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Journal of Research of the National Bureau of Standards-C. Engineering and Instrumentation

Vol. 63C, No.2, October- December 1959

Proposed Criteria for Defining Load Failure of Beams, Floors, and Roof Constructions During Fire Tests

J. V. Ryan and A. F. Robertson (July 30, 1959)

A .brief acc?unt is presente~ of procedures use.d in development of criteria for defining the pomt at ~hlCh fire test speCImens faJl to sus tam load durmg test. It is proposed that b.oth a deflectl~n of D j800d and an hourly rate of deflection of D j150d be taken as an indica­bon of load faIlure. In these formulas, L is the span between supports of the member or element found to be crItlcal under fire exposure, and d is the distance between upper and lower extreme fibers of the partlCular structural component or assembly.

1. Introduction R ecently an investigation was performed on the

effect of variations in ceiling fabrication on the fire endl!ranc~s. of a number. of floor constructions [1].1 DunnlS 1l1ltial tests of thIS study it became apparent that m many cases structural fail ure micrht be expected to occur before failure based on a defined temperature rise at the unexposed surface. Since the tesL procedure used [2] is not specific in defining methods for . determining the point at which t,he specimen fa~s to "sustain the applied load," it aP12eared desu'able to adopt laboratory procedures wluch would provide an objec tive method of deter­mination of this end point. The firs t attempt at selection of a criterion of load failure that of a critical deflection 2 of 3 in. [1], was ~elected for the particular type of floor construction used. It was chosen because it seem ed to r epresent a iO'ni­ficant indication of deflection and in addition bthe data then available, figure 1, example I showed'Lhat the corresponding rate of deflection ~\TaS so great that collapse of the construction might be expected to occur rather promptly.

It appears that a critical deflection method of specifying the t ime at which failure to carry the load occurs is not generally applicable to a wide vari~ty of constru~tion .types. This brief paper ou tlmes some conslderatlOns made in developinO' more general criteria of load failure for beam floot and roof constructions during fire enduranc~ tests:

2. Load Failure Criteria

2.1. Deflection

The selection of a critical deflection for defining ~oad failure, while possibly useful in specific cases, IS not applicable to the general case because of differences in specimen construction, span, manner of support, and materials of construction used. It would be preferable to specify a deflection in terms of the construction design. This was considered bu t i t alone was found deficient in properly allowing

1 Figures in brackets indicate tbe literature references at tbe end of this paper. 2 DeflectIOns for determmatlOn of load failure are tbose resulting from fire

exposure under design load, in excess of initial deformation due to application of tbe)oad.

for variations in longitudinal restraint at the ends of the load-carrying members of the construction.

2.2. Increase in Rate of Deflection

. T ests performed in which heavy steel beams were ll1corpol'ated as load carrying members showed the shortcomings of deflection alone as a criterion of load failure. In tests such as this it was not uncommon ~o :find. very larg~ deflections develop without any mdlCaLlOn of rapIdly ll1creasing ra te of deflection with r.esul tant impending collapse. T herefore, an analYSIS of some fire endurance data was made to determine the feasibility of usinO' an increase in rate of deflection as an indication of load failure. Figure 1, example II, illustrates the method used . The initial nearly constant rate of deflection RI was determined and then the time of load failure was assumed to occur at a time when this initial rate had ~een exceeded by a fixed percentage. In the case 11lus LraLed R2= 1.5RI . The difficul ty with this procedure was largely that of determining the point on the curve at which RI was to be measured. Therefore it seemed desirable that the limitinO' rate of deflection be defined on some other basis,b pref­erably dependent only on the structural features of the de~ign. Also, it seemed apparent that rate of deflectlOn alone was not an adrquate criterion.

Dc --------

TIME 1I

L'

!~~Q~------------

JII

F IGUR E 1. Typical curves of observed deflection data illustrating determination of failure time.

