|NON-LINEAR TRANSIENT AND QUASI-STATIC ANALYSES |
OF THE DYNAMIC RESPONSE OF BUILDINGS TO BLAST LOADING
BSc (Hons), MSc, MBGS
Consultant, Griffiths Cleator & Associates, London, UK
Lecturer, University of Westminster, London, UK
On Saturday 24th April 1993, a bombing incident took place at approximately 10:25 a.m. within the Bishopsgate area of the city of London. As a result, one person was killed and 34 people were injured. Damage to building structures, fabric and contents, within a radius of about 500 m of the device ranged from total devastation to minor damage. As a consequence of this incident, the author was involved, as a consultant to Griffiths Cleator and Associates (GCA), in the reinstatement of over ten commercial buildings of various sizes, construction and degrees of damage. Finite Element Analysis was carried out on two of these buildings using ANSYS. A non-linear transient dynamic analysis was performed on a 3-D model of a typical floor of the first building, and a quasi-static analysis was performed on a full 3-D model of the second building. This paper presents a brief overview of the bombing incident and its damaging effects on building structures, outlines the investigation and testing techniques used, discusses both types of FE analyses employed, presents the dynamic response of the two buildings as predicted by FEA, correlates the analysis results with the investigation and testing that was carried out on site, and discusses the reliability of using FEA in highlighting problematic zones in the structure.
At approximately 10:25 on Saturday morning, 24th April 1993, a terrorist bomb exploded in city of London. The device which was made of unknown quantity of home-made explosives was carried in the back of a vehicle that was parked on the Bishopsgate southbound carriageway in the position shown in Fig.1. One person was killed and approximately 34 people were injured. Building structures, fabric and contents, within approximately 500 m radius of the device exhibited different degrees of damage with the maximum being close to the bomb.
The 14th century St Ethelburga's Church, which was only about 7 m away
from the bomb, was practically levelled to the ground. The size of the
bomb was estimated to be approximately 850 kg TNT equivalent. This
estimation was based on specialist forensic evidence and study of the
crater measurements and the soil properties.
For the purpose of this paper the number of buildings discussed shall be limited to the ones modelled and analysed by FEA using ANSYS and they will be referred to as A93 (marked in red in Fig.1) and B93 (marked in green in Fig.1). The proximity of these two buildings to the source of detonation is 11 m and 75 m respectively.
Royal Ordnance, being a division of British Aerospace Defence Limited, was appointed to provide information on the magnitudes of the blast pressures experienced by the two buildings, externally and internally, in the form of time-history graphs at specific points of each structure using 3-D simulation packages named 'INBLAST' and 'CHAMBER'. This paper investigates the dynamic response of the two buildings as observed on site on one hand and as predicted by FEA on the other hand. It correlates the analysis results with the investigation and testing findings, and discusses the reliability of FEA as a tool not only for predicting the response but also in highlighting problematic zones that may not be easy to observe on site without major opening up and breakage of the structure.
2. CHARACTERISTICS OF BOMB BLAST
An explosion is an instantaneous conversion of a small volume of
solid, or liquid, into a large and highly pressurised volume of very hot
gases that undergo violent expansion. As a result, a blast wave is
formed by the rapidly moving compressed air which is characterised by an
instantaneous rise in pressure. This is followed by a decay over a period
called the positive phase duration (see Fig.2). As the energy of
the expanding gases becomes dissipated, their momentum falls and they
begin to contract, creating a suction phase known as the negative
phase. At this phase, the blast wave pressure is below ambient
As the blast waves radiate out within the confined city streets they will be reflected and refracted by adjacent buildings. The blast waves will travel over the tops of buildings and down light wells thus totally enveloping these buildings and subjecting them to large unbalanced transient blast loads such as pressure pulses, gas filling and linear windage all of which have different times of arrivals. The geometry of the individual buildings, and in particular their elevations, can further magnify the incident transient blast loads.
