1195

THE LOAD-BEARING BEHAVIOUR OF BIAXIALLY SPANNED MASONRY WALLS SUBJECTED SIMULTANEOUSLY TO HORIZONTAL AND VERTICAL LOADING

Prof.Dr.-Ing. W. Mann and Dipl.-Ing. V.Tonn Technical University Darmstadt 6100 Darmstadt Petersenstra~e 15 Federal Republik of Germany

SUMMARY

The condition of biaxially spanned walls with simultaneous ho­rizontal and vertical loading occurs, for example, when base­ment walls are subjected to lateral soil pressure or when ex­ternaI walls are subjected to wind pressure loading. The load­bearing behaviour of such walls is examined theoretically and compared to test results as given in [1]. The crack condition is determined in accordance with the plate theory and the fai­lure condition is determined in accordance with the yield line theory, which is extended for the bri ttle masonry wall mate­rial. The results show, that the yield line theory can only be applied with limitations.

Ng.tª_1:.:j,gn.I:l ... :.

lihid LiH

u 13z , 5 t i 13z , r

13K i ].l

13m Wr q\' i qR mx , r i mr, U

a!

Length, height and thickness of the wall Length and height of the masonry block (nominal working dimensionsl Overlap of masonry block in bond Tensile strength of the masonry block and the horizontal bed joint Compressive strength, shear strength of the wall Cohesion, friction factor Compressive strength of mortar Torsion resistance moment Vertical and horizontal wall load Carrying capacity moments Relationship failure load/1.maximum load

1196

Tests have shown that a masonry wall supported on four sides acts first of alI as a homogeneous plate when subjected to in­creasing horizontal load qo. Subjected to a 1.maximum load qH = ql, a 1. crack forms. Dependent on the geometry of the wall,the type of materiaIs and bond, as well as the relation­ship q\' /qH, this crack runs as shown in J:':j,gl,l:r:E:!+ ei ther hori­zontally (case A) or vertically (case B) within the zone, or diagonally in the corners (case C). The load-bearing capacity of the wall is thus normally not yet used up, and qH can be increased further. With a 2.maximum load qo q2 further cracking takes place where the crack formations A, B and C become superimposed. In spite of the extensive cracking, a further load increase up to failure load qH = q3 is possible. Non-elastic rearrangements take place so that the plate theory based on elastic materiaIs no longer applies. Calculations made on this basis, such as for example [2,3] are thus very much on the safe side. A yield line theory describes the behaviour more realistically . It is to be noted here that masonry walling as a brittle construction material behaves differently to such materiaIs as steel. Cracks do not plasticize, i. e. transfer neither tensile stesses nor moments. The usual yield line theory must be extended accordingly. Furthermore, attention must be paid to the fact that the relationship ~ = q3/ql can be very large. If one designs the wall with the usual factor of safety for the failure condition q3, the crack condition ql is possibly not yet covered. In practice cracks can already formo In the following, the conditions ql and q3 are examined.

y

qV~ J]\ case A case B case C

q'~I {~.ITJ D j, 1 L

1.crack criterium q.-q,

F=l ~ ~ LLl

2.crack criterium q.=qa failure criterium q.=q3

C1 LJ

FIG . l : State of cracking of masonry walls subjected to q. and qv

1197

lf the tensile strength of the wall 132. l' perpendicular to the horizontal bed joint is exceeded, then a horizontal crack oc­curs in the joint :

o, = n,/d + 6'm,/d 3 l I3z . , (pressure: n, negative) (1 )

~ .. ,~, .. +. ....... ... y.E:! .. ~.t:i, .c::: .. ª .. J, .. ç~ªc:::lt .... ªª .... ª ...... R.~ .. ª .. tl .. J,t ..... c:>J .... RtlPJtl.~ .. ~º.:f .. ..... t. .h.~ ... J1.ªª.ºn.~. y. ~Jºc:::lt

lf the tensile strength of the blocks I3z . st is exceeded, then a vertical crack forms through the block and the vertical joints . lf one assumes that the vertical joints do not transfer any tensile forces, then each block must accept the bending moments Mx = m, ·2· H acting on 2 courses, as shown inUgtl:r::_E:! _~ .ª ;

I Ox. st = 12·mx/d 2 == I3z . st ( 2)

For masonry blocks with a high tensile strength and with a mi­nimal applied loading nl', only minimal friction occurs in the bed joint. The blocks are turned out without cracking. The mo­ment Mx taken up by a masonry block is transferred as shown in .:f:i,gtl~~ . ~J? via friction as torsion moment Mr in two bed joints .

