What controls the Ultimate Load of a Glulam Dome?

A glued-laminated timber(glulam) dome (Fig. 1) is analyzed with the finite element method to determine the governing failure mode and ultimate snow loads. The dome consists of a triangulated network of curved glulam beam, roof decking supported by curved purlins, and a steel tension ring. The dome was modeled, analyzed, and post-processed by the commecial finite element programs I-DEAS and ABAQUS. Geometric and material nonlinearities are considered in the dome model. The dome is monitored as the nonlinear equlibrium path is tracked with the Risks method. The dome is subjected to a pressure composed of dead load pressure and live load presure resulting from snow load over the entire dome or over half of the dome. The project centers on the effect of the beam-decking connectors on the dome behavior. The beam-connectors are represented by nonlinear springs which model the nail connections between the beams and the decking.

The dome under study based on the Crafts Pavilion dome in Raleigh, N.C. The dome has a span of 133 ft, a rise of 18 ft, and a radius of 133.3 ft. The dome is cyclically symmetric and composed of six identical sectors (Fig. 2). Each beam of the dome is modeled by two straight, three dimensional, Bernoulli/Euler beam finite elements. The purlins and the tension ring are represented by truss elements. The effect of the decking on the behavior of the dome is investigated in three ways: (1) it is neglected; (2) it is represented by truss bracings; and (3) it is reflected in the beam-decking connector model, called connector element (Fig. 3). The connector element includes 16 nonlinear springs that provide lateral support for the beam element. The elongation of each spring is determined through interpolation functions from nodal displacements of the beam element. Hence, the springs do not add degrees of freedom to the assembly. Three normal stress-strain relations are used: linear, bilinear, and Conners' nonlinear model (Fig. 4).

A selection of analysis results is discussed in the context of Table 1. The critical pressure, corresponding to a bifurcation or limit point on the equilibrium path, is the ultimate pressure of the dome model. The buckling mode of the dome model with connectors under full snow loading is shown in Fig. 5. The equilibrium pats of various dome models under full snow loading are shown in Fig. 6. The buckling mode of the dome model with connectors under half snow is shown in Fig. 7. The equilibrium paths of various dome models under half snow are shown in Fig. 8.

As expected, the decking contributes significantly to the ultimate load capacity of the dome model, and connector failures seem to trigger failure of the dome model. However, nonlinear material behavior is closely linked with the failure mode for half snow load case.

This project was done by Dr. S. M. Holzer, Dr. J. D. Dolan, S.A. Kavi, and S. Tongtoe.

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