Tensile membrane action

Tensile membrane action is a term that the fire engineering sources cited in this article neither use nor define. The SFPE Handbook refers only to membrane action. In structural frames with many members, it states, load transfer or membrane action may let a heated steel member keep its integrity at temperatures above those usually associated with failure. The closest mechanism that the sources describe in detail is what NIST calls catenary action in its study of the floors of the World Trade Center towers. In that study, catenary action refers to the combined action that results when the bending capacity of a truss is exceeded and the floor system carries additional load as a tensile structure.

The tension in a sagging floor has to be anchored at its supports, where it pulls inward on columns and walls. In the towers, such pull-in forces from sagging floors bowed the exterior walls inward before collapse. In a full-scale fire test at Cardington in England, a floor sagged 0.64 m over a 9 m span, and no structural failures were reported. NIST does not attribute this result to membrane action, and the sources give no design method for membrane action in floor slabs.

From bending to tension

At normal temperatures, a floor carries its load by bending between its supports. In a fire, heated steel loses stiffness and strength, and the floor starts to sag. In its analysis of the World Trade Center floors, NIST listed three causes of sagging between supports. These were the loss of stiffness and strength of the steel trusses and the concrete slab at high temperature, and the yielding or buckling of the truss web members needed for bending. Failure of the connections between slab and trusses, which removes composite action, was the third.

When the bending capacity is exhausted, the floor can still carry load as a hanging cable. NIST's definition of catenary action for its study describes this change: once the bending capacity of the truss is exceeded, additional load is carried by the floor system acting as a tensile structure. Part of the load may still be carried by bending, through the residual moment capacity of the highly deformed floor. For a floor strip under a uniform load, NIST approximated the tension from this combination of bending and catenary behaviour as follows: $$T=\frac{0.5qx(L-x)-M}{d}$$ At midspan, where $x=L/2$, the first term in the numerator becomes the familiar maximum bending moment of a simply supported beam. Midspan is also where the worked example below applies the formula. The expression then reduces to: $$T=\frac{q{L}^2/8-M}{d}$$

Symbol	Description	Unit
$T$	horizontal tension in the floor strip	kN
$q$	uniform load per unit length of the strip	kN/m
$L$	span between supports	m
$x$	distance from the support	m
$d$	sag of the floor at distance $x$	m
$M$	residual moment capacity of the deformed floor	kN·m

The formula shows the two features that matter most. The tension equals the part of the bending demand that the floor can no longer resist, divided by the sag. A floor that sags less must therefore develop a larger tension to carry the same load. The supports provide vertical reactions of half the total load each, as in ordinary bending, plus the horizontal pull of the tension.

Worked example

The long-span floor trusses of the World Trade Center towers spanned nominally 60 ft (18.3 m) between the exterior walls and the core. In NIST's model of a single long-span truss under assumed fire temperatures, the largest downward displacement was 42.11 in. (1.07 m) after the web diagonals had buckled. This value belongs to a steel temperature of 700 °C, after the first connection failures, and lies away from midspan near the buckled diagonals. The example nevertheless uses it as a midspan sag, about one seventeenth of the span, to show the order of magnitude of the forces.

If the floor keeps no residual moment capacity, the midspan formula gives a tension of 18.3 / (8 × 1.07) = 2.14 times the total load $qL$ on the span. Each support then has to resist a horizontal pull about twice as large as the whole load that the floor carries. Two further cases assume that the floor keeps a residual moment of a quarter or a half of $q{L}^2/8$. The tension then falls to 1.60 $qL$ and 1.07 $qL$.

The sag has an even stronger effect. For two assumed sags with no residual moment, one fortieth of the span requires a tension of 5.0 $qL$, and one tenth only 1.25 $qL$. A floor can thus reduce the pull on its supports by sagging further, as long as it does not fail. This one-way calculation is a simplification. NIST used it to approximate the tensile forces in the floor system of the towers. It treats the floor as a strip spanning in one direction and leaves out any action of the slab in the second direction.

Development during a fire

Early in a fire, heated members expand, and restrained thermal expansion increases the loads in the heated elements. In the twin towers, the floors expanded in the early stages of the fires. As their temperatures rose, they sagged and began to pull inward on the exterior walls instead. In NIST's truss model, the floor first pushed the exterior columns outward. The columns were pulled in only after the web diagonals buckled at 565 °C and the sag became large.

The same truss model shows the later stages in detail. In the model, assumed steel temperatures were raised from 20 °C to 700 °C in 30 minutes and by a further 200 °C in the next 10 minutes. The shear studs on the spandrel failed below 275 °C, and the top chords yielded above 300 °C because steel and concrete expand by different amounts. At 565 °C, four compression diagonals buckled under high axial compressive force, and the floor sagged into a catenary shape.

The connections then carried the tension. At about 600 °C, before the gusset plate and the exterior seat bolts failed, the tension between the truss and the exterior columns was about 12 kip (53 kN). It passed through the gusset plate and the strap anchor. The interior seat bolts had sheared at 566 °C, and the gusset plate fractured and the exterior seat bolts sheared at around 680 °C. At about 700 °C, a tension of about 10 kip (44 kN) passed through the strap anchor alone, and at 730 °C the truss walked off its exterior seat. NIST notes that the actual failure modes and sequence in the towers may have been different, because the model used assumed rather than actual temperature histories.

