Here only a very short introduction will be given and the emphasis will be on rules and recommendations for practical application of the method to design. The strip method is based on the lower bound theorem of the theory of plasticity.

## A. Hillerborg-Strip Method Design Handbook-CRC Press (1996)

This means that the solutions obtained are on the safe side, provided that the theory of plasticity is applicable, which is the case for bending failures in slabs with normal types of reinforcement and concrete and normal proportions of reinforcement. As the theorem is usually formulated its purpose is to check the loadbearing capacity of a given structure. In the strip method an approach has been chosen which instead aims to design the reinforcement so as to fulfil the requirements of the theorem. The strip method is thus based on the following formulation of the lower bound theorem: Seek a solution to the equilibrium equation.

Reinforce the slab for these moments. It should be noted that the solution has only to fulfil the equilibrium equation, but not to satisfy any compatibility criterion, e. As a slab is highly statically indeterminate this means that an infinite number of solutions exist The complete equilibrium equation contains bending moments in two directions, and torsional moments with regard to these directions. Any solution which fulfils the equation can, in principle, be used for the design, and thus an infinite number of possible designs exist.

From the point of view of economy, not only is the resulting amount of reinforcement important, but also the simplicity of design and construction.

For satisfactory behaviour under service loading the design moments used to determine the reinforcement should not deviate too much from those given by the theory of elasticity. Torsional moments complicate the design procedure and also often require more reinforcement. Solutions without torsional moments are therefore to be preferred where this is possible.

Such solutions correspond to the simple strip method, which is based on the following principle: In the simple strip method the load is assumed to be carried by strips that run in the reinforcement directions. No torsional moments act in these strips. The simple strip method can only be applied where the strips are supported so that they can be treated like beams.

This is not generally possible with slabs which are supported by columns, and special solution techniques have been developed for such cases. One such technique is called the advanced strip method. This method is very powerful and simple for many cases encountered in practical design, but as hitherto presented it has had the limitation that it requires a certain regularity in slab shape and loading conditions. It has here been extended to more irregular slabs and loading conditions. An alternative technique of treating slabs with column supports or other concentrated supports is by means of the simple strip method combined with support bands, which act as supports for the strips, see Section 2.

This is the most general method which can always be applied and which must be used where the conditions that control the use of other methods are not met. It requires a more time-consuming analysis than the other methods. Usually only two directions are used, corresponding to the x- and y-directions.

Each strip is then considered statically as a one-way strip, which can be analysed with ordinary statics for beams. The load on a certain area of the slab is divided between the strips. For example, one half of the load can be taken in one direction and the other half in another direction. Generally, the simplest and most economical solution is, however, found if the whole load on each area is carried by only one of the strip directions. This principle is normally assumed in this book. We can thus formulate the following principle to be applied in most cases: The whole load within each part of the slab is assumed to be carried by strips in one reinforcement direction.

Pag e 11 In the figures the slab is divided into parts with different loadbearing directions.

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The relevant direction within each area is shown by a double-headed arrow see Fig. The load is preferably carried with a minimum of cost, which normally means with a minimum amount of reinforcement. As a first approximation this usually means that the load should be carried in the direction that runs towards the nearest support, as this results in the minimum moment and the minimum reinforcement area. From the point of view of economy, the lengths of the reinforcing bars are also important.

Where the moments are positive, the length of the bars is approximately equal to the span in the relevant direction. In such cases, therefore, more of the load should be carried in the short direction in a rectangular slab. A consequence of these considerations is that a suitable dividing line between areas with different loadbearing directions is a straight line which starts at a corner of a slab and forms an angle with the edges.

The dividing lines are shown as dash-dot lines.

Along these lines the shear force is thus assumed to be zero in all directions. The use of lines of zero shear force makes it possible to simplify and rationalize the design at the same time, as it usually leads to good reinforcement economy. For the choice of positions of the lines of zero shear force the following recommendations may be given.

A line of zero shear force which starts at a corner where two fixed edges meet may be drawn approximately to bisect the angle formed by these edges, but maybe a little closer to a short than to a long edge. Page 12 A line of zero shear force which starts at a corner where two freely supported edges meet should be drawn markedly closer to the shorter edge.

The distances to the edges may be chosen to be approximately proportional to the lengths of the edges, for example.

Where a fixed edge and a freely supported edge meet, the line of zero shear force should be drawn much closer to the free edge than to the fixed edge. The economy in reinforcement is not much influenced by variations in the positions of the lines of zero shear force in the vicinity of the optimum position.

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In cases of doubt it is fairly easy to make several analyses with different assumptions and then to compare the results. The use of lines of zero shear force is best illustrated on a simple strip or a beam.

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## Strip Method Design Handbook

The slab strip in Fig. The corresponding lines for shear forces and moments are also shown. The maximum moment mf occurs at the point of zero shear force. The parts to the left and right of the point of zero shear force can be treated as separate elements if we know or assume the position of this point. These separated elements are shown in the lower figure.

## Architecture Design Handbook: Copper Alloys - Introduction

The following equilibrium equation is valid for each of the elements:. The beam in Fig. This corresponds to strips in the y- direction in the central part of the slab in Fig. In many cases the loaded elements of the strips do not meet, but instead there is an unloaded part in between. This is the case for thin strips in the x-direction in Fig. Such a strip is illustrated in Fig. It can be separated into three elements, the loaded elements near the ends and the unloaded element in between.

The span.

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In a rigorously correct application of the simple strip method we would study many thin strips in the x-direction in Fig. This leads to a very uneven lateral distribution of design moments and a reinforcement distribution which is unsuitable from a practical point of view. For practical design the average moment over a reasonable width must be considered. In the first place, therefore, the analysis should give the average moments.

To calculate these average moments we introduce slab elements, which are the parts of the slab bordered by lines of zero shear force and one supported edge. Thus the slab in Fig. The load within each element is assumed to be carried only by bending moments corresponding to the reinforcement direction. Such elements are called one-way elements.

Each one-way element has to be supported over its whole width. The average moments and moment distributions are discussed in Sections 2. Cases which can be treated by means only of one-way elements can be found by the simple strip method. Even though the dividing lines between elements with different load-bearing directions, shown as dash-dot lines, are normally lines of zero shear force, there are occasions when the analysis is simplified by using such lines where the shear force is not zero.