FIRE RESISTANCE OF ASSEMBLIES MADE WITH HOLLOW CORE SLABS

CHAPTER 6 FIRE RESISTANCE OF ASSEMBLIES MADE WITH HOLLOW CORE SLABS

6.1 Introduction

building code requirements.

One of the attributes of hollow core slab construction is excellent fire resistance. More

6.2 Heat Transmission Through Floors or

than 30 standard fire tests (ASTM E119) have

Roofs

been conducted on hollow core floor assemblies. The standard fire test method, ASTM E119, The January, 1994 issue of Underwriters Labora-

limits the average temperature rise of the unex- tories, Inc. “Fire Resistance Directory” includes

posed surface, i.e., the surface of floor or roof not more than 50 design numbers for hollow core

exposed to fire, to 250 degrees F (120 degrees C) slabs which qualify for ratings of 1, 2, 3, or 4

during a fire test. This criterion is often called the hours. Constructions which conform to these de-

heat transmission end point.

signs are assigned ratings by most U.S. building For solid concrete slabs, the temperature rise of codes.

the unexposed surfaces depends mainly on the As an alternative to UL ratings, model codes

slab thickness and aggregate type. Figure 6.2 now include prescriptive requirements which can

shows the relationship between slab thickness and

be used to establish fire endurance ratings. For fire endurance as determined by the heat transmis- each fire endurance rating, strand cover and

sion end point criterion.

equivalent thickness provisions are given. Use of

6.2.1 Equivalent Thickness

such provisions eliminates the need for fire tests The information in Figure 6.2 is applicable to or UL ratings.

hollow core slabs by entering the graph with the Most U.S. building codes will also assign rat-

“equivalent thickness” of the unit instead of the ings to hollow core assemblies which do not con-

thickness. Equivalent thickness can be calculated form with the UL designs if it can be shown by cal-

by dividing the net area of the cross section of a culations made in accordance with procedures

hollow core unit by the width of the unit. given in the PCI manual, “Design for Fire Resis-

tance of Precast, Prestressed Concrete” (PCI

38 Fig. 6.2 MNL 124-89) Fire endurance (heat transmission) of that they qualify for the required

hollow core units

fire endurance. Readers can obtain more detailed

information from that manual on fire resistance of hollow core slab assemblies as well as informa- tion on fire resistance of concrete beams, walls,

and protection of connections. In Canada, The National Building Code of Canada requires that fire resistance ratings be de-

termined either on the basis of results of tests con- Lightweight (100 pcf) ducted in accordance with CAN/ULC-S101-M, Carbonate Aggregate

“Standard Methods of Fire Endurance Tests of

2 Sand-Lightweight (115 pcf)

Building Construction and Materials”, or on the

Fire Endurance, Hr

Siliceous Aggregate

basis of Appendix D, “Fire Performance Rat- ings”. While the general principles set forth in this 1

Manual are fully valid in that they are based on materials properties and structural engineering

procedures, users of the Manual are cautioned that 0

1-1/2 2 3 4 5 6 7

in Canada, fire resistance ratings should be deter-

Equivalent Thickness, in.,

mined strictly in accordance with applicable of Hollow Core Unit 6--1

In Figure 6.2, concrete aggregates are desig- for two hours or more. The addition of toppings, nated as lightweight, sand-lightweight, carbon-

undercoatings, fire resistive ceilings, roof insula- ate, or siliceous. Lightweight aggregates include

tion, or filling the cores with dry aggregates will expanded clay, shale, slate, and slag which pro-

increase the heat transmission fire endurance. duce concretes having unit weights between about

Figure 6.2.2.1 shows graphically the thickness of

spray applied undercoating required for heat replacement. Lightweight concretes in which

95 and 105 pcf (1520 - 1680 kg/m 3 ) without sand

transmission fire endurances of 2, 3 and 4 hours. sand is used as part or all of the fine aggregate and