The blast loads, although being transient in nature, would
nevertheless have been many orders of magnitude greater than the original
structural design loads for the buildings within the affected zone. Due to
the random nature of blast loads, damage to building structures is
notoriously unpredictable. Depending on the location of the explosive
device, the configuration of the surroundings and the quantity of free
space into which the gas may expand, the effects of a given explosive
device on a structure are notoriously unpredictable.
3. DESCRIPTION OF THE TWO BUILDINGS
3.1 Building A93
This was a grade II listed steel framed building, 7 storey high
constructed in 1928 (see Plate-2). Its architectural form can be described
as stone classical facade. Above 5th floor, the elevation steps inwards
and extends up the 7th floor where it was crowned with a cornice. Above
this was a steep slated mansard roof with dormer windows. The structural
frame was made up of plated mild steel R.S.J's (Beams and columns) or made
up plated beams secured with rivets and either riveted or bolted end
connections. The floors plates were generally insitu reinforced ribbed
slabs with permanent hollow tile liners used as shuttering. Part of the
3rd floor slab which was a later adaption was infilled using a timber
joist floor supported on steel beams.
3.2 Building B93
This property was constructed sometime between the late 1950's and early 1960's. The building had a basement, ground and five upper floors (see Plate-3).
Its construction consisted of a concrete cases structural steel frame
supporting hollow tiles reinforced concrete floor slabs. At 5th floor the
elevation stepped back and the perimeter cavity brickwork wall provided
support to the high level 5th floor roof.
4. DAMAGE INVESTIGATION AND TESTING
Immediately following the city bombing all efforts were naturally directed at damage limitation measures. The general condition of the fabric was recorded, photographed and videoed prior to it being removed, as this may give important clues on both the blast wave pressures and the manner in which they propagated through the structure. The preliminary bomb damage assessment report included a program of recommendations for further detailed inspections, opening up works and testing required to assess fully the effects of the blast on the structure.
Where visual evidence of distortions, deflections, and cracking to the structure and its finishes existed, selective local opening up of these elements were undertaken to establish if failure have occurred.
Having identified the areas of structure for detailed investigation, a regime of site and laboratory testing was prepared, starting from locations of greatest visible blast damage. Analytical methods proved very valuable here in terms of indicating areas of possible serious overstressing of the structure. Given the unpredictability of blast effects on buildings, it was found to be more cost and time effective to implement methods, such as finite element analysis that may highlight areas of damage prior to undertaking extensive opening of the structure.
Static proof load testswere carried out on floor panels which sustained maximum physical damage to compare actual deflections with analysis predictions. These results were compared with the results from a control area selected on the basis of least visual damage and similarly for all other materials tested. Also, plumb line surveys were carried out on the external elevations of both buildings, and FE analysis results were compared with recorded lateral displacements of the elevations of building B93.
5. BLAST OVERPRESSURE EXPERIENCED BY THE TWO BUILDINGS
What needs to be estimated first, is the magnitude of the blast pressures that the building may have experienced so that, FE technique, for example, can be used to obtain an indication of the dynamic response of the structure prior to it coming to rest. The consequences of this response on the structural integrity of the building can hence be evaluated. Royal Ordnance (a division of British Aerospace Defence Limited) were appointed to provide information on the magnitudes of the blast pressures experienced by the two buildings both on their external elevations and inside each structure through gas filling. Two distinct elements of calculations were carried out. The first, was to perform detailed external shock reflection modelling using INBLAST. For this analysis, 82 external test points on the elevations of building A93, and 88 external test points on the elevations of building B93 were selected by the author.
The second element of the calculation, was the analysis of the blast wave ingress into the structure and loads on internal slabs. This assessment used a program named CHAMBER which assesses the internal reflection and diffraction of blast waves entering through openings. For this analysis, 6 internal test points on a typical floor of building A93, and 5 internal test points on a typical floor of building B93 were selected.
