ _ pr y 5-2.9- . Plansand elevation of the specimen. considered -_(B6) fisi shown fin-e h Fig.L2.12'which al'so_ describes =the test rig. ' Plan dimensions, nut-to-out-of walls, of the specimen were 0.83

0.83~m (approx. 2.7-ft).

Wall ~ Lthickness was 0.08 m (approx. 3 in.). Lateral-loads were' applied!at.a

level;0.8 m (approx.=2.6'ft) above the top-of the. base slab.-

l Concrete strength was'reportedito be;256lkg/cm -(3600 ps'i) at time-of' test., As shown in Fig.l2.13 walls were reinforced with 6-mm' bars-(correspondingLapprox. to No. 2 bars). Vertical and h'orizontal bars = were. spaced at'13.2icm,:except.ne'ar the corners, resulting in a reinforce-ment ratio of.0.5 percent in the wall. sections away from the corners. Yield stress of.the reinforcement was 3910lkg/cm (561ksi).. i Umemura, et a1., calculated the maximum valuelof she. applied lateral-load to.be 34.3 tons (75.7 kips)' corresponding to.the development;of: E f the calculated flexural capacity. 1The curve identified by.the legend l1 "e-function method"'shows the. calculated response of the specimen for a monotonically' increasing lateral load. The lateral load.was applied alternately ~in opposite directions:using ~ the arrangement _of hydraulic jacks shown-in Fig. 2.12. 'The loading-I Ihistory'is documented.in Fig. 2.14. ~ Specimen B6 was loaded initially to 30ltons (66 kips).. The load 'was then reduced-to.zero.;-At-'that time"the walls. parallel.tolthe;. axes } of the Jacks would'have been cracked as shown ideally by;the sketch in t s cheffigure.- 'The specimen:may then be considered:as one.having,"precracks" because-the existing cracks were caused by a loading direction radica11yL [ different from.the-one it'"is to: sustain.-'Asjthe load is applied,in the' f 4 4 '= I e-- y, m+ r.s -.4.-+. ,y- ,.-g .w nes wr i fn - 4y,,4. q- + m .w--vg--*--+- ey M. -e.g.< g -a-3-mr-w- -a.4ep-i wr wg gwp sw,+g .m ggy a rm - yemy g p. ,%rp .ee l

2.10 . reverse direction (negative' values of load in Fig. 2.14), compressive stresses act on the crack planes while tensile stresses develop' parallel-to the crack planes. But the strength-of the' specimen is'not reduced. This observation can be rationalized on the-basis of the loading conditions. described earlier. Flexural strength is devsloped primarily by forces on the " flange" walls which are subjected essentially to alternating axial and tensile forces. It was discussed that there should be no critical decay'in axial compressive strength of the flange walls under the loading conditions considered. It can also be inferred'from Vecchic's test results (2.4) that the " web" walls carrying the shear would not be affected critically by'the existence of "precracks" at the beginning of loading in each direction in each cycle. Final states of cracks in the-web and flange walls are illustrated in Fig. 2.~1'5.- Concluding Discussion Internal resistance mechanisms in reinforced concrete members may be described by combinations of three simple conditions: axial compression,. -axial tension,.and shear..In fact, the last condition has to be treated independently only because the principal stress directions corresponding to the shaar stress are not usually colinear.with the directions of reinforcement. It has been shown, by-example where necessary, that existing cracks do not affect significantly the strength in tension, compression, and shear of properly reinforced concrete-elements.

2.11 O'erwh~elming. evidence:from the field and.from the laboratory-v ~ indicates that reinforced concrete structures will develop'their design strength even if they--do have."precracks", provided-the structure has ~ been proportioned and. detailed.to resist the design'-load combinations.~ a. The exa'mples discussed rationalize the experience. i t A I 6 i-i q '. l. L n l I, f 's i 4 1 I-y' 'W J -,. ,. 4., ..-.,.,_.,...u . - -. ~..

2.12 REFERENCES 2.1 F. E. Richart and R. L. Brown, "An Investigation of Reinforced Concrete Columns," Bulletin No. 267, University of Illinois ~ Engineering' Experiment Station, June 1934, pp. 48-54.. 2.2 J. A. Blume,'N. M. Newmark, and L. H.-Corning, " Design.of Multi ~ ' Story Reinforced Concrete Buildings for Earthquake Motions," Portland Cement Association, Skokie, 1961,'p. 130. 2.3 M. A. Sozen, " Hysteresis in Structural Elements," Applied'Hechanics in Earthquake Engineering, ASME Proc. of Winter Annual-Meeting, 1974, pp. 63-98. 2.4. F. Vecchio, "The Response of Reinforced Concrete to In-Plane Shear and Normal Stresses," Ph.D. Thesis submitted to the School of Graduate Studies, University of Toronto, December 1981, 332 pp. 2.5 It. Umemura,.H. Aoyama, and H.' Noguchi, " Experimental Studies on Concrete Members," Faculty of Eng., Dept. of Architecture, University of Tokyo, December 1977, pp. 32-48. 4 f w- -^ -e ~ w-' y y ..y

TABLE 2.1 (Reproduced from Reference 2.1) Srnr.xors or Cor.vuxe or ficates 3 ArTra Oss Yara Unosa Scaratsso LOADINO E.ch value represents the test roaults frote two colemas. Columa section. fio.2 forasural e Aumns. 33.4 for taed entumna. Nominal Denisa OJumna After Ona Year Columna After One Year Under eustained t =hns I;nder.No Loadans l'ercentase of Retaforce. - ("Itimate Imd. Pr t*1timate toed. P, hatio le. mens !b.per Ps/Pr Ib. per Ih. per a Ih-Ib. Vertical l Spiaal aq. in. y,,,, f.ananavont Arm Sir,ason 2000 1.3 2 23J OINI fiOIS 244 Thi 4 MS O'97 4 0 237 4858 4463 243 Edne 4 2dia 1.04 4 2 333 Men 6*M 345 700 6 440 0.98 6 2 33:1 250 7030 335 714 7 073 1.01 3.10 0 1.3 0 225 eino 4220 4 0 382 ;de teus 3n0 man 5 SM 0.99 4 2 40.3 lean mi.M 393 uns 7 MO 0.94 6 0 364 ENN) "AHat 6 1.2 364 300 7323 7410 0 1.3 2 3m3 200 7643 394 ann) 7 A40 3,0g 4 0 360 7tM 6915 413 eno - 7 763 1.12 4 2 Tde 'JM tPs74) 4s3 rem 9 neto 0.97 6 2-499 700 9940 id83 Ic0 10 Otto 1.01 Averese l 1.01 .\\torst !+mmust 2000 4 0 222 (kul 4 t *4