Figure 6.2.2.2 shows the thickness of sand-light-

weight concrete, insulating concrete and high designated as sand-lightweight. For normal

weigh less than about 120 pcf (1920 kg/m 3 ) are

strength gypsum concrete overlays required for 2, weight concrete, the type of coarse aggregate in-

3 and 4 hours. Figure 6.2.2.3 shows data for 2 and fluences the fire endurance; the type of fine aggre-

3 hr. roofs with mineral board or glass fiber board gate has only a minor effect. Carbonate aggre-

insulation with 3-ply built-up roofing. Data gates include limestone, dolomite, and limerock,

shown in Figures 6.2.2.1, 6.2.2.2 and 6.2.2.3 ap- i.e., those consisting mainly of calcium or magne-

ply directly to hollow core slabs made with sili- sium carbonate. Siliceous aggregates include

ceous aggregates and are conservative for slabs quartzite, granite, basalt, and most hard rocks oth-

made with carbonate aggregates or with light- er than limestone or dolomite.

weight aggregates.

6.2.2 Toppings, Undercoatings, or Roof Example 6.2.1 Equivalent Thickness Insulation

Determine the thickness of topping required to All 8 in (200 mm) deep hollow core units which

provide a 3 hr. fire endurance (heat transmission) are currently manufactured in North America

for the generic hollow core slab shown in Figure qualify for at least a one-hour fire endurance as

1.7.1. Both the slab and the topping are made with determined by heat transmission and some qualify

carbonate aggregate concrete.

Fig. 6.2.2.1 Hollow core units undercoated with spray applied materials (Heat transmission fire endurance)

Hollow core slab made with siliceous aggregate concrete

Sprayed mineral fiber or vermiculite cementitous material

or VMC, in. Thickness of SMF

0.2 2 hr

3.5 4.0 4.5 5.0 5.5 Equivalent Thickness, in. of Hollow Core Unit

6--2

Fig. 6.2.2.2 Floors with overlays of sand - lightweight concrete (120 pcf maximum), insulating concrete

(35 pcf maximum), and high strength gypsum concrete

Overlay Hollow Core slab made with

siliceous aggregate concrete

Sand-Lightweight Concrete

Insulating Concrete

1.0 Overlay Thickness, in.

Equivalent Thickness, in., of Hollow Core Units

High Strength Gypsum Concrete Overlay

3 1 in. G.C. Overlay

1/2 in. G.C. Overlay 2

Fire Endurance, Hr. 1

3.5 4.0 4.5 5.0 5.5 Equivalent Thickness, in., of Hollow Core Units

6--3

Fig. 6.2.2.3 Roofs with insulation board and 3-ply built-up roofing (Heat transmission fire endurance)

3-Ply built-up roofing

Mineral board or glass fiber board insulation

Hollow core slab made with siliceous aggregate concrete

0.50 3 hr

0.25 2 hr or Glass Fiber Board

Thickness, in., of Mineral Board

3.5 4.0 4.5 5.0 5.5 Equivalent Thickness, in., of Hollow Core Unit

Solution: the required thickness would be even less. Thus, Equivalent thickness

the roof qualifies for a fire endurance significantly t

eq = Area/width = 154/36

longer than 2 hours.

6.2.3 Ceilings

= 4.28 in Gypsum wallboard used as ceilings increases From Figure 6.2, the thickness of carbonate ag-

the fire endurance of the assemblies. Very few fire gregate concrete required for 3 hr. is 5.75 in. Thus,

tests have been conducted utilizing concrete the thickness of topping needed is:

floors with gypsum wallboard ceilings, and no such tests have been conducted utilizing hollow

5.75 -- 4.28 = 1.47 in core units. To be effective, gypsum wallboard

must remain in place throughout most of the fire

Example 6.2.2

endurance period. Because most hollow core Determine if a hollow core slab roof will quali- units by themselves have heat transmission fire fy for a 2 hr. fire endurance (heat transmission) if endurances of one hour to two hours and longer, the slabs are made with carbonate aggregate con- the wallboard must remain in place during fire ex- crete, have an equivalent thickness of 4.28 in, and posure for long periods of time. For a fire endur-

the roof insulation consists of a layer of 3 / 4 in thick

ance of 3 hours, a layer of 5 / 8 in (16 mm) Type X mineral board. The roofing is a standard 3-ply

gypsum wallboard can be used. The wallboard built-up roof.