5.1 Building A93
Bomb blast pressures are transient in nature and frequently of short
duration. On this building, this duration did not exceed 350 ms. The
maximum peak positive pressures ranged from 1,365 kN/m2 on the
north corner of the building (close to the bomb), to 91 kN/m2
on the south corner (away from the bomb). The arrival times of these
pressures were 12 m.sec and 138 m.sec respectively. In order to appreciate
the magnitudes of these pressures, it is worth pointing out that buildings
in the London region, including this one, are designed usually for a
maximum wind pressure of 1.5 kN/m2.
5.2 Building B93
All points on the rounded corner of the building between Bishopsgate
and Wormwood Street have seen very high blast pressures that reached a
maximum value of 131 kN/m2 at first floor level. The reason
being that this corner was approximately normal to the shock waves. This
is also 87 times the wind load that the building was designed for in the
laterally. At ground floor level, however, these pressures were less than
those at 1st floor level. This can be attributed to the frictional effects
of the ground on the shock waves.
6. FINITE ELEMENT MODELLING AND ANALYSIS
In the analysis of the dynamic response of a building structure to bomb blast, the following procedures must be followed [Esper & Keane, 1995]:
6.2 Building A93
The fifth floor slab of this building was modelled using ANSYS.
Two element types were used; shell element (shell 63) for the reinforced
concrete slab, and beam element (beam 4) for the steel beams. The total
number of elements in the model was 945, and the total number of nodes was
627. Each node had 6 DOF; three translations Ux, Uy, Uz, and three
rotations qx, qy, qz. The column locations were considered as support
points for the slab. Material properties of concrete and steel were
incorporated based on actual testing of the concrete cores and
examinations of the steel materials of the beams. The values used in the
analysis were as follows:
and for concrete:
The fundamental period of the plate was hence calculated and found to be equal to:
T1 = 1 / f1 = 0.080 sec = 80 msec
The positive phase duration was found on the internal pressures-time history graphs to be ranging between 20-45 m.sec. Since this was shorter than the fundamental period of the floor plate, a 3-D non-linear transient dynamic analysis was, then carried out in order to determine the response of the floor slab to the internal pressures.
The blast pressures were applied on the top and bottom faces of the concrete floor as pressure-time history graphs as produced by Royal Ordnance. Consequently, two graphs for every node of the model were obtained, one representing the deflections due to the pressures acting on the bottom face of the slab, and the other representing the deflection of the floor slab due to pressures acting on the top face of the slab. The two graphs were superimposed over each other so that the actual net deflection at any time can be estimated. As an example node 124 is considered and located near the middle of the bay next to the North stairs. It can be seen that the floor slab, at this point, was lifted upward by 16 mm before the pressures acting at the top of the slab were able to start pushing it downward.
It has been demonstrated by the FE analysis that when the soffit of the floor plate saw a positive peak pressure, it took 10 msec on average to develop its maximum deflection which ranged between 16 mm and 24 mm. It was observed that a 5 msec time lag in the pressures hitting the top surface of the slab was sufficient to result in a net upward deflection of approximately 16 mm above the horizontal. This momentary uplift of the plates will result in tension cracks to the top surface of the structural topping. This is combined with the subsequent rebound of the plate will cause crack aggravation over the supports, thus impairing the performance of the bond between the concrete and its reinforcement. This would result in failures similar to those that were recorded on the 5th floor load test, i.e. slippage of the reinforcement over the supports.
Further corroboration of these pressures, is the damage observed to the slab soffits which included cracking along the joints between the asbestos pots, hairline cracking of the concrete between the structural topping and the ribs. This cracking was reported in the petrographic tests of the cores that were taken from the structural slab.