19) feu) 3 370 0.h4 4

1.2 277 utM 3383 zum.*su 3 340 0.W7 4 2 321 Jte AJUO J31 tan 6 480 1.01 350ll 4 0 261 7t H 4s93 302 OU 3 eat t.13 4 1.2 3;ll Inse n643 327 tan G ssa 0.99 4 2 394 SVG 7 0-40 .TJ6 Idm 7 MM 0.99 fou0 4 0 331 TA) 6373 .sta tant 3 N05 0.10 4 1.2 4.14 ens Com3 4 t's tan M 313 ' o 97 4 3 4m:l ust 9610 4s2 Jtes 9 393 4.us - Ayersse j

0. W'l Grand Average Value of Itatio Pg/Pr ! 1 'O

" + t

10 -

TABLE 2.2 Properties and Test Results of. Laminae 'tubjected to Shear and. l Failing before Yielding of Longitudinal Reinforcement. -Reinforcement Long. Transv.- Shear Stress

l
t

'u g_ g Mark psi y y psi PV 9 1680 1.79 66.0 1.791 -66.0 542 PV 10 2100 - 1.79 40.0-1.79 40.0 575 PV 12 2320 1.79 ~ 68.0 .45' 39.0- '454' ~ PV 13 2640 1.79 36.0 0 0 292 PV 18 2830 1.79 62.5- .32 59.7 440 PV 19 2760 1.79 66.4 .71 43.4 573 PV 20 2840 - 1.-79 66.7 .89 43.1 617-PV 21 2830 1.79 66.4 1.30 - 43.8-729 PV 22 2840 1.'79 66.4 1.52 60.9 880 PV 26 3090.' 1.79 66.1 1.01 - 67.1 784 PV 27 2970 1.79 64.1. 1.79-64.1 920-PV 30 2770 1,79 63.3 1.01 - 68.4 '744 Note: Data from Reference 2.4 ? e-r g e - - ^ t 4 9--+ 9 9 -r,- -wy e r-S- g w ty-- e

I n +- I 2.1 Reinforced Concrete Element Resisting Axial Tension Very Stiff Bearing Plate j,' p

G___,

e -e ]r., ( 2.2 Reinforced Concrete-Element Resisting Axial Compression Dam /s Ei:~d.C' sh, a - wHb Cmen&,e y ~s m e 4,-tg

J

4 y k54 ..tG I b, if $ h 9 D l*l %D . I' 333 f i9 Lp.2;? pd]% -dq o s, ~. gV Tyces 3ed 4 2.3 Reinforced Concrete Column Tested by Richart and Biown (2.1)

e e RM i 4 i /, N Lorry RedA$% / 'dN [ )[#- 's v. .Q \\ snss n Carew. 4 9 9' "n" \\ \\n 9 \\\\ 1, /,, st six sna, a swi. c s no gi u% y\\s%(64 LW,hikM Q LW W6 IS%) Q st M b XNebJ [ / ?h s&4 f i 4 f y ~ 25 ,4 4 .n u N 3SAMb C.aocrate f Mrth,7f M !S 4 t::gmt gemfaremnt-4 -f Ar sempe F I $x 'o tw sw 4x

o too ex 300 Time Under Susfahrd Lxd h Days Reassinian Tins or Star _wra xx Coxcners AND STEEt, Deutso Mrsrusto Lusoixa 2.4. Stress Redistribution in Columns (Richart and Brown, 2.1)

1 Y Concrete Stress 4 O O = ~ +-- Cracks Closed ) / / Forces in Steel / / / / --_f-- / o o = -m ___u-.- Section St rain Stress Equivalent Couple 2.5 Idealized Mechanism for Flexural Strength

'- e e A,af58som .j s u ,- K A', el S8 so.n ? l ~.$ e i fi 83,000 psi IS e f, a 44,000 ps A ~* ' "1 8 f' =48.700 pse j i 0 i b I i Defl,eclKm,*n., l 4 i 9 8 7 6 5 4 3 2 6 8 2 3 4 5 6 7 8 9 I / S 40 I PM I/ i' .S l l-v! f@. !V S'.6* S' 6" Meesored Wee < Wen releWeasMps for e besen-eelusna conneeWen settested to reversels of lead. l l 2.6 Load-Displacement Hysteresis (Blume, et al., 2.2) I i l L

o ' Contilever Loaded At End -gEnd Of Cycle I f nd Of Cycle 2 E j N i. A Max. Deflection % gg, Deflection Progrom (c)

// / '

o

Force d

k ke / E H e'A ' Displacement p '/ f r (b) (e) / / (f) 2.7 Cc.icks in Various Stages of a Load Cycle

l e Links Outside flange seassanaan / Jack cocoartment r Stiffeners .m - y. r,,..a.==. e fk '::3 M p / 1.... T.y. y =

=== b ' '.I *..*r 4. - __ Test 5 pet.imen

i. '

~ = I,A . egg = m

==:

a mm= = a m=a e a E wql a. e e e m 4 = = = i:

==

N nside flange I e= =*ll N g uusvassues /Ht//Hi//H/st/H///itHHH/H//Hi/H/tH////H/////// ,, g, control bench 1 .m M u. M .m II.m 14 I .aq Shear key ]'. ' 1]J I I l 1Y.mii;. i A ka:!'ij"!;in:n-i I ..... !: :!Hii:I...., I IU'[I!!nk!!.l!-!'!N!! i musum I y;ijpij ri!!n!

:Eliri ;ui!im ai aa I

!ii lit::n:r : m:: 1 mi:p. h!!IM]99Cimeny S i.....

