Dataset Information

Stability of trusses by graphic statics.

ABSTRACT: This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell-Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar that arises due to the axial force that it carries. The prestress stability of any kinematic freedom may then be assessed using a weighted sum of these areas. The method is generalized to describe the out-of-plane stability of two-dimensional trusses, and to describe three-dimensional trusses in general. The paper also gives a graphical representation of the 'product forces' that were introduced by Pellegrino and Calladine to describe the prestress stability of trusses.

SUBMITTER: McRobie A

PROVIDER: S-EPMC8188010 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Stability of trusses by graphic statics.

McRobie Allan A Millar Cameron C Baker William F WF

Royal Society open science 20210609 6

This paper presents a graphical method for determining the linearized stiffness and stability of prestressed trusses consisting of rigid bars connected at pinned joints and which possess kinematic freedoms. Key to the construction are the rectangular areas which combine the reciprocal form and force diagrams in the unified Maxwell-Minkowski diagram. The area of each such rectangle is the product of the bar tension and the bar length, and this corresponds to the rotational stiffness of the bar th ...[more]

PMID: 34113449

Similar Datasets

Project description:Crushing and eating hard prey (durophagy) is mechanically demanding. The cartilage jaws of durophagous stingrays are known to be reinforced relative to non-durophagous relatives, with a thickened external cortex of mineralized blocks (tesserae), reinforcing struts inside the jaw (trabeculae), and pavement-like dentition. These strategies for skeletal strengthening against durophagy, however, are largely understood only from myliobatiform stingrays, although a hard prey diet has evolved multiple times in batoid fishes (rays, skates, guitarfishes). We perform a quantitative analysis of micro-CT data, describing jaw strengthening mechanisms in Rhina ancylostoma (Bowmouth Guitarfish) and Rhynchobatus australiae (White-spotted Wedgefish), durophagous members of the Rhinopristiformes, the sister taxon to Myliobatiformes. Both species possess trabeculae, more numerous and densely packed in Rhina, albeit simpler structurally than those in stingrays like Aetobatus and Rhinoptera. Rhina and Rhynchobatus exhibit impressively thickened jaw cortices, often involving >10 tesseral layers, most pronounced in regions where dentition is thickest, particularly in Rhynchobatus. Age series of both species illustrate that tesserae increase in size during growth, with enlarged and irregular tesserae associated with the jaws' oral surface in larger (older) individuals of both species, perhaps a feature of ageing. Unlike the flattened teeth of durophagous myliobatiform stingrays, both rhinopristiform species have oddly undulating dentitions, comprised of pebble-like teeth interlocked to form compound "meta-teeth" (large spheroidal structures involving multiple teeth). This is particularly striking in Rhina, where the upper/lower occlusal surfaces are mirrored undulations, fitting together like rounded woodworking finger-joints. Trabeculae were previously thought to have arisen twice independently in Batoidea; our results show they are more widespread among batoid groups than previously appreciated, albeit apparently absent in the phylogenetically basal Rajiformes. Comparisons with several other durophagous and non-durophagous species illustrate that batoid skeletal reinforcement architectures are modular: trabeculae can be variously oriented and are dominant in some species (e.g. Rhina, Aetobatus), whereas cortical thickening is more significant in others (e.g. Rhynchobatus), or both reinforcing features can be lacking (e.g. Raja, Urobatis). We discuss interactions and implications of character states, framing a classification scheme for exploring cartilage structure evolution in the cartilaginous fishes.

Dataset Information

Stability of trusses by graphic statics.

Publications

Stability of trusses by graphic statics.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets