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<br /> 3.0
<br /> 2.8
<br /> 2,6
<br /> 2.4
<br /> 2.2
<br /> 2.0
<br /> 1.8
<br /> 1.6
<br /> 1.4
<br />~ 1.2
<br />'"
<br /> 1.0
<br /> 0.8
<br /> 0.6
<br /> 0.4
<br /> 0.2
<br />
<br /> 111I111I1I!f'T 1- I
<br />'\. _111111114 ~ 1
<br />" 11111111111111
<br /> "- - - IIIIIIIIII)V
<br /> 90'WINGWALL
<br /> i".. ' :\... 960 w~ 450WINGWALL
<br /> ~, '("'" I I Illlllllllllll~
<br />F( R LENGTHS UP TO 200 FT 30' WW 1
<br />"- :k'
<br />-- --1'-] ] b r-..' " , I~
<br /> 11l1l1I1l1l1H~
<br />ALL SPILL TH OUGH ...--- I-........~'..r-..
<br />OR 450 ANO 50' WW
<br />I ABUTMENTS OVER ..... ~~ SPILLTHROUGH
<br />200 FT IN LENGTH,- ....... .
<br /> i ~ ......
<br /> , I
<br /> i ,-.....;;: ~
<br /> i -.......: ,~
<br /> ! ......
<br /> ~ :-....
<br /> ........
<br />
<br />o
<br />o
<br />
<br />0.3
<br />
<br />0.4
<br />
<br />QI
<br />
<br />0.2
<br />
<br />0,5
<br />M
<br />
<br />0,8
<br />
<br />1.0
<br />
<br />0,9
<br />
<br />0,6
<br />
<br />0,7
<br />
<br />Figure 6.-Backwater coefficient base curve8 (subcritical Bow).
<br />
<br />as a base coefficient and the curves on figure 6 are
<br />called base curves, The value of the overall back-
<br />water coefficient, K*, is likewise dependent on the
<br />value of M but also affected by:
<br />
<br />L Number, size, shape, and orientation of piers
<br />in the constriction,
<br />2, Eccentricity or asymmetric position of bridge
<br />with respect to the valley cross section, and
<br />3, Skew (bridge crosses stream at other than 90'
<br />angle),
<br />
<br />It will be demonstrated that K* consists of a base
<br />curve coefficient, K" to which is added incremental
<br />coefficients to account for the effect of piers, ec-
<br />centricity and skew, The value of K* is nevertheless
<br />primarily dependent on the degree of constriction of
<br />flow at a bridge.
<br />2.3 Effect of M and abutment shape (base
<br />curves). Figure 6 shows the base curves for back-
<br />water coefficient, K" plotted with respect to the
<br />opening ratio, M, for wingwall and spillthrough
<br />abutments. Note how the coefficient, K., increases
<br />with channel constriction, The lower curve applies
<br />for 45' and 60' wingwall abutments and all spill-
<br />through types, Curves are also included for 30'
<br />wingwall abutments and for 90' vertical wall abut-
<br />
<br />ments for bridge8 up to 200 feet in length. Tbese
<br />shapes can be identified from the sketches on figure
<br />6, Seldom are bridges with the latter type ahutments
<br />more than 200 feet long, For bridges exceeding 200
<br />feet in length, regardless of abutment type, the
<br />lower curve is recommended, This is because abut-
<br />ment geometry becomes less important to backwater
<br />as a bridge i8 lengthened, The base curve coefficients
<br />of figure 6 apply to crossings normal to flood flow
<br />and do not include the effect produced by piers,
<br />eccentricity and skew, Since the backwater coeffi-
<br />cient base curve, figure 6, has been modified in this
<br />book, the reasoning and the supporting data for
<br />making thi,;,change have been placed in section B.l,
<br />appendix B.
<br />2.4 Effect of piers (normal crossings). Back-
<br />water caused by introduction of piers in a bridge
<br />constriction has been treated as an incremental
<br />backwater coefficient desiguated ilK.. which is
<br />added to the base curve coefficient K. when piers
<br />are present in the waterway. The value of the in-
<br />cremental backwater coefficient, AK., is dependent
<br />on the ratio that the area of the piers bears to the
<br />gross area of the bridge opening, the type of piers
<br />(or piling in the case of pile bents), the value of the
<br />bridge opening ratio, M, and the angularity of the
<br />
<br />14
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