ML18026A353

Forwards Responses to Structural Engineering Branch Questions on Masonry Walls to Close SER Outstanding Issue 13.Justification for Use of Average Response Spectra Typical Wall Fix Diagrams Also Encl

ML18026A353
Person / Time
Site:	Susquehanna
Issue date:	05/14/1981
From:	Curtis N PENNSYLVANIA POWER & LIGHT CO.
To:	Youngblood B Office of Nuclear Reactor Regulation
References
PLA-760, NUDOCS 8105190400
Download: ML18026A353 (34)

Text

REGULATD T INFORMATION DISTRIBUTION O STER (RIDS)

ACCESSION NBR:8105190400 DUC ~ DATE: 81/05/14 NOTARIZED; NO DOCKET FAGIL:50"387 Susquehanna Steam Electric Stationr Unit 1> Pennsylva 0 7 50"388 Susquehanna Steam Electric Stationi Unit 2i Pennsylv 050003 8

.-AUTH'AME AUTHOR Al FILIATION CURT ISi u ~ n ~ Pennsylvania Power II, Light Co ~

REC IP ~ NAME RECIPIENI AFFILIATION YOUNGBLOODiB.J ~ Licensing Branch 1

SUBJECT:

Forwards responses to Structural Engineering Branch questions on masonry walls to close SER Outstanding Issue 13 'ustificat>on for use of average response soectra typical wall fix diagrams also CODE: 8001S COI'IES RECEIVED:LTR TITLE: PSALM/FSAR A>IDTS and Related Correspondence encl'ISTRIBUTION KNCL SIZE:

NOTES:Send ILE 3 copies FSAR L all amends.i cy:BWR"LRG P41(L ~ RIts) 05000387 Send IKE 3 copies FSAR II all amends.i cy:BAR LRG PH(CRIB) 05000388 REC IPIENT COPIES RECIPIENT COPIES IO CODE/NAvE LTTR ENCL ID CODE/NAI:E LTTR ENCL ACT ION ~ A/D LICENSNG 1 0 LIC BR 02 BC 1 0 RUSHBROOK<1~. 1 0 STARKrR ~ 04 1 1 INTERNAL: ACC ID EVAI BR2o 1 1 AUX SYS BR 07 1 1 CHEM ENG BR 08 1 1 CONT SYS BR 09 1 1 CO<K PERF 6R 10 1 EFF, TR SYS BR12 1 1 EHERG PREP 22 1 0 EQUIP QUAL oR13 3 3 GEDSCIENCES 14 1 1 HUH FACT ENG UR 1 1 rIYO/GEO BR le  ? ' 18C SYS BR 16 1 1 IaE 06 3 3 LIC GUID BR 1 1 LI C QUAL BR 1 l NATL ENG BR 17 1 1 i4IECH ENG BR 16 1 iHP A 1 0 NRC PDR 02 1 1 OELO 1 0 OP LIC BR 1 1 POWER. SYS BR 19 1 1 PROC/TST REV 20 1 1 QA BR 21 1 1 RA S BR22 1 1 RKAC SYS BR 23 1 1 EG F ILE 01 1 1 SIT ANAL BR 24 1 1 TWUC-T NG BR25 1 1 EXTERNAL: ACHS 21 lo 16 LPDR 03 NSLC 05 1 1 ggy 21 1S81 w'1 +I TOTAL NUMBER OF COPIES REQUIRE,D: LTTR 54 ENCL

PPaL TWO NORTH NINTH STREET, ALLENTOWN, PA. 18101 PHONE: (2 IS) 821.5151 NORMAN W. CURTIS Vice President Engineering & Construction 821-5381 May 14, 1981 ~%Ctt>R routnJ01 ISStort Rip, rp /

/ i Mr. B. J. Youngblood, Chief Docket Nos. 50-387 Licensing Branch No. 1 50-388 U.S. Nuclear Regulatory Commission Washington, DC 20555 SUSQUEHANNA STEAM ELECTRIC STATION SER OUTSTANDING ISSUE 13 ER 100450 FILE 841-2 PLA-760

Dear Mr. Youngblood:

Attached are the responses to the Structural Engineering Branch questions on masonry walls.

