EXAMINATION FOR DEGREES IN ENGINEERING.

DR. DOWNING.

1. A rectangular beam of American red pine timber, 7 inches wide, 9 inches deep and having a clear span of 11 feet, is placed on horizontal bearings and broken transversely by a weight of 6.235 tons laid on the centre. Compute from these data the value of a Constant which may be applied to determine the ultimate strength of rectangular beams of that material loaded in any assigned manner. State clearly the units of length and of weight to which the Constant you give is referred. As an example apply it in determining the ultimate resistance of a bridge consisting of five girders each 8 inches wide by 24 inches deep, and having a clear span of 40 feet, all of them being combined together by the transverse planking, &c., so as to offer a simultaneous resistance, and the load being uniformly distributed.

If the bridge be 12 feet wide, and loaded as close as possible with men; what, under your estimation of such load-is the co-efficient of safety, adding to the weight of the men six tons for that of the one span of the structure?

2. It is observed that the deflection of the experimental beam in No. I was on the average o 20823 inches per ton within the limits of elasticity. Calculate from this the value of a Constant by which the deflection of a given rectangular beam of this material under a given load may be assigned, and apply it to the case of a beam 12 inches wide by 12 deep and 15 feet in clear span with a load of eight tons on the centre. If the load was uniformly distributed over the span, what would be the deflection?

3. Several different arrangements as to the manner of payment to Contractors, during the progress of the work, are given in the several specifications of the various works in the Text book, draw out a clear and succint statement of them; and in some cases the applicability of the arrangement to the particular circumstances of the contract have been pointed out to you, note this also. In the case of extra works, how is the payment of such, and estimate of value, to be made?

4. Many different descriptions of masonry to which the denomination of AISLER is applied in practice have been pointed out to you from the Text book; enumerate and fully describe them, with a clear sketch in plan, end view and elevation, mentioning also the particular parts of a work, and other circumstances, which determine the use of any particular kind. Give the relative cost of each. Add a distinct account of Telford's specification for the bond of the aisler work of a sea-wall as set before you at Lectures.

5. In the Manual of Engineering are given specifications of temporary Fencing, also of the Permanent Fencing, give these clearly and succintly, stating for the latter the different kinds used and the subdivisions of each kind.

6. From the example of the detailed specification of a Railway Bridge by the same author (as in No. 5), give that for the foundations, the lower part of the masonry, and also for the girders.

7. Different methods of constructing and arranging the external plating of steam-boilers have been pointed out to you; explain these, and illustrate the explanation by sketches, shewing the rivetting; and compare the different systems. Specify for the material and workmanship in all parts. A boiler 5 feet in diameter and 30 feet long may be taken in the required illustration.

8. Describe and sketch the construction of the Birmingham Joint Station Roof, giving the leading dimensions, and point out the manner in which the irregularity in the plan of the ground covered by this roof was met in the design of the several principals.

Give clear detailed sketches, with figured dimensions in each case, of these principals at their bearings at each end, and of all the connections along the tie-rods, and also a transverse section of the main rib.

State also the distance apart of the principals, and the method of covering the roof and supporting it between the principals.

9. Describe and sketch the construction of the roof over the Midland Railway Terminus, St. Pancras, London, contrasting it with that in No. 8. Give a detailed sketch of the transverse section of one of the principals and of the manner of construction at their springings, their distance apart, and the mode of covering the roof and supporting the covering between the principals.

10. Explain the manner in which the pressure of the ground was taken off the front of a frame in the shield of the Thames Tunnel preparatory to its advance, and state generally how the forward motion of the several frames and of the whole shield was effected, giving a sketch of a horizontal section in illustration.

11. Give explanations of the use, and positions in the shield, of the Quadrants, the Top-Staves, the Slings, and the Universal Joint over the Snoes, and describe the several contrivances by which the Poling-boards were, in every way, rendered secure; in each case giving a sketch to aid the description.

