# Page:1902 Encyclopædia Britannica - Volume 26 - AUS-CHI.pdf/419

BRIDGES and veiy unequal loads, a parabola can be found which includes the curve of maximum moments. This parabola is the curve of maximum moments for a travelling load uniform per foot run. Let we be the load per foot run which would produce the maximum moments represented by this parabola. Then we may be termed the uniform load per foot equivalent to any assumed set of concentrated loads. Mr Waddell has calculated tables of such equivalent uniform loads. But it is not difficult to find we, approximately enough for practical purposes, very simply. Experience

Fig. 12. shows that (a) a parabola having the same ordinate at the centre of the span, or (b) a parabola having the same ordinate at one-quarter span as the curve of maximum moments, agrees with it closely enough for practical designing. A criterion already given shows the position of any set of loads which will produce the greatest bending moment at the centre of the bridge, or at one-quarter span. Let Mc and Ma be those moments. At a section distant x from the centre of a girder of span 2c, the bending moment due to a uniform load we per foot run is M = W- (c-x) (c+x). Putting x=0, for the centre section Mt= WeC" 2~ and putting x = ic, for section at quarter span 2 M ='_ 3w7ec T~’ From these equations a value of wt can be obtained. 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. In dealing with the action of travelling loads much assistance may be obtained by using a line termed an influence line. Such a line has for abscissa the distance of a load from one end of a girder, and for ordinate the bending moment or shear at any given section, or on any member, due to that load. Generally the influence line is drawn for unit load. In Fig. 13 let A'B' be a

Fig. 13. girder supported at the ends and let it be required to investigate the bending moment at O' due to unit load in any position on the girder. When the load is at F', the reaction at B' is mjl and the moment at C' is m(l -x)/l, which will be reckoned positive, when it resists a tendency of the right-hand part of the girder to turn

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