12.1
SECTION 12
BEAM AND GIRDER BRIDGES
Alfred Hedefine, P.E.
Former President, Parsons Brinckerhoff
Quade & Douglas Inc.,
New York, NY
John Swindlehurst, P.E.
Former Senior Professional Associate,
Parsons Brinckerhoff Quade & Douglas Inc.,
Newark, N.J.
Mahir Sen, P.E.
Professional Associate, Parsons Brinckerhoff-FG, Inc.,
Princeton, N.J.
Steel beam and girder bridges are often the most economical type of framing. Contemporary
capabilities for extending beam construction to longer and longer spans safely and econom-
ically can be traced to the introduction of steel and the availability, in the early part of the
twentieth century, of standardized rolled beams. By the late thirties, after wide-flange shapes
became generally available, highway stringer bridges were erected with simply supported,
wide-flange beams on spans up to about 110 ft. Riveted plate girders were used for highway-
bridge spans up to about 150 ft. In the fifties, girder spans were extended to 300 ft by taking
advantage of welding, continuity, and composite construction. And in the sixties, spans two
and three times as long became economically feasible with the use of high-strength steels
and box girders, or orthotropic-plate construction, or stayed girders. Thus, now, engineers,
as a matter of common practice, design girder bridges for medium and long spans as well
as for short spans.
12.1 CHARACTERISTICS OF BEAM BRIDGES
Rolled wide-flange shapes generally are the most economical type of construction for short-
span bridges. The beams usually are used as stringers, set, at regular intervals, parallel to
the direction of traffic, between piers or abutments (Fig. 12.1). A concrete deck, cast on the
top flange, provides lateral support against buckling. Diaphragms between the beams offer
additional bracing and also distribute loads laterally to the beams before the concrete deck
has cured.
12.2 SECTION TWELVE
FIGURE 12.1 Two-lane highway bridge with rolled-beam stringers. (a) Framing
plan. (b) Typical cross section.
Spacing. For railroad bridges, two stringers generally carry each track. They may, however,
be more widely spaced than the rails, for stability reasons. If a bridge contains only two
stringers, the distance between their centers should be at least 6 ft 6 in. When more stringers
are used, they should be placed to distribute the track load uniformly to all beams.
For highway bridges, one factor to be considered in selection of stringer spacing is the
minimum thickness of concrete deck permitted. For the deck to serve at maximum efficiency,
its span between stringers should be at least that requiring the minimum thickness. But when
stringer spacing requires greater than minimum thickness, the dead load is increased, cutting
into the savings from use of fewer stringers. For example, if the minimum thickness of
concrete slab is about 8 in, the stringer spacing requiring this thickness is about 8 ft for
4,000-psi concrete. Thus, a 29-ft 6-in-wide bridge, with 26-ft roadway, could be carried on
four girders with this spacing. The outer stringers then would be located 1 ft from the curb
into the roadway, and the outer portion of the deck, with parapet, would cantilever 2 ft 9 in
beyond the stringers.
BEAM AND GIRDER BRIDGES 12.3
FIGURE 12.2 Diaphragms for rolled-beam stringers. (a) In-
termediate diaphragm. (b) End diaphragm.
If an outer stringer is placed under the roadway, the distance from the center of the stringer
to the curb preferably should not exceed about 1 ft.
Stringer spacing usually lies in the range 6 to 15 ft. The smaller spacing generally is
desirable near the upper limits of rolled-beam spans.
The larger spacing is economical for the longer spans where deep, fabricated, plate girders
are utilized. Wider spacing of girders has resulted in development of long-span stay-in-place
forms. This improvement in concrete-deck forming has made steel girders with a concrete
deck more competitive.
Regarding deck construction, while conventional cast-in-place concrete decks are com-
monplace, precast-concrete deck slab bridges are often used and may prove practical and
economical if stage construction and maintenance of traffic are required. Additionally, use
of lightweight concrete, a durable and economical product, may be considered if dead weight
is a problem.
Other types of deck are available such as steel orthotropic plates (Arts. 12.14 and 12.15).
Also, steel grating decks may be utilized, whether unfilled, half-filled, or fully filled with
concrete. The latter two deck-grating construction methods make it possible to provide com-
posite action with the steel girder.
