# parabolic segment

## parabolic segment

[¦par·ə¦bäl·ik ′seg·mənt]
(mathematics)
The line segment given by a chord perpendicular to the axis of a parabola.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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We extend the approach in  considering an INF with a frequency characteristic consisting of six pieces, each piece being either a convex or a concave parabolic segment. There is a set of six convex parabolic pieces denoted as [A.sub.i], i = 1,2, ...
The pulses were generated by an INF with a piece-wise frequency characteristic consisting of four pieces using concave and convex parabolic segments.
Table I reports the coordinates of the end-points which define the six component parabolic segments. The equation that defines the proposed INF presented in Fig.
In Figure 3, parabolic segment (a) corresponds to the process in which A firstly takes the minimal acceleration for time [t.sub.s] and then switches to maximal acceleration for time t - [t.sub.s].
Similarly, parabolic segment (d) corresponds to the process, takes the maximal acceleration for time [t.sub.s], and then switches to minimal acceleration for time t - [t.sub.s].
Parabolic segment (c) corresponds to the process, takes the maximal acceleration until reaching [[??].sub.max](s, [a.sub.max], [v.sub.max]) at the time [t.sub.v], progresses with [[??].sub.max](s, [a.sub.max], [v.sub.max]) until time [t.sub.s] elapse, and then decelerates for time t - [t.sub.s].
Similarly, parabolic segment (f) corresponds to the process, takes the minimal acceleration until reaching [[??].sub.min](s, [a.sub.max], [v.sub.max]), progresses with [[??].sub.min]([a.sub.max], [v.sub.max]) until time [t.sub.s] elapse, and then accelerates for time t - [t.sub.s].
When the obstacles are polygons, the Voronoi diagram consists of straight and parabolic segments.
Two span beam with uniformly distributed loading A two span beam of 30 m span and 300mmX750mm cross section with 23 KN/m uniformly distributed loading (including self weight) and prestressing force of 938 KN has been analyzed by load balancing method with idealized parabolic profile and by Lin's method [Lin and Burns (1995)] with actual cable profile considering two parabolic segments at midspan and two reversed parabolic segments at the support (Fig.5).
The analysis considering two parabolic segments at midspan and two reversed parabolic segments at support, is very complex.
The beam is analyzed using load balancing method with parabolic and Lin's approach (6 parabolic segments), by STAAD Pro software and by our approach using PRES2D software.

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