This set of Prestressed Concrete Structures Multiple Choice Questions & Answers (MCQs) focuses on “Optimisation Techniques”.

1. The technique for selecting a new point depends upon:

a) Scope of the problem

b) Nature of the problem

c) Range of the problem

d) Analysis of the problem

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Explanation: In using the mathematical programming methods the process of optimization begins with an acceptable design point and new point is selected suitability so as to minimize the objective function and the search for another new point is continued is continued from the previous point until the optimum point is reached and there are several well established techniques for selecting a new point and to proceed towards the optimum point, depending upon the nature of the problem, such as linear and non linear programming.

2. In linear programming, the solution is based on:

a) Tensile properties

b) Strain properties

c) Elementary properties

d) None of the mentioned

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Explanation: In a linear programming problem, the objective function and constraints are linear functions of the design variables and the solution is based on the elementary properties of systems of linear equations and the properties of systems proportionally, additivity, divisibility and deterministic features are utilized in the mathematical formulation of the linear programming problem.

3. A linear function in three-dimensional space is a:

a) Midpoint

b) Plane

c) Laminar

d) Zero

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Explanation: A linear function in tree-dimensional space is a plane representing the locus of all design points in n-dimensional space, the surface so defined is a hyper plane and in these cases, the intersections of the constraints give solutions which are the simultaneous solutions of the constraint equations meeting at that point.

4. Linear programming problems can be solved by:

a) Revised simplex method

b) Termed method

c) Moment derivation method

d) Hollow method

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Explanation: Linear programming problems can be conveniently solved by the revised simplex method and the simplex algorithm for solving the general linear programming problem is an iterative procedure which yields an exact optima solution in a finite number of steps.

5. One of the most powerful techniques for solving non linear programming is to transform the:

a) Data

b) Problems

c) Materials

d) Labour

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Explanation: One of the most powerful techniques for solving non linear programming is to transform the problem by some means into a form which permits the application of the simplex algorithm and thus, the simple method turns out to be one of the most powerful computational devices for solving linear as well as non linear programming problems.

6. In non linear programming the boundaries of the contours of the function are:

a) Parallel line

b) Zig Zag lines

c) Straight lines

d) Trapezoidal lines

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Explanation: In non linear programming problems, the objective function and or the constraints are non linear function of the design variables and since the boundaries of the feasible region or the contours of equal values of the merit function are straight lines the optimum solution need not necessarily be at an intersection of the constraints.

7. One of the techniques developed for solution of non linear programming is:

a) Single programming

b) Multilinear propramming

c) Reverse programming

d) Dynamic programming

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Explanation: Over the years, several techniques have been developed for the solution of non linear programming problems and some of the prominent techniques are: method of feasible directions, sequential unconstrained minimization technique, sequential linear programming and dynamic programming.

8. The method of feasible direction can be grouped under the:

a) Direct methods of approach

b) Sequential method of approach

c) Terminate method of approach

d) Laminar method of approach

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Explanation: In non linear programming the method of feasible direction can be grouped under the direct methods of approach on general non linear inequality constrained optimization problems and two well known procedures which embody the philosophy of the method of feasible directions are Rosens gradient projection algorithum and Zountendijks procedure.

9. The first non linear programming procedure to be used in:

a) 1950

b) 1940

c) 1960

d) 1970

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Explanation: This method (method of feasible direction) was probably the first non linear programming procedure to be used in structural optimization problems by schmist in 1960 and this method starting from an initial feasible point, the nearest boundary is reached and a new feasible direction is found and an appropriate step is taken along this feasible direction to get the new design point and the procedure is repeated until the optimum design point is reached.

10. One of the element considered in the economy of prestressed concrete structural system:

a) Structural optimization

b) Beam optimization

c) Slab optimization

d) Transverse optimization

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Explanation: Structural optimization together with the efficient management of labour, materials and the use of new construction techniques, development and use of indigenous and new materials of construction would result in considerable economy in the overall cost of prestressed concrete structural systems.

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