Create a Rigid and Safe Grid-Like Structure

The failure of the building is not the consequence of the not strong enough elements of the structure in the majority of the cases, but the bracing elements inappropriate places. We consider a 4 × 4 and 4 × 5 braced frames to understand the connections between the lateral stiffnesses, and bracing graph to achieve the stiffest and the more safety design. In our consideration, we study those relationships that based on our frame using their finite element analyses and some new result in optimizations of structural design. We offer some conclusions, including perspectives and future developments in the rigidity of scaffolds and tall building as symmetrical and grid-like bar-joint frameworks

Applications of combinatorics to statics—rigidity of grids

AbstractThe infinitesimal rigidity (or briefly rigidity) of a bar-and-joint framework (in any dimension) can be formulated as a rank condition of the so-called rigidity matrix. If there are n joints in the framework then the size of this matrix is O(n), so the time complexity of determining its rank is O(n3). But in special cases we can work with graph and matroid theoretical models from which very fast and effective algorithms can be obtained. At first the case of planar square grids will be presented where they can be made rigid with diagonal rods and cables in the squares, and with long rods and cables which may be placed between any two joints of the grid. Then we will consider the one- and multi-story buildings, and finally some other results and algorithms

Applications of combinatorics to statics—a second survey

AbstractSome recent results are presented, concerning the algorithmic aspects of 2-dimensional generic rigidity, and 1-story buildings as tensegrity frameworks. Most of these results were obtained after the completion of the first survey (Recski, 1984) for a ‘Winter School’ organized by the late Professor Z. Frolík. Results in Sections 3 and 4 of the first survey are used throughout

Non-Euclidean braced grids

Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial part of the conditions is given in terms of a matroid for the bicoloured bipartite multigraph defined by the braces

Development of space truss systems in timber

Space trusses are a valuable structural form for architects and structural engineers due mainly to their efficiency in providing large unobstructed areas, associated with faster erection speeds and low maintenance cost. Most space trusses are made of steel and aluminium whilst a few are of timber. Interest is now shifting from the traditional use of timber in plane trusses of relatively short span, to new structural forms for medium to long spans. In adopting such systems in timber for non-traditional roofing applications, the challenge lies in developing structurally sound, visually neat and economically reproducible connectors for 3-dimensional configurations of timber members. The research aimed at developing a new connector for double and triple-layer space grids in timber, intended for medium-span lightweight roofing applications. The origins of the connector date back to 1995, when it was first proposed by Zingoni as the 14FTC-U Timber Space-Truss Connector, and subsequently tested under laboratory conditions over the three years that followed. Unlike connectors for timber space grids proposed by earlier investigators, or the proprietary connector systems that are available for constructions in steel and aluminium, the 14FTC-U connector features a central core of wood in the form of a cuboctahedron or its variants, upon whose faces are attached U-shaped metal brackets that take the timber members. Thus the connector unit is predominantly wood, giving it considerable aesthetic advantages over its all-metal counterparts. While promising, the structural performance of the original connector was not adequate for practical application, hence a programme of further development was embarked upon. As reported in the thesis, the improvements of the connector have culminated in a structurally viable unit that has been successfully employed in a prototype double-layer timber grid

On the Modeling of Elastic and Inelastic, Critical- and Post-Buckling Behavior of Slender Columns and Bracing Members

Analyzing tall braced frame buildings with thousands of degrees of freedom in three dimensions subject to strong earthquake ground motion requires an efficient brace element that can capture the overall features of its elastic and inelastic response under axial cyclic loading without unduly heavy discretization. This report details the theory of a modified elastofiber (MEF) element developed to model braces and buckling-sensitive slender columns in such structures. The MEF element consists of three fiber segments, two at the member ends and one at mid-span, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the crosssection that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test in the laboratory, with a linear elastic portion, a yield plateau, and a strain hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user-defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal coordinates at each iteration of a time step, and checking force equilibrium in the updated configuration. Inelastic post-buckling response is captured by fiber yielding in the nonlinear segments. A user-defined probability distribution for the fracture strain of a fiber in a nonlinear segment enables the modeling of premature fracture, observed routinely in cyclic tests of braces. If the probabilistically determined fracture strain of a fiber exceeds the rupture strain, then the fiber will rupture rather than fracturing. While a fractured fiber can take compression, it is assumed that a ruptured fiber cannot. Handling geometric and material nonlinearity in such a manner allows the accurate simulation of member-end yielding, mid-span elastic buckling and inelastic post-buckling behavior, with fracture or rupture of fibers leading to complete severing of the brace. The element is integrated into the nonlinear analysis framework for the 3-D analysis of steel buildings, FRAME3D. A series of simple example problems with analytical solutions, in conjunction with data from a variety of cyclic load tests, is used to calibrate and validate the element. Using a fiber segment length of 2% of the element length ensures that the elastic critical buckling load predicted by the MEF element is within 5% of the Euler buckling load for box and I-sections with a wide range of slenderness ratios (L/r = 40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic post-buckling of the Koiter-Roorda L-frame (tubes and I-sections) with various member slenderness ratios (L/r = 40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical approximations to the solution. The inelastic behavior of struts under cyclic loading observed in the Black et al. and the Fell et al. experiments is numerically simulated using MEF elements. Certain parameters of the model (e.g., fracture strain, initial imperfection, support conditions, etc.) that are not controllable and/or unmeasured during the tests are tuned to realize the best possible fit between the numerical results and the experimental data. A similar comparison is made between numerical results using the MEF element and the experimental data by Tremblay et al. collected from cyclic testing of single-bay braced frames. Finally, a FRAME3D model of a full-scale 6-story braced frame structure that was pseudodynamically tested by the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record, is analyzed iv and shown to closely mimic the experimentally observed behavior. To summarize, the MEF element is able to incorporate all the characteristic features of slender columns and braces that significantly affect their elastic and inelastic, critical and post-buckling behavior, and is remarkably effective in capturing the essence of said behavior, even with the vast uncertainty associated with the buckling phenomenon. To aid in the evaluation of the collapse-prediction capability of competing methodologies, a benchmark problem of a water-tank subjected to the Takatori near-source record from the 1995 Kobe earthquake, scaled down by a factor of 0.32, is proposed. The water-tank is so configured as to have a unique collapse mechanism (under all forms of ground motion), of overturning due to P - instability resulting from column and brace buckling at the base. A FRAME3D model of the tank reveals severe buckling in the bottom megacolumns on the west face of the tower, followed almost instantaneously by compression brace buckling on the north and south faces, when the structure is hit by the Takatori near-source pulse, resulting a tilt in the structure. Subsequent shaking induces P - instability resulting in complete collapse of the tank