The critical factor in establishing whether flashover conditions occur is the achievement of a critical irradiance for spontaneous ignition of materials in the lower part of the room. This irradiance is about 2W/cm2 in the case of cellulosic materials. For large areas, such as carpets, it is only necessary to exceed the critical flux for piloted ignition since the concentration of pyrolysis products at that exposure level could be high enough some distance from the source to be ignited by flames already present in the room. Assuming a radiation shape factor of 1/2, the ceiling would have to radiate 4W/cm2 which corresponds to a temperature of 650°C for a black surface and 700°C for one with a total emissivity of 0.9 which is typical of non-metallic materials in this temperature range. Note in figure 7 that with the AIB ceiling the temperature drop between the upper air and the ceiling was about 50°C at equilibrium regardless of the flame height, location, and gas flow rate. This suggests a critical upper air temperature of about 730°C to induce flashover after fairly long times.

As seen in the last section, the locations, horizontal as well as vertical, along with the burning rates of the combustibles, control the height of the transition plane BC which to a large extent determines the rate of air inflow for fixed doorway dimensions. The rate of air inflow, the burning rates of the combustibles, and the heat losses determine the air temperature. All three must be capable of estimation in order to build a prediction model for fire build-up. The effect of the burning rate on the elevation of the transition plane is through its effect on the flame height. The burning rate itself depends on the material and its temperature and radiation environment.

In the case of the gas burner the heating time can be extended as long as necessary to attain the maximum air temperature and thus, the maximum radiant flux. In the case of combustible contents the initial fire may be burned out before the wall and ceiling lining materials reach a sufficient radiating temperature to induce flashover. The rate of temperature rise of the surfaces of the walls and ceiling depends on the products of their thermal conductivity, heat capacity, and density (KC). If the KPC is low the surface temperature rises rapidly and radiation feedback increases the heat release rate of the burning contents. This enhancement may be enough to induce flashover when it might not otherwise occur. Thus, the KpC of the lining materials is very important in predicting the occurrence of flashover.

4. SUMMARY

4.1. Heat Balance

A satisfactory heat balance could be obtained during the fire buildup phase in the model where about 60 percent of the heat produced was carried out through the doorway with the exhaust gases and the remainder was distributed between heat conduction into the hot upper surfaces and heat radiation by these surfaces into the lower part of the room or out of the doorway. The portion radiated away increased with time up to about a half hour when steady temperatures were attained using a gas burner with a constant fuel flow rate.

1.

The elevation of the interface between the high and low temperature
air layers was lower in the model than it was in the prototype for
both combustible and non-combustible walls.
above the mid-height of the doorway.
doorway height was not scaled exactly.

In both cases it was
It should be noted that the

2.

3.

4.

5.

1.

2.

3.

The air velocities in the model were about 30 percent higher than the product of the square root of the ratio of the doorway heights and the measured velocities in the prototype. This may have resulted from improper scaling of the doorway. At any rate, the volumetric air flow rates were similar.

The upper air and ceiling temperatures in the model were similar to those in the prototype when non-combustible walls were used.

In the case of combustible walls, the temperatures in the model were higher than those in the prototype. This difference could be accounted for by the relatively larger combustible area.

Radiation fluxes on the floor were roughly similar for combustible walls. The higher ceiling temperatures in the model were partially compensated for by a decreased radiation shape factor.

4.3. Flame Height and Location

The high temperature air was confined to the region above a horizontal transition plane whose elevation was above the mid-height of the doorway. The air from this region flowed out of the doorway at high velocity. If a constant gas flow rate was maintained, the height of the plane increased with increasing flame height resulting from different burner locations within the enclosure. As the plane was raised the air inflow rate decreased and the temperature of the outgoing air increased.

The flame height increased as the constant fuel supply was moved
against a wall or placed in a corner.

There was a region between the mid-plane of the doorway and the high temperature region in which warm air heated by contact with the radiantly heated lower surfaces of the enclosure rose and passed out of the doorway at low velocity.

