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Urban Habitat Constructions under Catastrophic EventsFINAL CONFERENCE. Naples, 16th- 18th September 2010Chair of the Action: Federico Mazzolani, IT, fmm@unina.itCOST Science Officer: Thierry Goger, tgoger@cost.esf.org

COST Action C26

ON THE CATENARY EFFECT OF STEEL BUILDINGS

A.Formisano & F. M. Mazzolani Department of Structural Engineering, University of Naples “Federico II”

ABSTRACT: The vulnerability to progressive collapse of steel framed buildings subjected to sudden column loss is herein shown. Two steel framed buildings designed according to both the old and

new seismic Italian code, have been analysed, by considering the uncertainties on the material strength and on the applied loads. Linear static and non linear static analyses have been performed in

order to estimate the progressive collapse resistance of frames under different column-removed conditions. Also, the capacity curves of the structures under vertical loads have been drawn, they being

able to simulate their response in non linear dynamic range. The force-displacement curves obtained from the above analyses allowed to evaluate the Dynamic Amplification Factors (DAFs) to be used

when static analyses instead of the non linear dynamic ones are made. The comparison has shown that a DAF value less than 2 can be used, when the inelastic response of structures is considered.

The tragic event of the World Trade Centre collapse has pushed the scientific community to find the

way to reduce the occurrence of progressive (or disproportionate) collapse, what is related to the

improvement of the structural robustness under extreme accidental events.

Nowadays, different international codes [EN 1991-1-7 (2006), United States Department of Defense

(DoD, 2005), the United States General Services Administration (GSA, 2003), UK Building

Regulations (BS 6399-1, 1996)], starting from the collapse of the Ronan Point building in London

(1968), have provided different definitions for robustness and progressive collapse, providing at the

same time defensive measures for the construction protection. As an example, according to EN

1991-1-7, the robustness is intended as “the ability of a structure to withstand events like fire,

explosions, impacts or the consequence of human error, without being damaged to an extent

disproportionate to the original cause.” On the other hand, different meaning for progressive

collapse are used. In general terms, when one or several structural members suddenly fail due to

either accident or incidental conditions and subsequently every load redistribution causes in

sequence the failure of other structural elements, then the complete failure of the building or of a

major part of it occurs and the progressive collapse is attained.

Two different types of steel framed structures have been analysed aiming at evaluating their

robustness under the exceptional load deriving from the sudden column loss. The choice of the

frame types has been done according to a previous study performed by the Authors (Formisano

et al., 2009), where the robustness of new and existing steel frames under exceptional

earthquakes has been evaluated.

The selected framed buildings are made of S275JR steel profiles and subjected to permanent

and variable loads of 5.15 kNm-2 and 2 kNm-2, respectively. The first structure is composed of 3

transversal plane frames spaced 5 m each other, with a single 5m bay on two levels with inter-

storey height of 3.5 m. The longitudinal plane frames of the second structure develop on three

levels (H=3.50 m at 1st floor and H=3.00 m at 2nd and 3rd floor), with three 5m bays. Both

structures have been designed according to both the old (M.D., 1996) and the new (M. D., 2008)

seismic Italian code (Ferraioli & Lavino, 2007). For these structures, the randomness of both

material (coefficient of variation COVm of 3%-5%-7%) and vertical loads (coefficient of variation

COVl of 10%-20%-30%) have been considered at the light of a semi-probabilistic approach to be

used for the robustness analysis of new structures. Therefore, the combination of the above

COVs has led to nine analysis cases.

M.D. 96

CONCLUSIVE REMARKS

In this paper, the resistance to progressive collapse of steel framed buildings designed according to the old and the new seismic Italian codes has been assessed by using linear static, non linear static

and non linear dynamic analyses. The linear static analyses can be used when the column-removed building behaves substantially elastically. Contrary, in plastic field, the collapse resistance is better

estimated by means of the capacity curves, which can be obtained by a non linear static response, according to the energy conservation principle, with the purpose to simulate the structure NLD

behaviour. Linear static analyses accounting for the catenary effect have been also performed, they being able to assess in a simple way the real building behaviour in terms of stored energy. The

analyses have shown that the robustness index of buildings designed according to the new code is averagely 10% larger than the one of other buildings satisfying the old seismic provisions.

Furthermore, the use of DAFs has been assessed, for considering the dynamic effect due to the column removal, when static analyses are made. The obtained results have shown that the GSA US

code provisions are not on the safe side when elastic analyses are performed, since DAFs values are greater than 2, and that the dynamic amplification in the inelastic field depends on the maximum

allowable displacement. In particular, for the 2-storeys and the 3-storeys structure, a mean DAF value of 1.23 and 1.16 is respectively obtained, when the maximum allowable displacement is reached.

REFERENCES

Abruzzo, J., Matta, A. & Panariello, G. 2006. Study of mitigation strategies for progressive collapse of a reinforced concrete commercial building. Journal of Performance of Constructed Facilities 30 (4): 384-390.

British Standards (BS) 6399-1. 1996. Loading for buildings. Code of practice for dead and imposed loads. September.