Short-Span Stringers. For spans up to about 40 ft, noncomposite construction, where
beams act independently of the concrete slab, and stringers of AASHTO M270 (ASTM
A709), Grade 36 steel often are economical. If a bridge contains more than two such spans
in succession, making the stringers continuous could improve the economy of the structure.
Savings result primarily from reduction in number of bearings and expansion joints, as well
as associated future maintenance costs. A three-span continuous beam, for example, requires
four bearings, whereas three simple spans need six bearings.
For such short spans, with relatively low weight of structural steel, fabrication should be
kept to a minimum. Each fabrication item becomes a relatively large percentage of material
cost. Thus, cover plates should be avoided. Also, diaphragms and their connections to the
stringers should be kept simple. For example. they may be light channels field bolted or
welded to plates welded to the beam webs (Fig. 12.2).
12.4 SECTION TWELVE
For spans 40 ft and less, each beam reaction should be transferred to a bearing plate
through a thin sole plate welded to the beam flange. The bearing may be a flat steel plate
or an elastomeric pad. At interior supports of continuous beams, sole plates should be wider
than the flange. Then, holes needed for anchor bolts can be placed in the parts of the plates
extending beyond the flange. This not only reduces fabrication costs by avoiding holes in
the stringers but also permits use of lighter stringers, because the full cross section is avail-
able for moment resistance.
At each expansion joint, the concrete slab should be thickened to form a transverse beam,
to protect the end of the deck. Continuous reinforcement is required for this beam. For the
purpose, slotted holes should be provided in the ends of the steel beams to permit the
reinforcement to pass through.
Live Loads. Although AASHTO ‘‘Standard Specifications for Highway Bridges’’ specify
for design H15-44, HS15-44, H20-44, and HS20-44 truck and lane loadings (Art. 11.4),
many state departments of transportation are utilizing larger live loadings. The most common
is HS20-44 plus 25% (HS25). An alternative military loading of two axles 4 ft apart, each
axle weighing 24 kips, is usually also required and should be used if it causes higher stresses.
Some states prefer 30 kip axles instead of 24 kips.
Dead Loads. Superstructure design for bridges with a one-course deck slab should in-
clude a 25-psf additional dead load to provide for a future 2-in-thick overlay wearing surface.
Bridges with a two-course deck slab generally do not include this additional dead load. The
assumption is that during repaving of the adjoining roadway, the 1
1
⁄
4
-in wearing course
(possibly latex modified concrete) will be removed and replaced only if necessary.
If metal stay-in-place forms are permitted for deck construction, consideration should be
given to providing for an additional 8 to 12 psf to be included for the weight of the permanent
steel form plus approximately 5 psf for the additional thickness of deck concrete required.
The specific additional dead load should be determined for the form to be utilized. The
additional dead load is considered secondary and may be included in the superimposed dead
load supported by composite construction, when shoring is used.
Long-Span Stringers. Composite construction with rolled beams (Art. 11.16) may become
economical when simple spans exceed about 40 ft, or the end span of a continuous stringer
exceeds 50 ft, or the interior span of a continuous stringer exceeds 65 ft. W36 rolled wide-
flange beams of Grade 36 steel designed for composite action with the concrete slab are
economical for spans up to about 85 ft, though such beams can be used for longer spans.
When spans exceed 85 ft, consideration should be given to rolled beams made of high-
strength steels, W40 rolled wide-flange beams, or to plate-girder stringers. In addition to
greater economy than with noncomposite construction, composite construction offers smaller
deflections or permits use of shallower stringers, and the safety factor is larger.
For long-span, simply supported, composite, rolled beams, costs often can be cut by using
a smaller rolled section than required for maximum moment and welding a cover plate to
the bottom flange in the region of maximum moment (partial-length cover plate). For the
purpose, one plate of constant width and thickness should be used. It also is desirable to use
cover plates on continuous beams. The cover plate thickness should generally be limited to
about 1 in and be either 2 in narrower or 2 in maximum wider than the flange. Longitudinal
fillet welds attach the plate to the flange. Cover plates may be terminated and end-welded
within the span at a developed length beyond the theoretical cutoff point. American Asso-
ciation of State Highway and Transportation Officials (AASHTO) specifications provide for
a Category E
⬘ allowable fatigue-stress range that must be utilized in the design of girders at
this point.
