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An optimum preliminary strength design of reinforced concrete frames
A cost model consisting of fabrication, handling, cladding, foundation and erection costs is constructed and a suite of programs is developed to analyse, design, cost and optimize a family of precast concrete structures. These procedures are further illustrated with cost response surfaces which are generated by assigning the upper and lower bounds of any two primary variables. Conclusions are drawn on the significance of the resultant optimum structures to the precast concrete industry. Azad, A K 'Continuous steel I-girders: optimum proportioning' ASCE J. Struct. Div. Vol 106 ST7 (July 1980) pp 1 5 4 3 -
1555 The structural efficiency, economy and design flexibility of built up I-beams or girders have been reflected in their extensive use in engineering works. A procedure based on elastic analysis is presented to find an economical proportioning of a continuous built-up I-beam or girder that is symmetrical in cross-section, has an unchanged web of constant height, and is subjected to uniformly distributed load. The method determines the optimum locations of the assumed number of cutoff points for the flange plates required for an economical design. Krish, U 'Optimal design of truss by approximate compatibility' Comput. 5truct. Vo112 (1980) pp 9 3 - 9 8 Optimal design of elastic trusses is formulated as an approximate linear programming problem, Using the force method of analysis, the redundant forces are expressed in linearized terms of the design variables. An iterative procedure of solution is proposed in which both the design and the imaginary displacements are modified until the compatible optimal solution is reached. Each iteration cycle requires the solution of a linear programming problem. The proposed procedure provides more flexibility in the solution process than the usual algorithms based on a sequence of linear programs and may improve the convergence. Numerical examples illustrate the application of this procedure in optimal design of simple trusses. Govil, A K, Arora, J S and Hang, E J 'Optimal design of frames with substructuring' Comput. Struct. Vo112 (1980) pp 1--10 This paper presents a formulation for optimal design of large scale, 2D and 3D framed structures. Von Mises equivalent stress constraints and displacement constraints are imposed at all points in the structure. Member size constraints and constraints based on Schilling's approach for member buckling are also imposed. Three example problems of varying degrees
v o l u m e 1 3 n u m b e r 4 j u l y 1981
of difficulty are solved, using a gradient projection algorithm with state space design sensitivity analysis and substructuring. Results of these examples are analyzed and conclusions are presented. Crawford, A B and Jenkins, M 'Optimum design of some steel roof structures' Struct. Eng. Vol 58A No 10 (October 1980) pp 3 1 7 - 3 2 5 The o p t i m u m design of a range of steel roof structures is established using a combination of nonlinear programming method~. The objective function is cost oriented and a suitable cost model is described. The relative costs of seven types of roof structure are compared and conclusions are drawn as to cost effectiveness.
Davidson, J W, Felton, L P and Hart, G C 'On reliability-based structural optimization for earthquakes' Comput. Struct. Vol 12 (1980) pp 9 9 - 1 0 5 A formulation is presented for the minimum-weight design of a structure subjected to an earthquake ground motion and constrained by a specified upper bound on overall probability of failure. The formulation includes a probabilistic representation of earthquake response spectrum shape and structural stiffness characteristics. Examples are presented which provide insight into basic features of reliabilitybased earthquake-resistant designs, and also illustrate the effects of different material characterizations and different assumptions regarding parameter distributions. In addition, designs based on the probabilistic representation of response spectrum are compared to designs based on deterministic response spectra which compound to particular levels of probability of occurrence. Rosenman, M A, Radford, A D and Gero, J S 'Postoptimality analysis in dynamic programming' Eng. Optim. Vol 4 No 4 (1980) pp 207--214 A method is described for postoptimal stability analysis of a large class of serial and nonserial dynamic programming problems. The analysis examines the stability of an optimal policy subject to changes in the returns associated with values of the state variables or relationships between values at different stages. A practical worked example is presented and the usefulness of the results is demonstrated. Saka, M P ' O p t i m u m design of rigidly jointed frames' Comput. Struct. Vol 11 (1980) pp 4 1 1 - 4 1 9 In this paper a method is presented for the o p t i m u m , m i n i m u m weight design of rigidly
jointed frames. The problem is formulated using the matrix displacements method for which the design variables are not only the areas of members but also the displacements of joints. Both the stress and displacement requirements, as stated in BS 449, are taken into consideration. The resulting nonlinear programming problem is linearized by using the first two terms of a Taylor expansion. To ensure a feasible solution moving limits are employed so that the iteration procedure avoids the reduction of vital structural analysis equations to be solved during the optimization process. The design procedures developed do not require the structural analysis equations to be solved during the optimization process. Examples are given to demonstrate the method. Balaguru, P N 'Optimum design of singly reinforced rectangular sections' J. Civil Eng. Design Vol 2 No 2 (1980) pp 149-169 An algorithm for the cost optimum design of rectangular reinforced concrete beams is presented. Four differgnt types of problems with specified restrictions on dimensions of the beam and the amount of reinforcement are considered. The solution satisfies the structural bending equations as applied to the ultimate load design. The cost of concrete, steel and form work are considered to arrive at the total cost. Based on the numerical results obtained, it is recommended that a near optimum solution can be obtained using the maximum amount of steel allowed in the code of practice followed for the design and the minimum practicable breadth to depth ratio. Using the above recommendation, the optimum dimensions of the beam and the amount of reinforcement are obtained by solving a third order polynomial equation.
Gerlein, M A and Beaufait, F W 'An optimum preliminary strength design of reinforced concrete frames' Comput. Struct. Vol 11 (1980) pp 515-524 An optimization procedure is organized for the preliminary design of a multistorey-multibay, moment-resisting reinforced concrete frame. A reduced set of collapse mechanisms are used to define the kinematic constraints. Special constraints are defined in order to satisfy building code requirements and practical design considerations. In the proposed optimum preliminary design the total volume of reinforcing steel required by the members of the structure is minimized. A strong column-weak beam design results from the optimization study. An example is presented to illustrate the proposed method.
