40.- Structural Action of Brick-bearing Walls Exposed to Fire Temperatures

by C. B. MONK Jr. J. E. GOLDBERG, and V. JEARKJlRM ScltooJ 01 Civil Engilleerillg, PlIrdue Univl!rsil)', Laja)'ef/e, Indiana

A BSTRACT

In ,he s/andard Americon me/llods o/ tesrillg fire resiSlance, file end loading cOlldiliOI1S anel COllditiOI1S o/ exposure to jire are differenl for co/wnlls aliei IVal/s. This raises qlleslions of infer­prerGliol/ 01 lhe Qmilable dala, and ;11 rhis paper nwnerical methods hare beell IIsed in lhe /tear IralIs{er and strt/cllfral olla/ysis o[ load~bearing lral/s exposed to fire f rom ol1e side 011/y. The influence of loadillg (nlOgn'-· tude, direclioJl anel posirion). fhe bOlllldo,.y cOlldil iol15, and lhe Irallsienl ,herma! gradiel/[ are examilled fo r a 'srandard' jire anel a/50 for a ' nol1-sfalldard' fire bosed upon Iypica/ modem fire /ood cOlldilions.

NOTATION

Thermal Symbols li = general temperatu re va lue CF) T = specific temperature value C F) T.: = temperature of fire-exposed air

Action Portante des MllI's en Briques Exposés ali Feu

Dans /es méthodes américaines 1101'­

molisées d' essai de résislance ou Jeu , /es conditions moximo/es de charge el celles d'exposi/iol1 ou Jeu S0111 diffi!r­el1les pour /es pi/iers ef pOlir /es tnllrs. Ceci pose /e probleme de /' imer­pré/alio" des données disponibles. Dons cel arlicle 011 s'esl sel'l'i de métl/Odes numériques pOlir le Iral1s­ferI de chaleur el pour I'analyse de la slrtlClUre des murs porleurs exposés au Jeu l/l1iqllemem SUl' UI! cole. L'injluence de la charge (amplitude , direc/ioll el position), /es cOlldi/ions limites e f les gradients fhermiques transiroires sont examinés paul' 1/11 Jeu "standard' , de même paul' lfll [eu "noll standard' réa/isés à partir des cOl1dirions Iypes acruelles ell ce qui COI1Cerlle le Jeu.

Ball/iche Auswirkllng von Ziegel­maue"n, die Felle,'-Temperatlll'en aus-gestezt sind 'I

In den llOrmalen amerikanischen Priifmelhodell fi;r den Feuerwider­sland sind die Bedinglfllgen für die Elldbelasll/I/g und die Arr, wie sie dem Feuer ausgesetzl werden , bei Stützen u/ld Mal/ern l terschiedeJ/. Dadurch en/stehel1 fragwürdige Auslegungen der erreichbarell Dalen. 111 der I'ortleg­elldeu A rbeil lI'urden 1111merische Methoden [ ür {he Warmeüberlra­gllJlgs- und Slruktur-Analyse lasllra­gellder Mauem bei einseitiger Bean­spruelwl1g durell Feuer )ler1l'endel. Der EinflujJ der BelaslUlIg (Cr6jJe, Richllll1g til/c/ Lage), die Grenzbe­dingungell une! der nichtslatiollare Temperafllnerlaulwurden SOlI'Oh/ für ein StGndard-Feuer aIs allch Jür ein Nichlslandard-Feuer auf der Grwul­lage Iypisch modemer Fellerlasl­bedinglfl1gell gepriif/ .

y = eb fel = bottom- top eccentricit y ratio

Structural Symbols P = general load va lue (Ibf/ ft of \Vali) p , = appl ied structural load

Te.f = temperature of fire-exposed surface TII~ = temperature of fire-unexposed surface TI, = temperature of fire-unex posed air

PT = thermal axial load M y = general moment (ft Ib) M 1 = Pel = lOp applied moment Mb = Peb = bottom applied moment M T = therl1lal moment

)I = u/ Tu = dimensionless temperature )'jj = 1'= with finite difference notation V = T,/T" k = thermal conductivi ty (Btu/ h ft' °F/ft) c = specific heat (Btu/ lb °F) p = density (lb/ft J)

K = k /pc= thermal diffllsi vity (ft'/h) f, = exposed sUfface filll1 coefficient (Btll /h ft ' °F) J" = lll1exposed surface film coefficient (Btu/h ft' °F)

Dimensional Symbols H = wall height (ft) L = wall thickness (ft) e, = top eccentricity of applied load (ft) o: =et/L = dimensionless top eccentricity " = bottom eccentricity of applied load (ft) /3 =,,/L=dimensionless botlom eccentricity x = thickness distance measured from exposed side (ft) z = x /L = dimensionless d istance li = Llz = Ll x /L = incrementai distance i = index for distance increment b = wall length in perpendicular to h, I ft

247

~ =coefficient of linear expansion (in.fin . °F) E = modulus of elasticity (lbf/ in') mj =ch/ljJo = relative expansion value /1; = Ei/ Eo= relative modulus value A = area (ft') 1 = moment of inertia (ft4) C = di sta nce from neutral axis (ft) A* = transformed A } dUe to variable " = transformed 1 properties with T a = normal ftexural stress E'I' = transformed rigidity 'I' = g/h' = finite difference scale factor XA =distance between centroid of the transformed

section and the exposed surface (ft)

Time Symbols = general time value (h)

S = Kr/L2 = dimensionless time g = Lls= KLlr/L2 =incremental time j = index for time increment

248 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures 1. INTRODUCTION

A historical review of the fire testing of vertical building elements in lhe USA shows three series af column tests and one series ofwall tests. The first series was performed in Chicago at the Underwriter's Laboratories(l917- 1918), I and was primarily upon 5teel columns with a few re­inforced concrete and wood columns included. A 15-ft 8-in. specimen having an unsupported length of 12 ft 4 in. could be accommodated. The lower 12 ft was fired in a 7 x 7-ft furnace, providing fire exposure on ali sides. A study of the loading mechanism suggests a flat-ended condition top and bottom, loaded at the bottom through a 36-in.-dia. piston by water pressure (300 000 Ibf maximum).