!!Pli

!!si !Hi! iEii!F I m,,,,3;pai!!!f!' i f; ?!d.ii - p: ipw i b e 2 g m;eze

l.,1 l,I1,3 Links

/ 1 Rigid links

Jack

...w 2.8 Loading Scheme Used by vecchio (2.4) l l 1 1 ,,,__4 ,~. , _.. _. ~.. - -... - _ -,.., _.,, _ _.

Pin Anch:r plata A 'O @- * ' e * *T Transverse steel e- 'cw '. .e 1.'., f,( s,. .g ~ Concrete paneI T. Longitudinal steel \\ \\ Shear key "S t i r rup " F Internal Deta:' for Shear Key o Link .'l/ I / / s 45. / Shear Key / l s/ 45' e' h*\\ Tk \\ ,...l. - F ]\\ [' Link /,/,7

.irf f-N Test Specimen Shear key Specimen " * -

o o !o [X oh x ,\\ Shear key /, y fxXX xg ///g[x* o X x X X x* f /X o\\ !o x[/// x x[x[g // Xpb blN/ $((Z,{[gM4 //g/ [;t / \\ x[ [5[o/ \\

((/

/ X [x X )* \\o /x d, X Transverse ,x x z Longitudinal \\o ^f o/ reinforcing reinforcing o o 2.9 Test Specimen at.d Boundary Loading Details (2.4)

e 1400 l200 E. iOOO 0 PV26 O m 800 t O O PV30 600 o 0 k 8: (D 400 E () 02 200 OO 200 400 600 800 1000 1200 Pt X I, psi y 2.10 Variation of 14easured Shear Strength (2.4)

N / N / / / L / N 1 / \\ /\\ s I / \\ Lamina Equivalent Truss ~ (Reinforcing Bars Are Not Colinear With the " Diagonal" Truss Elements) 2.11 Idealized Mechanism for Resistance Mechanism of a Lamina Subjected to Shear Stress 4 -r i b

' ' ~ ~ ~ ~ ~ ~ 5 --~- Loading Arrangement i .,3.n. 3, s t le l 3 g b.ad reu l li d 4 et, e-rf I \\ .t a i I~ li A i 1 A 3r P

- - =

~ Zs ni u i~ >0 g'[

g I

I =ll l ti L l l \\ s.., I 'a' / ,/~ H-40nar answ 13 x 21 1 I Jo o a o o l'. I I. tj

,j j (ti LE Je"j 9(

Q I i I 9 6 2 Y! fI 7 I >* i I

o. + igj o.

+ l l 9 l al l I il os rom ris em $0 339) (b) 3%* l I

y

,.j g. ..._p _. - +- em -s n. sr' N 2- L4..;. [ 3 ;_ *[ p. y,. ..q I ~

7. 4 11 (.

c, 9

q.,.

e k . 41 i g, s >. t ': p g1-S

b..j l ;..

. -.. b., ? Il [ ~. ' ' ' 1.- \\. ' s.. . h.e t 'I) ' .Q h[ *,j.F-C * ~ ~. yg.. g 4.. ' ; ~; {' 4. - : ". ___3:,..,. . _ -. 5 -.-*3 ... '1 y t e :~-- ..\\ m. ,,a. 3* - F~... ;g'. {... ' L. ; 3,. I p,- ~ . ~. ,,;". e. '~ ' n'.... j }'. ,,_,---.. ~ ' [ ~..?. ' ~ ' _ g j,.,..l. ~ s, I 2.12 Loading Rig for Reinforced Concrete " Box" DG Tested at University of Tokyo (2.5) i ~.--,-_.-._--,,-.-.-~.,.-.-.--.-,.-n---,--------

i Y A s.ee s - s.n nn 21.,%H ~ = 2 o in+m. -t j cross [ t ? {

f

,y -. .m.- _I.! O 0 I 3 \\s I 5 3 s N e 16 i c. I .o b ,[ Ili ';

rr I

i g . l:! 1 i ll' ! I c,L 4 l 1 l y! aw 13 i i r -,1 y I r m l l', u-9l !I l iv ) g___ .r z, e E. l g 3 =\\ - x e e ~- f. n m a.\\ .mi < l# e s 7 i 1 . i o E '-., _--. --p---{ -- 5Am?*jn + + ll l e i 4 i l [. n:,n, w v: . sn tr re va Ya 13 IM

M IM

.,e

s. e 2.13 Dimensions and Reinforcement for Test Structure B6

s

P

(=Q1 i 1 @ shear craeb. i-N \\ //r fedt/dn htlll4//f t//N////g /g /////////g/g gg //fq//// Flesure Crack Fig-2.1 Load-Deflection Curves ~8 3 ~ g K.1 Initial Stiffness f No. B-6 d

7 20 50 P. = 0. 6 %

e n Q,,3 + 38. 2t 40 ~I I -34. 0: 15 /7 .i[ -y [ S* * ' e -Function M ethod s 30 a' /. / /i // F. = 255. 6ks/cm' to I'. !' !. l'

l l '

/j > Skear Crack > Viesure Crack I,/I/I, j' l 'jl . l. ' / i .j/'/ 5 fj',*/, 10 g ,/, (1/100) ( R = l/200) l ,g -8 -4 . 3, _,,9 ,o _ p.; /> 5'7~*" 8 12 16 20 - p (mm) 24 4 (1/100) ~(1/50) / ( R = l/2001 / g/ ,,- 10 d. d. 8,. 8 p -_ s ye ye ,e 3 As . 20 Q

' t 8

[ 5)].4 1. ii a' f : in ./ s w l ~~ 3 i n EI -- 40 w 8e 4 . - 50 d = #'+ #'+ #'+ #* W 4 R = d/4. r= Q/A,. A, : Gross Area i 2.14 Load-Displacement-History for Test Structure B6 t

