The Dynamics of Bell Towers - a Survey in Northeast England J.L

The dynamics of bell towers - a survey in northeast England J.L. Lund, A.R. Selby, J.M. Wilson

University of Durham, UK

Abstract

Full-circle bell ringing in the English system imposes large dynamic forces on to the bell tower, causing it to sway. A major survey of the dynamic behaviour of old masonry bell towers in the Northeast of England has been undertaken, which included two cathedrals and seventeen churches. In each tower, the heaviest bell was tolled, and accelerometers positioned around the tower were used to record both horizontal and vertical motions. Critical analysis of the form of the modes of deformation identified three components of sway: rocking, shearing and bending.

Introduction

In the English system, bells are rung by swinging them from mouth-up position through some 360<>, from 'up at handstroke' to 'up at backstroke' and back again. The clapper, which rotates faster than the bell, strikes the bell rim as the bell slows towards the end of the rotation, Wilson [1]. Towers contain a ring of bells varying in number from three to 12. A single bell may be tolled, or all the bells may be rung in defined patterns or 'methods'. The mass of the heaviest

'tenor' bell may be considerable, and within the present survey a bell in Newcastle Cathedral had a mass of 1900 kg.

As a bell swings through its 360° arc, usually in a N-S plane or an E-W plane, it exerts forces through the bearings into the bell frame and thence through the tower to ground. The bell tower responds dynamically to the forces, swaying laterally, with maximum deflection at the top of the tower, Selby and Wilson

[2], Wilson et al. [3]. The magnitudes of the bell forces can be calculated following a series of simple measurements on each bell, involving small amplitude oscillation frequency, and static load-rotation data, Heyman and Threlfall,[4].

46 Dynamics, Repairs & Restoration

A total of fifteen churches and one cathedral were studied in this exercise, and information was available from previously published work, Wilson et al [3],

Wilson and Selby [5]. Four church towers, the two St Cuthbert's, St Mary's and St Nicholas', are surmounted by a spire. The towers vary considerably in their height to breadth ratio, from 1.9 of Christchurch to 8.4 of St Nicholas in Durham. Most towers are nearly or truly square in plan, although St Matthew's is 9.2m by 7.2m. A sample of tower elevations is given in Figure 1.

Data Analysis

A typical record of data from one of some 24 sets at one church, in Figure 2, shows the characteristic form of response. At each swing of the bell a large response occurs which then decays sinusoidally until the bell swings again. The peak amplitude is used for mode shape definition, always by ratio to the reference signal. The characteristic decay of damped free vibration after the bell is held allows accurate measurement of the free vibration frequency of the tower, and also of damping factor.

Because of the high accuracy of the measured tower movements in this work it became possible to analyse the form of the tower response in some detail. The walls of the tower are of sandwich construction: inner and outer leaves of masonry, and an infill of loose mortar/rubble. The tower is sufficiently stubby for shear deformation to be of significance. The foundations of each tower are generally flexible to some degree. Consequently, the tower sway comprises three components of base rocking, beam shear, and beam bending.

The technique for computation of each component is as follows: i) The vertical displacement at ground level, divided by half-tower width gives the component due to base rocking. Displacement increases linearly with height. ii) The plot of vertical displacement, with the rocking deducted, and divided by the tower half-width gives the slope of the tower due to bending. The integral of the slope gives a non-linear curve of bending deformation. iii) Subtraction of the components of rocking (i) and of bending (ii) from the total measured mode shape of horizontal movements gives the component due to shear deformation at various heights up the tower.

A MATLAB program was written to make these significant computations. An example of the proportions of rocking, shear and bending is shown in Figure 3.

Results

The primary results from the comprehensive measurement programme include the tower dimensions, the natural frequencies of vibration, the mode shapes and their components, and damping factors. Table 1 gives a substantial summary.