The second series was performed in Pittsburg at the Bureau of Standards testing station (1917-1919).2 Ali columns were reinforced concrete, 8-ft 9-in. long. The furnace (6 x 6 ft in plan) completely engulfed 8 ft of the colurnn in ftames. The boundary condition must be assessed as flat-ended. Loading was through a 500-tonf hydraulic ramo

The third series was performed in Washington at the Bureau of Standards (1929- 1930).3 The steel specimens, protected with a variety of fireproofing systems, were 13-ft l-in. long, fired over the lower 8 ft in an 8 x 8-ft furnace providing fire ali around. The column was assumed laterally supported at the IO-ft 4-in. leveI. Again boundary conditions are reasonably assumed to be flat-ended and loading was provided by a 500-tonf hydraulic ramo

The bulk of loaded column testing has been done in the USA on this last facility at the Bureau of Standards. The points to be made in this brief review are:

(I) The lack of uniformity in length. (2) The exposure of the column over a portion of its

length and completely surrounded by fire.

(3) The limitation of the loading mechanism resulting in testing relatively small columns to full design load or

Stondard Fl fl! p,

:7i [1. 10

ê ~24001 u

o b o 8 ~

~" 4 h ~ -I h 2h

Ih rOmin u3000J 5 mio [Ocx::flJ

2 3 4 r im\!: [h]

r"'1 Non-ston dcrd Fir c [T. ] ~2400 ~ • I '6 ~ _---E 1800t-SÃ--- - ---~ • c.. 1200 E • >-

600

2 3 4 T im e [h]

I

I

I O

Õ x -• • I

I " .E ~

~

• • I I • O

:t O w '$ "ti

relatively large columns below full design load . (4) Flat-ended boundary conditions.

In contrast to column testing, load-bearing rnasonry walls have been characteristically fired from one side. A series of 167 specimens, 10-ft 6-in. high by 16-ft long, were tested in a vertical wall furnace at the National Bureau of Standards from 1921 lO 1927. The wall was loaded over its 16-ft length by a loose beam at its bottom, resting on top of four 200-tonf hydraulic rams, but the testing frame would only take a total load of 400000 Ibf (about 250 Ibfjin2 on an 8-in. wall). The bottom beam loading suggests a measure of bottom rotation was possible although the manner in which the test frame was clamped against the furnace probably restricted rotation in an unknown way. In contrast to column testing, lhe following points are emphasized for load­bearing wall testing:

(I) Uniformity in wall height.

(2) Unsymmetrical exposure of fire to one side of the wall over its full height.

(3) Boundary conditions ai lhe top were probably flat-ended but did permit a degree of rotation at the boltom in a manner freer than lhe column tests.

As in the column tests , lhe wall-loading mechanism was limited in magnitude.

This paper examines the structural significance of unsymmetrical fire exposure of load-bearing masonry walls. An analytical technique is developed to account for the thermal stress and deflection that must be added to the structural elfect. The study recognizes the influence of boundary conditions on both lhe freedom of end rotation and on restraint of change of length. Both the Iraditional standard fire' and a non-standard fire (based on more recent burn-out data) are compared. Based on the limited available data, the influence of the changes on physical properties as temperature increases is examined.

I To .. T,.

-' .' • v I x ~ • .

c '" " ;;: ~ o ~ • '$ ~ • ." • ~ ~_h_ to O c ~ x • Tl'mpe fo t ufcz Grad illnt c =>

FIGURE I-Fire and structural loading of bearing wall.

C. B. Monk Jr, J. E. Goldberg and V. Jearkjirm 249 2. THEORETICAL ANALYSIS shall be" t. Failure to fulfill this condition can result in

The fire and structural loading of a typical bearing wall divergence ofthe numerical method with finite differences. is illustrated in Figure I for both a standard fire and the The wall will tend to curl or deflect towards the fire non-standard fire. The latter is based on data accumulated For analytical convenience (Figure 2(b» the wall is first in the last decade in lhe USA from experimental studies assumed restrained against rotation and length change, offires generated by nuclear warfare5 and those conducted resulting in the thermal loading shown. This may be by the Ministry of Building Construction in Japan.6 expressed as a thermal axial force , Pr, and a thermal end Observed time- temperature relationships for different moment, M T • The thermal end mament may be released conditions and types of combustibles are replaced with to accommodate desired boundary conditions of end lhe standard time- temperature curve in these reports. rotation. Similarly, the thermal end force may be The fire load of the contents of many of the present-day released to study the influence of unrestrained length. buildings will peak in about I h and decay to zero at lhe A completely unrestrained wall will curl towards the fire end of 2 h. and grow in length. If the thermal gradient is linear, the

Because af lhe transient nature af lhe fire load, lhe thermal stresses are zero upon complete release af analysis fillst be treated as a dynamic heat flow problem. thermal restraining forces . For lhe transient heating The classical one-dimensional heat ft.ow equation is set studied here, the thermal gradient is non-linear; hence, out in Table I. Oimensionless parametersareintroduced upon full release of MT and PT residual thermal stresses and ali equations are expressed in tinite difference forms will exist. using forward differences and backward differences at Thermal loading equation5 are set out in Figure 3. the boundary position. The wall , 8-in. thick, is divided These equations have been specialized for the case where into ten thickness increments (i~ I to 10) (Figure 2(a). the physical properties are considered to vary with the 80th the time increment, g, and the space increment, h, temperature. As these are based on the tinite difference must be chosen to fultill the stability conditions that g/h2 equations, the dimensionless parameters, Ili = E! Eo for

TABU I - DYNAMIC HEAT FLOW THEORY

Classical Hem Flow EquatiolH:

0// 2 OU k K ;- = -;- where K = -

{} x l. ('I pc

ou ) k j)"X =-/" (T('-T~s) ® x = o

CU boundary cOllditions k à"X = -/11 (Tus-TII ) (! x = L

Dimell.Jionless Paramefer:

Dimellsionless Eqllatiolls:

óv2 OI' az2 = (Js

a' _ (f'L) Ir" T') . ' - 0 I a-;- k \T,/-r;; ® -, -

,= ~ 1-- ~ x = L O" (r.'L) (Tu,) I a, k Tu Nllmerical Operarional Notarion:

boundary condition~

1 I i = position increment Vij va ues, where Ij= time increment

Finire Difference Equarions:

V/.Ft"! = IJlvi+ !.J+(l~2'1') Vi . j + V'Vi_ L.j

where

'I'~gl'"

Stabilily criteria:

'1' ,.. lI/iria' cOlldiriofts:

:~'.~ :: ~) VI,s = 1

BOlllldary condiriom':

Vj,j + w('V Vo.j= ~ I +w-;--

II L) where lI'u= 1I \ k @, x = L

------------------- ------------

the change in modulus af elasticity with temperature and /11i =4>d4>o for lhe change in linear expansion with tem­perature are intraduced.

