. Concrete bridges and culverts, for both railroads and highways . rdinates found and this willgive a curve for uniform loads. The height T referred to above is the distanceto the line of pressure measured from a horizontalline through the point of rupture, which is not nec-essarily at the abutment face. The correct crownthrust cannot be obtained by using a distance T toany point below the point of rupture. When thepoint of rupture falls within the abutment face,the span length must be taken as the distance be-tween the points of rupture, and not the clear dis-tance between abutments. 134 COXC
. Concrete bridges and culverts, for both railroads and highways . rdinates found and this willgive a curve for uniform loads. The height T referred to above is the distanceto the line of pressure measured from a horizontalline through the point of rupture, which is not nec-essarily at the abutment face. The correct crownthrust cannot be obtained by using a distance T toany point below the point of rupture. When thepoint of rupture falls within the abutment face,the span length must be taken as the distance be-tween the points of rupture, and not the clear dis-tance between abutments. 134 COXCRETE BRIDGES AXD CVWERTS. For full dead and live loads, the line of pressureshould wherever possible, lie within the middlethird of the arch ring, and reinforcement used onlyfor resisting bending stresses due to partial liveloads. In Figure 26, the weight of the arch ringmay be assumed at its mean thickness at the quar-ter point, and the arch ring weight assumed ap-proximately as a uniform load. The weight of earthfilling, pavement and other material between the. extrados and roadway level, as well as the uniformlive load, is also uniform, and the center bendingmoment for these uniform loads is expressed by theequation: TIT W S^ M= 8 For a parabolic arch, the spandrel area shown REINFORCED CONCRETE ARCH BRIDGES. 135 hatched in Figure 26 is equal to . The center of 6 gravity of this area is equal to one-eighth of thespan length from the abutment face. Therefore,the bending moment at the center from spandrel filling is equal to The total moment is, 12 therefore, equal to the sum of moments from uni-form loads and from the spandrel filling. Dividingthe center moment by the rise gives the crownthrust or pole distance II for the force is a very convenient analytical method fordetermining the correct arch form for any systemor arrangement of loads. A combination of the an-alytical with the graphical method will simplifycomputation, as some results, like finding the crow:
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