These responses complete our action to close SER Outstanding Issue 13.

Very truly yours, N. W. Curtis Vice President-Engineering a Construction-Nuclear CTC/mks Attachment pool 810SXS04O <<~

PENNSYLVANIA POWER & LIGHT COMPANY

SUSCU1XAHNA SES UNIT 1 AND 2 DOGQ 7 NUMBERS 50-387 AND 50-388 CATEGORY I MASONRY WALLS PREAMBLE:

'afety related masonry walls are interior partitions whose primary function is to provide shielding and fire protection. Masonry walls are not used as primary shear walls for seismic resistance of the structure. All category I masonry walls are reinforced with all cells fully grouted. The infillmaterial of double wythe walls is either grout or concrete. The minimum specified canpressive strength for grout, concrete, and mortar is 2500 psi. %rtar infillis not used on SSES nasonry wa11s. Metal ties, between the wythes of double wythe walls, are provided at 24" spacing maximum in horizontal and vertical directions. Seismic design is in accordance with SSES FSAR Section 3.7. Allowable stresses are as noted in CESAR Section 3.8, Table 3.8-8 and Table 3.8-9. Safety related rrasonry walls are Q-listed and have been added to the FSAR Design Criteria Surmary (Table 3.2-1), in response to NRC, Quality Assurance Branch, Question No. 260.l-b (34).

QUESTION NO. 1:

In your response to Question 2, you indicated that Sm is the allcmble stress as specified in UBC. For extreme and/or abnormal loading combinations, you increase the alliable stress by a factor of 1.67, which is in conformance with the practice of SRP Sections 3.8.3 and 3.8.4, for reinforced concrete structures. Havever, concrete masonxy walls are quite different frcm reinforced concrete walls, particularly the unreinforced ones, the use of such a practice nay not result in an adequate design. Depending on the types of stress, that is, tensile, shearing or axial carpressive, the factor may vary from 0 to 2.5 (see enclosure 2). Specify the masonry design strength fm used in Susquehanna masonry walls and the allowable values for all types of stresses.

RESPONSE

Code allavable stresses for masonry tension, shear, ccnpression, a+2 bord are increased by a factor of 1.67 for load mnbinaticns involving abnormal and/or extreme environmental conditions which are credible but highly improbable. Since code alliable stresses are generally associated with a factor of safety of 3, the 1.67 increase provides a factor of safety against failure of 1.8 (3 -. 1.67) (see Table 4 for the increase allcwed for each type of stress). 'Ihere are no unreinforced masonry walls on SSES project. Susquehanna SFS masonry walls are designed based on an ultimate cmpressive strength, f'm, of 1500 psi as specified in UBC 1976, for solid grouted hollow masonry. Minima ccmpressive strength at 28 days for mortar, grout, and concrete is 2500 psi. Materials are in accordance with FSAR Appendix 3.8C.

The allowable stresses are as listed in Table l.

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~ q~>> s~ ~ ~y r ee ~ awemr ',',, ~ s ~ 'I ~ ye 8920 TM3LE l.

SSES MZQMABLE STRESSES Materials and Allowable Stress: UBC 1976 (1)

Stress 1~ HBsonry f'm = 1500 (see note 2)

Compression:

Flexural .33f 'm = 500 Axial .20f'm x (1-(h/40t) ) h = clear height, in.

t = wall thickness, in.

Flexural Shear 1.1 ~f'm = 43 Bond (deformed bars) 140 Bearing .25f'm = 375 Bed Joint tension Normal (See note 3)

Parallel Modulus of elasticity, Em 1000f 'm = 1,500,000 Modulus of rigidity, E 400f 'm = 600,000

2. Reinforcement:

Tension:

Grade 40 Steel 20,000 (used for ties, only)

Grade 60 Steel 24,000 Ccapression:

Grade 40 Steel 16,000 (used for ties only)

Grade 60 Steel 24, 000 Notes: (1) For stress increase allowed for abnormal, or extreme environmental load ccmbinations See Table 4.

(2) Ultimate compressive strength as specified in UBC 1976 for solid grouted hollow concrete units Grade N.

(3) Zero tension normal to bed joint is used.