The combined structural and thermal loading action is schematically shown in Figure 4. As the structural laading may be eccentric, it causes an elastic deflection that of itself increases the structural moment. As the fire is assumed to occur on the inside of lhe wall, the same side as the load eccentricity will probably oecur, its action will curl the wall thermally, producing a deflection op­posite to the elastic deflection. The thermal moment (released to produce the desired boundary rotation) will also oppose the structural moment. Three cases are shown in Figure 4:

Hinged Intermediate Fixed

H-H H-F F-F

Equations for the combined action shown in Figure 4 are displayed in Table 2. The final stress, a , is shown to be made up of:

(a) the initial thermal holding force, -E,ptJT;

(b) the given axial load , -P,IA ;

(c) the given bending due to load eccentricity, M" and the release of the thermal moment, M r , both contained

in My(±MyCfI);

(d) the thermal force , Pr, if length is unrestrained ( + PrIA).

The sign convention employed is + for tension and - for compression. When physical properties vary with temperature, a transformed section (A' + l*) is utilized (Table 2).

The influence of temperature on the k-factor for bricks and concrete is shown in Figures 5 and 6. It should be noted that for bOlh materiais the value increases with temperature for relatively low values but decreases for relatively high values. For building bricks considered here the value is assumed to vary linearly (Figure 7). From the sparse literature available both lhe specific heat and the modulus of elasticity are assumed to vary

250 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures

Solution ! Grid ~

E ~ u C

j~ n

j.3

j -2

§ j .. I

t- ) .. 0

-

-

- -:-- f- - -

!l! I;'

. !. . .!. . .!. ,! .! I . .!. .!...

Pos it ion r ncrOZ'~nt5_

<a)

---

,

K61 g-~'ÓS

h _ ..lU L ~ÓZ

PT - 'Z . __ .~ .~T p.

Actuol Thtzrmol Loadiog

v

M, 1 ~ M, P, f ··.··.~. __ ._._·.· ". ~ P, l=Ie!itrainlZd R.etation

Restroinord Length

PI Mr"'O

Pl -O "'00

. -. :-:--._. -_.-"-"

.... - --(b)

PTa O

M,-O

Um5tro ind RotatlOn RlZStro in~ Length

Unn'!)trolned RDtation UnrestroinOO LlZngth

FIGURE 2- Thermalloading aclion.

".U

l Vi,)

di = [?Vi.,T .... 'l!!..­:)[VI-It- Vi]

for Qny j

PhysicaJ Properties Variable 1I';lh Temperarure

lIi= EiIEo, mi= .piNo

Pr= Eo.pobLh [j~l ( Vj- ['~+Vi'l)"IIf/;_ IO] Physical Prope,.,ies Constan! wilh Tempera/llre " bLI[(VI-loi+VI.i) I]

PT ~ E4>bL" [;~, (VI- lo~+";,j)_JO]

MT~E~bL't.[,~,( ~+ VI,j+l) O-Ih+d)]

Pi= Eo'l'O I --2- II jl/l,-

.Yi= L(ih-dj)

_ _ EMi Mj = P iXi ".Xp= Pr

10 LhEllj(i- O·5)

_ i _ I XI/ = 10

Illi i~1

Mr= PT (.\',,-Xp)

FIGURE 3- Thermal loading equations.

C. B. Monk Ir, J . E. Goldberg'and V. Jearkjirm 251 ~~~

loodir'lg Dqf l«ct ion Curlin9

" P

H inljl«d CO !lCE [ H- H]

P

" " ?

lnt "rm «diotq Co!lZ [H- F]

I"

I FIX'ld Co S'l [F- F]

Structurol Eto stlC T hl!'rmol Thqrmo l lood ins ~n Curling Mamllnt

FIGURE 4-Combined structure and thermal loading action.

TABLE 2-COMBI NED STRUCTURAL ANO THERMAL L OADlNQ EQUATIONS

Hinged Case :

[ (l-Y}Y] (P) ( I ) [(Mr-Mr) M. ( y,)] My- M. I ----v- + El I- PIPE --2- (Hy-y2}-r; ( I-y) HY- /f - Mr

Intermediate Case:

[3 Y (HY y2 Y' ( PIEI )] My- Mr-{Mr-MT} 2/f- 4 - 2 + 4H I PIPe

Fixed Case :

M = O where J P = Pt+ Pr restraine:d length y l P= P, unrestramed length PE= Euler buckling load

Physical Properties Constam wirh Temperolllre:

a=-E.p.tJT- ~ =t= MyC wherei P= P t restrain~d length } { tension + A I P = P,-Pr unrestramed length compre5sion -

Physical Properties Variable with Temperature:

as shown in Figure 7. The available literature suggests that the coefficient af linear expansion is a constant at ali temperatures of interest in this study. (If quartz crystals are contained in the brick, the inversion at 573°C will tend to negate this assumption). Finally, the usual surface film coefficients aeeeptable at or near room temperature must be modified as the temperature in­creases. This has been done arbitrarily, as shown in Figure 7. Note that this coefficient is broken into two components: a convection effect and a radiation effect. The variation of physical properties with temperature is believed typical of the trend in change ; speeific cases may vary substantially from these assumed. The purpose of introducing these arbitrary values is to study the effect that such changes may have on the analysis.

3. INTERPRETATION OF ANALYTICAL RESULTS

Figures 8-11 show temperature gradients through the wall calculated by finite differenee analysis. Comparing Figure 8 and 9, or Figures 10 and 11 , substantial differ­enees in the gradients are noted depending upon whether the properties are assumed constant or variable with temperature. In general, the latter eondition tends to produce steeper and more non-linear gradients than the former. As noted before, this gradientcondition will tend to produce residual thermal stresses of a higher magnitude. For both sets of curves, the initial gradients at and prior to I h are very steep and very non-linear. The influence of the surface film coeffieient of heat transfer is most marked in comparing the variable property case with the

252 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures

10~ 8~

6 5

4

3

?2 u: o

-~J Or - 8-~

• 5 -=3 o :; 4 ~

3,.

