Volumes 6 through 9, comprising July 1879 - June 1881, unavailable online.
1881: Google Books has volume 10, covering July-December 1881.
July 16, 1881, The American Architect and Building News, The Albany Capitol. Page 32,
October 29 1881, The American Architect and Building News, THE LARGE GROINED VAULT IN THE ASSEMBLY CHAMBER OF THE NEW CAPITOL AT ALBANY, NY., An Analytical Examination, Page 203,
November 29, 1881, Vault of the Capitol, (Page 259 is missing from issue at Google Books)
December 3, 1881, The American Architect and Building News, THE VAULT OF THE ALBANY CAPITOL. Letter, Leopold Eidlitz, Page 235 & Reprinted Page 271
July 16, 1881, The American Architect and Building News, Page 32, The Albany Capitol.
— The State Legislature has already appropriated $950,000 for the new Capitol this year, and there remained $200,000 unexpended of the appropriation of last year when the Legislature met. For the present year, therefore, the sum of $1,150,000 is in the hands of the New Capitol Commissioners to expend. The Albany members, not satisfied with this large appropriation, introduced a bill a week ago appropriating $500,000 additional for the great structure. Senator Braman secured its passage in the Senate without difficulty. It was then considered by the Assembly, and notwithstanding several protests, it was passed by a vote of 69 to 30.
October 29 1881, The American Architect and Building News, THE LARGE GROINED VAULT IN THE ASSEMBLY CHAMBER OF THE NEW CAPITOL AT ALBANY, NY., An Analytical Examination, by H. W. Fabian, Page 203
I. Analytical Examination. It is generally known that a crack appeared in the lower third of one of the ribs of this vault, and that a new stone had to be inserted. It is also known that the possibility that the whole vault might fall was discussed in various quarters, and even in the legislature itself. Now since the legislative business of the State of New York is carried on under this roof, it seemed to me of the utmost importance that a thorough examination into its stability should be made. This I have done; and now I offer to the public the result of my researches.
Fig. 1, shows the ground-plan of a quarter part of the vault; Fig. 2, a longitudinal section, and Fig. 3, a transverse section of the same. The plan of the vault is a rectangle, whose sides measure 54' X 39' respectively. The vault is a groined vault; the details of its construction are given in the diagrams. The vaulting surfaces are pointed, and the radius of one principal arch is 31', while that of the other is 29'. The lines of the ridges of these vaults are not horizontal, but slope up from the apex of each principal arch to the key-stone of the vaulting; and this inclination is considerably greater in the long and narrow sections (Fig. 1 a), than in the others (Fig. 1 6); this can also be seen in Figs. 2 and 3. The diagonal rib which appears foreshortened in Figs. 2 and 3 is presented in its real form in Figs. 5, 6, and 7: while Fig. 4 shows a cross-section on a larger scale. Fig. 4 also shows the way in which the foot of the rib encounters the principal arch, the outline of which is here given. The rib forms a slightly pointed arch, as appears in Figs. 5, 6 and 7, the curves of which are not segments of a circle, but of an ellipse whose major axis measures 79', and minor axis 64', or its half 32'. The whole vault is supported at each of its four corners by a column which at the same time receives the arches and diagonal ribs of the smaller vaults which surround the principal one. Of these eight surrounding divisions shown in the plan (Fig. 8), only the four corner ones are vaulted; the rectangular spaces between them have a low flat ceiling, over which are placed the galleries for the public.
