axles spaced 12 ft. and wheels with an 8-ft. gage. Two-thirds of load on rear axle. Rear wheels 34 in. wide. For bridges in towns and country highways a 15-ton motor-truck with axles spaced 10 ft. and wheels with an 8-ft. gage. Two-thirds of load on rear axle. Rear wheels 18 in. wide. For bridges in remote mountainous highways an 8-ton motor truck with axles spaced 8 ft. and wheels with an 8-ft. gage. One-half of load on rear axle. Rear wheels 6 in. wide.

For additional data see article entitled "Concentrated Live Loads for Highway Bridges," by Milo S. Ketchum, printed in University of Colorado Journal of Engineering, October, 1916.

Ketchum's Specifications for Concentrated Moving Loads.-The author has adopted the following specifications for concentrated moving loads.

(a) That highway bridges on main roads or near towns or cities shall be designed to carry a 20-ton motor truck with axles spaced 12 ft. and wheels 6-ft. centers on axle, with 14 tons on rear axle and 6 tons on front axle. The truck to occupy a space 10 ft. wide and 32 ft. long. The rear wheels to have a width in inches equal to the total load in tons (20 in. for a 20-ton truck).

(b) That bridges not on main roads shall be designed for a 15-ton motor truck with axles spaced 10 ft. and wheels 6-ft. centers on axle, and occupying a space 10 ft. wide and 30 ft. long, with 10 tons on rear axle and 5 tons on front axle, and with rear wheels 15 in. wide.

(c) To provide for impact and vibration and unevenness of road surface thirty (30) per cent is to be added to the maximum live load stresses. Only one motor truck is to be assumed to be on a bridge at one time.

Motor trucks have narrower tires and are driven at greater speeds than traction engines, and therefore not only produce greater static stresses in the floor, but should have a greater impact allowance. In view of the above, it would not appear to be necessary to consider any road rollers or traction engines now in use in addition to the above motor-truck loadings.

DISTRIBUTION OF CONCENTRATED LOADS.-In designing floor slabs, floor stringers and floorbeams it is necessary to know the distribution of the concentrated loads.

Concrete Floor Slabs.-Tests of the distribution of concentrated loads on concrete floor slabs have been made by the Ohio Highway Commission, the results of which are given in Bulletin No. 28, published by the Commission; by Mr. W. A. Slater at the University of Illinois and described in Proceedings of American Society for Testing Materials, Vol. XIII, 1913, and by A. T. Goldbeck and E. B. Smith, described in Journal of Agricultural Research, Vol. VI, No. 6, Department of Agriculture, Washington, D. C., May 8, 1916.

Ohio Tests. The following conclusions drawn from the Ohio tests are of interest:

"The percentage of reinforcement has little or no effect upon the distribution to the joists, so long as safe loads on the slabs are not exceeded.

"The outside joists should be designed for the same total live load as the intermediate joists. "The axle load of a truck may be considered as distributed over 12 ft. in width of roadway. "The safe value for 'effective width' of a slab, where the total width of slab is greater than 1.33 L +4 ft. is given by the formula, e = 0.6L +1.7 ft., where e effective width (width over which a single concentrated load may be considered as uniformly distributed on a line down the middle of the slab parallel to the supports) and L span in feet."

=

=

Slater Tests. It was recommended that where the total width of slab is greater than twice the span, the effective width be taken as e = 4x/3d, where x is the distance from the concentrated load to the nearest support, and d is the width at right angles to the support over which the load is applied. While the depth of slab and the amount of longitudinal reinforcement had little effect on the distribution, it was recommended that the latter be limited to 1 per cent.

Goldbeck and Smith Tests.-Tests were made on three slabs, each slab being 32 ft. wide, 16 ft. span, and with effective depths of 10.5 in., 8.5 in. and 6 in., respectively. All slabs were made of 1-2-4 Portland cement concrete, and were reinforced with 0.75 per cent of mild steel.

DISTRIBUTION OF CONCENTRATED LOADS.

The following conclusions were drawn from these tests:

(1) The effective width decreases as the effective depth increases; the effective width for safe loads being 75.7 per cent; 81.1 per cent, and 109.3 per cent of the span, for the slabs having effective depths of 10.5 in., 8.5 in. and 6 in., respectively.

(2) For slabs in which the ratio of the width of the slab is not less than twice the span length, the effective width may be taken as

e= = 0.7L

where e is the effective width and L is the span length.

(34)

(Additional tests by Goldbeck, Proceedings American Concrete Institute, 1917, show that formula (34) may be used when the width of the slab is not less than the span.)

Watson's "General Specifications for Concrete Bridges," third edition, 1916, specifies that concentrated loads on reinforced concrete slabs may be assumed as distributed over a distance of 4 ft. at right angles to the supports, and a distance parallel to the supports equal to 2 ft. plus three-tenths of the span of the slab.

The State Highway Department of Ohio uses the following distribution of concentrated loads on floor slabs.