2

~

•

~""<Ó

"./' '?j\(f~ •

ó:.Q, "

~~a,6

~ "'''' .

• Zir Cra,Fire~k

y\tOZ 8(1

\t..'?o'i\~

,0'1 ! I I I

900 1000 1500 2000 2500

Tll mp ot rotura, [ORJ

FIGURE 5- Thermal conductivity for bricks.

0 4

0 3 'iV ~

S'P:

SpllCi f ic H'!o t ,

... \0 -;: .-'?1-\Q "

'7 ~ o .~

... Thcrmol Corduct lvity k

1-01

0'ft

• ,OX.

~ci ,,0 . .

,;>,"

~ 02 ~

e. 0. 5 , v ~

OI

'I~COO"<t. 1'1· 2' 1.1 by volumrz

~ 6 1009'0 .... otlzr contoznt IDormaQ

~ 5

"2 4 '

~

Ô 3

ã ~ 2

" O>

10-'

8

6

I I~e and 4 hydite by yo lum«

Sil- o -cel Cl conc~te

~ Lum mll,z c ozment corcrete ..------

5 1 ! -----.J 500 1000 1500 2000

Ttl:mperat ure ~RJ

FIGURE 6---Thermal conductivity for concrete.

~ u,

I

Mcxlulvs of Elos t icit)! E

,1\ E -1 ·35 1. IO· lbf/m2

~

ª I b lo lo I .

O O O

" ~ ~ I 8 lo I lo

O O Q o' ~-g !.-g o

Tc mpll rotunz ~FJ Tempcroturc ~F ]

>C! C'I àS '<l' - - N

Tcmp ot ro t ur e ~FJ

Cocff icilln\ of Thcumol Su r foce Film t , - 1-5 Btu Ih ft ~~ )In it io l or Exponsion rp -4 x 10-6 in/in'1= Coett ici ents · I . _ 6-0 Bt u/h f t ~ OF Con~tont Volu~s

f, - K, [r..r.J, K,I);<- r.,<J Wher e K,- 0.570 K, - 429 xO- 10

FIGURE 7- lnfluence Df temperature on physical properties.

constant property case. As the temperature increases, the convective turbulence plus the radiation exchange be­tween the luminous fire and the wall surface cause the exposed wall surface temperature, Tf'~, to approach the firo temperature, T,., itself. The decaying of temperature after I h is to be noted for lhe non-standard fire. Although thr fire has stopped at the end of 2 h, a residual thermal gradient of substantial magnitude still exists in the wall. The maximum thermal stress will oceur within 10 to 20 min after I h for the non-standard fire. In general , the transienl efrect of thermal loading is more marked when the variation of physical properties with tem­perature is taken into account.

A struetural analysis ofthe wall subject to the combined

structural and thermal loadings has been made. Thi s is presented in Tables 3 to 8. The tabulation of resuhs indicates a comparison between physical propert't,es constant and variable with temperature, length restrained and unrestrained , and fire that is standard and non­standard. Three basic boundary conditions are studied : fixed-end (F- F), intermediate (H- F), and hinged ends (H- H). The results are listed for three time intervals : 5 min , I h, and 2 h (or the time of maximum stress in the case of non-standard fire). Table 3 compares the three boundary conditions for the case a f zero eccentricity for the structuralload (10 000 Ibf). Table 4 is a complete tabulation of the intermediate case (H- F) for a variety of load eceentrieities (a= O, ,'" ~, t , ! ). Table 5 is a

C. B. Monk Jr, J. E. Goldberg and V. Jearkjirrn

. • , " > 1

500 \ \

1500

1000

500

68--- -:"-"63 O O

T. O o-! 0 -2 0'3 0 4 0-5 06 0·7 08 09 l-O T, Z - V OIU2S

FIGURE 8-Tempcrature gradient standard tire constant properties.

2

: 1000 , ,

" > 1

500

1500

1000

00

FIGURE 9- Temperature gradient standard fire variable propertics .

253

254 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures

FIGURE 10--Temperature gradient non-standard fire constan! properties. '"' "'-'

! ~ ,

'500

'000

:500

~/ o~, Õ'2:Z--:'4~ 0'9 ,i-~og z - Volues

'u:l 1oe, "-.J

'500

1000

• g

~ , FIGURE I J- Tempcrature gradient non-slandard fi re variable

properties.

500

f~ '--- -------~ 1~6B o·, 0·2 -CF) ·4 05 0·6 0'7 0·8 09 1,0,.

z-Vo lue!i

TABLE 3- COMPARISQN QF THE THREE BA5IC END CONDITIONS WITH ZERO ECCENTRICITY OF ApPLlED LOAD (P/ = 10000 lbf)

R~Jtraint

Jmif! Ih 2hormox, I I I 1-==-1 S/andard Nonstandard S/andard Nonstandard Sumdard Nonstandord

- 2924 _ 104 - 643 -104 - 9687 - 108 - 9574 - 106 - 12792 - 236 - 9574 - 210 F- F

1

-3 603 + 634 - 764 ~' -1'4 1 8 + j623 - 14882 + 5201 -2 1405 + 8376 - 15074 + 5716 H - F Constant properties I - 2420 - 608 - 561 ~ - S 118 - 4677 - 5424 - 4256 - 4675 - 8353 - 5 424 - 4849 H- H

- 4830 - 109 - 2231 - 104 8624 - 164 -9 152 - 155 - 9496 - 380 -9 152 - 475 F- F

Variable 1-5884 + 2778 - 2700 ~ - 16595 + 16170 -16503 + 15235 - 8072 - 3231 - 16503 + 15941 H-F propertit!$ - -I I 4077 -2174 1914 - 464 + 2009 - 2976 - 25 1 -18793 + 54902- -121577- + 7576 - 22697 H- H