..i...... B - 6 i d., . ik B-6..' 4 e s-' Ra*375 7..W>*: Ru=375 f. g.G' T'

i v

4. p. ......%u t -g..- %,b .,u. A,.f;', _$ f, 'g~ x;. i g){p;rh.. = > - m-A t -Gr ~. g . ?;:'..Q [f f l , m '-- .-~.--:--..y.-. ~ = _, .vi g, - ~ eP .,. B -6 l v- 's. d a- .q:_ ~ r, w 2.15 Crack Patterns for Test Structure B6 l 1 1.-_..-___._-.._--__.,._.____.___.___.____.____.__.__________.____________________,________,,_,_____

s ATTACHMENT 3 CRACKS IN CONCPITE UALLS Reprint of an article by Ake Holmberg and Sten Lindgren i l I. l I

Cracks in c:ncrete walls Nati nalSwedish Building Research nuna es Ake Holmberg & Sten Lindgren D7:1972 A n earlier inrestigation, " Crack Spacing be unreliable. All the data that were now Key words: and Crack Widths Due to Normal available have been analysed agam. and crack spacing, crack width. concrete c e or Bending Moment"(Document this analysis resulted in a new formula. walls, rigidity, imposed deformations D2t1970), published by the same which is similar in prmciple to that de-authors, has led to fundamental con-duced by Efsen and Krenchel. This new clusions regarding the di.stributiort and formula involves a slightly higher coetii-the width of stable cracks in concrete cient of variation than the previous for-structures. The available data on crack mula in its range. but covers the totality spacings was summarited in a crack of the test results under consideratioti. formula. The present report. however. The new formula was furthermore veri-rejects thisformula and presents a new fled by applying it to extensive results one which takes into account the full obtained by Nany, et al., from tests on range of experimental material avail-two-way slabs. This verification indicat. able, including material contained in ed that the formula in question might this report. The new crackformula has also be applicable to judicious predic-i a wider range of application, covering tion ofcrack widths in such slabs. as it does walls having diferent types The new formula is of reinforcement and also to a certain b',

extent slabs with two-way reinforcement.

s,,, = 0.055 + 0.144 The present investigation was made on the walls shown in FIG. I, which were where 0.2 m in thickness. The u ndisturbed area of observation on each lace of the wall

r. =

the finst (smaliest) mean crack was 1 x 3 m. Apart from a single excep-spacing. in metres, reached at tion, this investigation confirmed the high values of the stress, a,, earlier observations. The walls were m the remforcement r a crack strain ed in the test set-up shown in FIG.2. c the diameter of a reinforcing They were restrained so as to remain bar plane in the cases where the tensile force the diameter of that reinforcing was eccentric. The mean stra n over a i length of 3 m was increased in steps. bar in a group which has the smallest concrete cover, and and was maintained constant at the re-therefore produces a pre-spective values, viz.,0.125 per m 1,0.2 dominant efTect on crack form-per mil,0.35 per mil,0.65 per mil, and

II "

1.25 per mil. The time interval between two consecutive steps was I day. but the A, that maximum po;cion of the Document D7:1972 has been supported last interval was almost 2 days. gross cross. sectional area of the by Grant C 599 from the Swedish As the field of application was extend. concrete whose centre of grav-Council for Building Research to Cen-ed. the previous formula for the calcu-ity coincides with 15at of the. ter16f &.Holmberg. Ltd., Consulting l lation of the crack spacing was found to icinforcement Engineers, Lund, Sweden. l l 4 UDC 69.022:691.32 624.(M4 ! i-yr 69.059.2 t.- m t-o * +- g 3rg A

9..

W - W., .~4+ (21),(22) ISBN 91-540-2027-1 ,~- l L...... m Summary of: I Holmberg, A & Lindgren. S.1972, LA Cracks in concrete walls. (Statens insti-mi.*m m..m

,.

m.

n..m m-

.<. e .= e .at

..

tut (Ur byggnadsforskning) Stockholm. i e 1 Document D7:1972. 70 p., ill. 18 Sw.K r.

=

r-r 3F Sf,.*q 1 3r- - 3M 3C! 19 3 p* ? *

3a 3'l 3

y g.1 t e.[j. * *.'N!! "( !,!y*(.l'; *( lP(* l* .IF, ( v :.- t"* c12' The document is m English with Swed-

te t

l{ r It )a ish and English summanes. I

ta pa

+t-Ipte b b;a.) .j.) .q ,t 5- .m 3: l , d E.,.j df Eaa' 4* E d D ' b! ' 'll!

C i

e a u.i ~a. UE*'"b"'E*"; FIG. I. Walls subjected to the tests, including Walls Nos.11 to 16. which mere usedfor 1 shrinkaer measurements. The gauer points on the concrete un the end surfaces of the lat. Svensk Byggtjinst l ter mulls are marked v. All Jimensions are nominal, Jsmenswns m mnn 323 Ksto. Box l403. S-IlI 84 Stockholm 1 Type Kum sual rubbed bur. 23 mm in Jaumeter, yield stress ofreunforcement ubt 400.sf.V!m*. Smeden l Ssiti Ope Pl,an, round sust bar, ubt 700 st%ry ss.l.1 stras l*s.W a Twr Delurmed stal l bur. be ftN \\tMm'. a:J sur su s

r

'G a craed. e . The final crack width approaches as \\ a limit the crack spacing multiplied r-- 3 by c, = a/E,, trhere E, b the modu-g $ lus of elasticity of the reirforcement. O O l This statement holds good even if the. I action has not led to the final crack J

/

~ spacing. The variation in the crack g i---- -% width m a vertical direction, at right 'e --- - *~4 u angles to the reinforcement, is consid. ered to be a short-time effect. The coemcient of variation in s,,,,, is 0.2, and hence a reasonab'c maximum value is I A times the calculated value of 8,.. g 2. ~ The maximum crack width m. walls. etc., which are sufliciently long to N-__-_.__.___.____________._.D- [ contain the crack havmg a maximum e width is about 1.7 times the calculat-ed value of the crack width, and, for the magnification factor 1.7. the coer. ficient of variation is about 0.25. If a wall is teinforced at one face FIG. 2. Machine usedfor the tension tests on the walls, with controlled elongation. only, and if A, is smaller than the total cross-sectional area of the wall, then the crack formation on the face that is adjacent to the reinforcement 38 g il;;;; 4 ~ will be in accordance with the above-l;llt: i ii: l mentioned formula. On the other s hand, if the eccentricity of the reinforce. -5 . 'l N s I, mer t is great, then the crack devel-i w opment on the opposite face of the !8 '8 4 )18 M'-

il 8 5 wall may be considered to be entirely i

uncontrolled. With a slight exaggera-4 4 4 4 4 4 4 4 4 k4 4 tion, such a wall may be regarded as a reinforced wall that is contiguous to 7 . I 7 7 a non-reinforced wall, see FIG. 3. t i ' 'i7' ' una > The formula for the calculation of the M_i 3 PS) I te "*i r3

rat n ' l ' @ tat I 7~

crack spacing and, the above state- -N,' . g g.,j3,7 y s,,,,,g, M'