should be installed as shown in Figure 6.2.3. Solution:

From Figure 6.2.2.3 it can be seen that with an equivalent thickness of 4.28 in, a layer of mineral

6.3 Structural Fire Endurance of Floor or Roof

board 0.16 in thick with 3-ply roofing qualifies for

Assemblies

2 hours even if the slabs are made with siliceous During standard fire tests, specimens must sup- aggregates. With carbonate aggregate concrete,

port the anticipated superimposed loads through- 6--4

Fig. 6.2.3 Details of 3 hr. assembly consisting of hollow core slabs with a gypsum wall board ceiling

5 Max. 4 ’

Restrained Unrestrained

End Joint

Side Joint

1. Precast concrete hollow core slabs - Minimum equivalent thickness = 2.75 in

2. Grout - (Not Shown) - Sand - cement grout along full length of joint.

3. Hanger Wire - No. 18 SWG galvanized steel wire. Hanger wire used to attached wallboard furring channels to precast concrete units. Wire to be located at each intersection of furring channels and joints between hollow core slabs, but not to exceed 4 ft o.c.

4. Wallboard Furring Channels - No. 26 ga. galvanized steel, 7 / 8 in high, 2 3 / 4 in base width, 1 3 / 8 in face width and 12 ft long. Channels

to be installed perpendicular to hollow core slabs and spaced 24 in o.c., except at wallboard butt joints where they are spaced 6 1 / 2 in

o.c. Channels secured to concrete units with double strand of hanger wire looped through fasteners. At furring channel splices, chan- nels to be overlapped 6 in and tied together with hanger wire at each end of splice.

5. Wallboard - 5 / 8 in thick, 4 ft wide, Type X, installed with long dimension perpendicular to furring channels. Over butt joints, a 3 in wide

piece of wallboard to be inserted with ends extending a minimum 6 in beyond board width.

6. Wallboard Fasteners - 1 in long, Type S, bugle head screws. Fasteners spaced 12 in on center along each furring channel except at

butt joints where fasteners spaced 8 in on center. At butt joints, fasteners located 3 1 / 4 in from board edge. Along side joints, fasten- ers located 3 / 4 in from board edge.

7. Joint System - (Not Shown) - Paper tape embedded in cementitious compound over joints, and covered with two layers of cementi- tious compound with edges feathered out. Wallboard fastener heads covered with two layers of cementitious compound.

out the fire endurance period. Failure to support the ultimate moment capacity is constant through- the loads is called the structural end point.

out the length:

(Eq. 6.3.1) tural fire endurance of a floor or roof assembly is

The most important factor affecting the struc-

φ M n = φA ps f ps (d p -- a/2)

See Chapter 2 for evaluating f the method of support, i.e., whether the assembly

ps . If the slab is uniformly loaded, the moment dia-

is simply supported and free to expand (“unre- gram will be parabolic with a maximum value at strained”) or if the assembly is continuous or ther-

midspan of:

mal expansion is restricted (“restrained”).

M=w ℓ

(Eq. 6.3.2)

6.3.1 Simply Supported Slabs

Figure 6.3.1.1 illustrates the behavior of a sim- ply supported slab exposed to fire from beneath. Because strands are parallel to the axis of the slab,

6--5

Fig. 6.3.1.1 Moment diagrams for simply sup-

Where

ported beam or slab before and

w = dead plus live load per unit of length,

during fire exposure

k/in ℓ = span length, in

As the material strengths diminish with ele- vated temperatures, the retained moment capacity

becomes:

Fire

M nθ =A ps f psθ (d p -- a θ /2) (Eq. 6.3.3) in which θ signifies the effects of high tempera-

@ 0 Hr

tures. Note that A ps and d p are not affected, but f ps is reduced. Similarly, a is reduced, but the con-

crete strength at the top of the slab, f′ c , is generally not reduced significantly because of its lower temperature.