WP26/15-2

QUESTION B3. 2 In the note to your response to Question 2, you stated that the allowable shear or tension between masonry block and concrete or grout infill is considered to be equal to three percent of the canpressive strength of the block. 'The allowable shear or tension as specified by you is in the staff's opinion tco hich. To specify the allcwable shear or tension of the vertical joint between wythes in terms of the ccmpression strength of the block is in the first place unconservative and the use of seemingly 1cw percentage of 3% nay actually result in an allowable shearing stress greater than its corresponding strength. 'Iherefore, a revision of the stress criterion is required.

RESPONSE

The specified shear and tension, for the interface of masonry block and concrete or grout, infill, of three percent of ccmpressive strength, f'm, is based on the relationship 1.1 ~f'm given in ACI-531-79. For f'm = 1500 psi, this relationship yields a value of 43 psi ccmpared to 45 psi (.03 x 1500) allowed for evaluation of project masonry walls. The difference of 2 psi is justified by the fact that the ultimate canpressive strength of masonry f'm, is generally higher than 1500 psi.

The values for. shear and tension as specified above have been used only as a guide in evaluatinq double wythe walls, where infill thickness is greater than 8 inches (24" thick walls and larger).

For walls having an infill thickness of less than 8 inches (total of four walls), zero tension/shear is assumed for evaluation purposes; For SSES masonry wa11s, the actual shear stress, as determined by VQ/Zb for uncracked sections, and in the ccapression zone of cracked sections ranges frcm 5-10 psi; except for three walls. For these three walls shearing stress is in the range of 10-15 psi.

QUOI'ION NO. 3 In your response to Question 4: (1) It is indicated that response spectrum method is used for the dynamic analysis of which of the response spectra is used, ~

the concrete masonry walls. However, there is no mention as to response spectrum or the average of the two.

floor or lower floor It is required that an upper bound envelope of the individual flcor is used. (2) Though the use of ACI 318 forrmla the cracking of concrete masonry wall is considered. The use of such a formula is que'stionable in view of the fact that in a concrete masonxy wall the weakest section is the bed joint and the modulus of rupture is equal to that of neither the concrete block nor the mortar. Indicate hew the rxdulus of rupture is established in ycur ccaputation.

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RESPONSE ITEM (1):

=-892'esponse spectrum for the lcwer floor has been used for evaluation of cracked/uncracked behavior of masonry walls, as applicable, for vertical motion, and for walls cantilevered fran the flcor. For horizontal motion, the lcwer floor response spectrum has been used in the initial evaluation of cracked/uncracked behavior, as applicable, for walls spanning between two flcors and walls having side connection at concrete walls. These walls have also been re-evaluated based on the average acceleration of the upper and laser floors. Where the upper floor acceleration is less than the 1cwer flcor acceleration, the lower floor acceleration is used. For justification of using average acceleration, see Enclosure 1.

RESPGNSE ITEM (2):

Although ACI-318 formula is derived for cracked concrete sections, the use of the formula for masonry walls takes into consideration the difference in material strengths. 'Ihe difference between nasonry behavior and concrete behavior is recognized and allowances are provided in selection of seismic acceleration within a frequency variation of plus or minus fifteen percent of the natural frequency.

The mx2ulus of rupture (fx) for masonry is approximated by increasing the UBC allowable flexural tensile stress by a factor of safety of 3 and then applying a 33% reduction to arrive at a lcwer bourd value. M.s value is used only for stiffness and frequency calculations of the cracked section and not for strength. Allcwance for uncertainties in the nodulus of rupture is accounted for in the frequency variation of

+ 15% of the natural frequency.

QUESTION NO 4:

In response to Question 5, it is stated that when the design stresses of masonry walls exceed the allowable stresses, fixes are designed such that the criteria is satisfied. Indicate the number of walls where such fixes are needed and provide examples.

RESPONSE

The number of masonry walls requiring fixes for cracked section criteria is 36. Wall location, thickness, and elevation are as shown in Table 2. Typical fixes are shown in details type 1, type 2, type 3, and type 4 (see Enclosure 2).

