The Illinois Highway Commission requires that arches be designed for a live load of 125 lb. per sq. ft. or a concentrated load giving a maximum uniform load of 525 lb. per sq. ft., over an area 16 ft. wide and 3 ft. 10 in. long. Sidewalks to have a uniform live load of 125 lb. per sq. ft. The live loads specified by the author are given in Appendix II.

Allowable Stresses.—The allowable stresses in arches are given in the author's Specifications for Concrete Bridges and Foundations," in Appendix II.

General

Impact.—Where there is a crown filling of not less than one foot the effect of impact may be neglected. For open-spandrel arches with concrete slab floors the effect of impact should be considered the same as for other concrete bridges.

Distribution of Loads Through Fill.-The distribution of live loads when transmitted through filling has been studied but no standard specification has been adopted. A common specification is to assume that the load on a wheel is uniformly distributed over a square the side of which is equal to the width of tire plus twice the depth of the fill.

The Ohio State Highway Department requires that on masonry arches with spandrel filling three feet or more in depth, the weight of the concentrated load shall be assumed as distributed uniformly over an area 12 ft. wide and 20 ft. long in the direction of the roadway. Where a pavement is used the concentrated load is assumed as distributed over an area whose length is equal to twice the depth of earth fill plus four times the thickness of the pavement.

Allowance for Temperature.-Tests made at the Iowa State College of Agriculture and Mechanic Arts and described in Bulletin 30, show that for a latitude of approximately 40 degrees a temperature provision should be made in designing an arch for a variation of 40 degrees F. each way from the temperature of no temperature stress.

The Iowa Highway Commission requires that arches be designed for stresses induced by a temperature range of 80 degrees F.

The Illinois Highway Commission requires that arches be designed for range of 40 degrees F. either way from normal.

Watson's "General Specifications for Concrete Highway Bridges," 1916 edition, requires that arches be designed for a range of 35 degrees each side of normal for a latitude of 40 degrees, and that the limit be increased for higher latitudes and be decreased for lower latitudes.

Arch Loading.-Mr. Cochrane* calculated the stresses in arches by means of influence diagrams, and recommends the four typical arrangements of live loads, as shown in Fig. 12. Loadings 1 and 2 are for maximum positive and negative moments at the crown, respectively, and when combined cover the entire span. Loadings 3 and 4 are for maximum positive and negative moments at the springing respectively, and when combined cover the entire span.

If heavy concentrations are specified the method of influence lines should be used in calculating the stresses in arches.

Division of Arch Ring for = a Constant.—The arch may be divided in segments in

As
E.I

=

As
E.I

which g = a constant, by the graphic method shown in Fig. 13. The line A-B is made equal to one-half the length of the arch axis. The curve c-g-d is drawn through points whose ordinates are the values of I and whose abscissas are the corresponding distances along the arch axis from the springing line. A length A-f is then assumed for the length of the first segment, and the isosceles triangle A-e-ƒ is drawn. Starting from point ƒ, lines are drawn parallel to A-e and

e-f as shown. If the last division does not check at B the operation must be repeated. The base of each triangle is the length of As and the altitude is the mean value of I, and since all triangles are similar ▲s/I is a constant. The modification of the method shown by the dotted lines may be used.

=

=

span of arch, x = c.l

Best Shape of Arch Axis.*-If l distance of any point in arch ring from center line; y vertical distance of any point in arch ring from tangent to arch ring at center; r = rise of arch; 4 = angle between tangent to arch axis at springing and the horizontal, then the equations that give the best form of arch axis are

* Design of Symmetrical Hingeless Arches, by Victor H. Cochrane, Proceedings Engineer's Society of Western Pennsylvania, Vol. 32, No. 8.

It is very common practice to use a form for the arch such that there will be no tensile stresses in the arch for dead load.

Empirical Rules for Thickness of Arch Ring.*-Joseph P. Schwada gives the following formula for the thickness of highway bridge arches:

The thickness of highway bridge arches for different conditions are given in Fig. 14. In using formula (55) it is necessary to use an approximate value of d; if the calculated value and assumed value of d do not check, a new value must be assumed and the thickness recalculated.

Variation in Thickness of Arch Rib.f-Mr. Cochrane has made an analysis of the variation in rib thickness to give equal stresses throughout the arch rib. The variation in thickness is shown in Fig. 15. The thickness at the quarter point may be less than at the crown, but an arch of this design would be unsightly and difficult to build. The variation in thickness of arch rib shown by the dotted lines is recommended.

Reinforcement of Arch Rings.-Reinforcement in concrete arches makes the action of the structure more certain and permit higher working stresses in the conrcete than can be permitted * Engineering News, Nov. 9, 1916, p. 880.

† Design of Symmetrical Hingeless Arches, by Victor H. Cochrane, Proceedings Engineer's Society of Western Pennsylvania, Vol. 32, No. 8.

FIG. 15.

on plain concrete arches. Reinforced concrete arches can therefore be built with thinner arch rings and lighter abutments than plain concrete arches. More reinforcement is used than would be required to take the tensile stresses.

It is the best practice to use reinforcement near both surfaces of the arch ring to insure against positive and negative moments. The amount of steel at the crown varies from to I per cent. The author has specified I per cent of reinforcement at the crown in "General Specifications for Concrete Bridges and Foundations," in Appendix II. Transverse bars at right angles to the longitudinal bars are generally used to prevent cracks in the concrete and to assist in distributing the loads laterally. Web reinforcement is not ordinarily required for shear, but has the advantage of making the longitudinal and transverse reinforcement act as a unit, and web reinforcement should preferably be used.

For the calculation of stresses due to direct stress and flexure as in arch rings, see Chapter XVIII.

EXAMPLES. The arch bridge shown in Fig. 16 was designed by the Iowa Highway Commission. The bridge was designed for a live load of 100 lb. per sq. ft. or a 15-ton traction engine. The allowable compression in concrete was 650 lb. per sq. in. where no temperature stresses occur, and 750 lb. per sq. in. where temperature stresses are included. The allowable tension in steel was 16,000 lb. per sq. in., with 20,000 lb. per sq. in where temperature stresses were included. The arch rib was designed for a variation of 40 degrees F. from the mean. The arch ring, abutments and spandrels were built of 1-2-4 mix Portland cement concrete.

The arch bridge shown in Fig. 17 was designed by the Michigan State Highway Department. The bridge was designed for a uniform live load of 100 lb. per sq. ft. or an 18-ton road roller. The arch ring was built of 1-2-4 mix Portland cement concrete, while the abutments were built of 1-3-6 mix Portland cement concrete. The concrete in the arch rib was designed for a com pression of 650 lb. per sq. in. The allowable tension in steel was 16,000 lb. per sq. in. Rainbow Arch Bridge. The arch bridge in Fig. 18, built at Carmi, Ill. in 1916, has three arch spans of 90 ft. each between piers, with a rise of 18 ft. and a radius of 65 ft. 3 in. on the under side. It has an 18-ft. roadway. The arch was constructed by placing the structural steel reinforcing of the ribs first, connecting them rigidly in place by struts, floorbeams and hangers. The formwork was then built around the steel reinforcing. The reinforcing for the arch ribs is composed of four angles laced on four sides and with the backs of the angles turned outward. The concrete was 1:2:4 mix using gravel with a maximum size of 1 in.

The bridge was designed for a live load of 125 lb. per sq. ft. and a 20-ton road roller. The stresses were those required by the specifications of the Illinois Highway Commission. The plans were prepared by the Marsh Bridge Company, which has patented certain features of the bridge.

The cost of the bridge in 1916 was $21,960.