[ } j A ;,6 i-i ment involve by implication certain v

practical recommendations for des:gn. i ' Wy 8P( % 18 The rigidity of the wa!! varies in - m-Jo ^ W,ai L.& 4 4/ t 1ep i r ,o such a way that it und rgoes abrupt

,, L4 i 4 4 e, L4 4 4 4 changes within extreme limits which are determined by the uncracked con.

FIG. 3. Cracks in wall after completion of test. crete and by the bare reinforcement in the crack, respectively. The present 4 investigation alTords a basis for esti. mating the actual limits of the rigidity K a at a defined stress. I FIG. 4 shows in terms of numerical 3 values the decrease in the rigidity with increase in the mean strain, c.,, 9.aoas expressed by the factor x, in the re-2 l lation l i i 9= 0015 a, = E,c,,,x, A% i~ i f where O / EE z a, the stress in the reinforcement s m in a crack, So l E' the modulus of elasticity of the reinforcement, FIG. 4. Refution between n, and E,c,Ja, Extunic values at in = O M and a015, t.,,, the mean strain of the wall, deep beam, slab,etc., respectielA a, the stress in the reinforcement at the instant of appearance of j the first crack. l As may be seen from FIG. 4, the elTect of the ratio of remforcement, p. t l on the rigidity is slight. On the other hand, the efTect of the tensile strength of the concrete. which is in itself dim-I cult to determine and liabic to vaty, is by no means slight. If a system is highly statically indeterminate. then the design problem is to a certain ex. tent,, transferred from stataes to stausues.

ATTACHMENT 4 EVALUATION-OF CRACKING IN DIESEL GENERATOR _ BUILDING AT MIDLAND PLANT 4 i l construction technology laboratories.

TABLE OF CONTENTS Page INTRODUCTION ~. 4.1 - DESCRIPTION OF STRUCTURE 4.1 EVALUATION OF CRACKING. 4.11 Bechtel Crack Mapping. 4.14 CTL Observations. 4.27 RECOMMENDED PROGRAM FOR MONITORING STRUCTURAL INTEGRITY 4.30 Displacement Monitocing 4.30 Crack Monitoring. 4.33

SUMMARY

AND CONCLUSIONS 4.34 I ~5~ construction technology laboratnries ~

ATTACHMENT 4 EVALUATION OF CRACKING IN DIESEL GENERATOR BUILDING' AT MIDLAND PLANT-by -W. G. Corley and A. E. Fiorato* INTRODUCTION This report presents an evaluation of the significance of cracks observed in the Diesel Generator Building located at Midland Nuclear Power. Plant Units 1 and 2. Observed cracks in this structure are described. A program for future monitoring of structural integrity is described. I DESCRIPTION OF STRUCTURE A site plan for the Midland Nuclear Power Plant is shown in Fig. 4.1. The Diesel Generator Building is located 'directly t south of the Turbine Building. The building is a two-story I reinforced concrete structure. It is partitioned into four bays by load-bearing reinforced concrete walls. Elevations, plans, and sections of the Diesel Generator Building are shown in Figs. 4 2 and 4.3. Diesel: generators housed in the building are used to provide power to attain safe shutdown of the plant in case of a design

Respectively, Divisional Director, Engineering Development Division, and Eirector, Construction Methods Department, Construction Technology Laboratories, A Division 'of the Portland' Cement Association, 5420 Old Orchard Road, Skokie, Illinois 60077.
~

construction technology laboratories e ... ~...

i 1 l 1 l l %%_ - TITTABAWASSEE RIVER - l I COM ATION N EVAP AND ^ M AUX BOILER -.- (f l BLDG BORATED WATER COOUNG TOWER j TANK \\ V O l SOUD RADWASTEg j AUX BLDG O i REACTOR BLDG REACTOR BLDG l y UNIT 1 -b O UNIT 2 SERVICE WATER - i CONTROLTOWER SE V DG TURBINE BLDG PilMP STRUCTURE ) DIESEL GENERATOR

l l

DLDG ~,' N IRCULATING WATER O INTAKE STRUCTURE j OE 's K s \\g EMERGENCY COOUNG \\ j [} } \\ WATER RESERVOIR \\ i AFFLE DIKE 's _ _ _ p- _ / emu COOUNG POND j l FIG. 4.1 SITE PLAN I 1 I

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i i l basis accident, and to operate the plant in case of power outages. Because of its safety-related functions, the Diesel Generator Building is designed as a Seismic Category 1 atruc-ture. As such, it must maintain its structural integrity i during and after a design bacis accident, including a postu-lated safe shutdown earthquake. As shown in the elevations in Fig.-4.2, overall length of the Diesel Generator Building is 155 ft. Overall width, excluding external enclosures, is 75 ft-4 in. The basic layout of walls in the Diesel Generator Building is shown in Fig. 4.4. Table 4.1 contains details of selected walls designated in Fig. 4.4. Exterior walls of the structure running in the north-south and east-west directions are 2.5 f t thick. Primary vertical and horizontal reinforcement in these walls is No. 8 bars at 12 in. on centers at each face. Interior walls of the structure run in the north-south direction and are 1.5 ft thick. These walls contain No. 7 bars at 12 in. on center, each direction at each face. Specified concrete strength for walls of the Diesel Gener-ator Building is 4000 psi. Grade 60 reinforcement is used in the walls. Table 4.2 contains a listing of Bechtel drawings that were used to obtain data on member dimensions, and on amounts and arrangement of reinforcement. The Diesel Generator Building was founded on plant fill and constructed between the summer of 1977 and the spring of 1979. It has been reported that settlement of the Diesel Generator ~4.5-construction techisology laboratories