I, prechoscn critical deflection D c; lI, increase in rate of deflection by predetermined ratio, R2= KR! ' III , com binat ion of rate and de flection, both determined by size' and span of

stl'uctllJ'al clement (failure time T, or Td, whicbever is later).

517199- 59---4 121

TABLE 1. Effect oj new criteria on previously determined jail1,re times

~h is ~able com pares the times of failures, as determined by tbe testing personnel on the basis of the criteria listed in the second col umn , in tests of several types of fl oor constructions ,:vith the times derived by exam matlon of tbe test data in accord with the proposed load fa il m e cri teria . The criteri a define load fa il ure t ime as t he earliest time when a de ncctioD D ~ L'/800d an d 110urly rat e of deflectIOn R~ L'/l50d have botb been attained or smpassed. In these formulas, L~clear s pan, d~depth to most remote stressed fi ber. Most of the d ata are from tests performed before t hese for mnlas were considered.

KOTE; Times in parentheses ( ) , indicate no data after the given time, although given defl ection or rate not attained, net changes in ( ) correspond to these times.

Oonstruetion Failure criterion

ML, GP ___ __________ __ ____ Load fail ure ___ ______ _ _ Do _____ ___ __ __ _________ ____ _ do ________________ _

ML, pp ___ __________ ______ _____ do ____ ____________ _ ML, L P ___________________ Oollapse _____________ _ GB ________________________ Surf. tem p __ _________ _ GL, GP ___ ________________ L oad failme ___ _______ _ M L , GP ___________________ __ ___ do ________________ _

SJ 103, GS, GL, GP ________ R apid deft _______ _____ _ Do __ __ ____________________ _ do _________ __ . ____ _ Do _____________________ 3-in. defL ___ __________ _

~ ~mt~E:~~~~:~~~::::::: - ~~l~f:!~~~~: = :::::::::: Do ____________________ _ 3-in . deft ___ _____ _____ _ Do _____________________ Surf. temp __ ________ _ Do _____ ________________ 3-in. defl ____ ________ _ _

SJ81 , OS, G L , GP _________ R a pid deft ____ _______ _ SJl02, BR, ML, GP ____ __ _ 3-in. defl ______ _______ _

OS, Joists elTlbedded ___ ____ 1 Hole t.hrough __________ 1 OS , JOists embedded, GB __ Excess defl ___________ _ OS, Joists embedd ed _______ Surf. tem p ___ ________ _

Tile & concretr ____________ 1 OOllapse ______________ 1 Tile & concrete, GP _______ W aste ign ____________ . 00 ______________________ __ R apid defl ___________ _

Cell, c . w, CF __ ___________ Surf. tcm p ___________ _ D o _________ ______________ __ do __ __ ____________ _ Do ________________ _____ R apid dcft ___________ _ Do ___________________ __ Surf. temp ___ ____ ____ _

For'ijo~:_~_R~_?_~~~:::::::: Fla-~~-tIJ;.OUgh:: ~::::: Do _______ _____ _______ __ Surf. temp ____ _______ _ Do _____ ________________ . ____ do _____________ ___ _ Do _____ ____________________ _ c10 __ ___ ___________ _

