The Indoor Riding Hall in Bergpark Wilhelmsh?he

Overview

The master's thesis deals with the realistic modelling of historical timber constructions using the example of the indoor riding hall in the Bergpark Wilhelmsh?he in Kassel. The riding arena is a rectangular half-timbered building, in which the outer walls have a large inclination (see Figure 2) and the roof is secured with an emergency support (see also Figure 3). In the course of a repair, the future structural safety is to be determined.

In the work, documents available for the property were first studied in detail and the findings summarised. The results are a description of the condition, an analysis of the building type and a presentation of the construction history of the riding arena. It was shown that these three results are interrelated.

In order to be able to analyse the load-bearing effect of the "open roof structure" and the effects of the retrofitted elements, the general procedure was first developed. The aim was to create a three-dimensional FEM model of the riding arena that realistically represents the load-bearing effect, as this is particularly important in the case of open roof structures. The main focus of the procedure was to determine the stiffness of the carpentry connections. Practical building calculations for the stiffnesses were used on the basis of a guideline from the University of Applied Sciences Bern. Finally, three models were created to analyse the indoor riding arena, which represent the different situations of the existing reinforcement measures.

In order to be able to dismantle the emergency supports in the future and still ensure a functioning load-bearing behaviour, repair measures are necessary. Five different repair variants were developed, each based on a different load-bearing mechanism. The variants were then compared and a recommendation for the next steps was made.

Background

The subject of this master's thesis is the riding arena at the stables in the UNESCO World Heritage Site Bergpark Wilhelmsh?he in Kassel. It was built at the end of the 18^th century in the economic area of Wilhelmsh?he Palace, has been used repeatedly as an event venue in recent decades and is currently a shelter for garden tools and vehicles. The falling of components over the past decades indicates movement in the structure of the roof structure. This prompted an emergency stabilisation using several wooden supports.

The state institution "Hessen Kassel Heritage", which manages the building, would like to organise events in the indoor riding arena again in the future. To this end, the supporting structure is to be repaired in such a way that the emergency support can be removed again. Due to its size and complexity, the supporting structure requires an engineering investigation and modelling in order to initiate further planning steps.

The art of horsemanship was important in the Baroque court as horses were a symbol of the rulers. The riding halls have a special architectural-historical significance, as they span larger spaces with as few pillars as possible. The riding hall in Bergpark Wilhelmsh?he, built in 1789, is connected to the Marsstall complex located there.

The riding hall is a rectangular half-timbered building on a natural stone base with a gently sloping hipped roof. The building is approximately 18 metres wide and 30 metres long with a ridge height of 10 metres. The roof construction, which is visible today, originally had plastered wooden panelling that simulated a vault.

The half-timbered oak walls stand on a natural stone plinth made of tuff. Between the windows, the construction is double-shelled in two or three axes. This results in composite half-timbered supports consisting of four or six studs. These have a total depth of approx. 75 cm. The hipped roof, which is designed as an "open roof structure", sits on top of the half-timbered wall. The roof structure can be divided into trusses and empty trusses. The girder truss stands as a horizontal chair with a suspended structure, which is braced on the collar beam. The chair columns are usually designed as double chair columns. Typical of the open roof structure are the lack of a cross-beam layer and a cross-brace construction in the form of tongs made of wood and metal. At roof beam level, there are metal tie beams that were not built at the time of construction but were retrofitted later.

Structural analysis

The Baroque roof structures were designed on the basis of experience with proven constructions. Scientific calculations were not used in construction until the beginning of the 19^th century. The force flow of "open roof structures" cannot be intuitively read off due to the high degree of static indeterminacy, as is the case with rafter and purlin roofs, for example.

The structural stabilisation of historic buildings is part of monument preservation. It is important to know the load flow of the existing substance in order to develop securing concepts for this. The load flow must be determined quantitatively in order to dimension the components resulting from the concepts. This is not determined on the object itself, but calculated using abstract models that represent the load-bearing system. The more accurate the model, the more accurate the results that can be worked with. It is therefore important to convert the built load-bearing structure as accurately as possible into a calculable model. The calculation itself is carried out using computer programmes based on the finite element method (FEM).

Open supporting structures are particularly susceptible to modelling errors. The support situation of the roof base points in particular is decisive for the result. It is therefore important to consider this situation as realistically as possible.

In order to model historical structures realistically, it is important to know the load-bearing and deformation behaviour of carpentry connections, as these have a decisive influence on the overall load-bearing behaviour of a model. This mainly relates to the translational stiffnesses of a connection. Due to the small lever arm of a small connection surface, the rotational stiffnesses only have a minor influence on the load-bearing behaviour and have received little attention in research to date. The Bern University of Applied Sciences (BFH) developed a guideline for the practical application of the load-bearing and load-deformation behaviour of historical timber connections. According to the university, engineers did not have sufficient parameters available for the calculation of historical load-bearing structures, which meant that historical connections were often underestimated. The results were published in a research report in 2016.

The stiffnesses used in this master's thesis relate to compression connections, offsets, wooden nails and iron parts.

Load-bearing effect

The trusses act as truss girders with a buckled bottom chord. The lower sections of the cross braces, the tie beams, the suspended column and the upper head hinges are under tension (see Figure 4). Rafters and collar beams are subject to high compressive stress. The rafters are only lightly loaded at their base points. This is due to the cross braces, which absorb the load of the rafters due to their tensile stress and prevent horizontal displacement. The truss supports absorb the horizontal force and the resulting moment as a pair of forces. The outer support is subjected to compression, the centre support to tension.

Repair concept

As the roof of the indoor riding arena was built as a flat sloping open roof structure, horizontal forces occur at the base points of the roof. These must be transferred to the ground via the walls or the multi-part truss supports (see Figure 5). In order to work out the repair options in a targeted manner, the representation of the wall is first simplified. Based on the core width of foundations, the wall is considered as a cantilevered vertical component. The vertical load at a distance e from the centre of the wall support can act inside or outside the core width. In this case, the core width is the cross-section of the composite truss column. If the force acts inside, the truss column is overpressed.

The development of five variants, which solve the problem of a vertical load acting outside the core width in different ways, shows that it is most effective to reduce the horizontal force from the shear. It was found to be sensible and practicable to reinforce and strengthen the nodal points of the roof structure. The ceiling beam stubs are to be supported with additional cables and an alternating construction and the horizontal forces that occur are to be short-circuited.

To improve transparency, also in the course of opening the building to the public, it is recommended that the necessary measures and their causes are explained in a low-threshold manner on an information board or similar.

Summary

This master's thesis has demonstrated the realistic structural analysis of a baroque roof structure. The load flow and load-bearing behaviour of the structure were examined and various repair concepts were developed. Research has shown that the precise modelling of the structure, in particular the nodal stiffness, forms an important basis for further planning.