Dynamics, Repairs & Restoration 47

Table 1 Church tower properties and responses

Height Max u. cO) Bell Tower Nat. Damp CO 6 to displace

St. Oswald's, 8 EW 650 24.8 3.44 0.38 2.01 0.026 22 36 42 Durham 7 NS 447 0.27 2.05 0.026 30 23 47 St Mary's Schfe 6 NS 210 30.4 5.72 0.05 2.35 0.018 21 20 59 St Cuth's Ch le S 8 EW 966 43.5 6.01 1.27 1.59 0.028 20 36 44 0.33 2.56 0.026 16 72 12 All Saints' Lanch 6 EW 432 19.7 3.27 Christchurch 8 NS 822 16.3 1.9 0.4 2.48 0.078 6 87 7 Consett 6 EW 434 0.11 3.38 0.031 14 62 24 Newcastle Cath 12 NS 1913 32.8 2.98 0.22 2.04 0.014 6 58 36 St Michael's 8 NS 610 21.4 2.87 0.1 2.98 0.049 19 43 38 Houghton 7 EW 464 0.13 2.71 0.031 14 38 48 St Nicholas' 6 NS 516 43.5 8.4 0.62 1.38 0.014 6 34 60 Durham 1 EW 203 0.24 1.82 0.014 12 39 49 8 EW 660 16.5 2.66 0.1 3.13 0.045 14 32 54 St Margaret's Tanfield 7 NS 432 0.02 3.88 0.027 18 11 71 St Andrew's 10 EW 1155 20.5 2.65 0.002 5.28 14 25 61 Roker 9 NS 789 0.001 5.34 39 47 14 St Matthew's 8 NS 1588 28 3.06 0.4 1.92 0.026 22 60 18 Newcastle 7 EW 1103 3.89 0.84 1.49 0.028 9 60 31 St Andrew's 8 NS 609 23.2 3.22 0.12 2.51 0.065 26 44 30 B. Auckland 6 EW 356 0.17 2.2 0.051 27 45 28 St John's 8 EW 829 18.5 2.7 0.04 3.49 0.046 16 40 44 0.03 3.68 0.028 20 26 54 Shildon 7 NS 589 St Michael's 6 EW 782 16.2 2.69 0.09 3.16 0.023 9 64 27 Heighington 4 NS 432 0.04 3.63 0.016 6 64 30 St Edmund's 5 NS 533 25.4 3.48 0.16 2.28 0.018 40 47 13 Sedgefield 4 EW 469 0.21 2.2 0.017 35 46 19 St Brandon's 8 EW 693 20 3.57 0.23 2.59 0.02 Brancepeth 7 NS 498 0.22 2.84 0.032 St Cuthbert's 6 NS 643 33.8 6.74 0.12 2.25 0.026 Benfieldside 3 EW 263 0.08 2.27 0.027 Cathedral, 10 NS 1425 66 4.89 0.35 1.28 0.016 Durham 9 EW 1096 0.16 1.31 0.016

St Mary's 8 EW 559 24 4.06 0.13 2.55 0.038 25 59 16 Richmond 7 NS 408 0.05 3.04 0.029 29 32 39

Note the abbreviations of St Mary's in ShinclifFe, St Cuthbert's in Chester- le-Street, All Saints in Lanchester, and Newcastle Cathedral, where only one bell was tolled in each case.

Insufficient data were available from the previous surveys of St Cuthbert's in Benfieldside, St Brandon's in Brancepeth, and Durham Cathedral to allow estimation of the proportions of rock, shear and bending.

All the towers are of traditional sandwich masonry construction except St Andrew's in Roker which is outwardly similar but comprises an outer leaf of masonry backed directly by interior concrete. No damping factor could be derived from the very small signals at Roker.

Some conclusions are evident from the table. Firstly, the maximum dynamic responses of the towers, u^x, are very small, the maximum recorded value being 1.27mm in the spire of St Cuthbert's in Chester-le-Street. The more typical values, however, are of the order of O.lmm to 0.3mm. This contrasts strongly with the subjective opinions of the lay observer, who might commonly estimate movement of several millimetres, because of the very high sensitivity of the human frame to vibrations. The natural frequencies of free tower vibration lie in the range of 1.3 Hz to 3.9 Hz (except for the concrete tower in Roker).

The correlation between tower height and maximum displacement was found to be poor, with a correlation coefficient of 0.37, see Figure 4. Whilst the body of data relating to towers of rectangular elevation is clustered to the left side, the response of the tall spire of St Cuthbert's at Chester-le-Street stands out alone.

Both the tall Cathedral towers were so massive that their responses were low.

In Figure 5 a scatter graph is shown of the natural frequencies of the towers plotted against height. The two rogue high points relate to the concrete lined tower of St Andrew's, and should be ignored. Good correlation is shown by a curve drawn through the data. The lowest frequencies are for Durham Cathedral and for the churches of St Nicholas and St Cuthbert's which both have tall spires. The tall slender towers generally have lower frequencies than the short squat towers.

The proportions of rocking, shear and bending correlated poorly with aspect ratio. It thus appears that the rocking element was an effectively random function related to the unknown conditions of the foundations; the more 'stubby' towers showed generally rather higher shear deformation, while the more slender towers showed a higher component of bending.