In order that the columns may withstand the great thrust of the arches and ribs of the great central vault, a method of construction has been employed which must in the course of time become fatal to the stability of the structure. Immediately over the principal arches of the square corner vaults great half-arches have been raised, which of course are not visible, but whose skew-backs continually press against the columns, as is shown in Fig. 9. The half-arches are held together at the top by iron tie-rods, which run through the wall above the great principal arches, and connect one half-arch with the other as is seen in Figs. 8 and 9. This method of construction is a dangerous one, because variations of temperature affect iron and stone so unequally that a constant vibratory movement is kept up in the arches and vaults, which in the course of time must necessarily destroy the stone. Among several examples of the danger of this combination, I recall that of the Cathedral of Frankforton-the-Main. When the tower was rebuilt, experts asserted that one row of columns had been made unsafe by the employment of a system of anchoring through their vertical axes. The expansion and contraction caused by changes of temperature were a perpetual cause of disintegration. An architect should in the case of monumental buildings scrupulously avoid the combination of stone and iron. There is never any necessity for such a combination, as an architect thoroughly acquainted with the construction of vaults can always make use of buttresses, flying-buttresses, arches, piers, etc. Only by following this principle can truly artistic works be produced; while on the other hand great stone domes, vaults, etc., which are held together by ironwork will always fail to satisfy either the constructive or aesthetic sense of the intelligent observer. Larger and smaller arches and vaults, however, which meet together upon one single point of support and resistance, do not necessarily require auxiliary construction of any kind; but, as I shall show at the conclusion of this paper, can be so treated that they will maintain their own equilibrium in the vault. The load of the vaulting surface which is supported by the rib, when reduced to the material of the rib, and equally distributed through its whole length gives, taking the average thickness as the uniform thickness of the vault, the line of load c d; but on account of the inequality of the thickness of the vault, the real line of load of the vault is seen in the line c e. As it must naturally always be desirable to make the load of a vault as small as possible, the line ce would in an ideal S5 vault really be the line of load. In the vault under consideration, however, the load is in reality much greater, as it had to be in order to maintain the equilibrium.
The pointed arch is in itself a constructively weak line, because it has at the apex no radius which lies in the vertical axis of the arch, while every line of pressure at that point has a tangent which is horizontal. The natural tendency of the very flat line of pressure is to stretch far towards the base, since otherwise it would fall outside the section of the arch; and the consequence of this is, that the joint at the summit opens towards the top. If a similar effect is not observed in small arches and vaults, it is because the forces at work are too slight, in proportion to the thickness of the arch, to produce any noticeable effect. In the case of large vaults, however, some displacement of the stones inevitably results.
This was evidently what occurred in the case of the vault at Albany, and there was scarcely a point in it which did not seem to threaten danger. To obviate this difficulty, therefore, the first step taken was to load the vaulting surfaces at the summit near the principal arches; but it was also found necessary, in order to improve the equilibrium of the ribs, which likewise showed open joints above, to load the centre of the vault. Only a short space in the very middle of the arch of the rib remained free from this artificial load, as can be seen in the diagram Figure 5. Besides all this, the pockets of the vault have been so loaded with be'lon and walls that the result is the zig-zag line of load given in Fig. 5. That the load put upon the rib is perfectly enormous, and applied with very little system, a glance at the diagram is sufficient to prove.
In my investigation of the stability of the rib, I first employed the analytical method, by which I found that the horizontal thrust at the summit could not have been higher than it is drawn in the diagram, since otherwise the line of pressure would at one spot have approached too near the extrados of the arch, this spot being about where the joint makes an angle (a) of 65° with the horizon.
I studied the arch first for the following angles: 73°, 65°, 52°, 47°, 44°, 41°, and 25°, which all, except 73°, correspond with the angles of the zigzag line of load. The direction of the joints in an elliptical arch is found, as is well known, by bisecting the angle formed
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Page 206
by the radii of the ellipse. The foci of the ellipse now under consid" eration are marked on the diagrams.
I next divided the whole area of the load into sections, whose dividing lines are seen on Fig. 5, and the vertical forces represented by them are designated by lines marked Pt to P16. (P9 and P10 might have been combined; but I had based my calculation on the division of this force into two forces, and as this division had no influence on the result, I have allowed it to stand.)