12. One of the shafts of a railway tunnel through good clay has been carried down in brick-work nearly to the crown of the intended arch of the tunnel. State the further steps connected with the preparatory works, that must in the first instance be adopted before any of the tunnelling proper is commenced. If the ground had been of a wet and silty character, point out the changes in this part of the work which must be adopted.

13. Write out a full account of the finally successful method of closing the breach in the embankment excluding the tides, at Dagenham, on the north bank of the Thames, as given you in the course, and note the previous methods of attempting this operation at this place, which had failed, and then draw the contrast between them and the principle adopted,

14. Write also an account of plan pursued by Sir John Hawkshaw in analagous circumstances at the Middle Level inundation in Lincolnshire.

15. A rolled beam of wrought iron has the following dimensions in transverse section:-15 inches deep, and with flanges 6 inches wide, and of an average thickness of ths inch; what is the greatest span to

which it can be applied, as a horizontal girder, so as not to produce a greater strain in compression than 4 tons per square inch, the structure it has to sustain giving a uniformly distributed load of 16 cwt. per foot of span? What will be the weight of the above girder, the thickness of the vertical web being ths inch, and having a bearing of 1 foot 3 inches at each end?

16. A beam of American red-pine timber, 13 inches wide, and 14 inches deep, with a clear span of 16 feet, is intended to support a brick wall the weight of which is taken to be 112 lbs. per cube foot; to what height can the wall be built, the coefficient of safety being 8? The wall is to be the full width of the beam, that is, 13 inches. Compute the number of rods of brickwork in the above, giving a clear description of that mea

sure.

17. If the deflection at the centre of a beam by a uniform load be ğths of that caused by the same load concentrated at the same point, compute the deflection of the above beam, the value of the constant being 0.000462, where all dimensions are in inches.

18. Design a cast-iron beam to perform the same duty as that in No. 16, the tension in any part of the span not exceeding 14 tons per square inch. State fully the general proportions you propose to adopt in the beam; and give transverse sections at the centre, the ends, and at the point midway between these; and draw careful diagrams showing, to the same cale, the shearing forces, and the horizontal forces in the flanges in all points of the span under this load,

19. Give a design for wrought-iron trough girders, one under each rail, to carry a line of railway over a carriage road; the level of rails being 8 feet 6 inches above road surface, and from difficulties as to drainage, it is desirable to lower the road surface to as small an extent as possible, with which circumstance in view the girder must be designed. Figure all parts of the transverse section, and show by a detailed calculation their sufficiency, the heaviest engine in use being as in the sketch. The road is 16 feet in width, and has footpaths on each side 4 feet 6 inches wide; good foundations for the abutments can be obtained about 4 feet below the surface on each side,

20. Describe the cast-iron pillars adopted in the construction of the Corn Warehouses at the Sunderland Docks, as given in the Plates of the Text-book on the Resistance of Materials; pointing out their adaptation in detail to the wrought-iron girders that rest upon them and support the flooring; add an account of the details of the flooring.

21. Calculate the two numbers that are to be found in Bidder's Tables at the intersection of the several successive heights:

0-16; 16-24; 24-48; 48-0;

and by them the contents in cubic yards of an excavation with those heights from formation level to the original surface; and having a base of 33 feet; slopes 2 to 1; the four corresponding lengths being 330 feet, 400 feet, 600 feet, and 200 feet, respectively. Give in answer each part separately, and the total. No other method of obtaining the volume can be received in answer.

22. The following extract from a supplementary Table by Bidder

enables one to compute the area of the soiling of the slopes by means of one of the double numbers appertaining to any given end heights:

State fully how these multipliers were deduced, and give that for the above slope of 24, and compute the area of the soiling of the slopes in the above excavation by means of it; stating that for each separate part, and the total. No other method of obtaining the areas can be received in answer.