~ u

" ~ I.:: j. , ~L ~L

,

(b) ,{ "\ l ! ~

I I

~ .J :, / ' dr {a)~

I L-lLJ6'Mx r "-o=±-­da ' H

FIG.2: Bending moments m. parallel to the bed joints (a) bending moment of the masonry block (b) torsion moment in the bed joint

t=Mr / WT

WT =aT · d . u a

1198

lf one enters as an approximation Oy = qv/d in Coulomb's fric­tion law I3r = I3K + ll' Oy as a joint has not yet cracked, one obtains as á crack cri teria

I ~ = mx 'H/aT 'd'u Z ~ I3K + ll·qv/d (3)

The value aT for the torsion-resistance moment WT is between the values aT = 0,2 for u/d = 1 and aT = 0 , 33 for u » d with linear ~ distribution. With parabolic or rectangular ~ distri­bution, the aT-values are greater with the limiting value aT = 0,38 for a quadratic cross-section. lf my is considered wi th O~' or if even an open joint forms, then d is to be re­placed by an ideal thickness di for the residual bed joint subjected to compression. This distribution was used in Section 4.

~ ...•... ~. . ....... I).:j,ªg.9.nª.:), ..... _ç_;: .. ª.ç~ .. _ .... ª .ªªR..§!ª1,I,J .. t ..... ºf._ ..... m.~ ... .f. ......... ª .nª ... n.!· .. .

The blocks crack under the twisting moment loading mos , if the inclined main tensile stress within the block exceeds the ten­sile strength I3z. s t. As the vertikal joint does not transfer any twisting moment, the block has to accept the twisting mo­ment from 2 courses as a torsional moment MT = mxs ·2·H. With ~ = MT/WT . st it follows that

I

~ = mx r ·2· H/ aT . d· H 2 ,: I3z. s t (4 )

Section 2.2.2 is also applicable for the values aT.

Analogous with section 2 . 2 . 2, for the bed joint over one block half MT = mx y 'u and ~ = MT/WT = MT/aT ·d·u 2 •

Thus with ~ = I3r I

~ = mX y /aT ·d·u ,: I3K + ll·qv/d (5)

~ .• Af:i,;:ªtÇ;:ªçKÇgnª:i,~JgI}

The equations (1) to (5) give crack values for ms, mx and mx ~· or the thus derived loads qa. The 1.crack occurs with the low­est value qa = ql .

The known yield line theory was developed for non-brittle ma­terial. lt assumes that when failure takes place such large plastic deformations occur that the maximum bearing moments act at alI points of the yield line simultaneously. lf bearing moment Mu occurs at point i of the yield line, then this value must be maintained with increasing load and deformation until alI points of the crack have also reached their bearing momento This behaviour is met wi th in steel, for example, but not in masonry walling.

1199

Masonry walling should be examined to see if a zip-fastener effect takes place; should, for example, a masonry block crack at point i when subjected to Mu, then the bearing moment drops immediately to zero, prior to the other points attaining their maximun load-bearing capacity. This also applies to cohesion in the joint. Thus, in the following, the yield line theory is expanded for brittle material.

With a rotation around the horizontal yield line, it is assumed that the mortar joint allows a turning motion by plastic behaviour. In accordance wi th :f:Jgl,p::§!} one obtains:

d mf .U = nf'2'(1 - nf/d'(3w) (6)

d

" li ny =(3w ·d· (1-2'eu /d)

d ny eu =-. (1---)

2 (3w'd

i m~w I

my. u =ny . eu

FIG.3: Bearing moment my . U in the bed joint

},j,), Ve r t i k a lXJ§!+4.r.,:i,Jl§!ªêªR§!ê1J+i:9:f:J:1ªê9n:r;YJ?+99l:t ········· fªD1d~ .. ~

The fracture of the masonry block is a brittle failure.As no­ted in Section 3.1, attention is to be paid to the zip-fastener effect. One must make a distinction between 2 cases:

Çgn4.BJ9n. I:. If it is quite clear tha t the daigonal yield line only recieves its maximum bearing moment at the end of the de­formation process causing the failure, so that no further de­formations occur up to failure condition, then

d 2 I

mx . U = (3z . 5 t • 12 (7a)

If in doubt, then case condition II should be applied.