This determination of forces I based on the drawing shown in Fig. 5, on a scale of A of the natural size (£" = 1'). Then taking \", or half of this scale, as a unit of measure for these areas, there resulted the following values of forces: —
On the scale of Fig. 5, the unit of length here is naturally also =
To determine the line of pressure it is first necessary to discover the amount of the horizontal thrust. As this is ascertained by dividing the moment of that part of the arch which rests on the weakest joint taken about the i edge of the joint, by the arm of the horizontal thrust, we have first to establish the position of the weakest joint. Now this is at the point where the horizontal thrust has to be at a maximum in order to prevent the arch from falling in. To ascertain this maximum of the horizontal thrust, which is at the same time the real horizontal thrust, it is first necessary that for a number of joints the lines of weight of the loads resting upon them should be found. For the forces 1\ to P,„these lines can be ascertained directly from the diagram (Fig. 5). They have the following distances (») from the axis of Y measured on the axis of A'. The \ axis of F is here taken through the corner of the principal arch, a little outside of the inner initial point of the ellipse; and the axis of *—A lies in the major axis of the ellipse.
I now calculated for the angles 73°, 65°, 52°, 47°, 44°, 41°, 25° of the joints, the lines of weight of the loads resting upon them.
I now calculated for the angles 73°, 65°, 52°, 47°, 44°, 41°, 25° of the joints, the lines of weight of the loads resting upon them.
I calculated for each of these joints the sum of the moments (2Af) of all the superincumbent forces relative to the axis of Y, divided these values by the sum of the forces of the different sections (2 P), and thus found the distances of the lines of weight from the axis of Y, and the sum of the .-'^"^" several results. The following tables .2*-''"—" will make this more clear : — ~~
For the corresponding joints we now have the values shown in the following table : —
The forces represented in the columns 2 P marked in Fig. 5, from P 73° to P 25°. As we now know their exact size and position, we are enabled to ascertain their moments for any point of attack we choose. If we had to do it with an absolutely solid material, the arch itself would still remain firm, even if the point of attack of the vertical force were the inner end of the weakest joint. But since the solidity of the; material is simply mechanical, it follows that the break of the stone occurred very near to the two points in question.
Long and careful study of the subject of vaulted architecture has taught me that it is an a priori law that of all the lines of pressure which are possible in an arch, that is the real one which is th* most favorable one; that is, which deviates least from the middle line of the arch, and coincides with it. The manner of loading and the form of the arch, as they have here been shown, inclined nie in advance to the opinion that even the most favorable line of pressure possible under the circumstances would be a very bad one. Consequently I assumed that the distance of the point of attack from the inner line of the arch was very small, and fixed this distance at 7". The distance
- 5 ami
will be a line parallel to the inner line of the arch at a distance of 7" from it. The points of attack for the forces P 73° to P 25° are marked in Figure 5, . , with an x on their \^^-&A--^g^^\<iA-r;l^ettl c orresp o n d i n g joints; their arms are also marked in the same way.
In order to calculate the moments of these forces (ilia) their arms (u) relative to the axis of Y must be reduced to the distances (Fa) relative to their points of attack. This reduction, and the disposition of the moments is given in the following table : —
It follows that the horizontal thrust for the joints under consideration is at a maximum at a = 25°. To determine this maximum more precisely, however, it is necessary to examine a larger number of joints, and we will now proceed to examine the angles a = 30°, 23°, 22°, 20° and 18°.
a = 30° PsP = PKo — (P„-\-Plt); if Pj, is taken to signify the arc from 30° to 25° and P18 the part of the load resting upon it. Pu = 33.0 and P18 — 255.2. The arms of these forces are Va 17 = (—3.1) and Va 18 — — (5.6). Their moments will then be: — Ma 17= 33 X (— 3.1)=— 102
Ma 18=255.2 X (— 5.6) = — 1429
= 77242 A = 45; hence H=TTM = 1716
a = 18°:
PB = 45.6 and P„ = 131.6; Va 25 = (— 0.8) and Fa26=(— 3.2)
Ma 25 = 45.6 X (— 0.8) = — 36.5
Ma 26 = 131.6 X (— 3.2) = — 421.1
= — 457.6
Ma 18 ° = 4290.4 X 18.9 = 81088.6
— 457.6
80631.0
k = 47.5 hence H:
maximum of all the values for H is according to this at a = 22°. This joint is consequently the weakest joint and H = 1740.