Dimensions

L

ft:in. 12:10 12:10 12:10 12:10 12:10 12:10 12:10

12:10 12:10 12:10 12:10 12:10 12:10 12:10 ]2:10 12:.10 8:0

12:10

12:10 12:10 12:10

18:0 12:10 12:10

9:6 7:0 8:0 8:0 4:8 4:8 4:8 4:8 4:8

I d

in. ~n ~n ~n ~n ~n ~n ~n

10 10 10 10 10 10 10 10 10 8

10

9.25 9.25 9.0

7.0 1 4.375 5.25

5.1 5.6 5.6 5.6 1.5 1. 5 1.5 1.5 1. 5

r"---. -----J

D efl ection at failme Criteria

D eflection I R ate L'/800d

I L'/150d

Floors, wood joist

-h

in. 14 8.3 5. 7

16.+ 9.1 3 3.3

2.5 1.2 3.0 3.0 3.0 3.0 3.0 3.0 3.0 1. 4 3.0

in./hr 310 123 25.+

1,150.+ 468

9.+ 6.0

33 30 ] 6.0 47 12

4. 8 33 20 10. 8 3 0

10. 1

in. 3.04 3.04 3.04. 3. Q<l 3.04 3.04 3.04

Steel jois ts

~O ~O ~O ~O ~O ao ~O ~ O ~O 1. « ~O

in.jhr 16.2 16.2 16.2 16.2 16.2 16.2 16. 2

16.0 16. 0 16.0 16.0 16.0 16.0 16. 0 16.0 16. 0 7.7

16.0

P recast con crete joists

3.6 12 4.9 18 5.9 15.6

o oll apse 3.2 I 2.2 5. 1 14

2.4 0.8 1.7 0.8 1. 5 3.9 1. 6 0.7 o

1.2 0.1 1.1 0.1 3.9

15.+ 5.2 2.9 o

3.2 3.2 3.3

Slabs

8. 341 6. 78

5. 65

Steel decks

a2 1.6 ~oo ~oo ~7 ~7

~7 ~7 a7

17. 1 1 17. 1 17.6

44.41 36. 1 30.1

16.9 8. 4

11. 0 11. 0 14.3 14.3 14.3 14.3 14. 3

"'-

Time criteria reached

L ' jSOOd

hr:min 0:47 1:08 0:57 0:26 0:40 1:43 1:57

1:50 1:44 2:06 1:07 6:40 4:12 1:06 2:54 1:51 2:17 1:24

I

0:331 0:53 0:39

1:10 1 3:23 0:47

(6:45) (6:47) 3:18

(7:00) (2:10) 1:35 2:04 1:58

(3:12)

L'j l50d

hr:min 0:47 1:06 1:00 0:19 0:37 1:42

(2:00)

1:46 1:39 2:06 1:03 6:42 4:21 1:01 2:50 1:54

(2:17) 1:26

0:40 1 0:52 0:38

1:10 1 (4:07) 0:51

(6:45) (6:47) (3:25) (7:00) (2:]0) 1:26 1:49 1:58

(3:12)

~'- -~

Time to failure

R eported I

hr:min 0:51 1:12 1:06 0:29" 0:38 1:44 2:05

1:48 1:40 2:06 1:07 4:25 3:14 1:06 2:44 1:51 2:15 1:24

0:35 0:57 0:48

1:10 2:27 0:45

4:45 3:20 3:00 5:03 1:52 1:40 1:56 1:50 2:36

New criteria

hr:min 0:47 1:08 1:00 0:26 0:40 1:43

(2:00)

1:50 1:44 2:06 1:07 6:<;2 4:21 1:06 2:54 1:54

(2:17) 1:26

0:40 1 0:53 0:39

1:10 1 (4:07) 0:51

(6:45) (6:47) (3:25) (7:00) (2: 10) 1:35 2:04 1:58

(3:12)

Net chan ge of fire

endurance

min -4 -4 -6 -3~,

o - 1

(?)

+2 +4

o o o o o o

+3 (+2) +2

o - 4 - 9

o o

+6

o o

(+25) o o

-5 o o o

1"' ime to tom perature limit rises on Ull CX-posed surface

2500 F av \3250 F m ax

hr:min (0:50) (1:10) (1:05) (0:30) (0:45) (1:40) (2:00)

(1:50) (1 :45) (2:30) (1:10) 4:25 3:14

(1:10) (3:00) 2:01 2:48

(2:45)

(0:35) 1 1:10 0:48

(1:05) 1 3:08 (1:00)

4:45 3:20

(3:30) 5:03 1:52

(1:40) (2:00) 2:14 2:36

hr:min (0:50) (1:10) (1:05) (0:30) 0:38

(1:40) (2:00)

