Stability of trusses by graphic statics

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.

Tensegrity Informed Observations in Human Cadaveric Studies - A Clinical Anatomists Perspective

19th century anatomy took a systematic, uniform approach as efforts were made to give each anatomical structure a precise description. Concerning red contractile proteins observed within a gastor, descriptive words provided little or no information concerning the anatomy or physiology of such structures. Latin names were provided describing shape (i.e. trapezius), size (i.e. maximus), number (i.e. quadriceps) and anatomical location (i.e. posterior) but did little to inform learners concerning a global view of human form and function. Such a reductionist view concerning muscles was delineated by their assumed tendonous origin/insertion attachment to bone. Bespoke human dissections performed on embalmed cadavers, embracing a (bio)tensegrity focus, provides innovative insights concerning the topics of human anatomy, form and function. Such dissection shifts attention away from the solely mechanistic observations made since the time of Erasistratus (ca. 290 BC) and Giovanni Alfonso Borelli (1608-1679) which led to nebulous interpretations and isolated “parts”. Long held concepts such as muscle origins and insertions are not supported as factual evidenced by biotensegrity focused dissections. Borelli’s explanations of human movement, based on man-made objects, included wheels, clocks, watches and two-bar pinned joints. Mechanical models require construction materials such as 1st, 2nd and 3rd class levers, pulley systems with pins and screws for functional operation. Embryology does not require surgical intervention to attach an upper or lower limb, a liver, spleen or blood vessel. The embryo grows and develops such structures in a temporal sequalae orchestrated by the forces and the environment wherein it emerges. To-date it has been averred that the human body is a combination of ‘parts’ comprising of levers and pinned-joints. This observational-based report offers anatomically accurate cadaveric imagery supporting a paradigm shift in human anatomy moving towards a model dependent reality of continuity and wholeness, “Biotensegrity-Anatomy for the 21st century”.

Pullout Behavior of Steel Beam-Concrete Wall Pinned Joints with T- shaped Connectors

<p>Nowadays, reinforced concrete core wall-steel frame hybrid structural systems are widely used in mid-rise and high-rise buildings. In this type of structural system, the pulling resistant behavior of the steel beam-concrete wall joints (SBCW joints for short) plays a very important role in the seismic behavior. In this study, the pullout behavior of a new type of SBCW pinned joints with T-shaped steel connectors is tested, and the load- displacement curves and failure modes of the specimens are analyzed. Two failure modes are observed in the experiments: one is punching shear failure mode characterized by the pullout of concrete pyramid with lower strength and stiffness, and the other is web yield failure mode characterized by the yield of the web plate of the connector with higher strength and stiffness. The key factor to determine the failure mode is the embedded depth of the connector. Additionally, finite element models for the SBCW joint are established and nonlinear elastic-plastic analysis is carried out, which can predict the failure modes and pulling resistant capacity of the specimens with good accuracy. Based on the numerical model, a parameter analysis is conducted to study the influence of more factors on the capacity of the SBCW joint.</p>

Failure Analysis of Composite Pinned Joints Based on Continuum Damage Mechanics

The paper conducted bearing tests on composite pinned joints with four different stacking sequences. The bearing strength and bearing chord stiffness were obtained. The influence of stacking sequences on failure modes, bearing strength and bearing chord stiffness was discussed. Based on continuum damage mechanics, a three-dimensional finite element model of composite pinned joint under bearing load was built, where the maximum strain criterion was employed for initiation and bi-liner damage constitutive relation for revolution of fiber damage, while the physical-based Puck criterion was used for matrix damage initiation, and matrix damage revolution depended on the effective strain on the fracture plane. The failure mode, bearing strength and bearing chord stiffness of composite pinned joint were discussed with this model under which the non-linear shear behavior and in-situ strength effects were considered. Good agreements between test results and numerical simulations validates the accuracy and applicability of the finite element model.

A new method to assess the stiffness and rotation capacity of composite joints

Composite beam-to-column joints in buildings are mostly modelled as pinned joints in order to facilitate the design of the structure. In reality, due to the required reinforcement in the concrete slab, a certain joint rigidity and bending resistance is always available. The real joint behaviour corresponds therefore more to that of a semi-continuous joint. This is not only beneficial for the serviceability limit state but can also be advantageous at ultimate limit state. However, due to the lack of analytical design rules in EN 1994 to verify the rotation capacity of semi-continuous joints, these are commonly modelled as pinned joints, which impedes an efficient design of composite structures. In this context, a research program on the behaviour of composite joints, focusing on the ultimate rotation capacity, was initiated at the University of Luxembourg [1]. The aim was to identify the influence of two major joint components – the reinforced concrete slab and the steelwork connection – on the moment-rotation curves of composite joints under hogging bending moment. An experimental campaign comprising 8 tests on beam-to-column joints was conducted to determine the response of composite joints with variable reinforcement ratio and diameter of reinforcing bars. In addition to the experimental part, an FE model was developed with the software ABAQUS aiming to simulate the behaviour of internal beam-to-column composite joints. In this paper, the 3D finite element model and results of analyses are presented. The FE model has been defined by 3D solid elements with realistic contact definitions and non-linear material laws. The results of the numerical simulations presented a good agreement with the experimental data. Based on the experimental and numerical investigations, the influence of reinforcement and steelwork connection on the structural properties of composite joints is derived. A new analytical method to determine the stiffness and rotation capacity of composite joints is proposed. The accuracy of this new method is confirmed by existing experimental and numerical results.