çgng:i,i::i,gnJJ.:. After masonry block cracking occurs, then Mu in the yield line drops to zero

I I

mx. II o (7b)

1200

The cohesion ~K is not applicable with the necessary torsion in the yield line. Only the component 1: ll'Oy is permanently available. Analogous with (3) and with ~K = O one obtains:

m~ ~ t = ll'qv 'ar 'u1/H

Section 2.3.2 is applicable for the value ar.

3 ,) . 3 . -ªt::!ª;:JIlg _ ~º_Illt::!Il1::J:rl~ , \,

For mx.U either m~~u is valid, or the smaller of the values m~ . l' and m~ ~ ~

(7c)

rf one considers the diagonal yield line in detail as shown in t:i,g\g§! .. ~ as being stepped, then one can dissect the diagonal bearing moment md into the components my . U and mx . U.

I I I I-

_my.l'

rnx. l'

FIG.4: Bearing moment md.U

in the diagonal yield line

The yield lines are given from the stability of the partial areas in accordance with fJg~:r§!?

~_?t.:J:.?~_~ .. ~.?_~_._~ _:_ mx. u ,. O from (7 a) . around the supporting boundary :

h· a 2

Area 1 + 4 : q3 '-6- = mx . u 'h

c 1

EM

Area 2: q3 '6' (l + 2·b) my . U -I

e 1

Area 3 : q3 '6' (l + 2·b) 2· m}· . u '1

O for each partial area

(Sa)

(Sb)

(Se)

1201

Condition II: mX. E O. This does not mean that the partial areasiand4 fail. They are supported via shear force on the boundaries of areas 2 and 3. The section of the yield line with excess pressure qv (figure 4) are capable of doing this. The areas 2 and 3 therefor have to carry the loadings from the areas Ib and 4b. If one inserts the bearing moment for the most unfavourable sector wi thin the partial area 1 equal to mI x . u (this is possible as no zip-fastener effect occurs from this failure), then the stability conditions are given by :

a 2

Area 1 + 4 : qa 's I rnx . li (9a)

c 2

Area 2 : qa '6' (l + 2, (a + b) ) my. u , I (9b)

e 2

Area 3 : , qa '6' (l + 2, (a + b) ) = 2 'mr . u ,I (9c)

The 3 unknown a, c and qa are given by the 3 equations (8) and (9) •

case I: m • . • +<> case 11: mx . 0 2 0

1 b

c

h zO

e

'l> 'h~ m • • •• (c+e)

'I> ·1

Hmf .. ·2·a

~Y •• • b

'I> ·b

~ a ,

FIG.S: Yield lines and stability ot the partial areas - case I: plastic behaviour ot the vertical and

diagonal yield lines - case II:brittle behaviour

1 b

1202

In most of the cases that are of practical interest, the ap­plied load qv is small so that the influence of the moment from qa is predominant. In cases of large applied load qv, de­formation in accordance with the theory of the second order can be of importance. If one draws the system in accordance wi th ~~g\l:t:i;!§J.:>. in the deformed condition, then it can be seen that a moment ómy = qv·f has to be added to the stability requirements (8) and (9) for the partial areas 2 and 3. The maximum load q3 is thus reduced. The fracture deformation f can either be estimated from tests or calculated approximately from the theory of the second order. The values of f measured in [lJ lie between 0,10 ~ 0,15·d.

qv

(b)

!J. my =n~· . f

qv qv f

H 1 L .,

system 1 .order th. 2 .order th.

FIG.6: Stability by first-order theory (a) and second-order theory (b) on a deformed system

In order to verify the theoretical deductions, several results of laboratory tests which were pUblished in [lJ were examined. In these tests, walls supported at 4 sides were loaded with a constant vertical load qv and then the horizontal loads qa were increased until failure occurred. The equations (1) to (9) were used for calculation purposes. The base restraint was considered in the determination of the bending moments. This is not a full restraint but only acts partially due to crack formation in the base area of the wall. The results are shown inTªJ.:>.Ji;!J,·