- 2739 + 8 1 - 612 - 73 - 7788 + 1792 - 7884 + 1583 - 9229 + 3331 - 7884 + 2034 F- F

Constant j -3477 + 819 _ 734 + 47 - 135 18 + 7522 -13 192 + 6891 - 17837 + 11 944 - 15015 + 7794 H - F properties

U"rutraint I 1- 2 242 1 . .:_~~.:'J.=_.:'~.~_~ - HJJ 1- l.Ubl 1- 4JIJ 1- 19117 1 -- J432 1- 2461 1- 4313 1- 2045 1 H - H

-4624 1 + '09 F- F Variable 1- 5678 + 3397 H - F

properties -334 - 2 046 l '::"':":::"I~L:_2.~~J + I \34 1.:\0 282 1 + 6798 1- 7616 I H- H ----4---~I -~ 917 1- 1 429 1~

Um'.'Cp 1 Exp Unexp Exp Unexp Unexp Exp Unexp Exp "-Xp Unexp Exp

- For standard lesl, variable prope:rties and resl raint lenglh P-+PE aI 2 h (H-H case).

Struc­tIlral bound­aryend rondi­tions

C. B. Monk Jr, J. E. Goldberg and V. Jearkjirm 255

TABLE 4-INFLuENcE QF ECCENTRICITY OF ApPLlED LoAD FOR THE CASE OF INTERMEDIATE BOUNDARIES (Pt = 10000 l bf)

5 min J h 2 h (l~ max.

Standard NQ/lswndard Stalldard NQnSlandard Standard Nonsumdard -

I - 3 663 + 634 - 764 + 17 - 15418 + .'5623 - 14882 + 5201 -2 1405 + 8376 - 15 014 + 5716 O ------ ----------

- 3 637 + 608 - 738 - 8 - 15392 + .'5596 - 14 856 + .'5 175 - 21379 + 8349 15048 + .'5690 .; - - - ------ --- ----

I Consumi - ) 611 + S82 - 747 O - 15366 + .'5570 - 14830 + .'5 149 -2 1353 + 8323 - 15022 + 5663 I properties

-15340 - 3583 + 556 - 799 + 52 + 5544 - 14340 + 5 123 -21327 + 8292 - 14996 + 5637 I

-=-i559 --- -----------Restrainl + 530 - 851 + 104 - 15324 + 5518 14778 + 5097 li 300 + S 271 14970 + 5611 !

--- 5884 + 2778 - 2700 + 425 - 16595 + 16170 - 16 503 + 15235 - 8072 - 3231 - 16503 + 15941 O

Degree - 5873 + 2217 - 2676 + 397 - 16 570 + 16119 - 16480 + 15186 - 8149 - 3089 - 16480 + 15890 ir oi

Variable --------------------------------------------- eceen-properlies -5861 + 2716 - 2652 + 372 - 16 546 + 16070 -16 450 + 15137 - 8225 - 2946 - 16450 + 15839 I tricily

(Slrue--5850 + 2685 - 2629 + 345 - 16521 + 16019 16433 + 15089 - 8302 - 2804 - 16433 + 15788 I rural

- 5839 + 2654 - 2605 + 318 - 16496 + 15969 - 16 4 10 + 15040 - 8 378 - 2661 - 16410 + 15738 I load)

3477 + 819 734 + 47 - 13 518 + 7522 -13 192 + 6891 - 17 837 + 11 944 - 15015 + 7792 O

- 3 451 + 793 - 708 + 21 - 18 492 + 7496 - 13166 + 6865 -17811 + 11918 - 14 989 + 7766 -;-Constallt - 3 425 + 767 - 717 + 30 - 13 466 + 7470 - 13140 + 6839 - 17785 + 11891 -14963 + 7740 t properties

3 399 + 741 769 + 82 13440 + 7444 - 131 14 + 68 13 - 17 758 + 11865 - 14937 + 7714 I - 3373 + 71 , - 821 + 134 - 13 414 + 7418 - 13 088 + 6787 -17 732 + 11 839 - 14911 + 7688 I

Unreslmin/ I -5 678 + 3397 - 2 589 + 552 -15419 + 19 690 - 15437 + 18 428 - 19891 + 28945 - 15437 + 19473 -O - 5 666 + 3366 - 2 565 + 526 - 15395 + 19639 - 15414 + 18379 - 19858 + 28884 - 15414 + 19423 r--;-

Va,iable - 5 655 + 3 335 - 2542 ~ - 15370 + 19589 - [5 391 + 18330 - 19826 + 28823 - 15391 + 19 372 I-j {lfopertil's

- 5 644 +3304 - 2 518 + 472 - 15346 + 19539 - 15 367 + 18282 - 19 794 + 28763 - 15367 + 19321 I

5633 + 3273 2495 + 445 - 15 321 + 9489 - 15 344 + 18234 - 19 761 + 28703 - 15344 + 19270 I

Exp Unexp Exp Ullexp Exp I

Unexp Exp Unexp Exp Unexp Exp Unexp I

TABLE 5 - INFLUENCE OF VARIA BLE BorrOM LOAD ECCENTR1CITY CORRESPONDING TO Top LOAD ECCENTRICITY OF c.:=t FOR THE CASE OF HINGED BOUNDARIES (Pt = 10 000 lbf)

5 mill J h 2 h or max.

Srandard Nonsrolldord Standard Nons /andarrl Standard Nonstandard

-2527 i - 501 - 666 - 80 - 5242 - 4 552 - 5546 - 4134 - 4822 - 8206 - 5546 - 4722 -;---

1

2536 492 - 666 - 81 - 5211 - 4584 - 5515 - 4164 - 4785 - 8243 - 5 515 - 4754 I Constallf - 2 536 - 492 - 666 - 81 5 179 46 16 5484 - 4196 - 4748 - 8280 - 5484 - 4787 ()

properties - 2536 - 492 - 666 - 81 - 5 147 - 4648 - 5462 - 4228 - 471l - 83(7 - 5452 - 4819 -=I - 2536 - 492 - 666 - 81 - 5 114 - 4681 - 5419 - 4261 - 4673 - 8 355 - 5419 - 4853 --::-t

R" s/railll - 4126 - 2041 - 2008 - 355 - t 812 - 21570 - 421 - 18437 + 53906· - lJ9702· + 7279 - 21140 1 ----! - 4113 - 2076 -1967 - 403 - 1861 -21672 - 378 - 18 526 + 54155* - 120170· + 7354 - 22364 Ratios