It still remains to calculate the line of pressure, of which now two points are known, namely : the point of attack at the summit and the point in the weakest joint 7" distant from the inner line of the arch. Now since the moments of the horizontal thrust and the vertical forces must necessarily balance each other, we have the following equation, taking x as the distance of the line of pressure from the given points of attack, measured in the joint-line of the corresponding angle:
H (h — x sin. a) = P ( Va -f- x cos. a).
will be a line parallel to the inner line of the arch at a distance of 7" from it. The points of attack for the forces P 73° to P 25° are marked in Figure 5, . , with an x on their \^^-&A--^g^^\<iA-r;l^ettl c orresp o n d i n g joints; their arms are also marked in the same way.
In order to calculate the moments of these forces (ilia) their arms (u) relative to the axis of Y must be reduced to the distances (Fa) relative to their points of attack. This reduction, and the disposition of the moments is given in the following table : —
It follows that the horizontal thrust for the joints under consideration is at a maximum at a = 25°. To determine this maximum more precisely, however, it is necessary to examine a larger number of joints, and we will now proceed to examine the angles a = 30°, 23°, 22°, 20° and 18°.
a = 30° PsP = PKo — (P„-\-Plt); if Pj, is taken to signify the arc from 30° to 25° and P18 the part of the load resting upon it. Pu = 33.0 and P18 — 255.2. The arms of these forces are Va 17 = (—3.1) and Va 18 — — (5.6). Their moments will then be: — Ma 17= 33 X (— 3.1)=— 102
Ma 18=255.2 X (— 5.6) = — 1429
= 77242 A = 45; hence H=TTM = 1716
a = 18°:
PB = 45.6 and P„ = 131.6; Va 25 = (— 0.8) and Fa26=(— 3.2)
Ma 25 = 45.6 X (— 0.8) = — 36.5
Ma 26 = 131.6 X (— 3.2) = — 421.1
= — 457.6
Ma 18 ° = 4290.4 X 18.9 = 81088.6
— 457.6
80631.0
k = 47.5 hence H:
maximum of all the values for H is according to this at a = 22°. This joint is consequently the weakest joint and H = 1740.
It still remains to calculate the line of pressure, of which now two points are known, namely : the point of attack at the summit and the point in the weakest joint 7" distant from the inner line of the arch. Now since the moments of the horizontal thrust and the vertical forces must necessarily balance each other, we have the following equation, taking x as the distance of the line of pressure from the given points of attack, measured in the joint-line of the corresponding angle:
H (h — x sin. a) = P ( Va -f- x cos. a).
From this general equation z, and consequently the line of pressure can now be found. We have from it:
Hh, — IIx sin. a = Pea 4- Px cos. a
Hh — Pva = Px cos. a -f- Hx sin. a
Hh — Pea — x (P cos. a 4- H sin. a)
.,_ Hh-Pva
P cos. a -f- II tin. a All the following equations are solved by this formula. 5742. 3482 S70
The line of pressure in Figure 5 is drawn in accordance with these values, from the summit to the weakest joint, that is, to a = 22°. As it is however valuable to carry out the line of pressure as far as a = 0°, the calculation is continued to that point.
Pursuing the method followed in the foregoing examples, P„ denotes the arc from a = 25° to a = 0°; and P„ the part of the load which rests upon this arc.
P„ = 150, P„ = 250; Va 27 = (— 2.4) and Va 28 = (— 8.6)
Ma 27 = 150 (— 2.4) = — 360
Ma 28 = 250 (— 8.6) = — 900
= — 1260
It must be observed here that these moments are relative to the inner initial point of the ellipse, to which the collective moment also relates.
