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The Dynamic Behaviour of Some Bell Towers During Ringing J.M. Wilson

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The Dynamic Behaviour of Some Bell Towers During Ringing J.M. Wilson Transactions on the Built Environment vol 4, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509 The dynamic behaviour of some bell towers during ringing J.M. Wilson, A.R. Selby, S.E. Ross University of Durham, Durham, UK Abstract. When bells are rung to the English system they are swung full-circle through 360° from the mouth-up position. A body which is constrained to move around the arc of a circle experiences acceleration, and so a swinging bell imparts considerable force on to the bell frame and thence to the tower. This causes the tower to respond dynamically, primarily in swaying motion. The bell forces can be estimated from relatively simple measurements, and the motion of the tower can then be estimated computationally, using finite element methods. Three church towers in Northern England have been studied, and additionally, the dynamic movements of the towers have been measured for comparison with computed values. Introduction The traditional English church is of masonry construction and has a cruciform plan. A tower, sometimes surmounted by a spire, may be situated above the intersection of the nave and transepts or at the west end of the nave, or more rarely may be free-standing. Masonry towers are generally of thick-wall construction incorporating a sandwich of faces of ashlar or coursed stone and a filling of loose rubble. Large towers may be buttressed. The tower will normally house a ring of between four and 12 bells, depending on its size. The bells are carried in a bell frame, see Figure 1, and the ringers swing the bells by ropes from within a ringing chamber situated below. Traditionally bell frames were of timber, but modern frames are of steel construction or occasionally of reinforced concrete. In order to minimise the potentially damaging effects of the dynamic forces from the swinging bells, modern frames are relatively stiff, and are securely built into the tower structure. Transactions on the Built Environment vol 4, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509 492 Structural Repair and Maintenance of Historical Buildings In the English system of bell ringing, Wilson 1, the bells are rung full circle in various patterns of sequences, known as methods. Bells also may be rung in simple fixed sequences known as rounds, two or more bells may be 'fired' simultaneously, and single bells may be tolled individually. When a bell is swung full circle from the mouth-up position about an axis which is not coincident with its centre of mass it behaves as a compound pendulum undergoing non-linear oscillations. The forces transmitted to the bell frame and the tower depend on the mass of the bell and on the eccentricity of its centroid from the axis of suspension. A number of investigators have published work on the behaviour of bell towers in response to bell ringing. An important contribution to the practice of bell hanging and its consequences for bell towers was made by Heywood^, in which reference was made to the significant theoretical study of bell forces by Lewis^. More recently, Heyman and ThrelfalH found good agreement between theoretical predictions of inertial forces from bell ringing and those measured in laboratory tests. They also developed a useful method for deducing the inertial properties of a bell from simple in-situ measurements, namely timing the frequency of small amplitude oscillations of the bell and measuring the static rotation of the bell due to weights attached to the bell rope. Wilson and Selby^ extended the analysis to include the initial impulse provided by the ringer. While the horizontal and vertical force components are readily expressed mathematically as functions of angular position with respect to mouth-up, it becomes necessary to define the forces produced by the swinging bell as functions of time. An appropriate technique is the use of elliptic integrals evaluated numerically through standard computer algorithms, Wilson^. Typical time dependent forces are shown in Figure 2, for the complete oscillation of a bell involving two full circle swings during which the bell sounds twice. The duration of such an oscillation is typically of the order of five seconds with a ringing interval of half this time. For certain simple methods of ringing such as tolling or ringing rounds the forces acting on the tower are periodic and can be represented by Fourier series, Wilson^. In this study, three towers in the north of England were investigated: St. Brandon's in Brancepeth, St. Oswald's in Durham and St. Cuthbert's in Benfieldside. In each case the towers