Collated by Hari Murthy, University of Sydney, Australia
245
1555 The structural efficiency, economy and design flexibility of built up I-beams or girders have been reflected in their extensive use in engineering works. A procedure based on elastic analysis is presented to find an economical proportioning of a continuous built-up I-beam or girder that is symmetrical in cross-section, has an unchanged web of constant height, and is subjected to uniformly distributed load. The method determines the optimum locations of the assumed number of cutoff points for the flange plates required for an economical design. Krish, U 'Optimal design of truss by approximate compatibility' Comput. 5truct. Vo112 (1980) pp 9 3 - 9 8 Optimal design of elastic trusses is formulated as an approximate linear programming problem, Using the force method of analysis, the redundant forces are expressed in linearized terms of the design variables. An iterative procedure of solution is proposed in which both the design and the imaginary displacements are modified until the compatible optimal solution is reached. Each iteration cycle requires the solution of a linear programming problem. The proposed procedure provides more flexibility in the solution process than the usual algorithms based on a sequence of linear programs and may improve the convergence. Numerical examples illustrate the application of this procedure in optimal design of simple trusses. Govil, A K, Arora, J S and Hang, E J 'Optimal design of frames with substructuring' Comput. Struct. Vo112 (1980) pp 1--10 This paper presents a formulation for optimal design of large scale, 2D and 3D framed structures. Von Mises equivalent stress constraints and displacement constraints are imposed at all points in the structure. Member size constraints and constraints based on Schilling's approach for member buckling are also imposed. Three example problems of varying degrees
v o l u m e 1 3 n u m b e r 4 j u l y 1981
of difficulty are solved, using a gradient projection algorithm with state space design sensitivity analysis and substructuring. Results of these examples are analyzed and conclusions are presented. Crawford, A B and Jenkins, M 'Optimum design of some steel roof structures' Struct. Eng. Vol 58A No 10 (October 1980) pp 3 1 7 - 3 2 5 The o p t i m u m design of a range of steel roof structures is established using a combination of nonlinear programming method~. The objective function is cost oriented and a suitable cost model is described. The relative costs of seven types of roof structure are compared and conclusions are drawn as to cost effectiveness.
Davidson, J W, Felton, L P and Hart, G C 'On reliability-based structural optimization for earthquakes' Comput. Struct. Vol 12 (1980) pp 9 9 - 1 0 5 A formulation is presented for the minimum-weight design of a structure subjected to an earthquake ground motion and constrained by a specified upper bound on overall probability of failure. The formulation includes a probabilistic representation of earthquake response spectrum shape and structural stiffness characteristics. Examples are presented which provide insight into basic features of reliabilitybased earthquake-resistant designs, and also illustrate the effects of different material characterizations and different assumptions regarding parameter distributions. In addition, designs based on the probabilistic representation of response spectrum are compared to designs based on deterministic response spectra which compound to particular levels of probability of occurrence. Rosenman, M A, Radford, A D and Gero, J S 'Postoptimality analysis in dynamic programming' Eng. Optim. Vol 4 No 4 (1980) pp 207--214 A method is described for postoptimal stability analysis of a large class of serial and nonserial dynamic programming problems. The analysis examines the stability of an optimal policy subject to changes in the returns associated with values of the state variables or relationships between values at different stages. A practical worked example is presented and the usefulness of the results is demonstrated. Saka, M P ' O p t i m u m design of rigidly jointed frames' Comput. Struct. Vol 11 (1980) pp 4 1 1 - 4 1 9 In this paper a method is presented for the o p t i m u m , m i n i m u m weight design of rigidly
jointed frames. The problem is formulated using the matrix displacements method for which the design variables are not only the areas of members but also the displacements of joints. Both the stress and displacement requirements, as stated in BS 449, are taken into consideration. The resulting nonlinear programming problem is linearized by using the first two terms of a Taylor expansion. To ensure a feasible solution moving limits are employed so that the iteration procedure avoids the reduction of vital structural analysis equations to be solved during the optimization process. The design procedures developed do not require the structural analysis equations to be solved during the optimization process. Examples are given to demonstrate the method. Balaguru, P N 'Optimum design of singly reinforced rectangular sections' J. Civil Eng. Design Vol 2 No 2 (1980) pp 149-169 An algorithm for the cost optimum design of rectangular reinforced concrete beams is presented. Four differgnt types of problems with specified restrictions on dimensions of the beam and the amount of reinforcement are considered. The solution satisfies the structural bending equations as applied to the ultimate load design. The cost of concrete, steel and form work are considered to arrive at the total cost. Based on the numerical results obtained, it is recommended that a near optimum solution can be obtained using the maximum amount of steel allowed in the code of practice followed for the design and the minimum practicable breadth to depth ratio. Using the above recommendation, the optimum dimensions of the beam and the amount of reinforcement are obtained by solving a third order polynomial equation.
Gerlein, M A and Beaufait, F W 'An optimum preliminary strength design of reinforced concrete frames' Comput. Struct. Vol 11 (1980) pp 515-524 An optimization procedure is organized for the preliminary design of a multistorey-multibay, moment-resisting reinforced concrete frame. A reduced set of collapse mechanisms are used to define the kinematic constraints. Special constraints are defined in order to satisfy building code requirements and practical design considerations. In the proposed optimum preliminary design the total volume of reinforcing steel required by the members of the structure is minimized. A strong column-weak beam design results from the optimization study. An example is presented to illustrate the proposed method.
Collated by Hari Murthy, University of Sydney, Australia
245