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TABLE 2

~ SSES MASONRY NMLS WHICH REQUIRED FZKS H)R CRACKED SIXTION CRITERIA WALL BLDG. FZCGR EEZVATION t THICKNESS I NO. OF MALS REF. E4%.

Control 656'-0 8 II C-1301 Control 741'-0 6 II C-1304 Control 741'-0 8" 3 C-1304 Control 753 'W 8ll C-1304 Control 771'-0 8ll 16 C-1304 Control 783'-0 1'W" C-1307 Control 806 '-0 8 II C-1308 Control 806 '-0 1I ~ll C-1308 Reactor 728'-0 8 II C-1202 Reactor 799'-0 8ll C-1205 m26/15-5

38U2H QJESTION M). 5:

Provide justification for any deviation frcm the attached staff 's interim criteria in your desiqn and analysis of the masonry walls.

RESPONSE

Deviations and justification for differences between SSES criteria and SEB interim criteria are as noted in the following paragraphs.

Items which are not specifically addressed are in accordance with the criteria or not applicable to the project.

ITEM NO. 1: General R irments The materials, testing, analysis, design, construction and inspection related to the design and construction of safety-related concrete masonry walls shall conform to the applicable requirements contained in Uniform Building Code 1979, unless specified otherwise, by the provisions in this criteria.

RESPONSE

Uniform Building Cede, 1976 edition, has been used for design and evaluation of Susquehanna masonry walls. A carparison of 1976 and 1979 editions of UBC shows no significant difference in criteria applicable to SSES masonry walls. In addition, ACI-531-79 is used to supplement UBC allowable stresses, and ACI-318 1977 in stiffness ca1culations; ITEM HO. 2: Loads and Load Ccmbinations The loads and load ccmbinations shall include consideration of normal loads, severe environmental load, extrene environmental load, and abnormal loads. Specifically, for operating plants, the load canbinations provided in plant's FSAR shall govern.

For operating license applications, the following load ccmbinations shall apply for definition of load terms, (see SRP Section 3.8.4.11-3).

RESPONSE

For corrparison of SEB interim load combinations and load ccmbinations used for masonry walls evaluation see Table 3. Definition of terms is as shown below.

Notation D = Dead loa4 of- structure plus any other permanent loads contributing stress.

L = Live loads expected to be present when the plant is operating, including aavable eauipnent, piping, cables.

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P = Design basis accident pressure loads.

R = Steam/water jet forces or reactions resulting fran rupture of process piping.

TQ Therma 1 effects during normal operating conditions including temperature gradient and equipnent and pipe reactions.

Ho = Force on structure due to thermal acpansion of pipes under operating conditions.

Ta Added thermal effects (over and above operating thermal effects) which cccur during a design accident.

Ha Force on structure due to thermal expansion of pipes under accident conditions.

E = Load due to Operating Basis Earthquake.

E' Load due to Design Basis Earthquake.

W = Wind load.

W' Tornado wind load.

Ds = Force on bloc3nall due to story drift under Operating Basis Earthquake Loading.

D's = Force on blockwall due to story drift under Safe Shutdown F~hquake Loading.

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TABLE 3. IOAD COMBINATION COMPARISON IOAD COMBINATION

l. D+L 1. D+L

2. D+L+ E 2. D+L+E+Ds Service 3. D+ L+W 3. Not Applicable INo wind pressure(

load Condition la. D + L + To + Ro la. D + L + To + Ho 2a. D + L + To + Ro + E 2a. D + L + To + H + E 3a. D+L+To+Q+W 3a. Not Applicable )No wind pressure(

Fxtreme 4. D + L + To + Ro + E'.

4. D + L + To + H + E' D's envi-'onmental D + L + To + Ro + Wt D + L + To + Ho + W ISee note 2 I

atxmrmal 6e D + L + Ta + Ra + le5 Pa 6e D + L + (To + Ta) + R + ISee note 1 1.25 Pa + Ha abnormal/severe I 7. D + L + Ta + 1.25 Pa + 1.0 7e D + L + (To + Ta) + le25 Pa + R +

environmental (Yr + Yj + Ym) + le25E + Ra 1.25 E + Ds a?normal/ 8e D + L + Ta + Ra + leO P + 8e D + L + (To + Ta) + R + leO P +

extreme leO (Yr + Yj + Ym) + leOE 1.0 E' D',

environmental conditions Notes: (1) Abnormal load canbination in SSES-FSAR Table 3.8-9. Part C will be revised to read D + L + (To + Ta) + R + 1.5 Pa + Ho. All other load ccmbinations will remain unchanged.