A prediction method for fire build-up potential must be capable of estimating the ceiling temperature which controls the radiant flux level in the lower part of the room. When this level exceeds some critical value, full invoivement of the room occurs. This ceiling temperature is dependent on air temperature which in turn is determined from the heat release rates of the burning materials in the room, the heat losses, and the air inflow rate.

5. CONCLUSIONS AND RECOMMENDATIONS

This preliminary work, investigating the usefulness of the quarter scale model as a tool in the study of fire build-up in full sized rooms, is encouraging. However, the scaling rules used by IITRI, which work well for rooms with inert walls, are not adequate to scale rooms with combustible walls. It appears advisable to go to geometrical scaling (i.e., keep all dimensions proportional to the scale factor) in order to keep the heat release rate of the walls proportional to the area of the floor. At the same time it would be necessary to alter the doorway dimensions in order to maintain a constant ratio of air inflow to floor area. Because of the importance of the region above the doorway it would be desirable to keep the height of the doorway proportional to the scale factor and let the width of the doorway vary to provide the proper, air flow. The ratio of heat release rate to volumetric air flow must be kept constant to maintain the same temperatures in the model and the prototype.

Geometrical scaling has the added advantage of keeping the radiation shape factor constant. If the shape factors and the temperatures are the same, then the radiation levels which are responsible for flashover can be duplicated in the model.

The upper air temperature which is close to the ceiling temperature is the most important indicator of the degree of fire build-up in the room. It was modeled satisfactorily for the corner fire tests using the IITRI scaling criteria up to the time of ignition of the walls. When the walls were burning the rate of heat release in the model was too high for proper scaling of this temperature. Although the times to flashover and the radiation levels on the floor were roughly similar for the model and the prototype and the increase in air temperature in the model could be estimated in terms of the relatively greater surface area involved, satisfactory scaling for combustible walls requires alterations in the scaling criteria.

It has been practical to keep the thickness of the room lining materials constant between full and quarter scale and thus, maintain real time in the model.

The upper air temperature was found to depend on the height of the flame above the floor and the proximity of the flame to the wall, even when both the walls and ceiling are non-combustible.

[1]

[2]

[3]

[4]

Waterman, T. E., Determination of Fire Conditions Supporting Room Flashover, Final Report IITRI Project M6131, DASA Contract No. DA-49-146-XZ475 (Sept. 1966).

Heskestad, G., Modeling of Enclosure Fires, Fourteenth Symposium (International) on Combustion, The Combustion Institute, 1021-1030 (1972).

Gross, D. and Fang, J. B., Contribution of Interior Finish to the Growth of Fire in a Room, Fire Safety Research, Proceedings of a Symposium held at the National Bureau of Standards, Gaithersburg, Md., Aug. 22, 1973.

Thomas, P. H., Helselden, A. J. M. and Law, M., Fully-Developed Compartment Fires - Two Kinds of Behavior, Fire Research Technical Paper No. 18, October 1967, Fire Research Station, United Kingdom.

NATIONAL BUREAU OF STANDARDS SPECIAL PUBLICATION 411, Fire Safety Research, Proceedings of a Symposium Held at NBS, Gaithersburg, Md., August 22, 1973, (Issued November 1974)

AN ANALYTIC MODEL FOR CALCULATING THE FIRE RESISTANCE

OF SIMPLY SUPPORTED PRESTRESSED AND REINFORCED CONCRETE BEAMS

Lionel A. Issen

National Bureau of Standards, Washington, D.C.

At present the fire resistance of concrete beams is determined
either by running a fire test or by interpolation from existing fire
test data. The second method can only be used if the data are for
beams that are closely similar to the object beam. Other ad hoc
empirical methods are equally limited. To overcome these difficul-
ties an analytic model was developed for the rational analysis of
prestressed and reinforced concrete beams. This model will be
checked against available test data. A computer program based on
the analytic model is being tested and will be used for developing
graphical tools (graphs, nomograms, tables) for estimating the fire
endurance of simply supported prestressed and reinforced concrete
beams.

