Abbildungen der Seite
PDF
EPUB
[ocr errors][subsumed][subsumed]

per square inch) gives the maximum permissible value of à for each value of p; and these are plotted in a series of curves in Fig. 4, where each curve corresponds to a given range of temperature. If for any given pipe, the values of p and A be the coordinates of a point on the convex side of any curve in the Fig., then the pipe is stressed beyond the maximum permissible limit

[ocr errors][ocr errors][subsumed][ocr errors][ocr errors][ocr errors][subsumed][ocr errors][ocr errors][ocr errors]

by heating through the range of temperature belonging to that curve. For plotting the curves in Fig. 4 the values of A are calculated from equation (8), which may be written

[blocks in formation]
[subsumed][subsumed][ocr errors][ocr errors][ocr errors]
[blocks in formation]
[ocr errors]
[graphic]
[ocr errors]

The same values of E, a, and f, are used in Fig. 4 as in Fig. 3. The lower part of the diagram gives the values of λ for various values of D and 1.

As regards the "strut effect" referred to, it is evident that the maximum bending moment due to it occurs at the point of maximum deflection, and is equal to half that deflection multiplied by P, which acts at the point of inflection C, assuming O A to be undeflected by the force PB.

[merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][subsumed][subsumed][merged small][subsumed][subsumed]

The maximum deflection takes place where the slope is zero, so that

[merged small][merged small][merged small][merged small][merged small][ocr errors][subsumed][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][subsumed][merged small][merged small][merged small][subsumed][subsumed][merged small][ocr errors][merged small][subsumed][subsumed][ocr errors][subsumed]

Again, the maximum bending moment in the long arm due to PA occurs at O, and is equal to

[blocks in formation]

Comparing these two bending moments and neglecting the sign, since magnitudes only are being considered, it is seen that their ratio R

[blocks in formation]

Giving a the value corresponding to 300 lbs. per square inch. and evaluating, it appears that

[blocks in formation]

Now the effect of this bending moment is to increase the deflection of the long arm and so relieve the stress in the short arm. It has been shown that it is only of sensible magnitude, compared to the bending moment caused by PA, when p is very large (say 10 and upwards), and, consequently, σ is large (say 85 per cent. and upwards); hence any lengthening of σ, will be small, and will not much affect the stress B. Moreover, the curves are always on the right side. The strut effect in the short arm is obviously so slight that it need not be considered.

Consider, lastly, the compression in the long arm due to the direct thrust PR. It may conveniently be compared with the expansion which will produce the maximum permissible stress at B. Now the stress at B

[blocks in formation]

A being the sectional area of the copper in the pipe. The total

[blocks in formation]

4 Eσ D'

Εσ

[blocks in formation]

4 Εσ

the maximum compression for any given values of D, p and ƒ.

[THE INST. C.E. VOL. CXXXV.]

U

Now the expansion due to increased temperature being a L, the ratio of these expressions is

[blocks in formation]

But the largest value of λ on the Fig. is about 0·06, and the minimum value of σ is 0.5; hence the largest value to be considered is

=

1

460

4,000 × 0.06

0.5 x 4 x 16.5 x 106 × 0.00334

which may be neglected. The effect of this again is to decrease the stress at B.

The compression in the short arm is clearly much smaller, and although the thrust producing it tends slightly to increase the stress on the compression side at B, it may be neglected.

The comparisons instituted may appear to form a crude method of investigating these disturbing effects; but the full treatment in the original equations would be complicated, as the solution of the simultaneous equations of the second degree (1) to (4) is already somewhat troublesome.

It may here be noted that should the pipe be permanently deflected it will at the next equal expansion be stressed to the point at which it is about to take a further permanent set. If the pipe be given a deflection when fitted, the range of stress will be the same as the maximum stress would otherwise have been. Also, as a rule, a pipe is not warmed more than once a day, so that in 10 years it only receives about 3,650 loadings or repetitions of stress, and it may therefore be very near the elastic limit without danger, if submitted to no vibration.

EXPERIMENTS.

Several experiments were made, by deflecting pipes on a surfacetable, which tended to show that the elastic modulus of the pipes was about 16 millions; and though the elastic limit was much reduced by annealing, it did not appear that the modulus was much affected.

Experiments were also made by the deflection method at different temperatures to discover any change in the modulus of elasticity at the temperatures of steam at one or two pressures ; but the best of these experiments, that is to say, those in which

[merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][ocr errors]

modulus of the section, as solid-drawn pipes are rarely of the same section throughout.

Another experiment was made to obtain the linear expansion due to increase of temperature of a copper pipe. This appears to decrease slightly at higher temperatures and to amount to a total of 0.00275 for 300° rise from 60° F., or 0.0000092 per degree F. The figure, however, adopted in all these calculations is 0.00000955

[ocr errors]

the best precautions were taken to drain the pipe and so prevent deflection from unequal expansion, seemed to show that the difference is inappreciable at temperatures due to steam-pressures up to 150 lbs. per square inch. The experiments were of the workshop rather than of the laboratory order; but still the deflection method admits of considerable accuracy, the principal difficulty (apart from that of the draining mentioned) being to obtain the correct

Steel Plates thick

[merged small][ocr errors]
[merged small][ocr errors]

0 90

[merged small][ocr errors]

3-338 Steel

Angle Bar
G.M.Flange

Scale,

inch = 1 foot. APPARATUS TO ASCERTAIN THE STRESS IN COPPER PIPES DUE TO EXPANSION.

« ZurückWeiter »