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Hillman and Grassl gave the first proof that illuminates the role of hooks in 1976 by proving a special case of the Stanley hook-content formula, which is known to imply the hook length formula. [6] Greene , Nijenhuis , and Wilf found a probabilistic proof using the hook walk in which the hook lengths appear naturally in 1979. [ 7 ]
The direct stress is transferred from the concrete to the bar interface so as to change the tensile stress in the reinforcing bar along its length. This load transfer is achieved by means of bond (anchorage) and is idealized as a continuous stress field that develops in the vicinity of the steel-concrete interface.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
The following table gives formula for the spring that is equivalent to a system of two springs, in series or in parallel, whose spring constants are and . [1] The compliance c {\displaystyle c} of a spring is the reciprocal 1 / k {\displaystyle 1/k} of its spring constant.)
Reinforcing rebar is placed axially in the column to provide additional axial stiffness. Accounting for the additional stiffness of the steel, the nominal loading capacity P n for the column in terms of the maximum compressive stress of the concrete f c ' , the yield stress of the steel f y , the gross cross section area of the column A g , and ...
Rebar (short for ... Mass per metre length, kg/m 12 113 0.888 16 201 1.58 20 314 ... If a single strand of stirrup with a hook at each end was required, this would ...
In mathematics, specifically in representation theory, the Frobenius formula, introduced by G. Frobenius, computes the characters of irreducible representations of the symmetric group S n. Among the other applications, the formula can be used to derive the hook length formula .