-9*t-WEST 8 m i r c. WEST-CENTER - o r. mmm H e S U - m M A aR$_ CENTER zo to C x 5 -4 y ~. 1 x n . p. U - 4 . :g H-H Om. 5 -EAST-CENTER e Dg. P-O U . m EAST Z 1 y

c . TABLE 4.1 - DETAILS OF SELECTED WALLS IN, DIESEL GENEPATOR BUILDING Wall Primary Primary Wall Thickness, Vertical ' Horizontal Description ft. Reinforcement

Reinforcement
North Wall 2.5 No. 8 6 12" No. 8 9 12" South Wall **

2.5 No. 8 @ 12" No. 8 @ 12" West Wall 2.5 No. 8 @-12" No. 8 6 12" West Center Wall 1.5 No. 7 @ 12" No. 7 0 12" Center Wall 1.5 No. 7 @ 12" No. 7 @ 12" East Center Wall 1.5 No. 7 0 12" No. 7 6 12" East Wall 2.5 No. 8 @ 12" No. 8 9 12"

Reinforcement each face
- Reinforcement layout varies because of numerous wall openings.

l l l -4.7-construction technology laboratories

1 TABLE 4.2 - DIESEL GENERATOR BUILDING DRAWINGS Bechtel Revision Drawing Date Title pg, No. C-140 14 2/14/81 Project Civil Standards. Rein-forced Concrete General Notes and Details Sheet No. 1 C-1001 12 10/28/81 Concrete Outlines - Plan at El. 634'-6" Sheet No. 1 C-1002 14 10/28/81 Concrete Outlines - Plan at El. 634'-6" Sheet No. 2 C-1003 9 6/26/80 concrete Outlines - Plan at El. 664'-0" Sheet No. 1 C-1004 10 7/13/81 Concrete Outlines - Plan at El. 664'-0" Sheet No. 2 C-1005 4 1/31/80 Concrete Outlines - Roof Plan at El. 680'-0" Sheet No. 1 C-1006 3 2/28/79 Concrete Outlines - Roof Plan ~ at El. 680'-0" Sheet No. 2 C-1007 6 3/22/79 Concrete Ou tlines - Longitudinal Section C-1008 10 4/22/80 Concrete Outlines - Cross Section C-1013 6 3/20/80 Reinforcing Details - Foundation Plan Sheet No. 1 C-1014 3 1/13/78 Reinforcing Details - Foundation Plan Sheet No. 2 a C-1015 4 9/26/80 Reinforcing Details - Floor Plan at El. 634'-6" Sheet No. 1 C-1016 5 1/5/81 Reinforcing Details - Floor Plan at El. 634'~6" Sheet No. 2 C-1017 2 8/6/79 Reinforcing Details - Floor Plan at El. 664'-0" Sheet No. 1 "b'0~ construction technology laboratories 4 ,e-. m- ,r -r, ,-.,-.-e. ..-ee,. w -c-,--

i 8 O TABLE 4.2 - DIESEL GENERATOR. BUILDING DRAWINGS (Continued) Bechtel Revision Drawing Date Title y, No. C-1018 2 8/6/79 Reinforcing Details - Floor Plan at El. 664'-0" Sheet No. 2 C-1019 .2 9/10/79 Reinforcing Details - Roof Plan at El. 680'-0" Sheet No. 1 C-1020 3 9/10/79 Reinforcing Details - Roof Plan at El. 680'-0" Sheet No.-2 C-1021 4 1/6/78 Reinforcing Details - Wall Elevation Sheet No. 1 C-1022 4 1/6/78 Reinforcing Details - Wall Elevation Sheet No. 2 C-1023 4 1/9/79 Reinforcing Details - Wall Elevation Sheet No. 3 C-1024 4 1/9/79 Reinforcing Details -' Wall-Elevation Sheet No. 4 C-1025 3 1/6/78 Reinforcing Details - Wall Elevation Sheet No. 5 C-1026 4 3/30/79 Reinforcing Details - Wall Elevation Sheet No. 6 C-1027 4 3/30/79 Reinforcing Details - Wall Elevation Sheet No. 7 C-1028 4 4/25/79 Reinforcing Details - Wall Elevation Sheet No. 8 C-1029 4 4/27/78 Reinforcing Details - Wall Elevation Sheet No. 9 C-1030 2 1/6/78 Reinforcing Details - Sections Sheet No. 1 C-1031 4 1/9/78 Reinforcing Details - Sections Sheet No. 2 -4.9-construcilon technology laboratories ~.._.,.-__.__._-___________..._.____...__.2.._.._....

TABLE 4.2, - DIESEL GENERATOR BUILDING DRAWINGS (Continued) Bechtel Revision Drawing Date Title No. No. C-1032 0 7/21/77 Reinforcing Details - Sect' ions and Details Sheet No. 3 C-1033 0 7/21/77 Reinforcing Details - Sections and-Details-Sheet No. 4 C-1034 0 7/21/77 Reinforcing Details - Sections and Details sheet No. 5 C-1035 1 4/27/78 Reinforcing Details - Sections and Details Sheet No. 6 C-1036 4 8/13/80 Reinforcing Details.- Sections and Details Sheet.No. 7 -4.10-construction technology laboratories P---------

l Building exceeded the estimated settlement value given in the Midland Plant Final Safety Analysis Report. It has als been reported that the excessive settlement was caused by plant fill having a different compaction from that assumed in design. Footings of the north-south walls of the Diesel Generator Building are penetrated by electrical duct banks as shown in Figs. 4.5 and 4.6. It has been reported that when settlement of the buildings occurred, these duct banks were in contact with the footing. It is postulated that this support restrained vertical movement of the north-south walls. Contact between the duct banks and footings was eliminated in November 1978 by removing concrete at the duct bank-footing interface as illus-trated in Figure 4.5. EVALUATION OF CRACKING During construction of the Diesel Generator Building, cracks were observed in the concrete walls. It has been hypothesized that these cracks are related to two factors. The first is the normal cracking that can occut from restrained volume changes in reinforced concrete. The second is cracking that can occur because of differential settlement such as that reported in the Diesel Generator Building. In this report, evaluation of crack-ing is based on crack mapping reported by Bechtel, and on over-all visual observations of the building made by Construction Technology Laboratories (CTL) personnel. -4.11-construction technology Isboratories ~ _ _ - _ _.