1203

masonry-test h-2.16 bond mate- 'lo l.crack q, . C q,. T q;J . c q:J. T

no. 1 dw. I I rial [kN/m] [kN/m '] [kN/m'] [kN/m'] [kN/m'] [m] [em]

a 9 2.25 A 149.5 ver 21.5 20.0 32.4 37.0

11.5

a 10 2.25 A 304.8 ver 23.5 23.0 51.2 55.0

11.5

e 12 2.25 A 2484.0 dia 100.0 I 143.3 133 . O

24.0

a 14 3.75 A 203.6 hor 14 . 8 15.0 30.2 29.0

11 . 5

a 15 3 . 75 A 299.0 dia 23.0 20 . 0 37 . 9 37. O

11.5

b 38 2.25 B 148.8 ver 28.0 20.0 66 . 1 95.0

24.0

b 40 5 . 25 B 235.2 hor 39.0 I 71.3 80 . 0

24 . 0

b 42 5 . 25 B 348. O dia 46.0 50 . 0 100.4 100 . 0

24 . 0

a 60 2.25 C 87.4 ver 6 . 1 6 . 5 12.6 13. O

11 . 5

masonry bond: a = stretcher b ~ bonder c ,.. cross bond

materiaIs :

l . crack:

indices:

A brick ( fb = 6 . 0 N/ mm 2 ; s. a 5 . 0 N/ mm 2 )

B calcium silicate ( h :::I 25 , 0 N/ mm. 1 ; B. = 10.0 N/ mm 2 )

C pumice ( fb = 2 . 5 N/ mm 2 ; B. :z 2-, 5 N/ mm 2 )

hor horizontal

C calculation T test

ver -= vertical dia = diagonal

SLJ......-'. !U.-..L ql , C q" T

1.51 1. 85

2.18 2.39

1.43 /

2.04 1. 93

1. 65 1.85

2.36 4.75

1. 83 I

2 . 18 2.00

2 . 07 2 . 00

a) Tests and calculations concur satisfactorily, considering the deviation of the original data.

b) The failure load of a wall subjected to perpendicular loading can be determined with the aid of a yield line theory if this takes into consideration the brittleness of the masonry walling. This denotes: separate consideration of failure of the masonry block and failure of the bed joint; no application of tensile forces or cohesion in the bed joints; the bearing moment mx . u is taken as zero paraI leI to tne bed joint or is only used with caution; this is of importance as walls con­structed of blocks wi th high shrinkage properties tend to be

1204

subjected to restraining forces and thus from increased risk of cracking in any case.

c) The crack loading can be much lower than the failure loads, i. e. ql « qJ. The last column of Table 1 shows the relation­ship é!'! qJ /ql. If one dimensionst::hewall wi th the normal factor of safety, for example with the universal factor

'!"= 2, O, or the partial safety factor )ft = 1,35 .;. 1,50, then the safety factor against cracking under working loads is not assured wi th õ$ é!'! , and there is a danger of cracking occur­ring.

The failure load determined according to the yield line theory is the maximum possible with caution. Apart from should be provide an cracking.

loading, and should therefor be used the safety factor against failure, one adequate factor of safety against

REFERENCES

[lJ Schoner,W :Zur Biegetragfahigkeit von Mauerwerk unter Be­rücksichtigung axialer Auflasten;Mitteilungen aus dem Institut für Baustoffkunde und Materialprüfung der TU Hannover,Heft 41

[2J Mann,W. + Bernhardt,G.:Rechnerischer Nachweis von ein-und zweiachsig gespannten gemauerten Wanden;Mauerwerks­kalender 1984

(3J Mann,W. + Bernhardt,G.:Load Capacity of Masonry Cellar­walls under the Influence of Earth Pressure, V. IBMaC Washington

[4J Sawczuk,A. + Jager , T.:Grenztragfahigkeitstheorie der Platten, Springer Ver1ag 1963

[5J Schel1enberger,R.:Beitrag zur Berechnung von Platten nach der Bruchtheorie, Dissertation 1958

[6J Haase,H.:Ober die Bruchlinientheorie von Platten Dissertation 1957

[7J Tonn,V.:Das Tragverhalten von zweiachsig gestützten Mauer­werkswanden unter horizontaler und vertikaler Belastung, Dissertation in preparation

INDEX OF CONTRIBUTORS (VOLS 1-3)