Key words: Analytic methods; concrete; creep; elevated temperature;
finite differences; finite elements; fire endurance; fire tests;
isotherms; prestressed concrete; reinforced concrete; steel.

Structural elements such as beams normally carry a load. During a fire the materials of which the beam is made degrade; that is, they lose strength, they soften and flow as the beam is heated. The fire performance rating of a beam is related to the results of a standard fire test [1] during which the beam is subjected to a prescribed time-temperature exposure representing a fully developed fire.

Major U.S. building codes have fire resistance rating requirements based on these tests for the structural elements of buildings. These ratings may depend on the proposed building size, occupancy classification and, in some cases, fire district classification.

These fire tests are relatively expensive ($5,000, plus construction of the specimen in the test furnace) and in the case of concrete elements there may be a waiting period of several months while the test unit dries.

To overcome the problems of cost and waiting time, alternative procedures to the fire test have always appeared attractive. The alternative methods that are usually considered are interpolation methods, small-scale models and analysis of mathematical models.

In the interpolation method, as applied to estimating the fire resistance of beams, an effort is made to interpolate between the results of tests on similar beams to provide an estimate of the fire resistance of a particular beam. This method works best when the particular beam is similar to those beams comprising the test data. By similar is meant similar shape, material and load factor.

Experienced individuals can do this reasonably well. The process is not objective, being dependent on judgement, intuition and experience and therefore is not suitable for general use.

1.1.2. Small-Scale Models

Small-scale models have long been considered an attractive tool in engineering analysis. Their attractiveness lies in the fact that they are usually smaller, cheaper and easier to test than a prototype; the effects of a wide range of loading conditions can be studied and a check can be provided for a quick analysis. Small-scale models for fire tests are not feasible at the present state of furnace and material technology, because the thermal scaling relationships [2] require that the rate of temperature rise in the furnace be inversely proportional to the scale of the model. For instance for a 1/2 scale model the furnace temperature must rise at twice the rate for a test with a full size prototype.

The scaling relationships are difficult to satisfy exactly since the thermal and mechanical properties of materials, including concrete and steel, are not linear functions of temperature, and heat transfer by radiation, convection and conduction may not be in similitude.

Analysis of mathematical models is a popular method for estimating or predicting the performance of structures. The use of this method is limited in the case of thermo-structural analysis of structural elements because both the thermal and structural properties of concrete and steel (the main structural materials of interest) are non-linear with temperature and stress level. For these reasons closed form solutions to either the thermal or the structural parts of the problem have not been found and, therefore, it is necessary to use numerical methods.

The two methods of numerical analysis that are of interest here are the finite difference [3] and the finite element [4] methods.

The finite difference method is as old as the calculus; there is thus a long history of use and experience. In the method, the differential or integral equation is replaced by a series of algebraic equations which are solved using algebraic methods. Briefly described, the method divides the region of interest into a grid (1-, 2- or 3-dimensional), where the intersections of the grid lines are called nodes or node points. The values of the process (in this case temperature, stress and strain) are calculated at the nodes by the finite-difference equations which are comparatively easy to set up and solve. Difficulties arise if the grid is not regular, if the boundary of the region is other than simple, or if the material properties change with temperature or time.

The finite element method is quite recent, having been developed as a practical method in the late 1950's in the aerospace industry. As with finite differences the differential or integral equation is replaced by a set of algebraic equations. In the method, the physical body is divided mathematically into a number of elements, hence the name finite element, and the conditions along the boundaries of adjacent elements are matched up to give the values at the nodes, or vertices, of the elements (usual shapes are triangles or quadrilaterals for two-dimensional problems). The finite elements do not have to be of uniform shape so that irregular boundaries can be closely matched by the elements and varying temperature and time dependent properties can be easily incorporated into the equations. For these reasons the finite element method was selected for the thermal analysis.