R.M. Lawson, K.F. Chung, CIM Steel's Composite Beam Design to Eurocode 4 PDF

By R.M. Lawson, K.F. Chung, CIM Steel

ISBN-10: 1870004868

ISBN-13: 9781870004862

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Additional info for Composite Beam Design to Eurocode 4

Example text

Start Set the free space wavelength λ Select N for 2N equidistant sampling points for FFT Initialise: at z = 0, U ( x, 0) Calculate FFT of U ( x, 0) : V (k x , 0) = ℑ U ( x, 0) Calculate V (k x , L ) = V (k x , 0) e jkZ L Obtain U ( x, L ) by calculating inverse FFT of V (k x , L ) Stop ( ) optical beam shape, which makes the proposed Fourier method a very useful tool for studying optical beam propagation in a homogenous medium. Finally, it is noted that it is not necessary for the reader to be familiar with functional analysis to understand the presented material; however, further information on this topic can be found in a number of textbooks [7,8].

For this purpose U ( x, 0) has to be sampled at a set of equidistantly spaced points x l within a window of width MΔx where Δx is the sampling interval and M is the total number of samples. The set of samples U ( x, 0) can be used to calculate the DFT values at a set of spatial frequencies k xm = l/MΔx. 6, and the final summation is performed using the inverse DFT. Both the DFT and the inverse DFT can be easily and efficiently implemented on a computer using fast Fourier transform (FFT) algorithms that are readily available from most numerical modelling libraries and from standard reference books on numerical modelling [6].

The calculation window is 600 μm while the number of samples is 28 while the beam is propagated for 500 μm. The arrow indicates the direction of the optical beam propagation. M −1 ∑ 2 U (k xm , 0) = l =0 1 M M −1 ∑ U ( x , 0) 2 l l =0 and M −1 ∑ U (k xm , L ) 2 = l =0 1 M M −1 ∑ U ( x , L) 2 l l =0 2 2 Similarly, as in the previous case, it can be shown that U ( f x , L ) = U ( f x , 0) for 2 2 propagating waves and U ( f x , L ) ≠ U ( f x , 0) for the evanescent waves. indb 25 10/11/2014 10:47:10 AM 26 Photonics Modeling and Design The power conservation for an algorithm is closely linked with the reciprocity.

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Composite Beam Design to Eurocode 4 by R.M. Lawson, K.F. Chung, CIM Steel


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