M = applied moment

M = moment capacity n

@ 2 Hr M= applied moment

M = reduced moment capacity n θ

Fig. 6.3.1.2 Temperature-strength relationships for hot-rolled and cold-drawn steels

High strength alloy steel bars (tensile strength)

80 Hot-rolled steel

(yield strength)

Cold-drawn prestressing steel

Percent of Strength At 70 F

250 or 270 ksi (tensile strength)

Temperature, F o

6--6

Fig. 6.3.1.3 Temperatures within Fig. 6.3.1.4 Temperatures within carbonate aggregate concrete

siliceous aggregate concrete slabs during fire tests

slabs during fire tests

Siliceous Aggregate

Carbonate Aggregate 1500 Concrete (Normal Weight)

Concrete (Normal Weight)

Temperature, F 900 u = 3/4 in. From Exposed Surface

Temperature, F 900

u = 3/4 in. From Exposed Surface 1-1/2 in.

1-1/2 in.

Fire Test Time, Hr

Fire Test Time, Hr

Flexural failure can be assumed to occur when M

Fig. 6.3.1.5 Temperatures within sand nθ - is reduced to M. From this expression, it can

be seen that the fire endurance depends on the ap- lightweight concrete slabs

during fire tests

plied loading and on the strength-temperature characteristics of the steel. In turn, the duration of

the fire before the “critical” steel temperature is

Sand-Lightweight

reached depends upon the protection afforded to Concrete the reinforcement.

Test results have shown that the theory dis- cussed above is valid, not only for hollow core 1300

floors, but also for roofs with insulation on top of

1/4 in.

the slabs.

1/2 in.

Figure 6.3.1.2 shows the relationship between

temperature and strength of various types of steel.

Figure 6.3.1.3, 6.3.1.4 and 6.3.1.5 show tempera-

1 in.

tures within concrete slabs during standard fire

Temperature, F 900

u = 3/4 in. From Exposed Surface

tests. The data in those figures are applicable to

hollow core slabs. By using the equations given 1-1/2 in. above and the data in Figure 6.3.1.2 through

6.3.1.5, the moment capacity of slabs can be cal- culated for various fire endurance periods, as il- 600

3 in.

lustrated in the following example:

1 1-1/2 2 3 4 Fire Test Time, Hr

6--7

Example 6.3.1

w L = w -- w D = 170 -- 54 = 116 psf Determine the maximum safe superimposed load

(d) Calculate maximum allowable w at room that can be supported by an 8 in deep hollow core

temperature

slab with a simply supported unrestrained span of

25 ft and a fire endurance of 3 hr. Given:

f ps = 270

h = 8 in; u = 1.75 in; six 1 / 2 in 270 ksi strands;

A ps = 6(0.153) = 0.918 in 2 ; b = 36 in; d p = 8 -- 1.75 = 249 ksi

= 6.25 in; w D = 54 psf; carbonate aggregate con-

crete; ℓ = 25 ft

(a) Estimate strand temperature at 3 hr. from Fig- φ M n = 0.9(0.918)(249)(6.25 -- 0.75)/12 ure 6.3.1.3, θ s at 3 hr. at 1.75 in above fire-ex-

= 94.3 ft-kips

posed surface = 925 degrees F. (b) Determine f puθ from Figure 6.3.1.2. For

2 = 402 psf

cold-drawn steel at 925 degrees F:

f puθ = 33% f pu = 89.1 ksi With load factors of 1.4 (dead load)

(c) Determine M nθ and w

+ 1.7 (live load):

f 0.918 psθ 89.1 = 89.1 1 − 0.28

Conclusion: w L = 116 < 192; 116 psf governs = 86.8 ksi Note: Fire endurance for heat transmission 0.918  86.8 

0.85  = 0.52in 5  36  Table 6.3.1 shows values of u for simply sup-

should also be checked

M nθ = 0.918(86.8)(6.25 -- 0.52/2)/12 ported unrestrained hollow core slabs for various = 39.8 ft-kips

moment ratios and fire endurance of 1, 2, and 3 hours. The values shown are based on

A ps f pu /bd p f′ c = 0.05 and can be reduced by 1 / in

for A ps f pu /bd p f′ c = 0.10.

