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In geometry, a slab is a region between two parallel lines in the Euclidean plane, [1] or between two parallel planes in three-dimensional Euclidean space or between two hyperplanes in higher dimensions.
A two-way slab has moment resisting reinforcement in both directions. [24] This may be implemented due to application requirements such as heavy loading, vibration resistance, clearance below the slab, or other factors. However, an important characteristic governing the requirement of a two-way slab is the ratio of the two horizontal lengths.
In mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, [1] is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. [2] [3] [4] Thus it can be represented heuristically as
Waffle slabs are preferred for spans greater than 40 feet (12 m), because, for a given mass of concrete, they are much stronger than flat slabs, flat slabs with drop panels, two-way slabs, one-way slabs, and one-way joist slabs. [2] Section of a waffle slab including beam, ribs, and column head
Since the 1950s there have been several attempts to develop theories for arching action in both one and two-way slabs. [5] [6] [7] One of the principal approaches to membrane action was that due to Park [8] which has been used as a basis for many studies into arching action in slabs. Park's approach was based on rigid plastic slab strip theory ...
In an analogous way, one can obtain finite difference approximations to higher order derivatives and differential operators. For example, by using the above central difference formula for f ′(x + h / 2 ) and f ′(x − h / 2 ) and applying a central difference formula for the derivative of f ′ at x, we obtain the central difference approximation of the second derivative of f:
This formula is known as the symmetric difference quotient. In this case the first-order errors cancel, so the slope of these secant lines differ from the slope of the tangent line by an amount that is approximately proportional to h 2 {\displaystyle h^{2}} .
Marcus's method is a structural analysis used in the design of reinforced concrete slabs.The method was developed by Henri Marcus and described in 1938 in Die Theorie elastischer Gewebe und ihre Anwendung auf die Berechnung biegsamer Platten. [1]