adjusted density measurement methods on stairs

FIRE AND MATERIALSFire Mater. (2013)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fam.2204

SPECIAL ISSUE PAPER

Adjusted density measurement methods on stairs

Bryan Lawrence Hoskins*,†

Fire Protection and Safety Technology, Oklahoma State University, Stillwater, OK USA

SUMMARY

Density is calculated on the basis of the number of people per unit area. In order to properly calculate density,the measurements need to match how the space is actually used. Thus, how people space themselves could bedependent on the nature of the egress component. This study compares different methods of calculating densi-ties for people descending stairs based on the different components (treads and landings or just landings) that areobserved. The densities on the different components are not found to be equivalent unless factors (adjusted treaddepth and adjusted landing area) are applied. When these factors are applied to a second data set that had adifferent tread configuration, the densities are again equivalent. When the results are applied to a stair wherecultural factors could alter the findings, the adjusted landing area needs to be adjusted in accordance with theexpected change in behavior. Copyright © 2013 John Wiley & Sons, Ltd.

Received 8 February 2013; Revised 15 July 2013; Accepted 19 August 2013

KEY WORDS: evacuation; egress; stairs; fire safety; density; theory

1. INTRODUCTION

During a high-rise building evacuation, the stairs are used by most building occupants for a significantportion of their evacuation. The stairs also tend to be one of the last egress components that theevacuating people encounter. Understanding how stairs are used during egress can lead to moreaccurate predictions of evacuation time.

For stairs, the area used by the building population consists of two different types of components(the treads and the landings). The two types of components are very different from one another. Whentraveling along the treads, people are moving both horizontally and vertically. The spacing of the treadsrestricts how close two individuals can be; people must have their foot securely on a tread. On thelanding, people are only moving along a single plane and can space themselves at any desired distance.However, on many landings, the direction of travel changes 180º. This tuning action could influencethe area of that landing that is actually used during egress.

Because there are two different types of components, observations on one component should notarbitrarily be applied to the other. When density is used to predict movement speed, the units of densityare in persons per unit area. Thus, if one researcher measures density on the treads and another researchermeasures it on the landing (or a combination of treads and landing), both researchers would present theirresults with the same units. Due to the different behaviors on treads and landings, these two results mightnot be equivalent. Ideally, no matter what observation area is used to calculate the density, all methods tocapture a single person at a given moment should yield the same basic density value. Because this couldinclude just the treads, just the landings, or a combination of the two, a means of equating the different

*Correspondence to: Bryan Lawrence Hoskins, Fire Protection and Safety Technology, Oklahoma State University,Stillwater, OK, USA.†E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

B. L. HOSKINS

areas needs to be developed. There are no known previous studies that have compared how densitymeasured on the treads relates to density measured on the landings. When authors do not ensure that thesame measurement technique is used for their data and data that they are comparing their results with,densities collected by one measurement technique could be applied to a very different set of conditions.

Even if the samemethod is used to calculate the densities, the area used by the people on the stairs needs tobe calculated rather than simply considering the entire area to be used. For calculations to be consistent acrossdifferent researchers and within studies, the area measurements need to be calculated on the basis of how thestairs are used in practice. If people do not use the entire width or depth of the component, only the portion thatis actually being used should be included in the area measurements. Furthermore, the method should haveequivalent values when the density includes just treads, just landings, or a combination of treads and landings.

This study compares the density for evacuation drill participants when the area includes treads andlandings versus just the landings. When using the entire area (or just the effective width), the densitiesin the different measurement areas are statistically different. However, when appropriate factors areapplied to the tread depth and landing, the two density measurements are not statistically different.

2. PREVIOUS RESEARCH

Gwynne and Rosenbaum [1] present an equation developed by Nelson and MacLennon for calculatingmovement speeds descending stairs. They only provide equations for four different riser heights andtread depths and do not indicate which stair component (treads or landings) should be used to calculatethe density or how to handle data from different tread configurations. Hoskins and Milke [2] haveidentified over a dozen equations that exist in the literature for calculating speed descending stairs basedon density. These equations have a large variation for all possible density values. In addition, theyprovide data on the densities reported in previous studies. Figure 1 shows this range. Possibleexplanations for this range include the following: the authors are using different methods to calculatedensity, differences in human behavior across the studies, and differences in the design of the stairs.