(2) W'oes not include W, tornado missile. bhsonry walls are not used for protection of safety related equipnent against tornado missiles.

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ITEM K). 3: Allowable Stresses Allowable stresses p";ovided in chapter 24 of UBC-79, as supplenented by the follcwing rradifications/exceptions shall apply.

(a) When wind or seismic loads (OBE) are considered in the loading ccrnbinations, no increase in the allowable stresses are permitted.

RESPONSE

Design and evaluation of masonry walls is based on a 33% increase in the allowable stress. This increase is permissible per UBC, 1979 and per ACI-531-79. The factor is also ccrrpatible with the 25% increase in stress noted in SSES FSAR for Working Stress Design Method.

ITFÃ NO. 3: (b) Use of allowable stresses corresponding to special inspection category shall be substantiated by derrenstration of ccrnpliance with the inspection requirements of the NRC criteria.

RESPONSE

Stresses corresponding to special inspection have been used in the design and evaluation of SSES masonry walls. Inspection required to assure that masonry construction is in accordance with Appendix "D" and amendments to the PSAR, and to assure that. materials are in accordance with FSAR Appendix 3.8C, is implemented. Documentation of this inspection is in project jobsite files.

arm NO. 3: (c) For load conditions, which represent extreme envirornnental, abrnrmal, abnormal/severe enviroanental, and abnoxmal/

extreme environmental conditions the allowable working stresses may be multiplied by the factors shcwn in the following table: (See table 4).

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TABLE 4.

I,'AY -4 'c I,' 8 (J P [~

STRESS ZNCRFJSE FACIOR COMPARISON

'ACIOR FACTOR JUSTZFZCATZON/COMME%I'xial or flexural conpression 2.5 1.67 See Response Question gl Bearing 2.5 1.67 Reinforcement stress except shear 2.0 l. 67 See note 1 Shear Reinforcement 1.5 1.5 Anchor bolts are not usedl and/or bolts in safety related masonryl walls I

I Masonry tension Parallel to bed joint 1.5 1.5 Shear carried by masonry 1.0 1.67 See note 2 Masonry tension perpendicular to bed joint For reinforced masonry 0 0 For unreinforced masonxy 1.0 N/A No unreinforced I masonry walls I

(1) Shall not exceed .90 fy (2) The actual shear stress carried by masonry is within the allowable shear stress given in UBC Table 24-H with no increase factor applied.

RESPONSE

See table above.

NP26/15-10 QUESTION HO. 5: Design and Analysis Considerations ITEM In new construction, no unreinforced masonry wall is permitted, also all grcut in concrete masonry walls shall be conpacted by vibration.

RES KNSE

a. 'Ihere are no unreinforced masonry walls in SSES project.

b. Cell grout and/or infill grout or concrete is ccmpacted by either mechanical vibrators or by redding.

ITEM 4z Special constructions (e.g., multiwythe, carposite) or other items not covered by the cede shall be reviewed on a case by case basis for their acceptance.

RESPCNSE:

Double wythe walls are designed as carposite sections, except as noted in response to Question No. 2. Allowable stresses are per ACI-531-79.

~ETEM 4 Licensees or applicants for staff's review.

shall submit QK/QC information, if available,

RESPONSE

Applicable QA/QC information is available at SSES jobsite and will be submitted upon request.

WP26/15-11 -ll-

ENCLCSURE 1.

JUSI'IFICATHX'T FOR'HE USE OF AVERAGE RESPONSE SPECTRA (13 PAGES)

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JUSTIFICATION OF USING APPROXIMATION METHOD TO DETERMINE MAXIMUM WALL PANEL RESPONSES TO SEISMIC MOTION The evaluations herein demonstrate that: (l) The use of the average floor acceleration response spectra to calculate the response of the wall panel is appropriate, and (2) The use of uniform inertia load with magnitude equal to the average spectral acceleration for the fundamental mode, in calculating the maximum seismic responses is a good approximation, even considering the higher mode ef feet.