Abdullah, C.S., 316 Achyutha, H., 1108 Al-Hashimi, A.K., 571 Al1en, O., 1613 Amadei, B., 261 Ambalavanan, R., 1427 Ambrose, R.J., 583 Amjad, M.A., 342 Anand, S.C., 1049, 1205 Andam, K.A., 1059 Anderson, C., 1171, 1270 Andreaus, U., 1405, 1507 Angotti, F., 1768 Anstotz, W., 334, 1363 Anton, H., 823 Arinaga, S., 491 Arora, S.K., 446 Asthana, A.K., 1571 Atkinson, R.H., 261, 1693 Auciell0, N., 1217

Baba, A., 491, 884, 1340, 1519 Baker, L.R., 874 Beningfield, N., 118, 131 Ben-Omran, H., 304 Bergman, J.W., 14 Best, R., 1759 Binda, L., 205 Bishop, N.W.M., 1467 Bocca, P., 1027, 1657 Bonacina, C., 1238 Borchelt, J.G., 52, 1496 Bright, N.J., 1417 Brooks, J.J., 64,316,342 Brown, R.H., 894 Burland, J.B., 1637 Bursi, O., 716

Cabrera, J.G., 64 Calvi, G.M., 1665 Canavesio, G., 75 Candy, C.C.E., 1159 Cao, H.T., 194, 1184 Carpinteri, A., 1027

Ceragioli, G., 75 Chen, H., 1351 Chia, C., 653 Chiostrini, S., 1768 Chitharanjan, N., 1, 503 Colville, J., 372, 1089 Curtin, W.G., 571, 595

Dajun, D., 1531 Daou, Y., 665 Dawe, J.L., 516, 606 Day, R.L., 14 De Rosa, M.A., 1217 De Vekey, R.C., 925, 1270, 1673 Dickey, W.L., 1625 Di Paol0, A., 1507 Di San Filippo, P.A., 26 Dodia, J.T., 1270 Donegan, H.A., 846 Douglas, J.G., 217 Dowling, P.J., 774 Dyson, J.M., 1791

Edgell, G.J., 617 E1-Badri, M., 64 El-Mustapha, A.M., 631, 728, 740,

1119 El-Nawawy, O.A., 867 Ewing, R.D., 631, 728, 740, 1119

Farah, M., 867 Fontana, A., 205 Ford, R.W., 92 Franciosi, C., 1290 Franciosi, V., 1290 Fried, A., 1171 Frigerio, G., 205 Fudge, C.A., 1417

Gairns, D.A., 230 Gallegos, H., 1227 Ganesan, T.P., 1427, 1437

Ganz, H.R., 1447 Garrecht, H., 1682 Garrity, S.W., 642 Gates, R., 150 Ghazali, M.Z., 548 Glanville, J.I., 304, 1148 Gnanakrishnan, N., 981 Goodwin, J.F., 272 Gé)pfert, N., 958 Goulter, I.C., 1148 Grimm, C.T., 1040 Groot, C.J.W.P., 175 Guggisberg, R., 699

Haavaldsen, T., 242 Harndy, K.A., 467 Harnid, A.A., 653, 867 Harris, H.G., 653 Hart, G.C., 1131 Harvey, W.J., 1302 Haseltine, B.A., 1836 Hatzinikolas, M.A., 516 Hendry, A.W., 458 Hilsdorf, H.K., 1682 Hobbs, B., 665, 676, 1648 Hodgkinson, H.R., 1836 Hofmann, P., 292 Hosny, A.H., 467 Howard, J., 595 Huband, N.J., 936 Hughes, T.G., 1311 Huizer, A., 538 Hulse, R., 583

Jagadish, R., 1800 Jennings, A., 1320 Jung, E., 182

Kaliappan, T.P., 1 Kalyanasundararn, P.K., 1427 Karnimura, K., 1519 Kariotis, J.C., 631, 728, 740,

1119 Karisiddappa, 1108 Kasten, O., 334 Kavanagh, J.A., 1590 Khalaf, F.M., 752 Kingsley, G.R., 261, 1693 Kirtschig, K., 906, 1363, 1373 Knutsson, H.H., 350, 1282 Konig, G., 764 Kropp, J., 1682 Kupke, C., 836

11 /

Lai, L. F . W . , 1599 Lapish, E.B., 1579 Laska, W., 1003 La Tegola, A., 1067 Lauber, R., 150 Law, A.G., 857 Lawrence, S.J., 194, 981, 1184 Lawson, R. M., 1836 Lawther, R., 981 Lenczner, O., 324 Li, Z., 1351 Livingston, R.A., 83 Lomax, J., 92 Lao, Y-C., 1759 Lutman, M., 800