Ma 0° = 4290.4 X 19-7 = 84521
— 1260
= 88261
According to this, x is likewise relative to the inner initial point of the ellipse.
111012
4690.4 0
The line of pressure here given therefore approaches nearest to the lines of the arch at the following points and distances: 1. At the summit; 8" from the inner line of the arch.
2. At a =65°; 8'—(18i"+ 7") = 36" — 25J" = lOj," from the outer line.
8. At a = 22°; 7" from the inner line. 4. At a = 0°; ^" from the outer line.
Such a line of pressure would be impossible without strong buttresses at the ends of the arches, because a distance of only J" from the outer line of the arch far exceeds the bounds of possibility. This deviation of the line of pressure from its proper curve is not however especially dangerous in this case, as the pockets of the vaults are filled with solid masonry. The three first joints only, then, are dangerous, and the danger is greatest at a = 22°, since at this point the normal pressure is much greater than at the other two points. The three first distances given show, perhaps, that the line of pressure as it is here calculated is not absolutely the most favorable one; still it is easy to see that it would deviate very slightly from it. A second calculation of the line of pressure in which I followed the same method, resulted, with an almost identical line of load, in the following distances of the line of pressure from the lines of the arch:
1, at the summit, 11" from the inner line.
2, at a = 65°, 9£" " outer" 8, at a = 25°, 7" " inner" 4, at a = 0°, i" " outer"
Here also, H = 1740. This line of pressure is more favorable than the other only in so far as this, that the weakest joint has been raised a little higher, where the normal pressure is less. As for the rest, the extreme limit is reached in the approach of the line of pressure to a distance, of only 9^" from the outer line of the arch, though even this seems allowable, inasmuch as this distance is considerably more than one-third of the thickness of the arch, viz., !'. On this account the doubt remains whether in the arch tcith such a load laid upon it a line of pressure is possible which, at the most dangerous point, that is at the weakest joint, is more than ""from the inner line of the arch; at any rate a distance of more than 9" is impossible. In accordance with this, the dangerous point of the line of pressure is shown in the cross section in Figure 4; and an examination of this diagram shows that the danger of a break is even greater than it would otherwise be, owing to a perfectly unnecessary moulding of the arch, which weakens it considerably. In vaulted architecture it is a universal law, in order to secure the stability of the arch, that the'line of pressure should remain throughout within the inner third of the thickness of the arch, and at no point pass beyond it, since otherwise strains would take place in the arch which would certainly destroy the stone. This universal rule is far from being obeyed in the ribs of the vault at Albany, and on this account, and considering also the enormous load, and the weakening of the arch by unnecessary mouldings, it is impossible to repress grave fears for the result. The danger is increased by the above-mentioned use of tie-rods, which cause a perpetual vibration in the arches, with most injurious results.
Since making the above calculations I have found that the load is in reality somewhat different from what it was assumed to be, but this difference is not sufficient to affect essentially the result, as I shall show; the weakest joint is removed a little nearer to the summit of the arch, and so far only is the change favorable. The weakest joint then will actually be found at about a = 27°; and indeed it was in this part of the arch, as the line of pressure required, that the break occurred and the new stone had to be inserted. The most extraordinary hypotheses have been advanced to account for this break of the stone, and avoid impugning the stability of the arch itself. One suggested that the columns had settled unequally; another that the rib was flattened by the pressure of the half-arches held together by the iron tie-rods; another that the arch had been warped by the inequality of the weight of the superincumbent vault, etc. A closer examination, however, proves that all these hypotheses are untenable, and that the cause of the fracture can be found only in the vicious construction of the arch itself.
II. Synthetic construction of the Line of Pressure. In order to place the result of the foregoing analytical examination entirely beyond question, I now pass to the synthetical method; and shall thus give additional weight to any further remarks I may make in regard to the possibility of a fall of the great vault.
