# A measured protection

## Existing ways to determine the effectiveness of intumescent coatings on steelwork have included margins of error due to their theoretical nature. Hans van de Weijgert, principal engineer at International Fire Consultants, reports on a new assessment method that has equationed facts into the process.

In recent years many discussions have taken place over how best to characterise the contribution of intumescent coatings to the fire resistance of steelwork. Different assessment methods have been developed, however the general feeling is that while all of the existing techniques provide a way of predicting the performance times, none can do this with great precision. Therefore criteria for the acceptability of the assessment results have been added in many standards and guidelines.

There is a great need for a method that provides an exact prediction of the performance times of coatings based on facts rather than estimations. The recently developed 3D Interpolation Method is based on measured performance times obtained from fire tests and projecting them into a three-dimensional space.

Each test specimen and its performance time to a certain temperature is represented by a dot (x,y,z) in a three-dimensional space. Three dots construct a plane, the mathematical equation of which enables the performance time (z) for any combination of x and y within the plane boundaries to be predicted ie any point within the triangle of which the three dots form the corners.

The previous absence of a satisfactory, factual mathematical characterisation method is due to the complexity of the subject, which is actually a four-dimensional problem. The four dimensions are section factor (Hp/A), dry film thickness (DFT), performance time (t) and design steel temperature (T).

In order to grasp the behaviour this four-dimensional mathematical problem can be reduced to three dimensions in which the x-axis represents Hp/A; y-axis represents DFT; and the z-axis represents the performance time. As there is no room for a separate temperature axis this fourth dimension can be taken into account by repeatedly visualising a three-dimensional space for each design steel temperature separately. Hence, it is possible to construct a three-dimensional space for a steel temperature of 350°C, a separate one for 400°C and so on.

A test specimen can be identified by a combination of Hp/A and DFT. For example a steel section with an Hp/A value of 230m-1 and a DFT of 1.23mm would be represented as x,y = 230, 1.23.

If the specimen is subjected to the standard fire test it will take a certain time in order to achieve a specific design temperature; this is defined as the performance time (t). By putting the performance time on the z-axis a three-dimensional space is created in which every combination of Hp/A, DFT and t is represented by a dot (x,y,z) in the space formed by the x, y, and z axes.

This three-dimensional space represents one particular temperature only and shows for each of the test specimens the performance time achieved. The information is factual as the dots are measured values obtained from fire tests.

Once a series of dots has been created it is possible to identify three dots, each representing an individual test specimen, to create a triangle. It is also possible to draw straight lines through the dots, intersecting at the corners of the triangle. The lines enclose an area in the x,y-plane called the domain, which forms a collection of (xi,yi) dots for which the plane equation will be applicable. In the three-dimensional space the three dots can be imagined to lie in one plane.

By filling in a value for x and for y (x =Hp/A , y = DFT) in the plane equation the z-value can be obtained. In other words, the performance time can now be calculated for all combinations of Hp/A and DFT values that fall within the triangle.

In most cases manufacturers have test evidence that contains many more data points than only three test specimens. The principle of forming triangles can be extended to create more triangles in the Hp/A,DFT-plane: four dots will form two triangles; five dots will form at least four triangles and so on.

Each of these triangles forms the domain for which a combination of Hp/A and DFT within the triangle provides a performance time by using the plane equation. The planes intersect at lines that connect the measured performance times in the three-dimensional space. Figure 1 illustrates a sample data set showing the three-dimensional landscape that is created when all of the planes are combined.

An assessment of the performance of an intumescent coating will involve the performance time as a function of DFT and Hp/A. The performance time as a function of DFT is simply a vertical cross-section through the three-dimensional landscape. A vertical plane for a constant Hp/A produces the cross-section.

A vertical cross-section using plane Hp/A = constant can be taken for any value of Hp/A to provide the performance time as a function of DFT. This also shows where applicable test evidence does and does not exist. In other words it shows the lower and upper limitations of the DFT in the output directly as the performance time will be zero if there is no applicable test evidence.

Also, the performance time expressed as a function of Hp/A is purely a vertical cross-section through the landscape of a vertical plane for a constant DFT. This cross-section will show the lower and upper limitations for Hp/A for that particular DFT value.

The method enables previously unrevealed information about the behaviour of intumescent coatings to be visualised. When used to calculate the performance time as a function of Hp/A it reveals that in some cases a higher DFT does not necessarily provide a higher performance time; this is illustrated by local dips in the three-dimensional landscape. It also makes it possible to identify certain area’s of both Hp/A and DFT where improvement of the intumescent recipe may be possible, meaning more effective coatings may be produced.

There is no need for correction techniques to satisfy criteria of acceptability as the method is based on facts. The measured data points form literally the planes, therefore the difference between measured time and predicted time is zero. Over or under-prediction does not exist as the calculated times are identical to the measured times.