For the purposes of this evaluation, the seismic response of a simply-supported, uniform beam simulating a strip of the wall panel with unit width is considered, as shown in Figure l.

(1) Use of Avera e,S ectra The equation of motion of an undamped, simply-supported beam can be written in terms of the total displacement with respect to some fixed reference axis as:

m 3

St u + EI 34u ax4

=0 Where m and EI are the mass density and flexural rigidity of the beam. Denote the seismic excitations at the ends of the 1

EC-9

the beam as Ua and Ub. Then the total displacement u(x,t) can be expressed in terms of the two seismic motions and the relative displacement to the seismic motions as:

u(xg t) = (x/L) Ub + ( 1 -x/L) Ua + r(xg t) (2)

Where L is the length of the beam. The relation expressed above equation is shown in Figure 2. The relative dis-by'he placement r(x,t) needs to satisfy the following simply-supported conditions:

r(o,t) = r(L,t) = 0 a rl a rI 0 (4) ax Ix=o ax I x=L Substitute Equation 2 into Equation 1, the equation of motion in terms of relative displacement r(x,t) can be expressed as:

~~

2 ma r + EI a r m(x/L) Ub

~~

m(1 x/L) Ua at2 ax4 EC-9

The eigen-function solutions for the homogeneous equation associated with Equation 5 that satisfy the boundary condi-tions specified by Equations 3 and 4 are:

sin L

i n = l, 2, 3, and the corresponding frequencies of vibration are:

n= 1, 2, 3, n mL (6)

So, the solution of Equation 5 can be expressed as:

r(x,t) ='( a(t) sin n=l L Substitute Equation 7 into Equation 5, and multiply the latter by sin nmx, and then integrate L

it with respect to x over the full length of the beam, the equation of motion can be transformed into modal equations of motion as:

EC-9

HN-<'Gl '8 J2[)

~0 2 ~~ ~o n+ nan =r n Ua+U n = 1, 3, 5 2

(Sa) and

~0 2 I ~ 0 ~0 an + Q nan I' Ua Ub) n = 2, 4, 6,

"~ ~

i (Sb) where 1'n = participation factor (9) lf damping in the form of modal damping ratio is included, Equations Sa and Sb becomes:

~0 2 ~~ ~~

an + 2I-n"nan + > 'nan = n Ua + U 2

(10a) and

~y 2 %0 ~0 an + 2<n>n n + > n n = Fn Ua U n = 2,4,6,...

2 (lob)

Where gn is the damping ratio of the nth mode.

EC-9

Equation 10a means that the odd-number modes which are sym-metrical about the mid-span of the beam*will be excited by the average of the two seismic excitations; while equation 10b means that the even-number modes which are antisymmetrical about the mid-span of the beam will be excited by half of the difference between the two seismic excitations.

Expressing the maximum modal displacement response in equa-tions 10a aqd 10b in terms of absolute acceleration response spectra gives:

ap ng n) + b~~ n, n~1 n + n C

4mL4 a(< n,"n) + b(~ n,"n) n5,5EZ n = 1,2,3,...

This illustrates that the use of the average of two floor accelera-tion response spectra to calculate the modal response of a wall panel is appropriate.

EC-5

g -a'al .'802(1 (2) Contribution of Higher Modes From Equation ll, the relative importance of modes can be evaluated by examining the frequency ratios, modal partici-pation ratios, and maximum modal response ratios for constant acceleration which can be shown as

(d,1 lO 2

. hl 3

~

~ ~ ~ ~ 1 i 4 ~ 9 ~ ~ ~ ~ (12) r .r .r

~

2 ~

3

~ ~ 1 : -1/2  : 1/3  : . . . (13) td 1: 2: "3:

2 1 0) 2 2 0) 2

. ~ . = 1 32 1: 243 1:... (14)

For an SRSS method of combining maximum response, the contr'i-bution of higher modes is clearly negligible.

