In most mechanical systems the working stresses acting between the parts can be determined when the relative positions of all the parts are known; and the energy which a system possesses in virtue of the relative positions of its parts, or its configuration, is classified as "potential energy," to distinguish it from energy of motion which we shall presently consider.
But there are stresses which depend on the relative motion of the visible bodies between which they appear to act.
As subscribers' lines are invariably short, the smallest gauge of wire possessing the mechanical strength necessary to withstand the stresses to which it may be subjected can be employed, and bronze wire weighing 40 lb per mile is commonly used.
Availing himself of the admirable generalized co-ordinate system of Lagrange, Maxwell showed how to reduce all electric and magnetic phenomena to stresses and motions of a material medium, and, as one preliminary, but excessively severe, test of the truth of his theory, he pointed out that (if the electromagnetic medium be that which is required for the explanation of the phenomena of light) the velocity of light in vacuo should xvii.
Maxwell explained electric and magnetic forces, not by the action at a distance assumed by the earlier mathematicians, but by stresses in a medium filling all space, and possessing qualities like those attributed to the old luminiferous ether.
To prevent excessive bending stresses the diameter of drum and sheave must bear a proper ratio to that of the rope.
All metals are elastic to this extent that a change of form, brought about by stresses not exceeding certain limit values, will disappear on the stress being removed.
Was whether the mechanical impulsion was a direct effect of the light, or whether the radiation only set up internal stresses, acting in and through the residual air, between the vanes and the walls of the enclosure.
On the other hand, if the effects arose from balanced stresses set up inside the globe by the radiation, the effects on the vanes and on the case would be of the nature of action and reaction, so that the establishment of motion of the vanes in one direction would involve impulsion of the case in the opposite direction; but when the motion became steady there would no longer be any torque either on the vanes or on the case, and the latter would therefore come back to its previous position of equilibrium; finally, when the light was turned off, the decay of the motion of the vanes would involve impulsion of the case in the direction of their motion until the moment of the restoring torque arising from the suspension of the case had absorbed the angular momentum in the system.
The problem of the stresses in rarefied gaseous media arising from inequalities of temperature, which is thereby opened out, involves some of the most delicate considerations in molecular physics.
As far as the order to which he carried the approximations - which, however, were based on a simplifying hypothesis that the molecules influenced each other through mutual repulsions inversely as the fifth power of their distance apart--the result was that the equations of motion of the gas, considered as subject to viscous and thermal stresses, could be satisfied by a state of equilibrium under a modified internal pressure equal in all directions.
In later memoirs Reynolds followed up this subject by proceeding to establish definitions of the velocity and the momentum and the energy at an element of volume of the molecular medium, with the precision necessary in order that the dynamical equations of the medium in bulk, based in the usual manner on these quantities alone, without directly considering thermal stresses, shall be strictly valid - a discussion in which the relation of ordinary molar mechanics to the more complete molecular theory is involved.
Launhardt found that, for stresses always of the same kind, F = (t-u)/(t-fmax.) approximately agreed with experiment.
For stresses of different kinds Weyrauch found F
Whatever type of bridge is adopted, the engineer has to ascertain the loads to be carried, and to proportion the parts so that the stresses due to the loads do not exceed limits found by experience to be safe.
Development of theory has advanced poi passe with the demand for bridges of greater strength and span and of more complex design, and there is now little uncertainty in calculating the stresses in any of the types of structure now adopted.
But if hinges are introduced at crown and springings, the calculation of the stresses in the arch ring becomes simple, as the line of pressures must pass through the hinges.
The stresses were calculated to be 15, 17 and 12 tons per sq.
Of the internal stresses, which balance the external forces, shows that most of the material should be arranged in a top flange, boom or chord, subjected to compression, and a bottom flange Or chord, subjected to tension.
The horizontal stresses in the flanges are greatest at the centre of a span.
The stresses in the web are greatest at the ends of the span.
But girders may have curved chords and then the stresses in the web are diminished.
The earliest published theoretical investigations of the stresses in bracing bars were perhaps those in the paper by W.
Not only were the bracing bars designed to calculated stresses, and the continuity of the girders taken into account, but the validity of the calculations was tested by a verification on the actual bridge of the position of the points of contrary flexure of the centre span.
It is available for spans greater than those practicable with independent girders; in fact, on this system the spans are virtually reduced to smaller spans so far as the stresses are concerned.
Road to pass between the springings and ensured the transmission of the wind stresses to the abutments without interrupting the crossbracing.
(7) In some cases, especially in arch and suspension bridges, changes of temperature set up stresses equivalent to those produced by an external load.
I In Austria the official regulations require that railway bridges shall be designed for at least the following live loads per foot run and per track: It would be simpler and more convenient in designing short bridges if, instead of assuming an equivalent uniform rolling load, agreement could be come to as to a typical heavy locomotive which would produce stresses as great as any existing locomotive on each class of railway.
For all these reasons the stresses due to the live load are greater than those due to the same load resting quietly on the bridge.
The impact stresses depend so much on local conditions that it is difficult to fix what allowance should be made.
(4) The increase per cent of boom stresses due to impact is about the same as that of deflection; that in web bracing bars is rather greater.
A purely empirical allowance for impact stresses has been proposed, amounting to zo% of the live load stresses for floor stringers; 15 for floor cross girders; and for main girders, io% for 40-ft.
The weight of main girders increases with the span, and there is for any type of bridge a limiting span beyond which the dead load stresses exceed the assigned limit of working stress.
In the present day engineers are in accord as to the principles of estimating the magnitude of the stresses on the members of a structure, but not so in proportioning the members to resist those stresses.
For steel, was safe or more than safe for long bridges with large ratio of dead to live load, it was not safe for short ones in which the stresses are mainly due to live load, the weight of the bridge being small.
Be the breaking strength of the same bar when subjected to stresses varying from k max .
- k min ., if the stresses are both of the same kind, and kmax.
It was pointed out as early as 1869 (Unwin, Wrought Iron Bridges and Roofs) that a rational method of fixing the working stress, so far as knowledge went at that time, would be to make it depend on the ratio of live to dead load, and in such a way that the factor of safety for the live load stresses was double that for the dead load stresses.
Let t be the statical breaking strength of a bar, loaded once gradually up to fracture (t = breaking load divided by original area of section); u the breaking strength of a bar loaded and unloaded an indefinitely great number of times, the stress varying from u to o alternately (this is termed the primitive strength); and, lastly, let s be the breaking strength of a bar subjected to an indefinitely great number of repetitions of stresses equal and opposite in sign (tension and thrust), so that the stress ranges alternately from s to -s.
=0, where 4 is-For-according as the stresses are of the same or opposite signs.
= u (1+ (t - u) 4)/u) [Stresses of same sign.] fmax.
= u(1+ (us) Iu) [Stresses of opposite sign.] The working stress in any case is f max .
For shearing stresses the working stress may have o 8 of its value for tension.
To compare this with the previous table, tp _ (A+B)/A = r +P. Except when the limiting stresses are of opposite sign, the two tables agree very well.
Determination of Stresses in the Members of Bridges.
- It is convenient to consider beam girder or truss bridges, and it is the stresses in the main girders which primarily require to be determined.
- In the case of braced structures the following method is convenient: When a section of a girder can be taken cutting only three bars, the stresses in the bars can be found by taking moments.
Further, the range of stress to which they are subjected is the sum of the stresses due to the load advancing from the left or the right.
Then the bridge is designed, so far as the direct stresses are concerned, for bending moments due to a uniform dead load and the uniform equivalent load we.