MacLeod, I.A., 362 McCloskey, F.G., 1732 McSweeney, F., 1458 Ma, S.Y.A., 1467 May, I .M., 1467 Mann, W., 764, 1195 Mannion, M.P., 912 Manoharan, P . O., 503 Manos, G.C., 1779 Mansour, S.R.N., 1637 Materazzi, A.L., 1396 Matsumura, A., 1519 Matthys, J.H., 284, 707 Mattone, R., 33 Matty, S.A., 372 Maxwell, J.W.S., 1302 Mehlmann, M., 139 Melbourne, C., 991 Memom, A., 1739 Memom, A.A., 1739 Metje, W-R., 906 Meyer, J., 1373 Mo, T-B., 384 Modena, C., 716, 811 Moghaddarn, H.A., 774 Mohajery, S., 583 Morton, J., 925, 936 Motta, F., 1140 Munro, C., 150

Nannei, E., 1248 Naraine, K., 395 Narayanan, R.S., 936 Nelson, R.L., 150 Nieminen, P., 103 Noland, J.L., 1693

O'Connor, O.J., 846 Ohler, A., 1539 Ombres, L., 1067 Oppermann, B., 139 Orr, O.M.F., 253 Ossola, F., 75 ates, A., 764

Page, A.W., 479, 528, 538 Parducci, A., 1812 perry, S.H., 1637 Pfeifer, M., 1384 Phipps, M.E., 642 Pistilli, M., 150 Pistone, G., 1704 Plank, R.J., 1648 Prawel, S.P., 785

Qazi, S.A., 785

Radogna, E.F., 1396 Rahman, A.H., 1260 Rahman, A.M., 1049 Rahman, S.S.U., 1108 Raja, M.A., 1015 Ramamurthy, K., 1427, 1437 Rashwan, M.S., 1148 Reinhorn, A.M., 785 Riddington, J.R., 548 Roccati, R., 1704 Roman, H., 676 Romu, M., 103 Ryan, N.M., 1077, 1476

Saeb, S., 261 Saunders, J.O., 272 Schmidt, S., 150 Schneider, K-J., 1488 Schubert, P., 162, 406 Schwartz, J., 420 Scrivener, J.C., 230, 874 Seah, C.K., 606 Senbu, O., 491, 884, 1340, 1519 Seyl, J., 150 Sharada Bai, H., 1800 Sharp, B., 1824 Shaw, G., 1551 Shi, C-X., 435, 1563 Shi, G-B., 384 Shields, T.J., 846 Shrive, N.G., 479 Silcock, G.W.H., 846 Sinha, S., 395

III

Sivaraman, G., 503 Smith, O., 1171, 1270 Smith, F.W., 1302 Soliman, M.I., 467 Soric, Z., 946 Speare, P.R.S., 1015 Sreetharan, T., 362 Sriboon1ue, W., 707 Stark, C., 1089 Stevan, A., 1238 Stockbridge, J., 1713 Stockl, S., 292 Strada, M., 1238 Sture, S., 261 Sty1ianidis, K.C., 792 Sundararajan, R., 503 Suter, G.T., 1260

Takahashi, Y., 1519 Tanda, G., 1248 Tawresey, J.G., 686 Thürlimann, B., 420, 699, 1447 Tinker, J.A., 42 Tomazevic, M., 716, 800, 811 Tonn, V., 1195 Tulin, L.G., 946 Tutt, J.N., 1836

Usai, G., 26

Valente, S., 1027 Van Balen, K., 1751 Vandenberghe, O.G., 857 Van Gemert, O., 1751 Vaselli, R., 1812 Vernon, W.T., 52 Vignoli, A., 1768 Vilnay, O., 1311, 1330

Walker, P.J., 991 Wang, Q-L., 384, 1351, 1725 Wang, X., 1725 Wang, X-O., 435 Watanabe, M., 1519 Weck, T-U., 110 Westaway, R., 1648 Weston, J.H., 857 Wolde-Tinsae, A.M., 372, 1089 Wu, R-F., 1101

Xi, X-F., 1101

Ya1amanchi1i, K.K., 1205 Yan, Y., 1759 Yi, W-Z., 384 Y1a-Matti1a, R., 970 Young, J.M., 894

IV

Zhang, S., 559