Allowable-Stress Design of Bridge with Continuous, Composite Stringers

The structure is a two-lane highway bridge with overall length of 298 ft. Site conditions require a central span of 125 ft. End spans, therefore, are each 86.5 ft (Fig. 12.66a). The typical cross section in Fig. 12.66b shows a 30-ft roadway, flanked on one side by a 21-inwide barrier curb and on the other by a 6-ft-wide sidewalk. The deck is supported by six rolled-beam, continuous stringers of Grade 36 steel. Concrete to be used for the deck is Class A, with 28-day strength f’c = 4,000 psi and allowable compressive stress Æ’c = 1,600 Æ’c psi. Loading is HS20-44. Appropriate design criteria given in Sec. 11 will be used for this structure.
Concrete Slab. The slab is designed to span transversely between stringers..
A 9-in-thick, two-course slab will be used. No provision will be made for a future 2-in wearing course.
Stringer Loads. Assume that the stringers will not be shored during casting of the concrete slab. Then, the dead load on each stringer includes the weight of a strip of concrete slab plus the weights of steel shape, cover plates, and framing details. This dead load will be referred to as DL and is summarized in Table 12.81.

Sidewalks, parapet, and barrier curbs will be placed after the concrete slab has cured.
Their weights may be equally distributed to all stringers. Some designers, however, prefer to calculate the heavier load imposed on outer stringers by the cantilevers by taking moments of the cantilever loads about the edge of curb, as shown in Table 12.82. In addition, the six composite beams must carry the weight, 0.016 ksf, of the 30-ft-wide latex-modified concrete wearing course. The total superimposed dead load will be designated SDL.
The HS20-44 live load imposed may be a truck load or lane load. For these spans, truck loading governs. With stringer spacing S  6.5 ft, the live load taken by outer stringers S1 and S3 is

Stringer Moments. The steel stringers will each consist of a single rolled beam of Grade 36 steel, composite with the concrete slab only in regions of positive moment. To resist negative moments, top and bottom cover plates will be attached in the region of the interior supports. To resist maximum positive moments in the center span, a cover plate will be added to the bottom flange of the composite section. In the end spans, the composite section  with the rolled beam alone must carry the positive moments.
For a precise determination of bending moments and shears, these variations in moments of inertia of the stringer cross sections should be taken into account. But this requires that the cross sections be known in advance or assumed, and the analysis without a computer is tedious. Instead, for a preliminary analysis, to determine the cross sections at critical points the moment of inertia may be assumed constant and the same in each span. This assumption considerably simplifies the analysis and permits use of tables of influence coefficients. (See, for example, Moments, Shears, and Reactions for Continuous Highway Bridges,American Institute of Steel Construction.) The resulting design also often is sufficiently accurate to serve as the final design. In this example, dead-load negative moment at the supports. computed  for constant moment of inertia, will be increased 10% to compensate for the variations in moment of inertia.
Curves of maximum moment (moment envelopes) are plotted in Figs. 12.67 and 12.68 for S1 and S2 , respectively. Because total maximum moments at critical points are nearly equal for S1 , S2 , and S3 , the design selected for S1 will be used for all stringers. (In some cases, there may be some cost savings in using shorter cover plates for the stringers with smaller moments.)
Properties of Negative-Moment Section. The largest bending moment occurs at the interior supports, where the section consists of a rolled beam and top and bottom cover plates. With the dead load at the supports as indicated in Fig. 12.67 increased 10% to compensate for the variable moment of inertia, the moments in stringer S1 at the supports are as follows:

Allowable Compressive Stress near Supports. Because the bottom flange of the beam is in compression near the supports and is unbraced, the allowable compressive stress may have to be reduced to preclude buckling failure. AASHTO specifications, however, permit a 20% increase in the reduced stress for negative moments near interior supports. The unbraced length should be taken as the distance between diaphragms or the distance from interior support to the dead-load inflection point, whichever is smaller. In this example, if distance between diaphragms is assumed not to exceed about 22 ft, the allowable bending stress for a flange width of 16.6 in is computed as follows:

distance from an interior support, the top and bottom cover plates can be terminated where the rolled beam alone has sufficient capacity to carry the bending moment. The actual cutoff points, however, may be determined by allowable fatigue stresses for the base metal adjacent to the fillet welds between flanges and ends of the cover plates. The number of cycles of load to be resisted for HS20-44 loading is 500,000 for a major highway. For Grade 36 steel and these conditions, the allowable fatigue stress range for this redundant-load-path structure

In the center span, the resisting moment of the W36 equals the bending moment about 8 ft 4 in from the interior support. With allowance for the terminal distance, the plates may be cut off 10 ft 6 in from the support. Fatigue does not govern there.
Properties of End-Span Composite Section. The 9-in-thick roadway slab includes an allowance
of 0.5 in for wear. Hence, the effective thickness of the concrete slab for composite
action is 8.5 in.
The effective width of the slab as part of the top flange of the T beam is the smaller of the following:

Hence the effective width is 76.5 in (Fig. 12.69).
To resist maximum positive moments in the end span, the W36 x 280 will be made composite with the concrete slab. As in Art. 12.2, the properties of the end-span composite
section are computed with the concrete slab, ignoring the haunch area, transformed into an equivalent steel area. The computations for neutral-axis locations and section moduli for the
composite section are tabulated in Table 12.83. To locate the neutral axes for n = 24 and n  8 moments are taken about the neutral axis of the rolled beam.
Stresses in End-Span Composite Section. Since the stringers will not be shored when the concrete is cast and cured, the stresses in the steel section for load DL are determined with the section moduli of the steel section alone. Stresses for load SDL are computed with section moduli of the composite section when n = 24. And stresses in the steel for live loads and impact are calculated with section moduli of the composite section when n  8. See Table 12.68. Maximum positive bending moments in the end span are estimated from Fig. 12.67:

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