23. Calculate the rate of fall which must be given to a pipe 9 inches in diameter, so that it may be sufficient to supply a town having a population of 22,750, with water for domestic service, watering streets, flushing sewers, &c., all which have been assumed to amount to 25 gallons per diem for each inhabitant. Express the required fall as feet per

mile?

In proximity to the town the water has to be divided so as to supply different districts, namely, rds of the total supply to one, and the remaining 3rd to the other part. What must be the diameter of each, the rate of inclination being the same as deduced in the answer to the preceding question ?

24. Draw the transverse section of an embankment across a valley for impounding water, figuring and describing all the various parts, and explaining the objects sought to be obtained by them. Let the extreme height be supposed 70 feet, and the length on the top of the finished work 1100 feet. Mention the different modes of dealing with the floodwater of the stream during and after construction, and the method of drawing off the impounded water now generally adopted.

25. Describe in detail the filter beds, and by plan and section show all the various appliances required for their efficient working.

What area of the beds would be required for water-works intended to supply a town and district of 260,000 inhabitants with 25 gallons per diem for each person?

26. Calculate the height to which the water would rise over the crest of a gauging weir 8 feet in length, erected on the works in last question, and discharging the quantity above mentioned in No. 25.

27. What must be the diameter of the cast-iron pipe to convey the quantity in No. 25, the average inclination being 20 feet per mile ?

28. The line of pipes as in last question is supposed to pass over a very undulating country for about II miles, with great depressions at the transverse valleys. Give an account, with explanatory sketches of all the special details on the line, and such practical points as to laying the pipes as have been laid before you.

29. The greater number of practical formulæ in use for the mean velocity and for the discharge of water in channels have been given in the Text-Book; write out several of these, and show that they all very closely follow that adopted in it.

30. Give the transverse section, with full dimensions, of a quay-wall in a tidal river, the depth at low water being maintained at 18 feet, the

rise of springs being 16 feet, the coping 5 feet above high water, and at the place where the section is taken the depth below low water for a firm foundation was 5 feet to the bottom of the lowest footing. And generally, in the case of retaining walls, having in front a varying water-level, examples have been pointed out to you from which a rule as to thickness at the base might be deduced: quote some of these.

The wall indicated above is to have aisler facing with Portland cement mortar, and concrete backing intermixed with rubble stone.

What proportions should be used in the sand and cement for the front work at different depths, and in like manner what proportions of the several ingredients in the backing at different depths?

MR. GALBRAITH.

1. If the density of earth held up by a vertical retaining wall 20 feet high be 1.7, and if its natural slope be 40°, calculate the pressure on each running foot of the wall.

2. Investigate the expression for the curvature at any point of a beam deflected by external forces in terms of the bending moment, the cross section and the coefficient of elasticity.

3. Deduce the deflection of a beam supported at its extremities and loaded in the middle.

4. If two heavy spheres come into collision, determine their velocities after impact.

5. Deduce the expression for the moment of inertia of a triangle round a line passing through its vertex in terms of the perpendiculars let fall on it from the extremities of the base.

6. Given the dimensions of the different parts of a crane; show how the overturning moment of the post and the strains of the jib and tie rod may be calculated.

7. Describe Euler's formula for the strength of vertical pillars. Compare it with the experimental formula of Eaton Hodgkinson.

8. Describe the ballistic pendulum, and show how the velocity of the ball may be deduced from the angular deflection from the vertical.

9. Deduce the time of oscillation of a simple pendulum.

Io. Describe a roof strengthened by a King post and stretchers, and deduce the strains in these parts either by computation or by a diagram.

MR. LESLIE.

1. Form the fundamental equations on which the solution of questions connected with the working of double-acting engines depends.

2. Show how to find the maximum useful effect, and the absolute maximum useful effect in a double-acting engine.

3. Deduce the general equation in the theory of a locomotive.

4. Prove the relation connecting the velocity of the train and the pressure of steam in the cylinders.