Table 6.3.1 “u” inches, for simply supported unrestrained hollow core slabs*

Fire

Aggregate Type

Endurance

Sand-Lightweight (hr)

(in) (mm)

*“u” is distance between center of strands and bottom of slab with all strands having same “u”. Based

on A ps f pu /bd p f′ c = 0.05; conservative for values greater than 0.05. 6--8

Fig. 6.3.2 Equivalent concrete cover thickness for spray - applied coatings

2 Vermiculite Cementious Material (VCM) (slabs) Sprayed Mineral Fiber (SMF) (slabs)

Equivalent Concrete Cover Thickness, in.

Thickness of Spray-Applied Insulating Material, in.

6.3.2 Effect of Spray-Applied Coatings Fig. 6.3.3.1 Moment diagrams for continuous 2 -

The fire endurance of hollow core slabs can be

span beam before and during fire

increased by the addition of a spray-applied coat-

exposure

ing of vermiculite cementitious material or sprayed mineral fiber. Figure 6.3.2 shows the relationship between thickness of spray-applied coatings and equivalent concrete cover. Thus, if

strands are centered 3 / 4 in (19 mm) above the bot- tom of a hollow core slab and if 1 / 4 in (6 mm) of

sprayed mineral fiber is applied, the u distance to

Fire

Fire

be used in Figures 6.3.1.3, 6.3.1.4 or 6.3.1.5 is 3 / 4

in (19 mm) plus the equivalent cover of 0.9 in (23

mm) obtained from Figure 6.3.2.

6.3.3 Structurally Continuous Slabs

Continuous members undergo changes in

stresses when subjected to fire, resulting from

At 0 Hr

temperature gradients within the structural mem- M bers, or changes in strength of the materials at high - n θ

temperatures, or both. x Figure 6.3.3.1 shows a continuous beam whose 0

underside is exposed to fire. The bottom of the

beam becomes hotter than the top and tends to ex-

pand more than the top. This differential tempera-

At 3 Hr

ture causes the ends of the beam to tend to lift from their supports thereby increasing the reaction at

6--9

Fig. 6.3.3.2 Uniformly loaded member

Fig. 6.3.3.3 Symmetrical uniformly loaded mem -

continuous at one support ber continuous at both supports

the interior support. This action results in a redis- simply supported at the other. Also shown is the tribution of moments, i.e., the negative moment at

redistributed applied moment diagram at failure. the interior support increases while the positive

Values for M + nθ can be calculated by the proce- moments decrease.

dures given for “Simply Supported Slabs”. During the course of a fire, the negative mo-

Values for M − nθ and x o can be calculated: ment reinforcement (Figure 6.3.3.1) remains

 w because it is better protected from the fire. Thus, 2 ℓ

2 2M n +

cooler than the positive moment reinforcement

M nθ =w ℓ w 2

(Eq. 6.3.4)

the increase in negative moment can be accom-

x o =2 modated. Generally, the redistribution that occurs nθ (Eq. 6.3.5)

is sufficient to cause yielding of the negative mo- In most cases, redistribution of moments oc- ment reinforcement. The resulting decrease in

curs early during the course of a fire before the positive moment means that the positive moment

negative moment capacity has been reduced by reinforcement can be heated to a higher tempera-

the effects of fire. In such cases, the length of x o is ture before a failure will occur. Therefore, the fire

increased, i.e., the inflection point moves toward endurance of a continuous concrete beam is gen-

the simple support. For such cases, erally significantly longer than that of a simply

supported beam having the same cover and loaded

x o = 2M

(Eq. 6.3.6)