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DUCT BANK TYPICAL SECTION 4 Fig. 4.5 Diesel Generator Building Duct Bank $ayout

SECTION OF DIcSEL CENERATOR DUILDING LOOKING WEST EL. 580'-0* 3, i.9 3. g ;...,., g 0 i ?, 9 EL, 664*-0* . s.v. i w.... o. .L q. - ?h ?. ~ ?. 9 N TURBINE BUILDING A T.0* - - 6 C W.o 1 oo.ENERATOR PEDESTA(v***- 'G W m ::.... W.s.5'1 o. ?. -n MIy TOP OF SLAD WD MAT 0 ,,1 EL. 614'-0* I r DUCT BANKS }o .o.- p . o:. o'.. MINIMUM DUCT \\ *o.b:o' \\ DESIGN ENVELOPE \\ \\ j .\\ \\ .. 9,. s,.. i BOTTOM OF DUCT ELEVATION 593'-0*T ! N ... T'"

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Fig. 4.6 Diesel Generator Building Duct Bank' Elevation

. a Bechtel Crack Mapping-1 Cracks in walls of the Diesel Generator Building were mapped by_Bechtel personnel at several stages of construction. Figures 4.7 through.4.ll show cracks observed in the north-south walls of the Diesel Generator Building between elevations ~ 630 ft-6-in. and 664 ft-0 in. A key to wall designations is shown in Figure 4.4. In Figs. 4.7 through 4.11 only cracks with widths of 0.010 in. or greater are shown. Numbers show measured crack widths in thousandths to the nearest five thou-sand th. The drawings are based on cracks mapped in July 1981. Maximum reported crack width is 0.020 in. Cracking in the vicinity of duct banks is particularly evident in the center wall as shown in Fig 4.9. Cracks observed in north-south walls of the Diesel Generator Building between elevations 664 ft-0 in. and 681 ft-6 in. are 4 shown in Figs. 4.12 through 4.16. These figures are taken from Bechtel drawing SK-C-669. Cracks shown in this drawing were mapped in January 1980. Figures 4.17 and 4.18 show cracking observed in the north l wall of the Diesel Generator Building. These figures are taken from Bechtel drawing SK-C-659. The cracks were mapped in February-1980. Cracks in this wall were remapped by Bechtel personnel in July 1981. Results of the remapping are shown in Bechtel drawing SK-C-770, Revision A dated February 9, 1982. Although a few additional cracks with widths of 0.010 in. or greater were observed in July 1981, no significant differences in overall crack patterns were noted. -4.14~ construction technology laboratories ~.. _. -.,,. _ _. _.. _ _. _.. _ _..-._-....____ ___.___..... _._ _ _-. _ _, _. _ _ _.... ~ _ - -. - _ _ _ _. -

_l- - l -. EL'. 664'-0" m D~+'3L%% _ _ \\ vvs -s -s n,x,x m 4% 1 x v vvvVVX XXMu" 10 ' ,g T.O.G. EL 634'-O" in N#Y# EL. 630'-6" l I I l WEST WALL-EAST FACE _ /-_ __ /__ EL. 664'-O" m '5 J' ( l l 1 L X 20f') j / >( j to QO iak oo 0 4 /_ l' G ' s\\_ x r x ~ N Acc y Yx vy xx xv vv vv vx x 010 Oo io T.O.G. EL.634'-O"

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b *tE e EL. 630'-6" l l l WEST WALL-WEST FACE Fig. 4.'7 Cracking in West Wall of Diesel Generator Building From Bechtel Drawing No. SK-C-759 (Crack Widths -in 0.001" Increments) -4.15-

/ e EL. 664'-O" L WYXWYYYYYYYYYYYYYY \\t m888gweumpg c do k i ,io f'O f 0 T.O.G. EL. 634'-O" JI5 ,is in io Md m EL. 630'-6" j ~ l I I I I I WEST CENTER WALL-EAST FACE f1~ ~~ f ~ m EL. 664'-O" L 8884

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-}- -{- EL. 664'-O" m L-io), 15[ A h v\\ ( L (XXWWW>OCOOM Wnvvvvm2 QQAMW)C so ' Access' MMWWM ^ 40hotPt OfE bo /10 i T.O.G EL. 634'-O" 20 L 1 \\ Ul/ / R N EL. 630'-6" m l I I I I I~ CENTER WALL - EAST FACE / _j_ EL. 664'-O" m L L A mwnmwnn ex#o8888888888M88P h \\ W No Ac ess9 ss xxx s T.O.G. EL. 634'-O" h XX XNTAA g, EM EL. 630'-6" m l l l l l CENTER WALL - WEST FACE Fig. 4.9 Cracking in Center Wall of Diesel Generator Building From Bechtel Drawing No. SK-C-759 (Crack Widths in O.001" Increments) -4.17-

_f_ __ [ _ EL. 664'-0" m L i EM N h iotNi 20pw w\\ g j \\_ ' M v s.-1 )20Cx%d&y*w35& muw,<wa cammwmm66sooccamm9 1,15 hio ( bt:5 ,J q im J 10

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l I .I I I' ya EAST CENTER WALL - EAST ~ FACE -l- -}_ EL. 664'-O" m L 88888888FAMME A "5 \\_ "5 ands ~ 'Of jf ~~" 30 10 o / L / (/ ~ ot5 "10 o is I T.O.G. EL. 634'-O" 4 oio goj( o m i g ( Y#'I, EL. 630'-6" W 1 ~ l I I I I I EAST CENTER WALL-WEST FACE Fig. 4.10 Cracking in East Center Wal.L of Diesel Generator Building From Bechtel Drawing No. SK-C-759 (Crack Widths in 0.001" Increments) -4.18-