Figure 1. Densities values reported in Hoskins and Milke [2].

Copyright © 2013 John Wiley & Sons, Ltd. Fire Mater. (2013)DOI: 10.1002/fam

ADJUSTED DENSITY MEASUREMENT METHODS ON STAIRS

For measuring density, some past researchers (e.g., Fruin [3], Pauls [4], and Proulx et al. [5]) haveprovided density measurements but did not provide details of how these measurements were made. Allthat was provided was the number of people per unit area without a description of what exact area wasobserved. When the methods were provided, different egress components were part of the observationarea. For example, Proulx et al. [6] observed only the treads, and Pauls [7] observed both the treadsand landings.

Even when looking at the same component, the methods used to calculate the areas have also varied.Early researchers (e.g., Joint Committee [8] and London Transit Board [9]) used the entire area for theirdensity calculations. Then, Pauls [4] found that the effective width of treads should be 0.30m less thanthe total width. This decrease in width was to accommodate the boundary layer that people left betweenthemselves and the wall and/or handrail; people do not walk with their body scraping against the wall,and this accounts for the natural body sway.

In addition to how the areas should be measured, researchers have also focused on how stairs are used.For the width of the treads, Fruin [3] recommended that the stairs should be designed on the basis of exitlanes that are 76 cm wide based on the body ellipse and comfort. Templer [10] found a larger value forcomfort (88 cm per exit lane), but smaller values when the only concern was for the people being ableto move continuously (71 cm per exit lane) or with starting and stopping (61 cm per exit lane).

In addition to the width of the treads, Templer [10] studied the tread depth that allowed for thenatural gait of people descending stairs. He found that that tread depth had to be 29 cm for comfortand that treads less than 23 cm performed uniformly poorly and were not suitable for human gaits.

Researchers have also provided qualitative observations about how treads are used during evacuations.Kagawa et al. [11] and Proulx et al. [6] found that occupants tended to space themselves in either astaggered file or with pairs on every other tread. In either case, this resulted in an average of one personper tread when the stair was wide enough for two people. Proulx et al. [6] also observed the tendencyof people to stay to the right during light densities.

For the landings, most researchers have not identified the method that they used for calculating thearea. This could be the result of them simply using the entire landing area as performed by Peacocket al. [12]. Recently, Hoskins and Milke [13] provided two alternate methods for calculating thearea on landings. They provided equations based on both a path that was twice the tread width andone based on an arc that had a radius of half the tread width. Kuligowski and Peacock [14] now usethe arc method for calculating the area on landings.

3. EXPERIMENTAL

In this study, data from high-rise building evacuations conducted by the National Institute of Standardsand Technology [14] are used to develop area calculations on the basis of observations from evacuationdrills. These buildings were all office buildings located in the USA and the evacuation populationconsisted of the workers that were present on the day of the drill. Occupants were recorded onvideotapes as they descended stairs in each of the buildings with an overhead camera facing nearlystraight downward to capture at least three treads above and below the landing and most of thelanding area. Occupants were considered to be in the observation area when their first foot appearedto be flat on the step within the observation area and out of the observation area when their first footappeared to be flat on the step outside of the observation area, The number of occupants on the treadsand landings and just the landings were compared using paired t-tests to determine when the areaswere equivalent.

Data from three stairs in the National Institute of Standards and Technology data set were used. Theselected landings were chosen randomly amongst the floors in each building that were not dischargefloors and had at least 150 people observed. There were no indications that these landings were inany way different from others in the building. In all instances, the drills were conducted duringworking hours, and there were no known conditions that distinguished these buildings or theobserved populations from other office buildings. Also, all landings had the door to the floor locatedalong the back wall of the landing.


B. L. HOSKINS

Building 5 was a 10-story office building located on the west coast of the USA. The treads of Stair Awere 1.27m wide (1.22m between handrails), 18 cm tall, and 28 cm deep. During the spring of 2008 drill,385 people were observed on the third floor.