to the same moment intensity. Figure 6.3.3.3 shows a symmetrical beam or It is possible to design the reinforcement in a

slab in which the end moments are equal. In that continuous beam or slab for a particular fire en-

case:

durance period. From Figure 6.3.3.1, the beam

(Eq. 6.3.7) can be expected to collapse when the positive mo-

ℓ ∕8 − M nθ

M − =w 2 +

nθ

wx ment capacity, M 2 nθ , is reduced to the value indi-

and

(Eq. 6.3.8)

cated by the dashed horizontal line, i.e., when the

nθ

redistributed moment at point x 1 , from the outer

In negative moment regions, the compressive

support, M x = M + 1 nθ .

zone is directly exposed to fire, so calculations for

Figure 6.3.3.2 shows a uniformly loaded beam θ and a θ must be modified by (a) using f′ cθ from

Figure 6.3.3.4 and (b) neglecting concrete hotter or slab continuous (or fixed) at one support and than 1400 degrees F (760 degrees C).

6--10

Fig. 6.3.3.4 Compressive strength of concrete at high temperatures

40 40 Percent of Original Compressive Strength

Original Strength = f’ c 20 Average f’ = 3900 psi c

Stressed to 0.4f’ during heating c

Temperature, F o

6.3.4 Detailing Precautions

Example 6.3.2

It should be noted that the amount of moment Determine the amount of negative moment re- redistribution that can occur is dependent upon

inforcement needed to provide a 3 hr. fire endur- the amount of negative reinforcement. Tests have

ance for sand-lightweight hollow core slabs, 8 in clearly demonstrated that the negative moment re-

deep, 5 ksi concrete, 48 in wide, with six 7 / 16 in 270 inforcement will yield, so the negative moment

ksi strands and 2 in (4 ksi) composite topping. capacity is reached early during a fire test, regard-

Slabs span 25 ft of an exterior bay (no restraint to less of the applied loading. The designer must ex-

thermal expansion). Dead load = 65 psf, live load ercise care to ensure that a secondary type of fail-

= 100 psf. Strands are centered 1 3 / 4 in above bot- ure will not occur. To avoid a compression failure

tom of slab. The value for M + nθ can be calculated in the negative moment region, the amount of neg-

(by using the procedure discussed for simply sup- ative moment reinforcement should be small

ported slabs) to be 39.0 ft-kips. From Eq. 6.3.4

enough so that ω θ , i.e., A s f yθ /b θ d θ f′ cθ , is less than

(for use in Eq. 6.3.4):

0.30, before and after reductions in f y , b, d and f′ c w 2 = 4(65 + 100)(25) 2 /1000 are taken into account. Furthermore, the negative

moment bars or mesh must be long enough to ac-

= 412.5 ft-kips

commodate the complete redistributed moment (39.0)

nθ = 412.5 412.5 2 2−  412.5

and change in the inflection points. It should be

noted that the worst condition occurs when the ap-

= 26.9 ft-kips

plied loading is smallest, such as dead load plus Determine A s neglecting concrete above 1400 de- partial or no live load. It is recommended that at

grees F in negative moment region. From Figure least 20% of the maximum negative moment rein-

6.3.1.5 neglect 3 / 4 in above bottom, and assume forcement be extended throughout the span.

steel centered in topping.

d = 10 -- 3 / 4 -- 1 = 8.25 in

6--11

Assume f′ cθ in compressive zone = 0.8f′ c = 4 ksi

Fig. 6.4.1 Moment diagrams for axially

Assume d -- a θ /2 = 8.1 in

restrained beam during fire exposure.

Note that at 2 hr. M is less than M

A s = = 0.66 in 2

nθ

60 and effects of axial restraint permit  8.1 

beam to continue to support load.

0.66  60  check a =

= 0.24 in

0.85  4  48 T

d -- a θ /2 = 8.25 -- 0.12 = 8.13 in ≅ 8.1 OK

Fire

Use 6 x 6 - W2.1 x W2.1 WWF throughout plus #4 Grade 60 at 16 in in negative moment region.