6.3 Building B93
A full 3-D FE model of this building was generated using ANSYS. Two
element types were used here too; shell element (shell 63) for the
reinforced concrete slabs, and beam element (beam 4) for the steel beams
and columns. The total number of elements in the model was 5232, and the
total number of nodes was 3912. Each node had 6 DOF; three translations
Ux, Uy, Uz, and three rotations qx, qy, qz. From Plate-3, it can be seen
that this building has a large window area in each floor all the way
around except on the west elevation (flank wall). Taking also into account
the fact that it was reported by various sources [Royal Ordnance, 1993 and
later by Mayes & Smith, 1995] that normal glass, as a brittle
material, takes only 5-8 msec to break, it was found obviously sensible
not to include the glass panels in the FE analysis. This is true as long
as the glass panels are weak enough not to transfer any load to the
structural elements (such as frame members).
By carrying out a modal analysis first, using ANSYS, the natural frequencies for the building were given as follows:
f1= 1.899 Hz
f2= 1.961 Hz
f3= 2.586 Hz
The fundamental period of the plate was hence calculated and found to be equal to:
T1 = 1 / f1 = 0.527 sec = 527 msec
The positive phase duration was found on the internal pressures-time history graphs to be ranging between 50-80 m.sec. Since this was shorter than the fundamental period of the floor plate, the response of the building was impulsive, and the proper analysis that would be used is a non-linear transient dynamic one. Since the main concern was concentrated on the actual stability of the building, a quasi-static analysis was carried out as follows: The blast pressures were applied at different time intervals as a static load that has a variable value throughout all the elements forming the facades of the building. These values were extracted from the pressure-time history graphs produced by Royal Ordnance at each specific time interval considered in the analysis. This has allowed one to look at the maximum deflection that could have been experienced by the building with considerable saving of computer time and analysis efforts (such as feeding all the pressure-time history graphs to all the locations of the selected external 80 test points on all the elevations of the building).
7. CORRELATION BETWEEN DAMAGE AND FEA RESULTS
Tremendous damage was observed in the Bishopsgate incident. In
buildings close to the explosion, floor slabs were momentarily lifted,
load bearing walls moved and became out of plumb, and hidden damage
resulted. Hidden damage in building structures due to dynamic loading
became of more concern to engineers particularly after the investigation
of damaged buildings following the Northridge earthquake [NCE, 1994] and
the Kobe earthquake [Esper & Tachibana, 1995] where the same types of
damage described above were found.
In the case of Building B93, less damage was observed to the floor slabs because it was located much further than building A93 relative to the bomb. However, what was of a major concern in this building is the effect of the blast on the stability of the building and its residual strength to carry the original design load. This urged the need to look at the global behaviour of the structure and the magnitudes of permanent deflections in all three direction that may have resulted in the structure. Plumb survey was carried on the structure, along with all the other specified regular tests. Finite Element results from the 3-D quasi-static analysis over different time steps of the load showed good correlation with both the deformed shape and displacement magnitudes of the structure at corresponding points. Maximum deflection of 25 mm that was observed in the plumb survey on line V7, for instance, had a displacement value in the same direction of 22 mm in the FE analysis. Although these magnitudes may not seem particularly significant, design check calculations were carried out in order to predict the additional forces and moments values induced, in the structural frame, by the new displacements, and the adequacy of the frame to carry these forces and moments. Additional bracing was needed in this case for the structure to carry on functioning in the manner it was originally designed for.
Given the unpredictability of blast effects on buildings, it was found
to be more cost and time effective to implement methods, such as finite
element analysis that may highlight areas of damage prior to
undertaking extensive opening of the structure.
The author gratefully acknowledges the valuable contribution made by William Keane of Griffiths Cleator & Associates. The author also wishes to express his appreciation for the support provided by Griffiths Cleator and Associates, University of Westminster, and Taylor Woodrow Construction Holdings Limited. Finally, the support provided by the help desk and other members of the STRUCOM company on ANSYS is greatly appreciated.
Esper, P., and Keane, W., The St Mary Axe /
Bishopsgate Experiences on the Dynamic Response of Buildings to Bomb
Blast, A paper presented and discussed at the Institution of
Structural Engineers, Thames Valley Branch, on Wednesday 4th October 1995
at 6 p.m., London, UK.