Problems with fatigue cracking of the end weld and flange plate of older girders has
caused designers to avoid terminating the cover plate within the span. Some state departments
of transportation specify that cover plates be full length or terminated within 2 ft of the end
bearings. The end attachments may be either special end welds or bolted connections.
BEAM AND GIRDER BRIDGES 12.5
Similarly, for continuous, noncomposite, rolled beams, costs often can be cut by welding
cover plates to flanges in the regions of negative moment. Savings, however, usually will
not be achieved by addition of a cover plate to the bottom flange in positive-moment areas.
For composite construction, though, partial-length cover plates in both negative-moment and
positive-moment regions can save money. In this case, the bottom cover plate is effective
because the tensile forces applied to it are balanced by compressive forces acting on the
concrete slab serving as a top cover plate.
For continuous stringers, composite construction can be used throughout or only in
positive-moment areas. Costs of either procedure are likely to be nearly equal.
Design of composite stringers usually is based on the assumption that the forms for the
concrete deck are supported on the stringers. Thus, these beams have to carry the weight of
the uncured concrete. Alternatively, they can be shored, so that the concrete weight is trans-
mitted directly to the ground. The shores are removed after the concrete has attained suffi-
cient strength to participate in composite action. In that case, the full dead load may be
assumed applied to the composite section. Hence, a slightly smaller section can be used for
the stringers than with unshored erection. The savings in steel, however, may be more than
offset by the additional cost of shoring, especially when provision has to be made for traffic
below the span.
Diaphragms for long-span rolled beams, as for short-span, should be of minimum per-
mitted size. Also, connections should be kept simple (Fig. 12.2). At span ends, diaphragms
should be capable of supporting the concrete edge beam provided to protect the end of the
concrete slab. Consideration should also be given to designing the end diaphragms for jacking
forces for future bearing replacements.
For simply supported, long-span stringers, one end usually is fixed, whereas arrangements
are made for expansion at the other end. Bearings may be built up of steel or they may be
elastomeric pads. A single-thickness pad may be adequate for spans under 85 ft. For longer
spans, laminated pads will be needed. Expansion joints in the deck may be made econom-
ically with extruded or preformed plastics.
Cambering of rolled-beam stringers is expensive. It often can be avoided by use of dif-
ferent slab-haunch depths over the beams.
12.2 EXAMPLE-ALLOWABLE-STRESS DESIGN OF COMPOSITE,
ROLLED-BEAM STRINGER BRIDGE
To illustrate the design procedure, a two-lane highway bridge with simply supported, com-
posite, rolled-beam stringers will be designed. As indicated in the framing plan in Fig. 12.1a,
the stringers span 74 ft center to center (c to c) of bearings. The typical cross section in Fig.
12.1b shows a 26-ft-wide roadway flanked by 1-ft 9-in parapets. Structural steel to be used
is Grade 36. Loading is HS25. Appropriate design criteria given in Sec. 11 will be used for
this structure. Concrete to be used for the deck is Class A, with 28-day compressive strength
⫽ 4,000 psi and allowable compressive strength ƒ
c
⫽ 1,400 psi. Modulus of elasticityƒ⬘
c
E
c
⫽ 33w
1.5
⫽ 33(145) ⫽ 3,644,000 psi, say 3,600,000 psi.
1.5
兹ƒ⬘ 兹4,000
c
Assume that the deck will be supported on four rolled-beam stringers, spaced 8 ft c to c,
as shown in Fig. 12.1.
Concrete Slab. The slab is designed to span transversely between stringers, as in noncom-
posite design. The effective span S is the distance between flange edges plus half the flange
width, ft. In this case, if the flange width is assumed as 1 ft, S
⫽ 8 ⫺1 ⫹
1
⁄
2
⫽ 7.5 ft. For
computation of dead load, assume a 9-in-thick slab, weight 112 lb/ft
2
plus 5 lb/ft
2
for the
additional thickness of deck concrete in the stay-in-place forms. The 9-in-thick slab consists
