No_7_July_1969 — Page 41

position of neutral axis, moment of inertia and top and bottom section moduli.

An extension of the program has been written for sections composed of precast and in-situ concrete elements. Both these programs are regularly used by the Civil Engineering Office in connection with the Kowloon North East Corridor project. Although a con- siderable length of the proposed fly- overs is standardised, there are several points where short special lengths are required and individual designs have to be prepared. The two programs make it easy to consider rapidly a much wider range of shapes and sizes for the special lengths than would be possible using manual methods.

The consultants employed by the Public Works Department for the de- sign and construction of flyovers take beam design by computer several stages beyond the determination of section properties. A program has been pre- pared for 'I' beams and box beams acting compositely with in-situ con- crete. The data is processed on the Univac 1107 computer and the output gives the required prestressing force and eccentricity, together with transfer and final compressive and tensile stresses. The program takes into account limit- ing values of eccentricity and maxi- mum tensile stresses, and allows for shrinkage and creep.

Prestressed beams for the Lai Chi Kok Bridge and the Chatham Road Flyover, Kowloon, were analysed by this method, which enabled the most economical beam design to be chosen.

Pile loading

In designing a piled foundation the arrangement and number of piles to be used must be chosen so that the great est load likely to be imposed on any pile is not greater than its capacity. This is a simple enough matter where loadings are axial or nearly axial, but is more complicated where moments of any magnitude have to be resisted, particularly if the moments are bi-axial.

This situation arises when, for ex- ample, a flyover or elevated carriage- way is cantilevered out from single central columns so that transverse and longitudinal moments can be caused by wind forces, braking forces or unequal live loading. The possibility of the various forces acting together to cause uplift must also be considered, so both maximum and minimum pile loads have to be determined.

A program has been written for the Olivetti 101 which makes it possible to consider many sets of loading condi-

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tions. The computer prints out the maximum and minimum pile loads induced by each condition.

This program has been very suc- cessfully employed in connection with the Kowloon North East Corridor pro- ject. Here, the design of a variety of piers is at present being undertaken, and the program has been particularly useful for the Kowloon City section of the project, where the congested site requires many of the piers to be of the central column type. Not only does the full range of loading conditions have to be considered for each pier type but, as well, three kinds of pile are investigated for each pier type to ensure that the most economic design can be used.

Setting-out road curves and flyovers

In highly built-up areas, and when improving existing highways, the tradi- tional methods of setting out a curve are often very difficult, if not impos- sible. Points of intersection may well be inaccessible, lines of sight obscured, and in many cases the surveyor can only have access to limited sections of each curve due to traffic flow.

In these cases a complete mathe- matical analysis of the system of curves is made, such that the surveyor can then set out any point along the road curve without reference to any other part of the roadway except for check- ing purposes.

Most highway curves are designed with transition spirals where the re- lationships between chainage and co- ordinates can only be expressed in equations involving terms raised to the power of seven, eight, and higher. The work involved in producing parameters for many spirals by conventional methods would be completely pro- methods would be completely pro- hibitive, but with a computer they can be obtained in a few minutes. It is only necessary to enter a constant for the degree of curvature into the memory of the computer, and then to feed in the chainage to obtain a print- feed in the chainage to obtain a print- out of the co-ordinates of any point on the spiral. Also, by varying the value of constant, an infinite number of different spirals can be computed.

A computer program for this pur- pose has been used for setting out the San Po Kong interchange, Kowloon. Here a flyover linking Choi Hung and Prince Edward Roads spirals over two other carriageways, and in order to ensure correct pier clearances it was necessary to compute the intersection of the spirals with the underpassing curves, and finally to co-ordinate all pile and pier positions.

Surveys

In addition to setting out road curves, a wide range of survey data is being processed on the Civil Engineer- ing Office desk-top computers. Pro- grams have been prepared for most of the calculation for closed traverses and tacheometric reductions and for deter- mining areas and volumes. These are used, not only on highways, but also in other branches of civil engineering.

Sewage disposal

The effectiveness of sewage disposal by dilution in the sea depends on the efficient dispersal of sewage into the receiving waters. By the use of multi- port diffusers on the ends of submarine outfalls, a higher dilution of sewage in seawater can be achieved and the qualities of the waters in the disposal areas can be protected. A well-designed diffuser is one that has uniform dis- charge and full flow at every port for all expected variations of flow, does not require an excessive head at peak flow, and maintains self-cleansing velo- city even at low flow.

In order to satisfy these conditions, it is sometimes necessary to adopt varying port sizes and pipe diameters in the same diffuser. Without the use of computers the most suitable design can only be obtained by trial, which often requires a large number of com- putations to be made.

For this reason a computer program for the Olivetti 101 was applied to the design of submarine outfalls to be constructed in the harbour off Wan Chai Reclamation, Lai Chi Kok and Sham Shui Po. The program is so written that after feeding in the dia- meter and gradient of the diffuser pipe, size and spacing of port, friction factors etc., the computer will print out the port discharge, jet velocity, required head for discharge, velocity and frictional loss in the pipe.

Identical operations are carried out for each port in the diffuser. The re- sults, after each cycle of operation, are stored in the computer and ac- cumulated so that the total head re- quired for the accumulated discharge of any number of ports can be checked.

Part II

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In the second and final part of this feature to be published in the August Far East Builder, Mr. Armstrong-Wright will discuss the use of computers on Hong Kong's water supply projects and transportation studies and the part they play in the control of public works expenditure.

Far East BUILDER, July 1969

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