One of Germany's lasting reminders of the horrors of World War II, the 200-year-old Frauenkirche, is rising again inside an elaborate squirrel's nest of scaffolding. For Dresdeners it is an emotional sight, since the Frauenkirche in Dresden was a huge pile of rubble for four decades after the war.
For the rest of the world, the Frauenkirche is an example of engineering technology bringing back to life what the technologies of war once destroyed. It is not too much to say that the church is rising from its ashes.
The church is to be fully restored by 2005. The cross-shaped vault of the cellar has been in use since August 1996. Construction of the cupola is to begin after 2000.
Dedicated teams of engineers and skilled tradesmen have been hard at work since 1993 recreating this masterpiece of Saxon Baroque. The church was built between 1726 and 1743, but the rebuilders have a complete set of dimensioned drawings dating to refurbishments in the 1920s and '30s. Archeologists in 1993-'94 recovered 8,300 facade stones and about 90,000 lining bricks to be used in the reconstruction. Entire large sections survived the WWII collapse intact.
The rebuilders also have some problems that date back to the church's design in the height of the Baroque period, 1722-26. Because of ground settling and compression of the masonry foundations, some of the calculations of its designer and builder, Dresden Master Carpenter George Baehr, were a bit off.
The massive dome with its cross-topped stone lantern reaches 93 meters (307 feet) into the sky. But its weight, an estimated 8,300 tons, rests too heavily on eight slender, stone columns rather than the outer walls. Soon after the dome was completed, cracks appeared, especially in the interior columns.
Those cracks, said Prof.-Ing. Wolfram Jaeger, consulting engineer for the project's planning and engineering office for construction, "had kept generations of master builders busy considering solutions."
Unfortunately, the computer hardware available to Prof. Jaeger severely limited the finite-element modeling and finite-element analysis (FEM/FEA) calculations. Engineers took pains to do as much analysis as possible using linear solutions, since nonlinear solvers multiply the calculations more than a hundred-fold, according to Prof. Jaeger and fellow analyst Prof.-Ing. Helge Bergander.
With nonlinear methods, the engineering effort usually rises ten-fold or more, they added. Much of the additional engineering time goes into deciding optimal load increments.
Given masonry brittleness, linear solvers presented a major challenge. Most engineering analysis is based on the assumption-nearly always true-that materials fail slowly or at least predictably. This means reliable analyses can be generated with straightforward linear solvers (the mathematical underpinnings of FEM/FEA).
Because of its brittleness, however, masonry cracks and ruptures in ways which are not readily predictable. Engineers regard these situations as nonlinear.
The challenge was compounded by the fact that most FEM/FEA software is designed to analyze stresses and strains in homogeneous materials and in the joints between identical or very similar materials. Masonry, with its blocks and bricks, varieties of mortar, and multiplicity of joints, could hardly be more different.
Prof. Jaeger and his team face a number of difficult engineering hurdles:
For nearly all this work, Prof. Jaeger used the design verification and optimization capabilities of the ANSYS Academic product - University Research 5.0). "ANSYS was chosen because of some prestudies and experiences at the Technical University of Dresden" Prof. Jaeger said. "Other FEM/FEA programs in our office are much less efficient particularly with 3D problems."
Because the Frauenkirche is a Baroque masterpiece, a high degree of fidelity to the original design and building materials is required. The work is being financed by the Foundation Church of Our Lady in Dresden. One other important authority is the State Office for the Preservation of Historic Buildings and Monuments in Saxony.
Archeologists and art historians have taken a keen interest in the reconstruction. Neither they, nor the Protestant church, the reconstruction foundation, or the citizens of Dresden would tolerate easy, modern solutions like reinforced concrete structural components.
The reconstruction plans have led to a great deal of meticulous analysis of the sandstone masonry. Prof. Jaeger and his team have undertaken analyses for:
Using ANSYS Academic products, Prof. Jaeger developed formulae that accounted for the shortcomings of these materials, such as determining masonry's resistance to fracture. More than the usual number of distribution influences had to be considered, he reported. Especially helpful, he added, is the ANSYS Mechanical implementation of the Drucker-Prager approach to masonry analysis. "Drucker-Prager better evaluates masonry than do other solvers," he said. "Simulations of the building's construction can be assessed more realistically."
The Frauenkirche's ground plan is a 43 meter (m) square (about 143 ft. sq.). The main cornice has a height of 26 m (86 ft.) The main cellar is laid out in the shape of a Greek cross.
The church's astonishingly slim interior columns were originally an architectural design element. Baehr intended to support the high loads of the stone cupola not only with the columns but also the surrounding masonry. However, due to settling of the building and compression of the masonry, the loads shifted to the columns.
The result was that the interior columns had to absorb forces close to their load-bearing limit. By the mid-1700s, soon after construction of the cupola, the columns started to develop cracks. In the 1920s, a comprehensive refurbishment was undertaken, and the interior columns were reinforced with steel bands. The foundations were reinforced in the 1930s.
Baehr recognized the problems of cupola shear and the driving forces. "He was able to suspect or feel the flow of load distribution," said Prof. Jaeger, "but unfortunately the master craftsman was unable to substantiate his concepts with calculations."
Among the many evaluations carried out with ANSYS Academic software were shear-pressure and creep tests done with boundary elements. The creep tests showed that the stone does not experience any creep deformation. Creep is essentially limited to mortar, and then only during the first six months to one year.
The eight interior columns of the Frauenkirche in Dresden still play a key role in supporting the weight of the cupola and lantern. The loads on the columns have been subtly redistributed, so that the longitudinal forces as well as the bending moments are significantly reduced.
The cupola is a double-shell construction: an outer shell of 1.3 m to 1.5 m (4 ft. 3 in. to 4 ft. 10 in.) thick and an inner shell 0.25 m (10 in.) thick. The outer diameter is 26 m (86 ft.). To light the interior of the church, the cupola has 16 windows. The shells are connected by transverse masonry. The cupola is held together by wrought-iron rings and reinforced concrete anchors. The cupola is topped by a lantern about 18 m (59 ft.) high.
Because they comprise a dome, the original sandstone components of the cupola grow thinner as they rise in height. The space between the inner and outer shells also narrows. Despite the complex geometry, ANSYS academic products allowed the analyses to be carried out without time-consuming nonlinear methods.
The archeological reconstruction of the Church of Our Lady in Dresden represents a unique challenge to participating engineers. The building is a daring achievement of its master builder, George Baehr, whose ability and experience approached the limits of knowledge in the 18th Century. "This gives us an obligation to carry out the planning and supervision of the construction according to the best of today's science and technology," said Prof. Jaeger, "and explore new ways in the process."