The synthetical method depends upon a theoretical knowledge of the nature of every line of pressure; while the analytical method gives no special information about it. The general equation of the line of pressure is as follows: ro Z0 Z cos.8 a
In this formula a denotes the angle which the radius of curvature of the line of pressure makes with the vertical; p denotes the radius of curvature;r0 the radius of curvature at the summit; Z„ the height of the load at that point; and z the height of the load at any given point of the arch. Also the horizontal thrust, H =r r0 Z0; hence, taking G as the vertical force of that part of the vault, including the load which belongs to a; G = H tan. a; and the normal pressure N= yj Qi + v/s.
Figs. 6 and 7 show the line of load as it exists at present, varying slightly from the line as it was at the time of the break, as some changes have been made. It is extremely difficult to determine the line of load with perfect exactness; but there is no doubt that the one given in Figs. 6 and 7 comes sufficiently near the real one for all practical purposes, and that the line of pressure dependent upon it is not more unfavorable than the real one.
In constructing the line of pressure in Figs. 6 and 7 from the radius of curvature, small portions of the line of pressure were treated as arcs of a circle. Fig. 6 shows first a line of pressure which is impossible. As the unit of length the measure of 8' is taken. According to that r„ = 5.25, and Za =1.1; hence H — 5.25 X 1.1 = 5.78. From the formula for p given above, we obtain the following values for p:
It is evident that the construction on paper must keep pace with the calculation, as only in this way can the values of z, which correspond to the angles a, be obtained. As the unit now used is 16 times as large (8') as that upon which the diagram of Fig. 5 was based (), H here represents an H there of the value 5.78 X 16 X 16 = 5.78 X 256 = 1480. Although this horizontal thrust is not very much smaller than the former one of 1740, still the construction of the line of pressure proves that the real horizontal thrust must be greater than 1480 (that is, than 5.78), since the line of pressure in Fig. 6, even at a — 50°, begins to pass beyond the arch on the inner side. In Fig. 7, therefore, a second construction of the line of pressure has been undertaken. In this, ro = 6.5 and Za = 1.1; hence, H = 6.5 X M — 7.15, which corresponds to a former H of 7.15 X 256 = 1830, which is somewhat higher than 1740. Hence, we have the following values for p:
Fig. 7 shows that such a line of pressure does not to be sure at any point pass outside the bounding lines of the arch, but that at the summit and at a = 30°, it comes very near to them. It is therefore probable that the horizontal thrust is in reality a little smaller, and may be assumed to be 1740, the figure which was obtained by analysis. Accordingly the horizontal thrust at the summit will be somewhat higher than it is drawn in Fig. 7; and the line of pressure will then at a = 30° be somewhat farther away from the outer line of the arch, and come nearer to the inner line at the weakest joint than is shown in Fig. 7. But if this is so, then the synthetical construction of the line of pressure exactly corroborates the result of the analytical examination, and the following details may serve to assist in the formation of an opinion as to the probability of a fall of the vault.
Horizontal thrust. = 1740.
Distance of the line of pressure at the summit from the inner line of the arch 8J"
Distance of the line of pressure at a — 65° (circa) from the outer line of the arch ........ 9J"
Distance of the line of pressure at 27° {circa) from the inner line of the arch 9"
Distance of the line of pressure at a =0° from the outer line of the arch
As has been mentioned, however, it is not at all improbable that the distance at the weakest joint reaches 7", and at all events, the figure 9" given here cannot be considered as more unfavorable than the reality. As has likewise been observed, this position of the line of pressure in the weakest joint in no way prevents the occurrence of strains, and it is therefore probable, taking into consideration the other injurious circumstances, viz., the construction with tie-rods, and the injudicious moulding of the rib, that sooner or later a wider destruction of the ribs, and consequently of the whole vault, will take place.
With the want of system in the loading of the vault is naturally connected a want of system in constructing the line of pressure
from the radii of curvature. Figs. 6 and 7 show in this connection that the radii grow first shorter and then longer, then again shorter and again longer, whereas they ought only at first to have shortened, and then, after reaching their minimum, should have steadily lengthened.