Variable oi properries - 4089 - 2115 - 1920 - 457 1911 l[ 773 336 - 18615 + 54404· - 120640* + 7429 - 22470 O botlom

f:"j 10 top - 4084 -21 57 -1873 - 510 - 1960 - 21 875 - 293 - 18705 + 54654* - 121108· + 7503 - 22 584 eceen_

~ tricitie.f 4067 2201 I 825 364 2010 21 978 250 18794 + 54903· -121579* + 7578 - 22 699 ._-------------~ -2347 - 310 - 636 - 50 - 4038 - 1 957 - 4418 - 1 881 - 3537 - 2355 - 4418 - t 940

--------------- -------I-j - 2351 - 306 - 636 - " - 4006 - I 989 - 4 387 - 1913 - 3 507 - 2385 - 4387 - 1971 Conslan/ - --------properties - 2351 - 306 - 636 - " - 3965 - 2030 - 4344 - 1956 - 3471 - 2422 - 4363 - 2013 O

--- -=I - 2 351 - 306 - 636 50 4071 - 1924 - 4 499 - 1 851 - 3428 - 2465 - 4449 - 1907 --- --::-t -2351 - 306 - 636 - 50 - 4071 - 1924 - 4449 - 1 851 - 3 587 - 2306 - 4449 - 1907

Unrestraint --- ----~ 3963 - 1304 -1901 - 226 2 [46 7 518 3204 7 185 + 1001 - 10033 - 6638 - 7410

- 3 947 - 1347 - 1 856 -277 - 2120 - 7573 - 3 179 - 7237 + 1036 - 10097 - 6686 - 7464 ! Variabfe ---- ---- ----o properties - 3 926 - 1407 -1809 -33 1 - 2096 - 7633 - 3 15 1 - 7295 + 1072 - 10166 - 6748 - 7525

- 3 902 - t 469 - 1762 384 2059 - 7698 - 3120 - 7 360 + t 111 10239 - 6825 7590 ~ - 3880 - t 531 - t 713 - 438 - 2024 - 7769 - 3087 - 7429 + I 152 - 10316 - 6903 - 7661 -=t-

I - ---

Exp Unexp Exp Ullexp Exp Unexp Exp Unexp Exp Unexp Exp Unexp

• For standard test , variabJe properties and rest raint tength P-+PE aI 2 h.

256 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures

TABLE 6-CoMPARlSON OF THE THREE BASIC END CoNDITlONS WITH ZERO ECCENTRICITY OF ApPLIED LoAO {P, = 100 000 IbO

5m;n Ih I 1 li or max.

Slalldard NOI/SIO/rdard StandMd I NOII~·tam/(lrd Standard I NOlIsl~mlard I I COllstam

- 3862 1- 1041 - 1580 1- 1041 - lO 625 i - 1045 I - I0!l11 1- 1044 - 137301- I 174 1- 10" I 1-:Ji"48 F- F ---

prop('rI;t.f - 4600 1- 303 -1702 1- 920 - 16356 - 4685 - 15819 + 4264 - 22342 + 7438 1 - 16012 + 4778H-F

- ]]14 - 1689 -=!.i9I1-I 130 5617 1- 60!53 - 5969 5586 4726 - 10171 H69 6246 H- H R"flrllim

-5 1S9 - 1095 -3055 - 1049 - 90]8 - 1407 - \} !ISS - I 366 - 9988 - 1 839 - 9 !iS6 - 1661 F- F Yariablc ------

propnrirs - 6194 + 1741 - 3 518 - 52S - 9286 - 907 - 9845 - 759 - 7417 - 6819 - 14968 + 11328 H- F ---- 4365 - 3 272 2721 - I 427 + 52 16 -30 647 -r I 832 2S 211 254681' + 458562' + li 162 - 3l 038 H- H

---------- J 676 - 85. - I 550 - 101 1 - 8725 + 854 - 8821 + ." - 10162 + 2 393 - 8821 - 109. F- F

---Consta'" - 4415 - 117 - 1671 - 884 - 14 456 + 6585 - 14129 + 5954 - 18774 + 11006 - 14192 + 6854 H- F

proPCft;I'S - ----- --- ----- 3137 - 1395 - 1461 - 1100 - 4543 - 3228 - 4947 - 3228 - 3816 - 389 1 - 5969 - 8309 H- H

Unrl's/m;nl ------ ------------- ---- ---- - ---- - --- ---- --- 4 953 - 476 -2944 - 922 - 7863 + 2 113 - 8 490 + 1827 - 79Q3 + 4342 - 8 490 + 2355 F- F ---- ---- -------- ---

V(/f;abf,' - 5 988 + 2360 - 3 407 - 398 - 15668 + 18108 - 15 693 + 16907 - 20125 + 21 013 - 14 609 + 17 876 H - F properti!'of ---------- - -- ---- ---- - --- ------------

- 4211 - 2 511 - 2 613 -1296 - I 653 - 10626 - 28 17 - \O 052 + 2548 - 15327 + 5918 - 10491 H- H

------ - ----- -------------- ---- - ------- -----------Exp Unexp Exp Un('xp EI'p UI/('xp Ex!' Uncxp Exp Unl'xp E;>.°p UIII' .>::{I

• For vari.ble prop:nies. 5l."dard leit. reslraint length and H-H case ai 2 h P > PE-

TA8LE 7- I NFLUE:-ICE OF ECCENTRICITY OF ApPUED LOAD fOR THE CASE QF INrERMEDlATE BOUNDARIES (P/ = 100000 Ibr)

5 m in fi, lharft/ax

Slondar!1 NOflSlandard S IQ/lllttrlJ NOl/sw/Illar./ Stul/dard NOIlSlanda,,1

------,- 4600J~j - 1 102 i~ - 16356 !- 4 685 - 158 19 1 .... 4264 -22)42 + 1438 - 16012 + 4778 O

- 4383 - 520 j -2 101 - 520 - 16095 ;+ 4425 - 15559 40.)4 -22082 ..... 7178 - 15751 + 4 518 o,~ COI/SUIIII 1-------pmrwrti('f - 4803 j 0 ! - 2622 O 15105 + 4164 - 15N'J 37H 21821 + 6917 15491 + 4257

