The conditions at. indicate that there are several wheels which give large moments; but according to Article 46, wheel 11 gives the maximum moment. When this wheel is at L„ wheel 1 is off the truss, and 15 feet of uniform load are on the truss. The moment of z all the loads about the right support is 19 304 + 304 X 5 -I- X2 = 20 849, from which should be subtracted the moment of wheel 1 about the right support. This moment of wheel 1 is 10 X 124 = 1 240, and the moment about L, of all loads on the truss is 20 849 — 1 240 = 19 609. The left reaction is: In the case of L„ the reactions and the moments for the two positions are: For wheel 12, R1 = 16 364 - 120 = 136.4 136.4 X4 X 20 — 6 708 = 4 204 000 pound-feet.
For wheel 13, R, = (16 364 + 5 X 284 + 5' 2 _ 120 = 148.4 if,=148.4X4X20-7668 = 4 204 000 pound-feet, which shows that each wheel gives the same moment, and also that the moment is greater than that at the corresponding point on the left-hand side of the center of the truss. As is the center of moments of then, if the center of moments for falls at L, (that is, if acts), the stress in will be greater than the stress in when wheel 6 is at Of course, if the engine came on the truss from the left, would receive the same stress that now receives. According to the shears, always acts, and therefore the center of moments for does fall at L,.
The various moments are written in order, as such action will facili tate the remainder of the computa tions.
The chord stresses are now found to be When the load comes on from the left, the stresses in and will be —168.2 and + 168.2 respec tively, which are the maximum live load stresses for these members.
Instead of placing the values of the stresses on a truss outline, they are sometimes put in tabular form, as in Table VII.
48. Impact Stresses. 'When an engine is at rest on a bridge, the stresses in the members are the same as those computed for that loading. When the loads move across the bridge at any speed, the vibrations and the shocks produced by the counterweights in the drivers and by other causes create stresses in the various members in excess of those computed by aid of the engine diagram. The excess stresses are designated as impact stresses. This term, however, is mislead ing to a certain extent, as causes other than the impact or pounding of the engine wheels help to produce the stresses referred to.
It is a well-known fact capable of mathematical demonstration, that a load, if suddenly applied, will produce a stress equal to twice that which it will produce as a static Load; also, that as the ratio of the weight of the load to the weight of the structure increases, the vibrations produced by the impact will be less. These two facts are
the basis of most of the empirical formulae for impact stresses; and empirical formulae are used to obtain these stresses, as the existing conditions and producing causes are not such as to make them sus ceptible of mathematical treatment. The result of experiments on actual bridges under the effect of passing engines and trains, have been the basis of many formulae. One of these is: f = S where 1 = Impact stress in the member; S = Live-load stress in the member caused by the engine load when at rest; L = Length of that part of the bridge which is loaded when the stress S is produced; and 300 = A constant .value derived from experiments.
This formula was proposed by C. C. Schneider in 1887, and is given in the "Transactions" of the American Society of Civil En gineers, Vol. 34, page 331. While it does not take into considera tion the relative weights of the bridge and the live-load loads, this formula does make allowance for the time it takes to produce the stress, by introducing L, the distance over which the engine passes before causing the stress S. It is seen that the smaller the distance L, the greater will be the impact stress for any given value of S. When L becomes exceedingly small, the effect would be that of a suddenly applied load, and the impact stress would equal the stress S. Table VIII gives the values of , which is called the impact coViii gives the values of , which is called the impact co- efficient, for different values of L. Values not given may be inter polated.
For example, by consulting Fig. 92, which gives the position of the engines for the maximum live-load stress in it is seen that 93 feet (the distance from'wheel 1 to the right support) is the loaded length. From Table VII, it is seen that the stress in produced by this loading is +118.6; and from Table VIII, the impact coefficient for 93 feet is found to be 0.763. The impact stress is now computed: Table IX gives the necessary information for computing the impact stresses, and also gives the impact stresses corresponding to the maximum live-load stresses in the members of the truss of Article 47.