The horizontal stresses in the flanges are greatest at the centre of a span.
The impact stresses depend so much on local conditions that it is difficult to fix what allowance should be made.
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.
Road to pass between the springings and ensured the transmission of the wind stresses to the abutments without interrupting the crossbracing.
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 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.
The axis becomes, therefore, a line of resistance, and in reasoning of the stresses on frames we may treat the frame as consisting of simple straight lines from joint to joint.
It is found in practice that the stresses on the several members do not differ sensibly whether these members are pinned together with a single pin or more rigidly jointed by several bolts or rivets.
A frame used to support a weight is often called a truss; the stresses on the various members of a truss can be computed for any given load with greater accuracy than the intensity of stress on the various parts of a continuous structure such as a tubular girder, or the rib of an arch.
Many assumptions are made in treating of the flexure of a continuous structure which are not strictly true; no assumption is made in determining the stresses on a frame except that the joints are flexible, and that the frame shall be so stiff as not sensibly to alter in form under the load.
These stresses will be unknown quantities, which the designer cannot take into account, and such a combination should if possible be avoided.
Bow (Economics of Construction), and is convenient in applying the theory of reciprocal figures to the computation of stresses on frames.
On this account it is usual to neglect the tensile strength of concrete in designing structures, and to arrange the material in such a way that tensile stresses are avoided.
It is never exhibited except by rocks which have been sub jected to the tangential stresses set up in the earth's crust by folding.
These stresses may operate in several ways.
(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.
Reciprocal figures are easily drawn by following definite rules, and afford therefore a simple method of computing the stresses on members of a frame.
Rankine gives the approximate rule Working deflection =5= l a /t o,000h, where l is the span and h the depth of the beam, the stresses being those usual in bridgework, due to the total dead and live load.
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.