If for example, the fundamental frequency "1 is above 8 Hz, the second frequency is above 32 Hz which is already in the rigid range, i.e., in the range of no amplification. Thus the Sa and Sb values associated with modes other than the fundamental will be the Zero-Period-Acceleration (ZPA) values of the two seismic motions Ua and Ub. Using the absolute sum (ABS) method of combining the modal maximum responses., the con-tribution of higher modes is not more than 4% of the fundamental mode.

EC-9

~ ~

~

'he relative importance of modes can also be evaluated by examining the moment and shear responses in the beam for each mode, as shown in the following.

The moment in the beam due to the nt mode can be evaluated by:

M (X) an sin L

('15 )

I

,( 4mL a(<n "n) b (<n,"n) sin nmX n

n = 1,2,3,...

The moment at the mid-span of the beam is contributed only by the symetrical modes and can be expressed as follows-a(<n,"n) + (<n,"n) b (16)

EC-9

yg -g 'u(,'892 H For a constant spectral acceleration, the contibution to the mid-span moment of the beam from each mode can be expressed in the following ratio:

H (k) 52~ 27 125 Using the SRSS Method of combining modal responses, the con-tribution of the higher modes to the mid-span moment is less than 1% of that from the fundamental modes. Using the ABS method of combining modal responses, the contribution of higher modes is less than about 5%.

The shear force in the beam due to the n mode can be eval-uated as-'3 0 (X) = EI n >X3 a

n sin nsX L

C 4mL a(<n ~n) + b (~n,"n) cos ( nmX n Tt q L n = 1,2,3,4,...

EC-9

The maximum shear occurs at the support of the beam and can be expressed as: I 1

a(<n,"n + (<n,"n)

(4mL b (19) n n2 2 n = 1,2,3,4,...

The contribution of the higher modes to the maximum shear at the beam support relative to that of the fundamental mode can be evaluated by comparing the modal effective masses (MEM) associated with the fundamental mode and the higher modes. The modal effective mass of the fundamental mode is MEM 0.81 mL (20a) 1 .2 The modal effective mass associated with modes higher than the fundamental mode can be calculated as MEM1 = (1 0.81)mL = 0.19 mL (20b)

T The ratio of C

MEM1 TO MEM1 is 0.19/0.81 = 23't. That is the contribution of higher modes to the maximum shear is at most 23% of the contribution due to the fundamental mode. This ratio does not take-inte-account the ratio of the spectral EC-9

~ ~

~

~

n 4 oi gg JP()

acceleration for the fundamental mode to the ZPA value for the higher modes. When the difference in spectral accelera-tions is accounted for, the contribution of higher modes to the maximum shear would be less than 23%. For example,, if the spectral acceleration for the fundamental mode is 1.5 ZPA, then the ratio of higher mode contribution would be 0.19/(0.81 x 1.5) = 16%.

(3) Uniform Inertia Load Approximation Using the modal responses, the maximum moment and shear of the beam can be calculated. This moment and shear can then be compared to the moment and shear based on a uniform inertia load using the average of the two floor spectral accelerations.

at the fundamental mode of the beam.

The maximum moment occured at the mid-span of the beam induced by a uniform load with the following magnitude:

f(X) = m a (<1'~1) + b (<1'~l) (21) can be expressed as:

M*

L mL 2 Sa (~1'"1) + b (~1'1) (22) 2 8

~4

.4 C

From Equation 16, the moment at the mid-span of the beam due to the fundamental mode is:

(Ill+]) + Sb (0] i+1') (23)

The maximum difference between the moments from Equations 22 and 23 is about 3%.

The maximum shear occurred at the support of the beam induced by the uniform load expressed in Equation 21, can be written as:

Q*(0) mL a (<1'"1) + b (<1'"1) (24) 2 From Equation 19, the shear at the support of the beam due to the f undamental mode is:

Sa (<1 "1) + Sb (<1 "1 (25)

Q (O) (4mL 1 2 EC-9 g1

The shear from'qua tion 24 is greater than the shear from Equation 25 by about 25%. This margin can well cover the contribution to the shear due to the higher mode ef feet, as discussed previously.

From the above comparison, it can be concluded that the use of a uniform inertia load with the magnitude of the averaged floor spectral acceleration at the fundamental mode, provides a good approximation for calculating the seismic response in the wall panel .

EC-9

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