To obtain the working of the forces and the pressure acting on the material in pounds requires the following calculation.
The load weighs to the cubic foot 147 pounds. For one foot in depth of the rib then, the horizontal thrust will be expressed as follows, since J' is taken as the unit of length.
H= 1740 X ^2 = 1740 X 1740 X 36.75 = 63945 lbs.
The figure which is produced when a solid is destroyed by pressure, is, as is well known, a double-cone, whose axis lies in the direction of the pressure, and where the two cones meet at the apexes. Hence follows, that for practical purposes it has to be assumed that the area of resistance in vaults is twice as large as that which reaches from the bounding line of the arch to the line of pressure.
In the present case the area of resistance at the summit = 2 X 8.5 X 12 = 204D", whence the pressure per square inch on the material amounts to 63946 = 818.5 lbs. 204
The weight of the vault with its load at the weakest joint between PBo and Pjp (Fig. 5), is expressed in the following equation:
2 X 4290.4 — (33.0 + 255.2) 8580.8 — 288.2 8292.6 .,.„„ 2 = 2 =~r~= 4146-3
The normal pressure, therefore, is y/ii46.& -f- 1740, = 4500, or expressed in lbs., 4500 X = 165875 lbs. for one foot of thickness of the rib. Since the area of resistance in the weakest joint amounts to 2 X 9" X 12" = 216D"; the pressure on the material per □" = J**?!6. = 765.7 lbs.
216
For sandstone the allowable load per □" is generally reckoned at just 260 pounds, and the breaking load at 800 pounds. Hence it follows that in the vault at Albany the allowable load is far exceeded, and that at the weakest joint even the breaking load is reached. The sandstone which has been employed is certainly extremely firm; if this were not the case, more symptoms of disturbance must already have appeared in the rib; and it is therefore beyond question that a fall is far from impossible, especially when we remember that in the calculation of the area of resistance, its weakening by the niouldingof the rib has been entirely disregarded.
Even if the line of pressure coincided throughout with the middle line of the rib, the load would still bo the greatest allowable. The pressure per would then be ^p-= 191 pounds; or, taking into account the moulding of the rib, about 200 pounds.
The question now arises whether anything can be done to obviate the danger of a fall. To obtain complete security seems impossible, as little can be taken from the load without bringing the equilibrium of the vault again into danger.
Nothing definite could be stated on this point unless every single arch in the vaulting were examined as thoroughly as I have examined the rib. But even if it could be assumed that by a diminution and better distribution of the load the line of pressure at the weakest joint could be carried 1" farther away from the inner line of the arch (10" that is, in the whole), even then very little would be accomplished.
If the arch were a perfect ellipse, sufficient stability could bo obtained provided the load were arranged according to the line of load f g, Fig. 5, which is deduced from the formula* for p. Nothing, however, can be done to supply the place of the missing piece at the summit, as not only the vertical forces but also the points of weight which are represented in it influence the line of pressure.
There is no ideal line of load for the pointed arch, and in that respect round and elliptical arches will always be preferred, even though they have not such lines of load as are practically possible, since they require at the skew-back a load-height of an infinite ordinate. Theoretically, then, these arches also are on this account to be avoided. Logically, also, they would be condemned, because infinite load-heights imply infinite thickness of skew-backs, which of themselves are inconsistent with the nature of the arch.
The weakness resulting from the variance between the line of the arch and the line of pressure is so great in the arches of the great vault in the Assembly Chamber of the new Capitol at Albany, that a fall sooner or later is seriously to be feared. Absolute security can be obtained only by tearing down the whole vault, and building another in its place.
November 12, 1881, The American Architect and Building News, Page 235
THE VAULT OF THE ALBANY CAPITOL New York November 3 1881 To the Editors of the American Architect, Dear Sirs: Referring to an article published in your paper of the 29th ultimo entitled The Large Groined Vault in the Assembly Chamber of the Capitol at Albany, NY, I desire to say, That the line of the arch and the quantity and distribution of the load as there represented are not in accordance with the facts and that the line of pressures is therefore not the true line for this reason, as well as for reasons involved in the theory advanced by the author of that paper.
