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From it, project several extensions, the den- drites, as well as a single tubular fiber, the axon, which in turn, ramifies into a number of small branches. The dendrites serve as receptors for signals from ad- jacent neurons. The role of the axon is the transmission of the neural activity to other nerve cells. The synapses are the junctions between the neurons. Schematic view of a biological neurone. ANNs have been applied to a number of problems with variable success[1,3,4]: speech recognition, image processing, pattern recognition, classification, opti- mization problems, robotics and control, and medical and commercial applica- tions.
Artificial Neural Network Architecture Different ANN topologies exist, the well known are[6,7]: Competitive learn- ing network, the Boltzmann machine, the Hopfield network, and the Back- propagation multi-layered network. The latter type gets its name from the way it learns, by back-propagating the errors seen at the output nodes. The back-propagation network model is the most widely used by most neural net- work application developers. A typical example of a back-propagating network architecture is shown in Fig.
Each neural network has an input layer, an output layer, and a number of hidden layers. The latter compute complicated associations between patterns, and the propagation takes place in a feed-forward manner, from the input layer to the output layer. Architecture of a back-propagation neural network. These weights are modified during the training of the neu- ral network in an iterative process.
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When the iterative process has converged, the collection of connection weights captures and stores the information present in the example used in its training. This initiates the feed-forward process. Schematic representation of processing within an artificial neuron. Both the function and its derivatives are continuous everywhere. Artificial Neural Networks in Structural Engineering These activation values are the output of the neural computations. The training of a back-propagation neural network can be envisaged as fel- lows: during the forward propagation step, the input patterns generate a forward flow of signal from the input layer to the output layer.
The error of each output node is then computed from the difference between the computed output and the desired output. The second stage involves adjusting the weights in the hid- den and output layers in order to minimize the difference between the actual and desired output. This training is classified as a supervised training algorithm. Thus, the network learns how to respond to patterns of data presented to it. Dif- ferent learning algorithms exist for training neural networks.
The most com- monly used one is the Delta rule or back-error propagation algorithm , which can be applied to adjust connections weights so that the network can predict un- known examples correctly. The behavior of an ANN depends on its topology, the weighting system used, and the activation function. The choice of the activation function is based on the types on input and outputs desired and on the learning algorithm to be used. In addition , there is no direct way of determining the most appropriate number of nodes processing units to include in each hidden layer.
The choice of the number of layers, the size of each layer, and the way each layer is to be connect- ed is left to the developer to experiment with. Increasing the number of hidden layer nodes makes the network more powerful, but the training time and opera- tion of the network will be increased. A general rule is to start with a simple network with one hidden layer, and then increasing the hidden layers and ob- serve the performance of the network until the best architecture of the network is reached.
ANN could be developed using special development tools. For example, sever- al software programs are spreadsheet-based. Other software tools are designed to work with expert systems as hybrid development tools. Also, there are some neu- ral network shells which exist for commercial use. The advantage of these shells is that programming experience is not required and programming time is reduced.
For example NeuroShell is an ANN development environment based on back propagation and is best for stand-alone systems. References[10 and 11] list some of the used ANN development systems. ANN can also be implemented directly as semiconductor circuits, or using electro-optical technology.
The example is included here for clarification purpose. This ex- ample involves the computation of the deflection of a cantilever beam subjected to a point load as shown in Fig. The input values were normalized to be in the range The output layer contains one single node which represent the normalized deflection.
The hidden layer contains 3 nodes. The normalized deflection was used as the de- sired output value. Sample training patterns, testing data, and the comparison of the theoretical and predicted deflections can be found in reference. Example application. Structural Engineering Applications Research on the application of ANNs to civil engineering problems is grow- ing rapidly. The use of ANNs in structural engineering has evolved as a new computing paradigm, even though still very limited.
It has been applied for dif- ferent areas such as: structural design, material behavior modeling, damage as- sessment, structural analysis, and FE analysis. In the following section some prototype applications in structural engineering are briefly described.
