【正文】 eable floor area to an indoor/outdoor climate. These generally narrow buildings count on the courtyard for daylight. Steel and glass shells offer a unique solution to this design challenge. The historic context for these shells imposes a series of design constraints within which the designer has the freedom to develop the shell’s form. The boundary conditions often include height restrictions and limits upon the maximumextra load that can be imposed on the existing building, particularly in a horizontaldirection. The British Museum Court Roof is supported on sliding bearings so that no horizontal thrust is exerted on the historic masonry walls of the museum (Williams 2021). In the reviewing the design of recently realized steel shells, the driving design factor more often seems to be architectural scenographic esthetics rather than structural performance. Sculptural Architectural Esthetics With the available geometric digital modeling tools, more architects base their work on esthetic (and often subjective) considerations to achieve scenographic effects. This sculptural design intent can be appreciated for its inventiveness of plastic forms, but not for its consideration of gravity loads. This particular design approach thus raises questions from a structural point of view with respect to the resulting lack of structural efficiency. Unfortunately, the structural solutions necessary to make these sculptural shapes possible typically use an awkward and significant accumulation of material. These freeform shapes often lead to unfavorable internal forces and under loading do not allow membrane stresses to develop within the surface. These shapes then rely on bending action—the least effective of all basic load carrying methods. Designers often ignore the fact that the free form is made up of conventional constructional and structural means. Frank Gehry, the Pritzker prizewinning architect, promotes this architectural process, which expresses sculptural intentions but is disconnected from any sculptural intent (Shelden 2021). A rationalization is needed at the preliminary design stage that goes beyond this scenographic experience and concentrates on the structural integrity of the design (Leach et al. 2021). The evolution of an initial sculptural shape into a constructable structure needs a strong team of engineers and contractors. For example, the conceptual design for the shell of the Nuovo Polo Fiera Milano, Italy (built in 2021) (Guillaume et al. 2021) was developed by the architect Massimiliano Fuksas and then handed over to the engineers Schlaich Bergermann and Partners and contractor Mero TSK Group for the development of the structural and constructional rationale for the project (see Fig. 2) (Basso et al. 2021). Geometric Shape Geometry is a tool that has been used since antiquity for the development of architectural shapes. These forms are thus limited by the rules imposed by analytical geometry and the designer’s imagination. Through the centuries, architecture has developed around ―simple‖ geometries chosen for their constructive or structural qualities. [Examples can be found in the design of the cupola of the cathedral Santa Maria del Fiore, Italy (built in 1436), by Filippo Brunelleschi and more recently the thin concrete shells by Felix Candela (Moreyra Garlock and Billington 2021).] Surfaces of revolution, translational surfaces, and scaletrans surfaces lend themselves excellently to shell action and discretization into subelements. In this context, the work of J Schlaich and Hans Schober on steel shells is innovative. They devised a method to find the right translational or scaletrans surface that can be divided into foursided planar meshes. The HippoHouse of the Berlin Zoo, Germany (built in 1996), designed by architect Grieble and Schlaich Bergermann and Partners (Schober 2021, Glymph et al. 2021) exploits this approach in an elegant steel shell, as shown in Fig. 3. Structural Efficiency through Form Of all traditional structural design elements (ranging from material choice, profile sections, node type, global geometry, and support conditions), global geometry mostly decides whether a shell will be stable, safe, and stiff enough. The shell spans large distances with Fig. 2. Nuovo Polo Fiera Milano (Italy, built in 2021。ade. The four corner nodes are pinned in all directions. At the intersection of the nodes, the gravity loads caused by the selfweight of the steel members and glass covering is modeled。 and Lt1Dt m 5 current length of member m at time, calculated using Pythagoras’s theorem in three dimensions. This process is continued, cycle by cycle, to trace the motion of the structure. So far, no damping has been introduced and, thus, the grid continues to oscillate. This phenomenon can be prevented by introducing ―kiic damping‖ in all the velocities that are set to zero when a kiic energy peak is detected. This process will never truly converge, but once the residual forces are measured in, for example, thousandths of Newtons, convergence has occurred for all practical purposes. At that point, a shape is found that is in static equilibrium and that holds the ―correct‖ spatial surface. This formfinding process yields a 3D cupola with a height of m, as shown in Fig. 5 (ratio height/span 5 ). The steel skeletal shell mainly works in pression under selfweight. As to be expected, large tensile forces arise in the ring beam framing the shell. The structural elements radiating out from the corners experience the largest pressive forces. Although all boundary nodes can transmit vertical forces onto the fa231。 yiT_ e7T Thespring stiffness, si, is chosen to be proportional to the plan area in the region of the ith vertex. This will have the effect of pulling the roof toward the form z