(1:50) (1:45)

b2:26 (1:10) 4:46 3:19

(1 :10) 2:44 1:59 2:40 2:38

0:36 1:13 0:51

(l :05) 2:58

(1:00)

4:53 3:3i 3:30 5:06 1:57

(1:40) 1:56 1:50 2:57

I ~

( )

(

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? : ~

i ~

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" '" " .0

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g 0

"" i e Po;

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§~~ ~$$ ~ r:.:;.::jC'?C'l e C"l ~

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OOO-le--' O-l

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~ ~~ 8;g$ ':";~ "j 0 ":"; ':::

~$~8:;r;~ ':"; ~~e~ ";";

t-oo.Ol'- tOo:> -I '<::I""" Ct')lf";)~

,.:....;ro~ .t-5 ~~

1- 0000 00 00 00

odd~~ ~ -I -I ...... _ C'I C'I

C'l C'l C'ltO to O ............... tO tO

C"i~CO':iM~~

0 0 000

ci ~8 ~;; g

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MO+O~ C') MOO u? ot:i C'i..."i

oO t-I ..... '-O;' O:>

ci~~~ aic:P

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0.0 tr.l LQ , .... 00 """'''''''''I'' lQ C'-l sse':"; ":";

f6;;5 !; +~ 2ic.O<:O Ci ':"";

I.Q "" .!':I Ol '" '<t<'d" ....,.. ....,..c-., .8se ,:,,; ,:,,;

LQ ·n '!':I I-OO ....,.. <o;1' ~ <f':IC',

ees ~":";

"I1' C"I ,....; MC't:I

...roc:P dc.=i _ ~C'I"' C'I

O '~ r-... , .... If'';) 0)0)

C"ic-:i ,r.i ...,.i~

~6C'1 -p.Q ci ~ "":M I"";

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OO ...... u - C"l O

oC"i ....r...o s

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to_~ _ _

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00 ~ ...... I(;() to "<:1'1 LQO ,...., ""' ''1 00 .:.i c-lcoc..i.nc'i

::I! - oo C'loO O"" O oO - O M ..... c--i .:.; ~M 0 c..;

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cOdd 'QU;~ C\1 C'IC'l C'l C'I C'I

O'lOlQ) I'- t--l'-

..,,; '<ti..,r~...,.i ~

Ol'-oO:>OC'l

oC'-iu:i "";.....; c6 "" ~

.., CO I-C'l Ol C'-lOO

OO M ~C'i~C"i

2.3. Deflection and Rate of Deflection Method

Previous experience had hown Lha t to be useful a criterion of load failure must be applicable to a variety of construction variables including variou s types of end res train t, loading, and construction dimensions and materials. The lal'ge number and complexity of these variables, no t to mention th e effects of thermal strain , seem to require a special analysis of each structure. This seemed impractical for the purposes intended alld as a r esul t a com­promise method was developed. This involves t.he requirement that both a deflec tion and ra te of deflection be exceeded as an indica t ion of load failure . The requiremen t of bo th criteria is bclicved to provide a practical substitute for detailed analysis of each structure tes ted.

The deflection of a beam 01' a floor constru ction in a fire test is the res ult of several fac tors, including the deflec tion du e to th e flexllI'al s tresses produced by t he loads, that resulting from changes in tem­perature, and that res ulting from movements of mois­ture in the materials. D eflec tions due to shearin g deformations usually are small in comparison to those caused by flexUl'e; for OllI' present purpo e t hey win be neglected . The usual assump tion will be m ade th a t all transverse planes remain plane aft er bending. Then following the reasoning of 11alley [3], it can be shown that th e maximum deflection of a beam 01' floor of constant flexural rigidi ty t hrough­ou t its length is given by :

(1) 111 whiell

7c = numel'ical cons tant ; Lh e value of W11ich de­pends upon the L~'p e of support and the methods of loadin g.

