By DRMashhour a Ghoneim
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Extra info for Design of reinforced Concrete Structure Volume 1
23) (a so-called ‘boxcar’ function) we want to investigate its frequency content. 24a) and the graph of F(ω) is sketched in Fig. 4. 24b) Note that in this particular example F(ω) is a real function (and this is because the real function f(t) is even). In general, this is not so, as the reader can verify, for instance, by transforming the simple exponential function Fig. 4 Fourier transform of even ‘boxcar’ function. Copyright © 2003 Taylor & Francis Group LLC which we assume to be zero for t<0.
B)–(e) Bending of bars. Copyright © 2003 Taylor & Francis Group LLC Other examples are shown in: • • • • Fig. 11(b): cantilever with fixed-free boundary conditions and force F applied at the free end, k is the local stiffness at the point of application of the force, Fig. 11(c): fixed-fixed bar of length L with transverse localized force F at L/2; k is the local stiffness at the point of application of the force; Fig. 11(d): fixed-fixed bar of length L with uniform transverse load w (N/m), k is the local stiffness at the point of maximum displacement; Fig.
6b) (or eq. 10)). 10). 8)) converges to the function x(t). s. 10)). Various sets of conditions have been discovered which ensure that these assumptions are justified, and the Dirichlet theorem that follows expresses one of these possibilities: Dirichlet theorem. 6a) converges to x(t) at all the points where x(t) is continuous. At jumps (discontinuities) the Fourier series converges to the midpoint of the jump. Moreover, if x(t) is complex (a case of little interest for our purposes), the conditions apply to its real and imaginary parts separately.
Design of reinforced Concrete Structure Volume 1 by DRMashhour a Ghoneim