- 5-424 1- 520 L= __ :.~~ 580 1- 15574 -:-3 904 - 1~038 1 3482 - 21561 + 6657 - 15230 + 3991

- 5945 1+ 104I j -3 663 + 1041 1- 15314 + 360 - 14718 j' 32~3 -27300 + 6396 - 14 970 + 3136

--= 6194 +I7.il-=-i5i"8~I-=9""2S6 -=-907 --=~-fuj-=~-=--74i"9--=--68i9~+IiJi8--0-

- 6082 + 1432 - 3589 - 501 - 9789 + IH - 10314 + 221 - 8329 - 5121 - 14754 + 10866 1 ,~ V(Uillbll' 1-_____ " __

Rtftrail/I

pro"mi('o~ 1- 596') ~ - 4012 ~~1 - 1029:.....1~~788 ~ 202 ~ - 3422 - 14540 + 10405 __ 1_

~ + 869 - 4484 + 568 '- IOH7 1+ 2189 - 11251 + 2183 - 10148 - 1124 - 14325 + 9943 j 1

- 6161 + 1486 - 4951 + 1103 - 11300 1+ 3222 - 11120 + 3 164 1- 11058 - 25 - 14112 + 9982 ! ------1 1- 441 5 _ 117 - 1671 _ 839 - 14456 + 6585 - 14129 t- 5954 1- '8774 + 11006 - 141 92 ... 6854 , O

- - - ------------------ ---- --------------- _ 0 0- 0 ___ • o 0 __ __ 0 _

~_=___ .. :::..J -2071 ~~I+ 6324 - 13869 1"'" ;}O'.lJ I - L(I;) L4 1-r 'U / 'fO - I J":IH -r "''1'f I ,~

- 471 8 ..... 185 - 2592 + )0 - 1J33S 1+ 6064 - 13609 + 5 433 - 18253_ 1 __ + 10485 - 13671 + 6334 • Com'la", prop(''''''$

Ullrt'Struill t 1----..,1

Voriabfl' prop;>rt/ef

- 5239 + 706 --=--3iI2 ~-=-i367S + 5804 - 13348 ) ..... 5 172 - 17993 1+ 10225 -=tJ'4iI + 6073 1.-;-

-5 760 -!- 1227 - 3633 + 1071 -JJ 414 + 5543 '-= 13088 '+4912 - 11732 + 9964 - 13151 ~-I

- 5988 + 2360 -3 467 ~ - 15668 + 18108 - 15693 1+ 16907 -20125 + 27013 - 14609 1+ 17876 _ 0_

- 5875 + 2051 ' - 3428 - 374 1- 15423 1+ 17604 1- 15 460 ..... 16421 -19801 + 26409 1- 14359 + 17365 ,\

- 5763 ---- 1743 -3901 +I601~ + 17100 '- 15228 1- 15934 1- 19477 + 25804 - 14109 + 16856 1-j-

- 5670 + 1488 - 4314 + 695 1- 14 93 1 1""""+ 16596 - 14 9961

.... 15448 - 19153 + 25 199 - 13858 + 16346 - j-

_____ 1 _____ 1- 5895 + 2105 - 4847 ~1- 1468 5 1+ 16092 :- 14764 1 ..... 14961 - 18830 + 24595 - JJ608 + 15837

I Exp Um'xp I EX{I U"e..>:p I Exp UI/,'.'op E.I'" I Unexp Exp Untxp I Exp UIII!X{l

S/(m"-'",aI OOUflll-arl' <nd condi-tion_f

---

Degre<',,' ,I eccl'l/­Iricity (StlllC­tllra! foall)

tabulation of the hinged case (H-H) for a variety of f3 values (f3= I, t, 0, -t, -I) at a load eccentricity of a=a. Ali tables give the stress at both the exposed and unexposed surfaces of the walls using the sign convention of plus for tension and minus for compression. Tables 6. 7 and 8 repeat the above for a 100 OOO-Ibf load.

(2) Comparing the influence of physical properties variable with those constant with temperature reveals that , for the standard fire, stress decreases with time when variable but increases when constant, while for lhe non-standard tire, stress increases to lhe time of lhe maximum value.

An examination of the tables shows:

(I) The boundary conditions significantly alfect computed stresses (Table 3).

(3) The maximum stress of the non-standard fire is frequently greater than the standard fire value.

(4) The elfect of the structural load (assumed initially

c. B. Monk lr, 1. E. Goldberg and V. learkjirm 257 S I'Iln I h 2h or M(I)(

F F H- F H-H F F H- F H ~ H F F H F H-H

J....Q.. EQ.. EU E JL EJ,L EU ..s..JL EU EJL L" LuL"Lu lRLuLJ-v ~luLRLu LRLu~Lu LFlLuLRLu L"Lul.p,Lu L"Lu4Lu L4-V4.L:.J LR~Lu_

2

, 10

6

• , .. , 2

10' a •

'r !

-

:a o o

~3 c 8 t • 2 ·

Ui 101

.. ' --

. ~ 8 · ' rAA

• 5 ~ .. ~ , u

· ., o

'"

2

10 ,

2

, .. , • 6f-

, 4 , , ,

10 .r r

2

, 4

'r ,

.!

•

·

•

aa o o •• 110 • o o • . , t· •

D.

00 '. ooh t. .. q"

• ... " ." • o • t.

t. o

A

• D

• • •

'r I 1 1 1 1 1 1 1 1 1 1 1

• II '8 •

•

A

o o

~

•

I LI 1

2

-• I O'

-a , - , ..

• , • ~! .. :, • • a h •

I o· -. • D a • • • g 8 8 ~ 00 -,

,ia 8f ' o .. • <) - ,

• : 2 • • • • l)

• I

• 6 O'

-, , , - -. -, , B -2

I O'

-2

-, -4

: : - 6

I <) •

O'

-• g - 2

• , 1 , _4

8~ • " , é a • A .. , .. 8 i , , •

e • • I o·

I ·t - 2

• =, • =i ,

11 "" 1 111 1111 111 1 6

I O'

{ Sto,'o,' M" o ) • ) Load rOOOOOlb, No n- stondord Fir~ o Propcrtiu. Propcrtiu

{ Stondord Fire C Corlttont . Vorioblc

lo od IOOOOlbf Non.,tondord Fire A •

FIGURE 12- Graphical plot of Tables 3 and 6.

in lhe analysis, namely 10000 Ibf/fl of wall) is relatively minar compared 10 lhe thermal load, as is clearly shown in Table 4. When lhe load is increased lo 100 000 Ibf/fl of wall the thermal elfecl is st ill dominant.