In Building 7, Stair 3, 158 people were observed on the 13th floor during a spring 2008 drill. Forthis 18-story building on the east coast of the USA, the treads were 1.12m wide (0.91m betweenhandrails), 19 cm high, and 25 cm deep. Both of these stairs were dextral (turning left whiledescending) stairs.

Building 8, Stair S was 31-story sinistral (turning right while descending) stair located on the eastcoast of the USA. During the fall of 2008 drill, 327 people were observed on the 14th floor. Thetreads were 1.38m wide (1.26m between handrails), 18 cm tall, and 27 cm deep.

The conditions within the stairs covered a wide range of conditions with the density varying fromoccupants descending in isolation to approximately 3.5 persons/m2. Just as there was variation in thedensity, there was a large range of observed descent speeds. The maximum speed was slightly morethan 2m/s while some occupants were forced to come to a complete stop. With the range ofobserved conditions, any effects of either light densities or heavy densities should be accounted for.

As with all stairs, the evacuees encountered two different types of components as they descended. Thefirst are the landings. The path on the landing can be described as a series of straight lines as performed byPredtechenskii and Milinskii [15] or as an arc as described by Hoskins and Milke [13]. In either case, thearea is centered on this path. For the second component, the treads, there could be an effective width aswell as an adjusted depth. All of these measurement methods are examined in order to determine whatfactors are needed to equate the two different density measurements.

A difference between treads and horizontal surfaces like corridors is the inability of individuals tohave complete freedom on selecting the interpersonal distance between themselves and others: theirfoot is on either one tread or the next tread. The steps create a literal step function of possiblespacings. Where this is relevant for density measurements can be illustrated using a basic exampleand the qualitative observations of Kagawa et al. [11]. If the treads are 0.254m in depth over a totaldistance of 3.05m (12 treads), six evacuees could be located on every other tread. If 0.305m deeptreads are used instead, 3.05m is spanned by just 10 treads. In this case, every other tread would onlyaccommodate five evacuees. For evacuees to maintain the every other tread spacing, a factor isneeded to relate the different tread depths. None of the previous studies on building evacuations haveconsidered the adjusted depth of the treads.

The limitation of this approach is that people applying the equations from researchers can apply aspeed and density equation to data where the density has been calculated in a different manner.Factors for adjusting the density on treads and landings to be comparable will allow a single data setto be compared with data collected under different conditions.

In order to test what the different factors might be, the density for each evacuee was calculated fortwo different times within a single camera observation area. The first observation area included threetreads above the landing, the landing, and three treads below the landing. The number of peoplewithin this area when the evacuee entered the area were counted and divided by the area. Thesecond observation included only the landing. For this observation, the procedure was similar withthe number of people on the landing being counted when the evacuee descended onto the landing.These observations were typically a few seconds apart.

By focusing on two points within the field of view of a single camera, it is possible to directlycompare the two different conditions experienced by a single evacuee. The exact density values willfluctuate because of the relatively small numbers of people that are visible, but the fluctuationsshould not show a trend to favor one component over the other when the measurement methods areequivalent. Thus, factors for the tread depth and landing area will be developed. These factors willbe based on the findings of previous researchers about how people use stairs and will be adjusteduntil the pairs of density measurements are statistically similar.

With a large sample size, it is possible to see these general trends. While there will be some variationfor a given individual based on whether someone is just inside or outside of the observation area, thereshould be no trend where one set of measurements is always greater than the other. Paired t-tests aredesigned to compare two similar populations for trends between the paired values, as is the casewith this data. Thus, the paired t-tests will help to determine when the difference between the two



area measurements across all evacuees is not statistically different. Also, by comparing an individualwith themselves, any personal preference on the spacing is controlled.