L = length of specimen between support s. cl = clepth of specimen (s trictly t Jl e distance,

normal to the ncutral plane, between the planes of el an d e2)'

el- e2= algcbraic difference between thc strains in 01' neal' the two surfaces of the specimens , measured in th e direction of th e span , in planes separated by th e distance d.

The equation applies for strains in th e elas tic ran ge. On examination, it appears that th e ra tio D id migh t be useful in expressing limitations on deflection eve n wh en plastic deformation OCClli·S . Th e usefulness of D id for such limitations is demonstrated b.\T study of th e da ta from a number of fire tes ts . All these t es ts, which did not include those from r cference [1], had been performed, and th c time of faillU'c to "sustain th e applied load" establish ed , prior to our consideration of th e use of th e term D id in th e criteria for failme. In addition , th e tes ts were selected as representa tive of constructions w11ich were con­sidered to have failed to sustain th e lop.d during th e test . Various cons tan ts were considered prior to selection of botl) :

a deflection of D ?, D /800cl and

an hourly deflection r ate R ?, D /150cl

123

as representing the best fit between the empirically specified load failure time and that predicted in the form of the proposed criteria.

To investigate the effect of applying such criteria for identification of time of load failure of structures during a fire test, data of 50 experiments were ana­lyzed. The results are presented in table 1. Two columns of data are presented under the main caption "Time to failure." The first of these entiLled "Reported" lists the reported failure time for the construction. In some cases this was limited by load failure, in others by temperature rise or ignition of waste. The second subcaption entitled "New criteria" indicates the time at which load failure would be indicated by application of the criteria proposed. In cases where the defined limiting con­ditions of ignition of cotton waste or temperature rise due to heat transfer occurred at earlier times than determined by these criteria, such earlier limiting conditions would determine the fire en­durance of the specimens. The column entitled "Net change of fire endurance" indicates the change which would occur on application of the proposed criteria. The entries here recognize the fact that in some cases term perature rise, etc., may limit eJl­durance. In other respects, the table is believed to be self-explanatory.

Study of the table indicates that application of the criteria to the specimens listed would have the effects of increasing the endurance in 13 instances, reducing it in 14 , and in 23 instances there would either be no change or it would be uncertain. It thus becomes evident that use of the criteria is quite successful in selection of load failure times which are reasonably consistent with behavior as analyzed by the operator in charge of the test . Tbe requil'ement that both a given deflection and rate of deflection be achieved is believed to present a useful method of defining the point of load failure of beams, floors, and roof constructions testcd on end supports but regardless of the type of restraint applied at these ends.

3 . Conclusion

The investigation performed seems to justify use of th e following criteria for dcfining the time at which a specimen should be considered as havin g failed to sustain the load during a fire test.

A beam, floor , or roof construction mounted on end suppor ts and subjected to a fir e endurance test ':' under design load will be considered to fail to I

"sustain the applied load " at that time when both / the maximum net deflection resulting from fire I

exposure has equaled or exceeded D j800d, and the '\ hourly rate of deflection has equaled or exceeded I

D j150d.

In these formulas :

L is the span between supports of the structural component or assembly found critical under fire exposure;

d is the distance between th e upper and lower extreme fibers of the structural component or assembly.

D, L, and cl are all in the same units of length; / R a rate of the same length unit per hour.

) >

111'. D. E . Parsons suggested the advantages to be . gained by use of criteria of the type proposed.

4. References

[1] J. V. R yan and E. W·. Bender, Fire endurance of opcn­web steel- joist floors with concrete slabs and gypsum ceilings, KBS Building Materials and Structures Report 141 (1954).

[2] Standard methods of fire testR of building construction and materials , ASTM Designation E119, ASTM Standards.

[3] G. A. Maney, Relation between deformation and deflection in reinforced concrete beams, Am. Soc. T esting Mate­rials Proc. 14, II, 310 (1914).

WASHINGTON, D.C. (Paper 63C2- 15)

124

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