A s =8  0.021   0.20  = 0.768 in + 48 2

@ 0 Hr, T=0

Calculate x o for dead load plus one-half live load.

@ 2 Hr.

M − nθ = 0.768 (26.9) = 31.3 ft-kips

loading = 4(0.065 + 0.050) = 0.46 k/ft;

T(d - - ) T a_ θ

M n = 34.0 ft-kips (calculated for room tem- peratures) (curved due to beam deflection)

From Eq. 6.3.6 temperature rise of the unexposed surface rather 2M −

than by structural considerations, even though the 2(34.0) x o =

= 5.91 ft

steel temperatures often exceed 1200 degrees F

(650 degrees C).

Half of #4 bars should extend 7 ft each side of inte- The effects of restraint to thermal expansion rior support and half 5 ft.

can be characterized as shown in Figure 6.4.1. Use #4 Grade 60, 12 ft long at 16 in and stagger.

The thermal thrust, T, acts in a manner similar to an external prestressing force, which tends to in-

crease the positive moment capacity. If a fire occurs beneath a portion of a large floor

6.4 Restraint to Thermal Expansion

Methods for calculating fire endurance of “re- or roof, such as beneath a concrete floor slab in

strained” floors or roofs are given in PCI MNL one interior bay of a multi-bay building, the

124-89. It is seldom necessary to make such cal- heated portion will expand and push against the

culations, as noted below. The beneficial effects surrounding unheated portion. In turn the un-

of restraint are recognized in ASTM E119. The heated portion exerts compressive forces on the

standard presents a guide for determining condi- heated portion. The compressive force, or thrust,

tions of restraint. The guide includes Figure 6.4.2. acts near the bottom of the slab when the fire

In most cases, the interior bays of multi-bay floors starts, but as the fire progresses, the line of thrust

and roofs can be considered to be restrained and rises and the thermal gradient diminishes and the

the magnitude and location of the thrust are gener- heated concrete undergoes a reduction in elastic

ally of academic interest only. It should be noted modulus. If the surrounding slab is thick and

that Figure 6.4.2 indicates that adequate restraint heavily reinforced, the thrust forces can be quite

can occur in interior bays and exterior bays of large, but they will be considerably less than those

framed buildings when:

calculated by use of elastic properties of concrete “The space between the ends of precast units and steel, together with appropriate coefficients of

and the vertical faces of supports, or between the expansion. At high temperatures, creep and stress

ends of solid or hollow core slab units does not ex- relaxation play an important role. Nevertheless,

ceed 0.25 percent of the length for normal weight the thrust is generally great enough to increase the

concrete members or 0.1 percent of the length for fire endurance significantly, in some instances by

structural lightweight concrete members”. more than 2 hours. In most fire tests of restrained

Sketches illustrating typical conditions de- assemblies, the fire endurance is determined by

scribed above are shown in Figure 6.4.3. 6--12

Fig. 6.4.2. Examples of typical restrained and unrestrained construction classifications (from

Appendix X3 of ASTM E119 - 88)

I. Wall Bearing: Single span and simply supported end spans of multiple bays a (1) Open-web steel joists or steel beams, supporting concrete slab, precast units or metal decking

unrestrained (2) Concrete slabs, precast units or metal decking

unrestrained Interior spans of multiple bays: (1) Open-web steel joists, steel beams or metal decking, supporting continuous concrete slab

restrained (2) Open-web steel joists or steel beams, supporting precast units or metal decking

unrestrained (3) Cast-in-place concrete slab systems

restrained (4) Precast concrete where the potential thermal expansion is resisted by adjacent construction b restrained

II. Steel Framing: (1) Steel beams welded, riveted, or bolted to the framing members

restrained (2) All types of cast-in-place floor and roof systems (such as beam-and-slabs, flat slabs, pan joints, and waffle slabs) where the floor or roof system is secured to the framing members

restrained (3) All types of prefabricated floor or roof systems where the structural members are secured to the framing members and the potential thermal expansion of the floor or roof system is resisted by the framing system or the adjoining floor or roof construction b

restrained III. Concrete Framing:

(1) Beams securely fastened to the framing members restrained (2) All types of cast-in-place floor or roof systems (such as beam-and-slabs, flat slabs, pan joists, and waffle slabs) where the floor system is cast with framing members

restrained (3) Interior and exterior spans of precast systems with cast-in-place joints resulting in restraint equivalent to that which would exist in condition III(1)

restrained (4) All types of prefabricated floor or roof systems where the structural members are secured to such systems and the potential thermal expansion of the floor or roof system is resisted by the framing system or the adjoining floor or roof construction b

restrained IV. Wood Construction

All Types unrestrained a Floor and roof systems can be considered restrained when they are tied into walls with or without tie beams, the walls being designed and detailed to resist thermal thrust from the floor or roof system.

b For example, resistance to potential thermal expansion is considered to be achieved when: (1) Continuous structural concrete topping is used.

(2) The space between the ends of precast units or between the ends of units and the vertical face of supports is filled with concrete or mortar.

(3) The space between the ends of precast units and the vertical faces of supports, or between the ends of solid or hollow core slab units does not exceed 0.25 percent of the length for normal weight concrete members or 0.1 percent of the length for structural lightweight concrete members.

Fig. 6.4.3. Typical examples of restrained floors or roofs of precast construction

Hollow-Core Slabs or Double Tees

Hollow-Core or Solid Slabs

To be considered as restrained: c 1 +c 2 < 0.0025 ℓ for normal weight concrete c 1 +c 2 < 0.0010

Example: Determine maximum value of c ℓ for lightweight concrete 1 +c 2 for normal weight hollow core slabs with a clear span of 30 ft

Solution: c 1 +c 2 = 0.0025(30 x 12) = 0.90 in

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Example 6.4.1

strength, the assembly will generally be satisfac- Hollow core floor slabs were installed in a

tory structurally.

building several years ago when a 1 hr. fire endur- ance was required. The occupancy of the building will be changed and the floors must qualify for a 3 hr. fire endurance. What can be done to upgrade the fire endurance? Given:

Slabs are 4 ft wide, 8 in deep, prestressed with five 3 / 8 in 270 ksi strands located 1 in above the bottom of the slab, and span 24 ft. Slabs are made with 5000 psi siliceous aggregate concrete, have an equivalent thickness of 3.75 in, and weigh 47 psf. The slabs are untopped and the superimposed load will be 50 psf. Solution:

There are a number of possible solutions. The appropriate solution will depend on architectural or functional requirements and economics.

For some parts of the building, the slabs might

be made to qualify as “restrained” in accordance with Figure 6.4.2 and Figure 6.4.3, in which case those slabs would qualify structurally for 3 hours, but would still have to be upgraded to qualify for 3 hours by heat transmission.

A gypsum wallboard ceiling installed as shown in Figure 6.2.3 would provide three hours both structurally and for heat transmission. Calcula- tions of the ultimate capacity and stresses should

be made to assure that the added weight of the ceil- ing can be adequately supported.

A spray-applied undercoating of vermiculite cementitious material or sprayed mineral fiber can also be used. For heat transmission, the re- quired thickness for three hours of undercoating is

0.6 in (see Figure 6.2.2.1). From Figure 6.3.2, it can be seen that with a thickness of 0.6 in of VCM or SMF, the equivalent thickness of concrete cov- er is more than 2 in. Thus, the equivalent “u” dis- tance is more than 2 in plus 1 in or more than 3 in. From Figure 6.3.1.4, with u more than 3 in, the strand temperature will be less than 600 degrees F at three hours, so the strength of the prestressing steel will be 65% of its 70 degrees F strength (Fig- ure 6.3.1.5) or more than 0.65 x 270 = 175.5 ksi. Calculations can be made in accordance with the procedures in the section headed “Simply Sup- ported Slabs”, but if the strand strength is reduced less than about 50% of its room temperature

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