For the initial development of the factors, the 13th floor of Building 7, Stair 3 will be used. As statedpreviously, there are no known features of this stair, landing, or building population that would causethe results to be different than other dextral stairs. Once these factors are developed, they will beapplied to other landings to test the reproducibility of the results

4. RESULTS

As stated previously, two different density measurements were made for each of the 158 individualsobserved on the 13th floor of Building 7, Stair 3. To see the relationship between the two densitymeasurements, the difference between the density for the landing and treads combined is subtractedfrom the density on the landing. Positive data points indicate that the density on the landing isgreater than the density on the landing and treads. A negative data point means the opposite. Thetrend line indicates if the difference in the measurement methods is different for the two methods.Ideally, the trend line for the data will be nearly horizontal along the x-axis. For all measurements,the 15 cm boundary layer found by Pauls [4] will be applied.

The first comparison used the total area of the treads and the rectangular landing area that is one treadwidth in depth and two tread widths in length. This is shown in Figure 2. The density on the treads andlandings is calculated using Equations (1) and (2). respectively. As seen in Figure 3, when the

Figure 2. Initial measurement areas.

Figure 3. Density comparisons without new factors.


B. L. HOSKINS

difference is plotted against the density for the combined treads and landings, most of differences arepositive. This indicates that either the landing density is too large or the stair density is too small.

T ¼ 6 * b * d (1)

L ¼ 2 * b * b � 0:15* 0:15 mð Þð Þ (2)

where T is the tread area, L is the landing area, b is the tread width� 2 * 0.15m, and d is the tread depth.The paired t-test for this data resulted in a t-statistic of 14.3. The large t-statistic indicates that the two

measurement methods are significantly different at the 95% confidence interval. Thus, applying the totalarea of the treads or landings to a data set including the other component is not expected to givecomparable values.

Several factors can now be adjusted to equate the two areas to make them equivalent. The firsthypothesis is that the adjusted area on the landing is the area traced by arcs from the edges of the usedtread area as described by Hoskins and Milke [13] as shown in Figure 4. Equation (1) is used for thetread area, and Equation (3) is used for the landing area. This increases the landing area and thusdecreases the density on the landing. The results for the 13th floor of Building 7, Stair 3 are seen in Figure 5.

L ¼ 0:5 * π * b þ 0:15mð Þ2 � 0:15 mð Þ2� �

(3)

where L is the landing area and b is the tread width� 2 * 0.15m.

Figure 4. First hypothesis measurement areas.

Figure 5. Density comparisons with arc paths.



Once again, the data points indicate that the density differences are positive. The t-statistic is 12.5,and the results are significantly different at the 95% confidence interval. While the two sets ofmeasurements are more similar, the landing density is still too large relative to the density for thetreads and landings. Further adjusted measurements need to be applied in order to make the twoarea measurements equivalent.

The second hypothesis is that the area on the treads is a single adjusted value for all stair depths thatare observed. Based on the work of Templer [10], the minimum tread depth for people to notsignificantly alter their stride is approximately 23 cm. This is shown in Figure 6. The landing area iscalculated using Equation (3), and Equation (4) is used for the tread area. When a tread depth of23 cm is applied to calculating the tread area, the results are shown in Figure 7.

T ¼ 6 * b * 0:23 m (4)

where T is the tread area and b is the tread width� 2 * 0.15m.The t-statistic is 9.9, and the results are still significant at the 95% confidence interval. While the

results are headed in the right direction, these measurement methods are still not equivalent. Afurther change in the landing (or treads) area is required.

The third hypothesis is that the occupants, once on the landing, spread out regardless of tread widthas shown in Figure 8. Equation (4) is used for the tread area, and Equation (5) is now used for thelanding area. When the arc width is 1.30m (1.00m with a 0.15m boundary layer on each side), theresults are shown in Figure 9. This is an approximation because the exact landing dimensions wouldnot allow for a perfect arc.

Figure 6. Second hypothesis measurement areas.

Figure 7. Density comparisons with adjusted tread depth.


Figure 8. Third hypothesis measurement areas.

Figure 9. Density comparisons with adjusted landing area.

B. L. HOSKINS

L ¼ 0:5 * π * 1:00þ 0:15 mð Þ2 � 0:15 mð Þ2� �

(5)

where L is the landing area.The data in Figure 5 appears to be randomly arranged above and below the x-axis. The t-statistic

confirms this with a value of 0.3. Because the two measurement methods are not significantlydifferent at the 95% confidence interval, the adjusted spacing on the treads matches the adjustedspacing on the landings.