Demands on supports and connections

The tension in a sagging floor becomes an inward pull on whatever supports it. NIST found that substantial sagging of the tower floors produced pull-in forces at the column connections and led to inward bowing of the exterior wall. A floor with tensile forces at its connections does not restrain the exterior wall from bowing inward. In the global analyses, floors with a large sag likewise did not restrain the exterior columns against buckling.

Sagging can also overload the supports of the floor itself. NIST noted that floor sagging between supports may cause tensile failure of the truss seats, or tensile forces that pull the columns inward. NIST also summarised an earlier study of the towers by the University of Maryland and the Israel Institute of Technology. That study postulated, without supporting calculations, that the floors would sag and fail at their connections to the columns. Progressive collapse would then follow as the floors below also failed.

NIST reports connection failures in other fires as well, without attributing them to tension from sagging floors. In the 1970 fire at One New York Plaza, steel beams were deflected by several inches and their connecting bolts sheared off or failed. No floors collapsed, but there were connection failures and distortion of the floor beams. In World Trade Center 5, bolts tore out of fire-weakened beam webs at field-bolted connections, and large sections of floor failed.

Evidence from tests and fires

NIST uses the Cardington test building of the BRE in England as one of its comparison cases. This eight-storey steel braced frame was completed in 1993 to represent a typical office building, with simple shear connections and bays of 9.0 m along its length. Seven fire tests were carried out in it.

In Test No. 6, office furniture with a fire load of 46 kg/m² burned in a test area of 135 m². Gas temperatures exceeded 900 °C within 10 minutes and reached just over 1200 °C within 40 minutes, and the heat release rate was calculated to peak at 58 MW. No structural failures were reported, but the floor sagged by up to 0.64 m in a span of 9 m, about one fourteenth of the span. In Test No. 3, with compartment temperatures of about 960 °C, the largest floor beam deflection was 428 mm, also in a 9 m span. NIST cites these tests as a comparison with other building fires. It does not analyse how the Cardington floors carried their load at such deflections, and it does not attribute the result to membrane action.

Modelling and its limits

Milke notes that the response of a structure to fire was traditionally analysed one member at a time. In frames with many members, load transfer or membrane action may occur, and capturing load transfer requires a frame analysis. Such frame analyses range from algebraic methods to finite element models and belong to the tools of structural fire engineering. Milke also cites a review of the finite element models for structural fire protection available at the time. According to that review, all of them assumed perfect composite action between steel and concrete and disregarded torsion, and none modelled large displacements accurately.

NIST's own models show what was included in practice. In the truss model of the towers, the concrete slab was given different strengths in tension and compression. At the interior end of the slab, separate break elements represented the temperature-dependent tensile capacity of its steel reinforcement. The model of the WTC 7 floor likewise included the contribution of the welded wire fabric to the tensile capacity of the slab. In the global models of the towers, by contrast, the floors were shell elements that could not capture key failure modes at high temperature, including floor sagging.

NIST analyses the tension in sagging floors as catenary action of the floor system and its connections, and it does not call this membrane action. It uses the term membrane action only for the in-plane transfer of load from the core to the exterior walls through the floor shell elements of its global models. Milke's remark on membrane action concerns structural frames of many members. The NIST studies thus describe catenary action of floor strips and full-scale observations, but they give no design method for membrane action in floor slabs. The worked example shows the scale of the forces involved rather than a design check.

See also

• Finite element analysis
• Critical steel temperature
• Fire resistance
• Strength reduction at elevated temperatures

References

• Gross, J. L., & McAllister, T. P. (2005). Structural fire response and probable collapse sequence of the World Trade Center towers (NIST NCSTAR 1-6). National Institute of Standards and Technology.
• McAllister, T. P., Gann, R. G., Averill, J. D., Gross, J. L., Grosshandler, W. L., Lawson, J. R., McGrattan, K. B., Pitts, W. M., Prasad, K. R., Sadek, F. H., & Nelson, H. E. (2008). Structural fire response and probable collapse sequence of World Trade Center Building 7 (NIST NCSTAR 1-9, Vols. 1–2). National Institute of Standards and Technology.
• Milke, J. A. (2002a). Analytical methods for determining fire resistance of steel members. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 4-209–4-238). National Fire Protection Association; Society of Fire Protection Engineers.
• National Institute of Standards and Technology. (2005). Final report on the collapse of the World Trade Center towers (NIST NCSTAR 1).
• Zarghamee, M. S., Bolourchi, S., Eggers, D. W., Erbay, Ö. O., Kan, F. W., Kitane, Y., Liepins, A. A., Mudlock, M., Naguib, W. I., Ojdrovic, R. P., Sarawit, A. T., Barrett, P. R., Gross, J. L., & McAllister, T. P. (2005). Component, connection, and subsystem structural analysis (NIST NCSTAR 1-6C). National Institute of Standards and Technology.
• Zarghamee, M. S., Kitane, Y., Erbay, Ö. O., McAllister, T. P., & Gross, J. L. (2005). Global structural analysis of the response of the World Trade Center towers to impact damage and fire (NIST NCSTAR 1-6D). National Institute of Standards and Technology.