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Planes and axes of motion
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
In a two-dimensional (2D) example (like the page of this text that you are reading) we have two dimensions of space. Vertical and horizontal (or height and width) are terms that are used to express two-dimensional space. The pages of this text will have a vertical distance (height) and a horizontal distance (width). In this context, we often use X and Y axes to represent the two-dimensional space we are considering. The X axis would be drawn in the horizontal direction and the Y axis would be drawn in the vertical direction. The X axis is often termed the abscissa and the Y axis as the ordinate. The point at which the two axes intersect (cross) is called the origin. In three-dimensional (3D) space a third axis is needed to describe the movement and this is usually denoted as the Z axis. This axis also acts through the origin but is perpendicular to both the X and Y axes described previously.
Strength Hierarchy at Reinforced Concrete Beam-Column Joints and Global Capacity
Published in Journal of Earthquake Engineering, 2018
Ali Sahin Tasligedik, Umut Akguzel, Weng Yuen Kam, Stefano Pampanin
The load path can be defined as the force flow mechanism within a structure. The effectiveness of this force flow depends largely on the proper design of the structural members and member-to-member connections. A typical reinforced concrete building consists of vertical and horizontal structural elements. The primary vertical structural elements are structural walls and columns. The primary horizontal structural elements are beams and floor diaphragms [Elnashai and Di Sarno, 2008; Taly, 2003]. A continuous load path requires all these members to be designed and connected in order to resist the design earthquakes at the ultimate limit state (ULS). It should be noted that the structure will be pushed to deform into the inelastic range at higher magnitude earthquake events and even then the structure is expected to transfer the earthquake forces via a continuous load path. Therefore, the design and detailing of the member-to-member connections are crucial to achieve an effective load path and seismic performance of the structure as a whole. For the application of the method reported in this paper, a continuous load path is assumed to be present between the floor diaphragm and the lateral restraint structural elements under consideration. However, in real scenarios, the load path continuity has to be checked at the connections to the diaphragm.
Microstructural characterisation and analysis of coarse aggregates in asphalt drill cores
Published in Road Materials and Pavement Design, 2023
Tim Teutsch, Lukas Gönninger, Matthias Ruf, Holger Steeb, Wolfram Ressel
Finally, the research is complemented by the analysis of the aggregates' orientation. Therefore, a fitted ellipsoid representing the measurements, location and orientation is determined for each aggregate. For the definition of the alignment its three orientation angles (α, β, γ) are used (see Figure 10b). Again, a distinction is made between the vertical and horizontal direction. The vertical alignment is characterised by evaluating the angle β, as it is defined as the rotation around y-axis, which causes the longest dimension of the aggregate to tilt around the centre. This allows predictions about whether the aggregates are standing or lying. The results show that the largest amount (approx. 2/3) of the aggregates have a lying position, while only about 6% are considered standing (see Figure 15a). For the remaining aggregates, the position is uncertain as their orientation is in between the two definitions. It also turns out that the aggregate form has an influence on the orientation. Thus the percentage of lying aggregates increases with decreasing SPH (see Figure 15b). This aggregate orientation behaviour can be most likely caused by the paving and compaction of the asphalt, i.e. the aggregates tend to align in the paving respectively horizontal compaction direction. This hypothesis is supported by the research described by Hofko et al. (2016), which demonstrates a non-isotropic behaviour of an asphalts' performance, dependent on the direction and type of the compaction. The consolidates the conclusion that the aggregates tend to orientate alongside the compaction direction.
Scattering problems of the SH Wave by Using the Null-Field Boundary Integral Equation Method
Published in Journal of Earthquake Engineering, 2018
Jeng-Tzong Chen, Shing-Kai Kao, Yin-Hsiang Hsu, Yu Fan
In this paper, this approach was extended to solve SH-wave scattering problems of a semi-circular hill containing a circular tunnel or inclusion and elliptical-arc hill (shallow-shallow case). For the half-plane problem of a hill, the half-plane fundamental solution subject to traction-free boundary condition results in an interior unknown displacement when constructing the Green’s third identity as shown in Fig. 1. Therefore, the decomposition is required not only for seismic wave but also for water wave. Lee [1990] had studied the wave-induced oscillation in harbors of arbitrary geometry by using the decomposition technique to solve problems with convex domain. The original problem is divided into abstract subdomains by taking a free-body diagram. One region is an interior problem of a circular boundary, which is a circular region including the hill, another is a half-plane problem containing a semi-circular cut containing a ground surface subject to the Neumann boundary condition, and the other is a circular inclusion. Instead of finding admissible wave expansion bases, six constraint equations were constructed from the null-field BIE formulation after matching boundary conditions and continuity conditions on the interface. In addition, the scattering problem of an elliptical-arc hill is also considered. The deep and shallow hills are shown in Fig. 2(a) and 2(b) where major axes are vertical and horizontal, respectively. For such cases, analytical solutions are available [Amornwongpaibun and Lee, 2013; Lee and Amornwongpaibun, 2013]. However, the analytical solution for the shallow–shallow hill (Fig. 2(c)) is not derived to authors’ best knowledge. Therefore, our present semi-analytical method may provide a reference solution for such a benchmark example. Several numerical examples as shown in Figure 3 are presented to verify the validity of the proposed method.