Truss

Abstract: In this article, the authors propose a simplified MCFT (modified compression field theory) and demonstrate that this simplified MCFT is capable of predicting the shear strength of a wide range of reinforced concrete (RC) elements with almost the same accuracy as the full theory. The authors summarize the results of over 100 pure shear tests on reinforced concrete panels. The ACI approach for predicting shear strength as the sum of a diagonal cracking load and a 45-degree truss model predicts the strength of these panels poorly, with an average experimental-over-predicted shear strength ratio of 1.40 with a coefficient of variation of 46.7%. The modified compression field theory (MCFT), developed in the 1980s, can predict the shear strength of these panels with an average shear strength ratio of 1.01 and a coefficient of variation (COV) of only 12.2%. The authors contend that their new, simplified method gives an average shear strength ratio of 1.11 with a COV of 13.0%. They demonstrate the application of this new simplified method to panels with numerical examples. They conclude that, on many occasions, a full load-deformation analysis is not needed and this quick calculation of shear strength is appropriate and useful.

Abstract: A wide variety of high-performance applications require materials for which shape control is maintained under substantial stress, and that have minimal density. Bio-inspired hexagonal and square honeycomb structures and lattice materials based on repeating unit cells composed of webs or trusses, when made from materials of high elastic stiffness and low density, represent some of the lightest, stiffest and strongest materials available today. Recent advances in 3D printing and automated assembly have enabled such complicated material geometries to be fabricated at low (and declining) cost. These mechanical metamaterials have properties that are a function of their mesoscale geometry as well as their constituents, leading to combinations of properties that are unobtainable in solid materials; however, a material geometry that achieves the theoretical upper bounds for isotropic elasticity and strain energy storage (the Hashin-Shtrikman upper bounds) has yet to be identified. Here we evaluate the manner in which strain energy distributes under load in a representative selection of material geometries, to identify the morphological features associated with high elastic performance. Using finite-element models, supported by analytical methods, and a heuristic optimization scheme, we identify a material geometry that achieves the Hashin-Shtrikman upper bounds on isotropic elastic stiffness. Previous work has focused on truss networks and anisotropic honeycombs, neither of which can achieve this theoretical limit. We find that stiff but well distributed networks of plates are required to transfer loads efficiently between neighbouring members. The resulting low-density mechanical metamaterials have many advantageous properties: their mesoscale geometry can facilitate large crushing strains with high energy absorption, optical bandgaps and mechanically tunable acoustic bandgaps, high thermal insulation, buoyancy, and fluid storage and transport. Our relatively simple design can be manufactured using origami-like sheet folding and bonding methods.

Abstract: Strauss, R. E., and F. L. Bookstein (Museum of Zoology, The University of Michigan, Ann Arbor, Michigan 48109) 1982. The truss: body form reconstruction in morphometrics. Syst. Zool., 31:113-135.-In principle, any measured distances between landmarks of a form may serve as characters for morphometric analyses. Systematic studies typically are based on a highly biased and repetitious sample of these. But collections of landmarks and the distances among them must be homologous from form to form for comparisons to be meaningful, and an adequate character set should at least permit the full reconstruction of the original configuration of landmarks. We describe a geometric protocol for character selection, the truss network, which enforces systematic coverage of the form and which exhaustively and redundantly archives the landmark configuration. Reconstruction of the form from truss measures provides Cartesian coordinates for landmarks and allows estimation of, and compensation for, measurement error. Samples of forms may be averaged and standardized to one or more common reference sizes by regression of measured distances on a composite measure of body size, followed by reconstruction of the form using distance values predicted by the regression functions at some standard body size. Principal component loadings of distance measures may be indicated directly on the truss network to display patterns of within-group allometry or between-group shape differences. Because the truss enforces use of cross measurements, discrimination among groups may be enhanced. Composite mapped forms are useful in biorthogonal analyses of differences in shape because they allow the comparison of averaged forms among samples. Certain patterns of principal component loadings are concordant with, and provide an initial sampling of, the biorthogonal grids for these deformations. [Allometry; biorthogonal analysis; discriminant analysis; fishes; morphometrics; multivariate analysis; principal components; triangulation; truss.]