were surveyed and the bell parameters were obtained using the method of Heyman and Threlfall. The dynamic forces computed from these measurements were imposed on to a finite element model of the masonry tower, to produce an estimate of the sway of the tower as a function of time. In addition, measurements were taken of the sway of each tower using sensitive velocity transducers, which gave specific information about the fundamental natural frequency, mode shape and damping. Comparison between measurements and estimated values gave an appreciation of the accuracy of the finite element representation of the tower structure. Transactions on the Built Environment vol 4, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509 Structural Repair and Maintenance of Historical Buildings 493 The Churches In The Study. 1. St Brandon's Church, Brancepeth. This church has been studied over several years, and measurements and analysis were reported by Selby and Wilson?. Additional measurements of tower sway response have since been made. The church dates from the 12th century and was built using local sandstone. The tower is located at the west end of the nave and is some 20m high. It houses a ring of eight bells, and the heaviest, tenor, bell has a mass of 693 kg. 2. St Oswald's Church, Durham. This church dates in part from the 12th century, although the tower and other parts of the structure were added in the 14th and 15th centuries. It was constructed from local yellow sandstone. The tower is of sandwich construction and is located at the west end of the nave. It is some 25 m high and square in cross section. Access to the ringing chamber is by stone spiral staircase, which allows measurements of sway at regular intervals as well as in the ringing chamber and above the bell frame. The ring of bells comprises eight bells, with the tenor having a mass of 651kg. 3. St. Cuthbert's Church, Benfieldside. St Cuthbert's was constructed during the 1840's of dressed masonry, and was consecrated in 1850. It stands on the side of a steep hillside, and because of this feature it is unusual in that the nave runs north-east to south-west. In this text, for convenience, the altar will be described as the 'east' end. The bell tower is at the true west corner of the masonry church. The square tower is small both in plan and elevation, and is surmounted by a masonry spire, being some 35m in height overall. The ring of six bells are hung on a steel frame on two levels, the heaviest bells being on the lower level. Characterisation Of The Bells. The first stage of each study was to estimate the properties of all the bells in each ring of bells. The masses, m, of the bells were available from foundry records for all three towers, and could be accepted as reliable; however a 20% addition was made in every case to make allowance for the headstock and ropewheel, Heyman and Threlfallt Weights of up to 600N were applied incrementally to each bell rope, and rotation of the bell was measured; from these measurements the distance from the support axis to the centroid of mass, h, of the bell was estimated. Next, small oscillations of the bell were then timed, over 50 cycles, to give the period, T, and thence an estimate of the moment of inertia, mk^. These parameters are recorded in Table 1, for the heaviest bells swinging E/W and N/S in each church, and can be used as input to a computer program to derive dynamic forces as a function of time, as in Figure 2. Transactions on the Built Environment vol 4, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509 494 Structural Repair and Maintenance of Historical Buildings Table 1. Bell data. Church Bell Mass (kg) k(m) h(m) T(s) St. Brandon's 7(N/S) 498 0.390 0.338 1.780 Brancepeth 8(E/W) 693 0.426 0.387 1.855 St. Oswald's 7(N/S) 447 0368 0.282 1.750 Durham 8(E/W) 651 0.406 0.302 1.848 St. Cuthbert's 3(E/W) 338 0.329 0.322 1.627 Benfieldside 6(N/S) 643 0.406 0.313 1.837 Finite Element Modelling Of The Towers The modelling of structural behaviour by the finite element method is now commonplace, but considerable care is necessary in constructing the model if realistic results are to be obtained, especially in transient dynamic analyses. A church tower can be modelled by either a vertical cantilever using Timoshenko beam elements or as a fully 3-dimensional structure using 'brick' elements. However it is necessary to make several assumptions for either model. First, the detailed behaviour of a sandwich wall of outer masonry skins with rubble infill is approximated as a solid wall which has an effective elastic modulus, Egg; much reduced from the elastic modulus, E, of intact sandstone; typically E is about 17 GPa for Durham sandstones, while an appropriate value of E^ff varies between 3 and 6GPa.
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