They developed a multi-layer feedforward network model for the ini- tial design of reinforced concrete rectangular single-span beams. They used two hidden layers and 8 nodes in the input layer. One node each was selected for span, dead load, and live load. For type of steel, one node each was assigned for the three grades of steel.
Similarly, for the two possible grades of concrete, M- 15 and M, two nodes were provided. The network has been tested to predict the probable values of different beam parameters for new examples.go to site
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Abdallah and Stavroulakis developed a back-propagation neural network model that uses experimental steel connections data for an estimation of the me- chanical behavior of semi-rigid steel connections. Two types of steel structure connections have been considered: single-web-angle beam-to-column and sin- gle-plate beam-to-column connections. The design variables used for the train- ing and testing of the neural network are: number of bolts, web angle, thickness of the plate, and length. These design variables were taken as input data, and the measured moment-rotation curve is considered as the output data for the neural network.
Chen et al.
University of Wisconsin Platteville
Their model consists of two parts: Neural Emulator Network to represent the structure to be controlled; and Neural Action Network to determine the control action on the structure. The neural em- ulator network is constructed with a four-node input layer, a four-node hidden layer, and a one-node output layer. The input data to the network are displace- ments on the roof and ground floor, the output of the network is the displace- ment on the roof at the next time step.
The aim was to publish a yearbook to reflect progress in "ferro-concrete" structures until - as the book's first editor, Fritz von Emperger , expressed it - the "tempestuous development" in this form of construction came to an end. However, the "Beton-Kalender" quickly became the chosen work of reference for civil and structural engineers, and apart from the years has been published annually ever since.
The structural challenges of building metres into the sky are substantial, and include several factors which do not affect low-rise construction.
This book focusses on these areas specifically to provide the architectural and structural knowledge which must be taken into account in order to design tall buildings successfully. In presenting examples of steel, reinforced concrete, and composite structural systems for such buildings, it is shown that wind load has a very important effect on the architectural and structural design.
The aerodynamic approach to tall buildings is considered in this context, as is earthquake induced lateral loading. The Empire State Building, the Burj Khalifa, Taipei and the HSB Turning Torso are just a few examples of the buildings whose real-life specifications are used to explain and illustrate core design principles, and their subsequent effect on the finished structure.
Nearly 40 practice problems with step-by-step solutions help sharpen your problem solving skills and demonstrate how to arrive at solutions most efficiently. Numerous charts, tables, and figures make it possible to work most exam problems using just the Reference Manual.
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A complete, easy-to-use index will save you valuable time during the exam when it helps you to quickly locate important information needed to solve problems. The structural PE exams require a thorough familiarity with relevant codes, and the Structural Engineering Reference Manual, Fourth Edition, is updated to the latest exam code specifications.
The Structural Engineering Reference Manual is part of PPI's best-selling exam review series, used by more than 1 million engineers to prepare for their licensing exams. From the Publisher: I do not know of an equivalent textbook that has the scope of this one. I know of no other book that covers such a range of topics including: water retaining structures, comprehensive treatment of the Strut-tie method with a link to finite element output.
Proper background to design of statically indeterminate structures with a proper treatment of joint rotation capacity, comprehensive treatment of: yieldline method, Hillerborg's strip method, design using elastic stress fields, etc and the design of whole structure as opposed to individual elements only.
Of special importance are the examples that cover complete systems and components rather than just single topics. This new edition of the bestselling reference, Fundamentals of Building Construction: Materials and Methods provides the complete, up-to-date coverage of building construction practices that thousands of professionals and students of architecture, engineering, and construction technology have been relying on for years.
It's organized around a detailed treatment of the structural systems most widely used in North America: heavy timber, wood light frame, masonry, steel, light gauge steel, and reinforced and precast concrete. Fundamentals of Building Construction, Fourth Edition makes available to students and professionals an array of construction information that is unprecedented in scope and quality.
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