Most respectfully yours Leopold Eidlitz
2 X 4290.4 — (33.0 + 255.2) 8580.8 — 288.2 8292.6 .,.„„ 2 = 2 =~r~= 4146-3
The normal pressure, therefore, is y/ii46.& -f- 1740, = 4500, or expressed in lbs., 4500 X = 165875 lbs. for one foot of thickness of the rib. Since the area of resistance in the weakest joint amounts to 2 X 9" X 12" = 216D"; the pressure on the material per □" = J**?!6. = 765.7 lbs.
216
For sandstone the allowable load per □" is generally reckoned at just 260 pounds, and the breaking load at 800 pounds. Hence it follows that in the vault at Albany the allowable load is far exceeded, and that at the weakest joint even the breaking load is reached. The sandstone which has been employed is certainly extremely firm; if this were not the case, more symptoms of disturbance must already have appeared in the rib; and it is therefore beyond question that a fall is far from impossible, especially when we remember that in the calculation of the area of resistance, its weakening by the niouldingof the rib has been entirely disregarded.
Even if the line of pressure coincided throughout with the middle line of the rib, the load would still bo the greatest allowable. The pressure per would then be ^p-= 191 pounds; or, taking into account the moulding of the rib, about 200 pounds.
The question now arises whether anything can be done to obviate the danger of a fall. To obtain complete security seems impossible, as little can be taken from the load without bringing the equilibrium of the vault again into danger.
Nothing definite could be stated on this point unless every single arch in the vaulting were examined as thoroughly as I have examined the rib. But even if it could be assumed that by a diminution and better distribution of the load the line of pressure at the weakest joint could be carried 1" farther away from the inner line of the arch (10" that is, in the whole), even then very little would be accomplished.
If the arch were a perfect ellipse, sufficient stability could bo obtained provided the load were arranged according to the line of load f g, Fig. 5, which is deduced from the formula* for p. Nothing, however, can be done to supply the place of the missing piece at the summit, as not only the vertical forces but also the points of weight which are represented in it influence the line of pressure.
There is no ideal line of load for the pointed arch, and in that respect round and elliptical arches will always be preferred, even though they have not such lines of load as are practically possible, since they require at the skew-back a load-height of an infinite ordinate. Theoretically, then, these arches also are on this account to be avoided. Logically, also, they would be condemned, because infinite load-heights imply infinite thickness of skew-backs, which of themselves are inconsistent with the nature of the arch.
The weakness resulting from the variance between the line of the arch and the line of pressure is so great in the arches of the great vault in the Assembly Chamber of the new Capitol at Albany, that a fall sooner or later is seriously to be feared. Absolute security can be obtained only by tearing down the whole vault, and building another in its place.
November 12, 1881, The American Architect and Building News, Page 235
THE VAULT OF THE ALBANY CAPITOL New York November 3 1881 To the Editors of the American Architect, Dear Sirs: Referring to an article published in your paper of the 29th ultimo entitled The Large Groined Vault in the Assembly Chamber of the Capitol at Albany, NY, I desire to say, That the line of the arch and the quantity and distribution of the load as there represented are not in accordance with the facts and that the line of pressures is therefore not the true line for this reason, as well as for reasons involved in the theory advanced by the author of that paper.
Most respectfully yours Leopold Eidlitz
November 26, 1881, The American Architect and Building News, The Vault of the Capitol,
Page 259 is missing from Google Books online. Must reference the following letter from Eidlitz. Find Hard Copy
December 3, 1881, The American Architect and Building News, THE VAULT OF THE ALBANY CAPITOL. Page 271
To The Editors Of The American Architect: —
Dear Sirs, — In answer to a letter on the vault of the Albany Capitol, in your issue for November 26, 1881, I beg to refer your readers to my letter of November 12.
Most respectfully, Leopold Eidlitz
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