While the area for the treads and landings was found to yield similar densities for individuals on agiven landing, other landings need to be examined in order to determine if the results are applicableto a wider range of scenarios. As mentioned previously, the treads in stair Building 5, Stair A aredeeper and wider than the treads in Building 7, Stair 3. Figure 10 shows the difference between thetwo density methods versus the adjusted density on the treads and landing measurement method forBuilding 5, Stair A.

As can be seen in Figure 10, there is no obvious trend in the data, and the points appear to berandomly spaced along the x-axis. The t-statistic is 0.0, and the values are significant at the 95%confidence interval.

When the adjusted factors for the treads and landings are applied to a dextral stair (Building 8, Stair S),the results are shown in Figure 11.

As can be seen, the data tends to be negative. This is the opposite effect as was seen previously. Forthis data set, the density on the landings needs to be increased or the density on the treads needs to be


Figure 11. Density comparisons Building 8, Stair S with dextral stair adjusted factors.

Figure 10. Density comparisons Building 5, Stair A.


decreased. The t-statistic is �11.6, and the two density measurements are statistically different at the95% confidence interval.

One possible method for altering the adjusted factors is to decrease the landing area. If the arcbounding the landing area is reduced by 0.2m, the results are shown in Figure 12.

The t-statistic is 1.1, and the two density measurements are not statistically different. Thus,in the dextral stair, less area on the landing results in the density between the two methodsbeing equivalent.

Figure 12. Density comparisons Building 8, Stair S with sinistral stair adjusted factors.


B. L. HOSKINS

5. DISCUSSION

The current methods for determining the density on stairs involve using the entire tread depth as well asthe landing area. There are two issues that are not addressed by this current application of the densitydata collected for people on stairs. The first stems from the incompatibility of unadjusted data collectedfrom the two different types of components (treads and landings). The second stems from people on thetreads not being able to have an unlimited number of spacing options due to the nature of the treads.Both of these issues are addressed by findings in this paper.

The first statistical test compared the density for a combined tread and landing measurement comparedto just the landing measurement. The measurement methods used were ones that are found elsewhere inthe literature. Thus, there was no adjusted depth applied to the treads or was there an adjusted landingarea based on an arc. In other words, it is representative of the values currently available in theliterature. The results were statistically different as the landing density alone was systematically greater.It is not surprising that people would space themselves differently while on the treads than they wouldwhile they were on the landings. This indicates that using equations developed from measurements onjust treads for instances when landings are included (or vice versa) are not a valid application of thedata; with the currently available data, comparison should only be accurately made when the stairconfigurations are the same.

In order to decrease the area on the treads, the first factor was determined on the basis of the minimumdepth found by Templer [10]. The assumption being made is that the 23 cm is the minimum space that aperson can occupy, and this would therefore be the amount of space that is actually used by the peopleduring the evacuation drill. Thus, it was selected as the basis for converting between landings andtreads as well as between different tread depths. The adjusted depth also relates to the staggered file thathas been qualitatively observed as people descend stairs. As shown in the example of the 25.4 and30.5 cm treads, a few additional centimeters are not expected to result in more people being found onthe stairs because they will choose spacing based on the number of treads to the next person rather thanon the exact linear distance.

Even with this change, the density on the landing was still too large. Fruin [3] and Templer [10] foundthat the amount of space that an individual required was greater than half of the stair width. Their valuesfor an exit lane ranged from 61 to 88 cm depending on the design criteria. This led to the assumption thatthe people on the landing, no longer confined by the stair walls, might choose to increase the width of thearea that they were occupying. While the people were expanding the area that they were occupying, theywere still not calculated to be present in the entire landing area; the corners were excluded. At this point,the value for that depth was varied until the two density measurements were statistically similar. Theresulting depth was within the values provided by Templer [10]. While the assumption was made thatthe path was a semicircle, this was based on a qualitative assessment of how people were observed onlandings. Path tracing could reveal a more elliptical path, which would be consistent with both thedecreased area on the sinistral stair and the width of the arc being greater than the landing width inBuilding 7.