Computer and Structures, Inc. (CSI). 2008. SAP 2000 Non linear, version 11. Berkeley, California, USA.

Department of Defense (DoD). (2005). Unified Facilities Criteria (UFC): Design of Structures to Resist Progressive Collapse. Washington, D.C.

EN 1991-1-7. 2006. Actions on structures – Part 1-7: General Actions – Accidental actions. January.

Ferraioli, M. & Lavino, A. 2007. Performance evaluation of steel framed structures by means of simplified non-linear analysis methods (in Italian). Proc. of the XXI C. T. A. Italian Conference, Catania, October.

Formisano, A., Marzo, A. & Mazzolani, F.M. 2009. Robustness based design of new and existing steel structures. Proc. of the 6th Int. Conference on the “Behaviour of Steel Structures in Seismic Areas” (STESSA 09), August 16-20, Philadelphia.

Lin, B. H. 2007. Progressive collapse analysis and evaluation of an earthquake-resistant RC building. Master thesis, National Pingtung University of Science and Technology, Taiwan.

Mazzolani, F.M. & Piluso, V. 1996. Theory and Design of Seismic Resistant Steel Frames. London: Champan & Hall.

Ministerial Decree of Public Works (M. D.). 1996. Technical codes for constructions in seismic zones (in Italian). Official Gazette of the Italian Republic published on January 16th.

Ministerial Decree of Public Works (M. D.). 2008. New technical codes for constructions. Official Gazette of the Italian Republic published on January 14th.

Starossek, K. 2006. Progressive collapse of structures: nomenclature and procedures. Structural Engineering International 16 (2): 113-117

Tsai, M. H. & Lin, B. H. 2008. Investigation of progressive collapse resistance and inelastic response for an earthquake-resistant RC building subjected to column failure. Engineering Structures 30: 3619-3628.

United States General Services Administration (GSA). 2003. Progressive Collapse Analysis and Design Guidelines for New Federal Office Buildings and Major Modernization Project. Washington DC.

United States National Institute of Standards and Technology (NIST). 2007. Best Practices for Reducing the Potential for Progressive Collapse in Buildings. Technology Administration, U.S. Department of Commerce, Washington, D.C.

ROBUSTNESS AND PROGESSIVE COLLAPSE OF STRUCTURES THE STRUCTURES UNDER STUDY

RESISTANCE TO PROGRESSIVE COLLAPSE

MURRAH FEDERAL BUILDING

Oklahoma City , April 19th, 1995)

RONAN POINT

(London, May 16th, 1968)

WORLD TRADE CENTER

(New York City , September 11th, 2001)

M.D. 08

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M.D. 96 M.D. 08

Analysis methodology

When a column is removed from a framed structure, its robustness can be assessed

in terms of progressive collapse resistance, intended as the maximum loading

capacity to be sustained before failure. Different analysis types, namely linear static,

non linear static and non linear dynamic, are usually performed to evaluate the

progressive collapse of framed buildings (Tsai & Lin, 2008).

Dynamic non linear

response obtained from

static non linear one

Linear static (LS) procedure: a step-by-step scheme of inserting moment-release

hinges is used to simulate the inelastic structural behaviour. In this analysis, the

vertical loads applied to the structure are gradually increased up to achieve the

progressive collapse of the building. Catenary effect is neglected and only flexural

failure mode is considered.

Non linear static (NLS) analyses: a displacement control procedure is used. A

vertical displacement is gradually applied to the column-removed point, up to the

attainment of the maximum building resistance. Generally, this analysis type provides

a progressive collapse strength lower than the one obtained by linear static

procedures.

Non linear dynamic (NLD) analyses: the real progressive collapse resistance of

buildings is estimated. This analysis typology, which provides a lower collapse

resistance than static analyses one, is to difficult to be carried out for practical

applications. As a consequence, an alternative method has been proposed in order to

precisely estimate the building collapse resistance under the described exceptional

situation instead to perform NLD analyses (Abruzzo et al., 2006 – see figure).

Analysis results

2-storeys building: the first and the second level columns of the central frame have been removed separately

from the structure (two threat-independent column-removed conditions). 3-storeys building: the columns of

the 1st, 2nd and 3rd level belonging to the external and internal alignment of vertical elements have been

removed one by one from the central frame (six threat-independent column-removed conditions).

0

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Displacement (m)

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M. D. 96 - COVm = 7% and COVl = 10%)

1st storey column 2nd storey column

M. D. 08 - COVm = 7% and COVl = 10%)

1st storey column 2nd storey column

In the above pictures, LS analyses accounting for the catenary effect have been also plotted. These curves

are able to assess the real building behaviour in terms of stored energy, since the area under these curves is

equal to the one enclosed under the NLD curves.

NLD

LS

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M.D. 96 - int. col.

M.D. 96 - ext. col.

M.D. 08 - int. col.

M.D. 08 - ext. col.

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M.D. 96 - int. col.

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M.D. 08 - ext. col.

2 storeys - M. D. 96 2 storeys - M. D. 08

3 storeys: change of DAFs with respect to

the column removal at different storeys