For spans less than 6 ft. the percentage, p, of the wheel load carried by one foot in width of (35) slab for a span in feet, l, is given by the formula while for spans greater than 6 ft. the percentage, p', of the wheel load carried by one foot in width of slab for a span in feet, l, is given by the formula

P = 42 - 4/

= 20

0.41

For a span of 5 ft., from formula (35), Þ as carried by a slab 5 ft. wide, applied on a For a span of 10 ft., from formula (36), p'

(36)

= 20 per cent, and the concentrated load is assumed parallel to the supports.

line

113

16 per cent, and the concentrated load is assumed

as carried by a slab 6.67 ft. wide, applied on a line parallel to the supports.

The U. S. Bureau of Public Roads specifies that wheel loads be distributed on concrete slabs as follows: with a fill of ballast or paving of 8 in. or less, 9 to 17 in., inclusive, and 18 in. or more, an area of distribution of 4 ft. square, 5 ft. square, and 6 ft. square, respectively.

Plank Floor on Steel Stringers.—A series of experiments to determine the distribution of concentrated loads on a timber floor supported on steel stringers has been made at Iowa State College of Agriculture and Mechanic Arts by T. R. Agg and C. S. Nichols, and published in Engineering Experiment Station Bulletin 53. The floor consisted of a 3-in. plank floor supported on 6-in. The concentrated loads I-beams spaced 12 in. centers and also spaced 19 in. centers; and a 3-in. plank floor supported on 7-in. I-beams spaced 24 in. centers and also spaced 27 in. centers. were applied through wheels 6′ 8′′ in diameter and 24 in. wide. The wheels were spaced 6 ft. A summary of the tests shows:

centers.

(1) For stringers spaced 12 in. centers the maximum load carried by a single stringer was 25 per cent of a wheel load.

(2) For stringers spaced from 24 in. to 27 in. centers the maximum load carried by one stringer was 55 per cent of a wheel load. A top floor of 2-in. plank laid longitudinally reduced the concentration under a wheel slightly.

(3) The concentration on stringers immediately under the wheels was slightly increased when the ends of the floor planks were not bolted down.

(4) The concentration on the outer stringer increases rapidly as the load approaches the side, and the outer stringer should have the same section modulus as the intermediate stringers.

These tests check the rule that the percentage of a concentrated load carried by one stringer is equal to the stringer spacing in feet divided by four feet.

Floor Stringers and Floorbeams.-The Illinois Highway Commission specifies that longitudinal stringers be spaced not more than 24-ft. centers, and that each stringer be designed for 20

per cent of the rear axle load concentrated at the center of the span when a concrete sub-floor is used, and 25 per cent of the rear axle load when a plank floor is used. Transverse stringers or floorbeams, spaced not more than 24-ft. centers, shall be designed to carry 40 per cent of the rear axle load distributed over the middle 10 ft. of the stringer. Floorbeams shall be designed for maximum stresses due to concentrated load.

The Iowa Highway Commission specifies that one-third of a wheel load be assumed as carried by one joist, when a concrete floor slab is used, and that one-half of a wheel load be assumed as carried by one joist, when a plank floor is used.

The Massachusetts Railway Commission specifies that the wheel load on plank doors be distributed over a width in feet equal to the thickness of the floor in inches, with a maximum distribution of 6 ft. With solid floors each wheel load is assumed as distributed over a width of 6 ft.

Watson's "General Specifications for Concrete Bridges," third edition, 1916, specifies that the part of the concentrated load carried by one stringer shall be found by dividing the stringer spacing by the gage distance of the concentrated load. With a gage distance of 6 ft. this gives one-third the total load for a stringer spacing of 2 ft.; one-half the total load for a stringer spacing

of 3 ft.; the total load for a stringer spacing of 6 ft.

=

General Specification for Steel Highway Bridges adopted 1918 by the Engineering Institute of Canada specifies that roadway stringers or joists shall be designed to carry proportions of the motor truck loads as given by the formula C = P.d/g, where C = proportion of front or rear wheel-load supported by one stringer; P concentration on one wheel, front or rear; d = distance center to center of stringers; g = gage, center to center of wheels. The U. S. Bureau of Public Roads specifies that loads be distributed on stringers and floorbeams as follows: For bridges with a timber floor and longitudinal stringers, stringers spaced 2 ft. centers shall be assumed as carrying one-half the wheel load, stringers spaced 3 ft. centers shall be assumed to carry three-fourths the wheel load, and proportional for other spacings. For bridges with concrete floor on steel or reinforced concrete longitudinal stringers, stringers spaced 4 ft. centers shall be assumed to carry two-thirds of the full load, stringers spaced 6 ft. centers shall be assumed to carry the full load, and proportional for other spacings. Outside stringers shall be placed inside the curb and shall have at least as much strength as the interior stringers. For bridges with concrete floor carried on steel floorbeams without stringers, each floorbeam shall be assumed to carry the full load for spacings of 5 ft. to 10 ft. For spacings of floorbeams less than 5 ft. the fraction of the load carried by one beam shall be equal to the spacing of the floorbeams in feet divided by 5 ft. The wheel load shall be assumed as uniformly distributed along the floorbeam for depths of ballast or paving of 8 in. or less, 9 in. to 17 in., and 18 in. or more, a distance of 9 ft., 10 ft. and 11 ft., respectively.