An interesting comparison between the observed maximum displacements of the towers of Christchurch in Consett and of St John's in Shildon can be observed from Table 1. These towers are both short, squat towers of similar dimensions, and the masses of the tenor bells are 822kg and 829kg respectively. The maximum displacements recorded, however, were 0.4mm for Christchurch and 0.04mm for St John's. While there may be some differences in the foundations and in the condition of the mortar joints, the reason may lie elsewhere. It was observed that the ratio of tower frequency to bell-ringing frequency was 12.00

Transactions on the Built Environment vol 15, © Dynamics1995 WIT Press,, Repair www.witpress.com,s & Restoratio ISSN 1743-3509n 49

in the case of Christchurch, and 22.4 in the case of St John's. The significance of the ratio is not its magnitude but the proximity to an integer. The phenomenon of excitation of large oscillations by a tuned periodic force is well known. It would be interesting to investigate further the potential for this condition.

Conclusions

A survey of the dynamic behaviour of the bell towers of churches and cathedrals in the north-east of England has shown that despite the considerable forces imposed by the full-circle tolling of the tenor bell, the displacements of the towers were very small, rarely exceeding 1mm. The natural frequencies of the masonry towers reduced with tower height, the lowest being in Durham

Cathedral at 1.28 Hz.

The detailed records of the form of the variations of vibrations around each tower structure allowed estimation of the contributions to displacements from base-rocking, from shearing and from bending. Future analysis of the several towers can move towards estimates of factors of safety of the tower in each of the three modes.

Acknowledgments

The permission from the many vicars to enter the church towers and to ring the bells was gratefully appreciated, as were the efforts of the many bell ringers who made the work possible.

References

1. Wilson, W.G. The Art and Science of Change Ringingfaber & Faber, London, 1965.

2. Selby, A.R. and Wilson, J.M The Dynamic Response of a Church Tower to Bell-Ringing', in STREMA2 (ed. Brebbia, C.A.) Vol. 2, pp 3-16, Proc. of 2nd Int. Conf. on Structural Repair and Maintenance of Historic Buildings, Seville, 1991. Comp.Mech.Publ. Southampton, 1991.

3. Wilson J.M, Selby A.R. & Ross SE The Dynamic Behaviour of Some Bell Towers During Ringing' in STREMA3 (ed. Brebbia, C.A. & Frewer RJB) Vol. 3, pp 491-500. Proc. of 3rd Int. Conf. on Structural Repair and Maintenance of Historic Buildings, Bath, 1993. Comp.Mech.Publ.

Southampton, 1993. 4. Heyman, J. and Threlfall, B.D. 'Inertia Forces Due to Bell Ringing', Int. J. of Mech. Sci. Vol. 18, pp 161-164, 1976. 5. Wilson, J.M. and Selby, A.R., 'Durham Cathedral Tower Vibrations During

Bell-Ringing', in Engineering a Cathedral (ed. Jackson MJ). pp77-100. T.Telford, London 6. Lund J.M. The Dynamic Response of Church Bell Towers to Bell Ringing'. Unpublished report, Durham University, 1994.

50 Dynamics, Repairs & Restoration

IIOUCHTON I.K-SPRING. CONSP:TT. CIIPJSTCIIURCH

_J cj (N/S) ^ 2.48 H/.. ; (N/S) = 2.98 H/.. w (E/W) 3.38 Hz. ; (E/W) = 2.71 Hz. 8 HEI.IS. Mass(No8) ---• 821.5kg. 3 CELLS. Mass(NoB) = 609.6kg

NEWCASTLE. CATHEDRAL CHURCH OF DURHAM. ST. NICHOLAS

u (N/S) - 2.04 Hz. w (N/S) = 1.38 Hz. u (E/W) = 3.38 Hz. w (E/W) = 1.02 Hz. 12 BELLS. Mass(Nol2) = 1912.8kg 6 DELI^. Mass(No6) =-- 516.2kg.

POSITION OK KEKERENCt; ALL DRAWINGS TO SCALE 1:400 TRANSDUCER FOR CLARITY. AVERAGE WIDTHS AND X POSITIONS OF ROVING WALL THICKNESSES ARE INDICATED

Figure 1 Some tower elevations showing accelerometer positions.

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Figure 2 Typical traces of tower response at two positions.

52 Dynamics, Repairs & Restoration

DURHAM, St Oswalds, Bell No8.E/W

25-

0.5 1 1.5 2 2.5 3 3.5 Horiz Accel, referenced to Ringing Chamber

Figure 3 Proportions of rock, shear and bending, St Oswald's.

1.4 - 6 T • 1.2 5

• 0.8

0.6 •

u ma x m 2 -- 0.4 • •• • • 0.2 .: . ,f : Q PL^^«" '

0 20 40 60 80 20 40 60 80 height m height m

Figure 4 Displacement/height Figure 5 Frequency/height scatter plot scatter plot