The analysis should take into consideration the interac tion, where appropriate, of the axial, flexural, and torsional
10.4.2 Empirical methods
10.4.2.1 Limitations-The method described here ap- plies to monolithic concrete deck slabs carrying highway loads (AASHTO-1983). It should not be used where the skew angle exceeds 20 deg (0.35 rad).
For greater skew, the slab design should be based on mod- el tests, a rational analysis based on principles of the theory of plates, or other The reinforcement at the obtuse comers of skew spans should receive special 10.4.2.2 One-way slab-The design of one-way should be based on the analysis of a strip of unit width at right angles to the supports considered as a rectan- gular beam. Bending moment per unit width of slab, due to a standard truck load, should be calculated according to em- pirical formulas given below, unless more exact methods are used. In the following:
M = = E =
live load moment per foot width of slab, in ft-lb (kNm/m)
clear span length of slab, in ft (m)
effective width of slab resisting a wheel or other concentrated load, in ft (m)
= load on one rear wheel of truck, in lbs (N): 12,000 lbs for HS 15 loading (54 kN), 16,000 lbs for HS 20 loading (72 kN)
a. Main reinforcement perpendicular to traffic [spans 2.0 to 24 ft (1.7 to 7.3 m), inclusive]. The live load moment for simple spans should be determined by the following formula
M (lb ft/ft) = (ft) + 2) P(lb)/32 [M (kNm/m) = (m) + 0.61) P (kN)/9.7]
In slabs continuous over three or more supports, 80 per- cent of the previous calculated value should be used for both positive and negative.
b. Main reinforcement parallel to traffic. Longitudinally reinforced slabs should be designed for the appropriate HS truck or lane loading, whichever causes larger de- sign moment. The effective width of slab resisting a wheel load should be estimated to be E (ft) = 4 + 0.06 (ft), [E (m) = 1.22 + 0.06 (m)], but not to exceed 7.0 ft (2.1 m). The effective slab width resisting lane load should be 2E.
For simple spans, the maximum live load moment per ft width of slab, without impact, may be approximated by the following formulas
HS 20 loading:
Spans up to and including 50 ft (15 m): M (lb ft/ft) = 900 (ft); [M (kNm)/m) = 13.1 (m)] Spans 50 to 100 ft (15 to 30 m):
{M(kNm/m) = 14.6 [1.3 e,(m) - 6.1]} HS 15 loading:
Use 75 percent of the values obtained from the formulas for HS 20 loading. Moments in continuous spans should be determined by a suitable analysis using the truck or appropri- ate lane loading.
Edge beams should be provided for all slabs having main reinforcement parallel to traffic. The beam may consist of a slab section additionally reinforced, a beam integral with and deeper than the slab, or an integral reinforced section of slab and curb. The edge beam should be designed to resist a live load moment of 0.10 Penfor simple spans. For continuous spans, 80 percent of the previous calculated value should be used for both positive and negative moments, unless a great- er reduction results from a more exact analysis.
10.4.2.3 Two-way slab-Two-way slabs are supported on all four sides by beams, girders, or walls and are rein- forced in both directions. For rectangular slabs simply sup- ported on all four sides, the proportion of the load carried by
the short span of the slab may be estimated by the following For load uniformly distributed, = +
For load concentrated at center, = + ); where
p = proportion of load carried by short spans = length of short span of slab
= length of long span of slab
Where exceeds one-and-one-half times the entire load should be assumed to be carried by the short span. For a concentrated load, the effective slab width E for the load carried in either direction should be determined in accor- dance with Section 10.3.2(a) and (b).
Moments obtained should be used in designing the center half of the short and long spans. The area of reinforcement in the outer quarters of both short and long spans may be 50 percent of that required in the center. For other supporting conditions at the edges, the formulas for p can be adjusted to account for the restraining effects at the edges. At the ends of the bridge and at intermediate points where the continuity of the slab is broken, the edges should be supported by dia- phragms or other suitable means.
10.4.2.4 Ribbed slabs-A two-way system consisting of a slab with closely spaced ribs of similar size, equally spaced in two directions, may be analyzed by the empirical methods as an equivalent two-way slab. For two-way systems in which the ribs are not equally spaced or are of different size, an elastic analysis may be used in which the system is treated as an equivalent orthotropic plate or a A model analysis may also be used.
10.4.2.5 Cantilever slabs
a. Truck loads. Cantilever slabs may be designed to sup- port truck wheel loads, ignoring the effect of edge sup- port along the end of the cantilever.
1. Main reinforcement perpendicular to traffic. The effective slab width in ft (m), perpendicular to traffic, for each wheel load should be E = 0.8 + 3.75 (0.8 + 1.14), where = distance in ft (m) from load to point of support.
2. Main reinforcement parallel to traffic. The effec- tive slab width, parallel to traffic, for each wheel load should be E = 0.35 + 3.2 (0.35 + 0.98), but not to exceed 7.0 ft (2.1 m).
b. Railing loads. The effective width of slab resisting rail- ing post loadings should be estimated as E = 0.8 + 3.75 (0.8 + 1.14) if no parapet is used, and E = 0.8 + 5.0 (0.8 + 1 if a parapet is used. In the previous expressions, is the distance in ft (m) from the center of the post to the point under investigation.
10.5-Distribution of loads to beams
Analysis based on elastic theory is recommended to find the transverse distribution of the bending moment. For the analysis, the structure may be idealized in one of the follow- ing ways:
a. A system of interconnected beams forming a grid. b. An orthotropic plate.
c. An assemblage of thin plate elements or thin plate ele- ments and beams.
Several methods of analysis are which can be applied with the use of a computer. In addition to the mo- ments in the direction of the span, the computer-aided anal- ysis can give moments in the transverse members. A theoretical analysis is particularly recommended for bridges which have large skew or sharp curvature.
10.5.1 T-beam or precast i-girder and box girder bridg-