Ketchum's Specifications for Distribution of Concentrated Loads. From a study of the various tests and specifications, the author has adopted the following rules for calculating the stresses in slabs, stringers and floorbeams:

(a) The distribution of concentrated wheel loads for bending moments in reinforced concrete slabs with longitudinal girders shall be calculated by the formula

with a maximum limit of 6 ft. for e, where e = effective width (distance that the load may be considered as uniformly distributed on a line down the middle of the slab parallel to the supports), span, and c width of tire of wheel, all distances in feet. See Fig. 1.

=

=

(b) The distribution of concentrated wheel loads for bending moments in reinforced concrete slabs with transverse girders shall be calculated by the formula

e = 21/3+ c

with a maximum limit of 6 ft. for e, where e = effective width, wheel as defined in paragraph (a). See Fig. 2.

(38)

=

span, and c = width of tire of

(c) The distribution of concentrated wheel loads for bending moments in slabs of girder bridges in which the span of the bridge is not less than the width of bridge center to center of girders, shall be calculated for spans of 9 ft. or over by the formula

with a maximum limit of e = 12 ft., where e = effective width, and I = span as defined in paragraph (a).

TABLE I.

DISTRIBUTION OF CONCENTRATED LOADS ON SLABS.

Effective Width of Slab for Concentrated Load Distributed on a Line.

Effective width on line along center of beam for moment, and near end of beam for shear. Minimum effective width of shear is 3 ft.

(d) The effective width for shear in beams carrying concentrated loads shall be taken the same as for bending moment as calculated by formula (37) or formula (38), with a minimum effective width of 3 ft. and a maximum effective width of 6 ft.

The total shear for an effective width of 3 ft. shall be considered as punching (pure) shear. The total shear for an effective width of 4.5 ft. and over shall be considered as beam shear (a measure of diagonal tension), for effective widths between 3 ft. and 4.5 ft. the total shear shall be divided proportionally between punching shear and beam shear. Beam shear shall be used in calculating bond stress and as a measure of diagonal tension.

(e) In the design of longitudinal joists or stringers with concrete floors, the fraction of the concentrated load carried by one stringer for spacings 6 ft. or less shall be taken equal to the stringer spacing in feet divided by 6 ft.; with plank floors the fraction of the concentrated load carried by one stringer for spacings 4 ft. or less shall be taken equal to the stringer spacing in feet divided by 4 ft., the maximum in each case being the full load. Outside stringers shall be designed for the same load as intermediate stringers.

(f) In the design of transverse stringers or floorbeams with concrete floors, the fraction of the concentrated load carried by one floorbeam for floorbeams spaced 6 ft. or less, shall be taken equal to the floorbeam spacing divided by 6 ft. For floorbeams spaced 6 ft. or over the entire reactions are assumed as carried by one floorbeam. Axle loads are assumed as distributed on a line 12 ft. long.

The distribution of concentrated loads calculated for different auto trucks for formulas (37) and (38) are given in Table I.

UNIFORM LIVE LOADS FOR TRUSSES.-The uniform live loads for trusses of steel highway bridges as specified by the highway commissions of Illinois, Iowa and Wisconsin, the American Concrete Institute, 1916, and the uniform loads as specified by the author for classes D1 and D2 are given in Table II. The D1 and D2 loadings are to be taken as proportional for intermediate spans, and are to be increased for impact.

It will be seen that the D1 loadings with impact added are practically the same as the Illinois loadings; while the D2 loadings with impact added are practically the same as the Iowa and Wisconsin loadings.

General Specification for Steel Highway Bridges adopted 1918 by the Engineering Institute of Canada specifies uniform live loads for trusses as follows:

Class A, city bridges, 100 lb. per sq. ft. for spans of 100 ft. or less; 80 lb. per sq. ft. for spans of 200 ft. and over, and proportional for spans between 100 ft. and 200 ft. Minimum load per lineal foot, 1,200 lb.

Class B, town and country bridges, 80 lb. per sq. ft. for spans of 100 ft. or less, 60 lb. per sq. ft. for spans of 200 ft. and over, and proportional for spans between 100 ft. and 200 ft. Minimum load per lineal foot, 900 lb.

Class C, remote highway bridges, 70 lb. for spans of 50 ft. or less, 40 lb. for spans of 200 ft. and over, and proportional for spans between 50 ft. and 200 ft. Minimum load per lineal foot, 600 lb. All of above loadings are used without impact.