_a _/_ EL 664'-O" m l '? s ~- y K ~- i x_ i T.O.G. EL. 634'-O" is EL. 630'-6" e l I I I I I EAST WALL-EAST FACE - } _l- ~ EL. 664'-O" e l \\ (xYMWNvVYMN1 s ? y 30 7 10 10 T.O.G. EL. 634'-O" j#SNr EL. 630'-6" e l I I I I I~ EAST WALL-WEST FACE Fig. 4.11 Cracking in East Wall of Diesel Generator Building From Bechtel Drawing No. SK-C-759 (Crack Widths in 0.001" Increments) -4.19-

o. 4 d EL. 681'- 6" I i I . \\lO S I E L. 664'-O* I I I 4 g1 I I WEST WALL - E AST FACE P ta E L. 6 81'- 6" i .. < >20 I E L. 664*-O" 15 10 10 10 '10 \\ L 'l I \\'O l 4 WE ST WA LL - WE ST FAC E l I Fig. 4.12 Cracking in West Wall of Diesel Generator Building. From Bechtel Drawing No. SK-C-669 (Crack Widths.in 0.001" Increments)

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4 f EL. 681'-6" g-L f-f m I \\TsjoI Ik CfIS k* I f f5 fs O C \\ to j, f St "5 0 I ( th ( ( i o "o oo o , 'o o Lo "o ]* fs \\o 8 __ 1. _ _ _*/ ii 1 'r ts \\o yj _s!' /

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Figures 4.19 and 4.20 show cracks mapped in the south wall of the Diesel Generator Building. These figures were taken from Bechtel drawing Number SK-C-658. Based on overall review of Bechtel drawings, it appears that many of the cracks shown are attributed to restrained volume changes that occur in concrete during curing and subse-quent drying. However, the patterns observed in several north-south walls of the Diesel Generator Building indicate that cracks could have resulted from differential settlement of the f walls between the duct banks and the north and south portions of the suructure. It is possible that differential settlement was caused by extra support provided by the duct banks when they came in contact with the wall footings. CTL Observations Visual observations of cracking in walls of the Diesel Gen-erator Building were made by CTL personnel on January 12, 1982 and February 9, 1982. Construction Technology Laboratories personnel did not do detailed mapping of cracks. CTL inspec-tions were made to obtain an overall impression of cracking in the structure and to correlate this impression with that obtained from review of Bechtel crack mapping drawings. In general, impressions obtained from the visual inspection at the site were consistent with those obtained from review of the 1 l Bechtel drawings. Because the observed pattern of cracks in the center north-l south wall of the Diesel Generator Building was most indicative of cracks caused by differential settlement, one face of this -4.27-construction technology laboratories I.-... -..,- -. _..- -. - -.,....-.- ___ -...._-,._ _._ - -,-:,-.-. . ~.

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EL. 62s'-O" SOUTH WALL-SOUTH FACE Fig. 4.20 Cracking in South Wall - South Face of Diesel Generator Building From Bechtel Drawing SK-C-658 (Crack Widths in 0.001" Increments)

wall was remapped by CTL personnel on February 9, 1982. Figure 4.21 shows cracks observed in the center wall on the east face. Maximum measured crack width was 0.025 in. The pattern of cracks at the electrical duct penetration is consistent with a pattern that could occur because of differential settlement about the duct. Development of settlement cracks is discussed by Dr. M. A. Sozen in the main body of this report. RECOMMENDED PROGRAM FOR MONITORING STRUCTURAL INTEGRITY It is recommended that future integrity of the Diesel Gen-erator Building be monitored by periodic measurements of dis-placements of the structure and by periodic inspection of cracks. Displacement Monitoring Displacement measurements should be made periodically to monitor absolute and relative movement of walls of the Diesel Generator Building. Figure 4.22 shows approximate locations of recommended displacement measurement points. These measurements will confirm that current estimates of settlement limits are not exceeded and will provide a means to verify structural integrity. Measured displacements should be recorded as a func-tion of time.- The frequency of measurements will be selected in relation to the observed rate of displacement. It is also. recommended that the time history of displace-ments be submitted on a regular basis to qualified engineers familiar with reinforced concrete behavior and design. The qualified engineer will provide recommendations on whether wall ~4.30-construction to. %otogy laboratories

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1 i m 4 ..y [ i i 1 I i a e I EL 630'-O" CENTER WALL-EAST FACE 'l Fig. 4.21 Cracks Observed in Center Wall - East Face of Diesel Generator Building on February 9, 1982 I 4 e 1

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displacements are of-significance with regard to structural integrity of the building. Crack Monitoring As. a supplement to the displacement monitoring program, periodic visual inspections of the Diesel Generator Building ] should be made to determine if new cracking has developed or if. existing cracks have changed in width or length.. Crack

inspections should be conducted by qualified personnel.

t Because the Diesel Generator Building is not being under-pinned, it is not anticipated that the crack monitoring program will be as rigorous as that for ' the Auxiliary Building. However, as a minimum, the following steps should be included. Initially a crack survey should be made for the entire structure. This will provide a base for future evaluation of changes in crack patterns or crack widths. All visible cracks should be marked and recorded. Selected cracks should be measured to obtain an estimate of maximum crack widths. If displacement measurements indicate that building settle-ment exceeds the predicted values, cracks in the structure should be remapped. Within four weeks after observation of the cracks, an engineer f amiliar with reinforced concrete behavior and design should provide a written report that describes significance of observed cracks and recommendations for main-taining structural integrity of the building. l 5 -4.33-cm'aucuan technology Isboostories

i SUMARY AND CONCLUSIONS This report presents a description of observed cracks in the Diesel Generator Building-at Midland Nuclear Power Plant Units 1 and 2.- Cracks observed in this structure ' by Bechtel personne1'and by Construction Technology Laboratories personnel are attributed to: 1. Restrained volume changes that occur during curing and drying of concrete. 2. Reported differential settlement between the duct banks and the north and south portions of the building. It is proposed that measured displacements be used as the primary means of monitoring future behavior of the structure. If displacement measurements exceed predicted values, cracks should be remapped and evaluated to insure that structural integrity of the building is maintained. Displacement and crack monitoring should be reviewed by an engineer knowledge-able in reinforced concrete behavior and design. i 1 0 h 1 I -4.34~ construction technology Isboratories .}}

ML20041C141

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