While the values matched for a single landing, that could have been caused by the particular buildingpopulation and does not prove that the results are reproducible. To verify that the results were not limitedto just this one set of data, the methods were applied to a second set of data. There were several keysimilarities and differences between the two buildings In this instance, the stair turned in the samedirection was the same type of building occupancy (office building) and was from the same county(although a different region in the country). However the physical dimensions of the stairs were not thesame with different tread widths and depths.

For this second building, the factors developed for the previous stair were applied without anyalterations. Just as was the case with the first building, when the factors were applied, they led to thetwo area measurements being statistically similar. Thus, there is reproducibility of the results when theadjusted depth of the treads is 23 cm, and the area on the landing is within a 1.3m arc. Even on a stairwith different tread dimensions, the same factors led to the treads and landing within the cameraviewing having similar densities.

The next data set was a stair that was different in a meaningful way. When a stair that turned theopposite direction was examined, a smaller landing area was needed in order to achieve the similarity



in the density measurements. In North America, Templer [10] and Proulx et al. [6] have identified thetendency of people to stay to the right. Because the inside lane for descent on this stair was to theright, the smaller area could be caused by this phenomenon. For a broader perspective, it alsoindicates that there could be cultural differences that will alter the factors for buildings with differentcultural norms.

In summary, without adjusted factors applied, the density measurements on treads and landings arenot interchangeable. The current assumption that the entire depth of treads should be used in thedensity calculation also appears to not be valid for comparing treads of different sizes. When using adensity correlation developed by a previous study that does not use the adjusted factors developedhere, it is important to ensure that the methods and components used to calculate the density arecomparable. With the application of adjusted factors, it is possible to convert the data from onestudy to another and to be equivalent.

6. CONCLUSIONS

Previous studies have measured density on treads and/or landings, but the methods used have been leftunspecified or varied from one study to another. When the methods were described, authors did notconsider the adjusted areas used by people on these different components. Instead, all areas weregrouped together. Similarly, the depth of treads was calculated in a linear manner rather than on theanecdotal reports of typical spacing.

For this study, the measured density experienced by evacuees when treads were included andexcluded was compared. Without applying any adjusted factors, the two densities were statisticallydifferent. Adjusted factors were then developed on the basis of the findings of how people actuallyuse stairs. When an adjusted tread depth (23 cm) and used landing radius (1.3m arc) were applied,the two areas were statistically similar. These factors allowed the densities on the two differentcomponents to be directly compared. When these values were applied to a stair landing in adifferent building that turned the same direction but had a different tread configuration, the twodensities were again statistically similar.

To build upon these results, more stairs need to be observed in order to better develop the factorspresented here for determining the areas used for density calculations of the different staircomponents. Furthermore, detailed path tracing can be used to determine the exact area that peopleare occupying as they descend the stairs. However, based on the observations by previous researchersas well as the results here, the entire area of the treads should not be counted. A small increase in thetread depth will increase the available area, but people will not be able to use that additional areabecause their spacing is limited by the number of treads rather than the linear depth of the observedarea. Similarly, while there is no the same limitation on spacing, it does not appear as if the entirearea of the landings is used.

It should be noted that the factors developed here do not account for the comfort of the people on thestairs; the values are only the point at which the two areas are mathematically similar. Also, at the veryminimum values, safety for occupants that are slightly larger than average could become an issue.Thus, the adjusted values are not intended to be the basis for component design. Instead, they are onlyintended for density calculations in order to obtain equivalent values from observations on the twodifferent types of components within stairs.

Attention should also be given to cultural effects because the results for the sinistral stair were whatwould be expected if people stayed to the right. Based on cultural preferences for personal space aswell as the tendency to stay to a particular side of the stair could lead to different factors being required.Also, there could be a difference based on the type of occupancy and the familiarity between theoccupants. How people use stairs is dependent on both their physical requirements as well as theirsociological requirements.

By incorporating adjusted factors into the calculation of density, the results of studies should bemore applicable to future situations. This could help eliminate some of the variability that iscurrently found between data sets.


B. L. HOSKINS

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