(5) The unrestrained length reduces the resultant compressive stresses tending to produce greater tensile stresses which may be critica i for brittle material systems.

The main conclusions is lhal ullsymmetrical heating of a vertical building elemenl can produce slress elfecls which may outweigh the probable design load. Boundary

conditions both as to end rotation and restraint of lenglh affect results sign ificantly. The meaning of fire resistant rat ings o n columns symmetrically exposed to fire is called into questiono Greater attention should be given in the standard' fire lest to the influence of boundary conditions upon structural behaviollr under unsym~

metrical heating so lhat the designer can extrapolate from a known bOllndary in the test to an actual condition prevailing in his design o Figure 12 is a graphical plol of Tables 3 and 6.

258 Structural Action of Brick-bearing Walls Exposed to Fire Temperatures TABLE 8-INFLUENCE OF VARIABLE BOITOM LOAD ECCENTR ICITY CORRESPONDING TO Top LOAD ECCENTR ICITY OF t\=! FOR THE CASE DF

HI NGED BOUNDARIES (?r = 100000 IbO

5 min 'h 2 fi or ma.\" . I

Standartl NQl1slantlard Standort/

-4473 - 430 - 2634 + 12 - 6982 - 4688

4411 - 492 2541 - 81 - 6619 5051

COl/slallt 4411 - 492 -2541 - 81 - 6220 - 5450 properril's

- 4411 - 492 - 2541 - 81 - 5 795 - 5875

I - 4411 - 492 - 254! - 81 - 5330 - 6320

RI.'Slraint 4905 - 1792 - 3 770 - 239 + 2890 - 2488

- 4558 - 2742 - J 226 - 855 + 3102 - 26 309

Variabfe 4496 - 29 12 2754 1 389 + 3822 - 27787 prQPl!rI;I!S

4271 8520 2281 - 1925 + 4550 - 29 281

! - 4045 - 4148 - 1808 - 2460 + 5285 - 30787

- 4278 - 254 - 2601 + 40 5683 - 3187

4226 - 306 - 2511 - 50 - 5336 - 2534

CO/ISlall/ - 4226 - 30. - 2511 - 50 - 4891 - 2979 proper/i~s --- - -----

- 4226 - 30. - 25 11 - 50 5946 J 924

- 4226 - 30. - 2511 - 50 - 5946 - J 924 Ullres/rai/ll

- 471 5 - I 127 - 2651 - 122 - 2886 - 8099 ----------45 15 - I 675 - 3 11 5 - 788 - 2560 8765

vt/r;a/>/t' - 4290 - 2298 1- 2643 - J 262 - 2206 - 9490 propu/In

- 4065 - 29 /1 - 2170 - I 798 - 1828 - 10264

3839 - 3 529 - 1697 - 2333 - 1432 - 11078

Exp Unt!xp Evp Urrt!xp Exp U Ilt!Xp

·For Slandard test, ",ariable prop.!rlies and restrainl lenith . at 2 h P > PE.

REFERENCES I. INGBERG and others, Fire Test of Building Columns. Bur. Sral/d.

Wash. Tech. Papo 184. 2. HULL, W. A. and INGBERG, Fire Resistance ofConcrcte Columns.

Dur. S/ando Wash. Tech. Papo 272. 3. MITcHELL, N. '8., Fi re Test of Columns Protected with Gypsum.

Dur. Sral/tI. J. Wash. 10, R.P.563, January, 1933.

1 NOlIstalldarrl Srmu!ard Nonslulltlard ,---- - ------- 1-----

- 7306 - 4249 - 6360 - 8543 - 7306 - 48S!! I - ---~ 6946 - 4609 - 5940 - 8960 - 6946 - S 223

- 6544 - SOlO - .5 51 1 - 9392 - 5922 - 5624 O ---- ---- 6113 - 544 1 - 5066 - 9837 - 685 1 - 60.50 -I

- 5661 - S 893 - 4610 - 10 293 - 6995 - 6494 r:-;-+ 47. - 20 377 -21 4296- + 382660· + 6957 - 26118 I

- 105 - 21 596 - 224403* + 401 882- + 8016 - 27859 1---;- Ra/ ios

234531- I'+42Õ742* " .97 22835 + 9091 -29622 O bottom ta top

1296 24089 244677· + 489835· + 10177 31041 ; I!CCl'Ir· Ir;rll/!'s

- 1902 - 25358 - 254720- + 458736- + 11271 - 33 [94 - I

- 6088 - 2087 - 5017 - 2750 - 6088 - 2164 I

- 5734 - 2440 - 4693 3074 568. 25 15 ;

- 5277 - 2898 - 4303 - 3464 - 6238 - 2961 -.-6324 - I 85 I - 3859 - 3908 - 6324 - 1907 -j

- 6324 - I 85 I - 3 373 4394 6324 - t 907 -I

- 3967 - 7643 - 823 - 12080 - 6 184 - 7948 I

~ 3662 - 8 281 - I 263 - 129 19 - 5975 - 8615

- 3329 - 8980 - 1738 - 13 802 - 5718 - 9 436 ---.;-- 2970 - 9729 - 2229 - 14728 + 6173 - 10 133 -=-!

-- 2593 - 10 520 - 2739 - 15686 + 6958 - 10 959 - I

~ ---Exp UI/exp Exp Urr~xp Exp UI/exp I -----

4. AMERI CAN SOCIETY FOR TESTING MA TER IALS. Standard MClhod of Fire Tests of BlIilding Const rllc lion and Materiais, EI1 9-69.

5. NATIONAL FIRE PROTECTIO N ASSOCIATION, Handbook of Fire Protection. 12th edition, Junc, 1962.

6. K AWAGOL. KUNIO, Fire Behaviour in Rooms. RepOr! No. 27. Building Rcsearch Institute, Minislry of Constructi on, Ja panese Governmcnt , September, 1958.