The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.
A new approach to acoustic quality assessment of churches during simulation tests is proposed in the article. The numerical global index, based on four partial indices: reverberation, speech intelligibility, music sound index and a proposed new one - sound strength index, assesses the acoustic parameters of the model of the tested church in a complex manner. The global single number index was obtained from 17 simulations of acoustic adaptation options of the investigated church's interior. The equation of the approximate global index has been obtained by means of singular vectors, obtained from Singular Value Decomposition (SVD) of the Index Observation Matrix of Simulation Variants (IOMSV). The weights of four partial indices and a universal equation of the global index have been calculated using the SVD technique to solve the problem of correlated acoustical parameters. The global index may be a helpful tool during simulation tests of acoustic quality assessment of churches. The proposed final equation of the global index does not require knowledge of the SVD technique and the values of acoustic parameters preferred for churches. Therefore the methodology proposed is easily applicable.
The paper presents an innovative approach for the index assessment of the acoustic properties of churches. A new formula for an approximate single number index to assess selected acoustic parameters of church interiors, such as reverberation time (RT), speech intelligibility index (RASTI) and music clarity index (C80), is presented in the paper. The formula is created by means of the Singular Value Decomposition (SVD) method. An innovative approach for calculating the weights of partial indices is shown by solving the problem of redundant information, i.e., the system of overdetermined linear equations, using a computed pseudoinverse matrix. The new procedures for calculating the values of three partial indices and the single number index to assess selected acoustic parameters are presented. The proposed method was verified by measurements in several selected churches.
In parallel with research conducted using conventional methods, a uniform index method for assessing the acoustic quality of Roman Catholic churches has been developed. The latest version of the index method has been created using the index observation matrix of 12 churches which have been rated by means of the single number global index. Assessments of the acoustic quality of any Roman Catholic church, using two calculation models: the Global Acoustic Properties Index (GAP) and the Global Index (GI), are shown in the article. The verification was performed on the example of one church, showing the way of calculating global indices to assess the acoustic quality of a new facility. The next stages in the development of the index method for assessing the acoustic quality of churches were taking into account the audience, using simulation tests and determining the spatial distribution of the single number GAP index in an examined church. An attempt to use the GAP and GI calculation models to assess the acoustic properties of some churches is also shown in the article.