Fall '91 - Focus on Bridges |
In 1986, the AASHTO Subcommittee on Bridges and Structures took
the first step in replacing the Standard Specifications
for Highway Bridges—an assessment of the document to compare
its contents to non-U.S. design specifications and alternative design
philosophies. Upon completing the assessment in 1987, the subcommittee
judged the Standard Specifications to include “discernible
gaps, inconsistencies, and even some conflicts.” Furthermore,
the current specifications did not embody the load and resistance
factor design (LRFD) philosophy that is considered to be the state
of the art in bridge design.
Subsequent to the assessment, the development of a completely new
code, the LRFD Specifications, was undertaken. This five-year
effort was completed in 1993, and the LRFD Specifications
was adopted by AASHTO as a parallel specification to the Standard
Specifications. At the time, AASHTO voted to consider phasing
out the Standard Specifications. With the majority of states
still designing bridges in accordance with the Standard Specifications,
however, the question became not whether the LRFD Specifications
would replace the Standard Specifications, but how long
it would take to make the transition.
Overview of LRFD for Concrete Structures
To be sure, the LRFD Specifications is a completely new
document. Its overall organization is different, as are its chapter
numbering, content, articles and equation numbers. Nevertheless,
to understand the ramifications of the new specifications from a
preliminary perspective, it is helpful to think in terms of major
changes to the Standard Specifications. In this respect,
the most significant changes are:
- The concept of limit states
- New live load model, distribution factors and impact factors
- New load factors
- A unified approach to concrete design
- A modified compression field theory for shear and torsion design
- A new flexural resistance formulae
- New thermal gradient profile
- Parallel commentary.
Load and Resistance Factor Design
The LRFD Specifications are founded on the concept of probability-based
limit states design, whereby load and material resistance factors
are determined through statistical studies that measure for variability
of these factors and calibrate them accordingly. The basis for this
methodology can be summarized by a simple formula. For the four
limit states defined in the Specifications, each component and connection
of the bridge must satisfy the following equation:
hSgiQi<fRn=Rr
where:
h =
A factor relating to ductility
gi
= Load factor
f =
Resistance factor
Qi = Force effect (i.e., forces, moments, and shears)
Rn = Nominal resistance
Rr = Factored resistance
= fRn
Limit States. A limit state is defined in LRFD
as a condition beyond which the bridge or a component of the bridge
fails to satisfy the provisions for which it was designed.There
are four such limit states:
- Service, which places restrictions on stresses,
deformations, and crack widths under normal service conditions
- Strength, which relates to strength and stability
of the structure
- Fatigue and fracture, which consist of a set
of restrictions on the stress range in a component
- Extreme event, which accounts for unique occurrences
in the life of a bridge, such as a seismic event or a vessel collision.
Each limit state has one or more subcategories, and all limit
states are considered to be of equal importance.
Loads. Loads are classified as either permanent
or transient. Permanent loads include dead load, superimposed dead
load, and earth pressure. Structure dead load is now split into
two categories:
- Dead load of structural components and nonstructural attachments
- Dead load of wearing surfaces and utilities.
The primary reason for creating two categories is to recognize
their difference in variability and be able to adjust the corresponding
load factors accordingly.
The basic LRFD vehicular live load-designated HL-93-consists of
two parts: either a design truck or a design tandem each combined
with a design lane load (Figure 1 on page 18). The design truck
is essentially the same as the axle load portion of an HS20-44 truck,
and the design tandem is the same as a military load with the exception
of the axle weights, which are 111 kN (25 kips) each, rather than
107 kN (24 kips).
The design lane load is a uniform load of 9.34 kN/m (0.64 klf).
The impact factor, or dynamic load allowance as it is now called,
is fixed at 15 percent for the fatigue and fracture limit state
and at 33 percent for all other limit states, but is not applied
to the design lane load. This constitutes a major change in the
live load model for bridge design with potentially significant changes
in design requirements, particularly for long-span prestressed concrete
structures.
Load Factors and Combinations. Another area of
major change has to do with load factors and load combinations.
Because the philosophy and calibration methods of LRFD differ fundamentally
from those of the Standard Specifications, the load and
resistance factors are virtually all different. Load combinations,
too, bear little resemblance to prior combinations.
For example, for the design of prestressed girders of a conventional
beam-slab type bridge, three limit states will have to be checked
typically for flexural design: Service I, Service III and Strength
I:
- Service I. The load factors for limit state
Service I are much as before—all 1.0.
- Service III. This is a special limit state
created specifically for checking tension in the precompressed
tensile zone of a prestressed beam. The load factor for live load
for Service III is 0.8, which reduces the effects of the heavier
HL-93 live load, tending to have a compensating effect.
- Strength I. The load factors of Strength I
are substantially different—1.25 is used for all dead loads
except for wearing surface and utilities, which have a load factor
of 1.50, and live load has a load factor of 1.75.
Figure 1: The HL-93 Vehicular Live Load Model of LRFD Consists
of Two Parts. |
Analysis. In general, LRFD permits the use of
any method of analysis that satisfies the requirements of equilibrium
and compatibility and utilizes stress-strain relationships for the
proposed materials. Several acceptable methods are given in the
specifications. Regarding live load distribution for girder bridges,
empirical equations that are given in specifications can be used
in lieu of a detailed analysis if certain criteria are met. These
distribution factor equations are relatively straightforward to
use, although more complicated than the ones of the Standard
Specifications. If the criteria prescribed for their use are
not met, however, the alternative is a cumbersome, refined (e.g.,
grillage or FEM) analysis, which can be very time-consuming.
Shear Design for Concrete Structures. Two methods
of shear and torsion design have been adopted that are completely
different from the method of the Standard Specifications:
- A sectional model, based on Modified Compression Field Theory
(MCFT)
- The strut-and-tie model, which is a useful and very powerful
tool for designing areas near supports and other disturbed zones.
These new methods provide a simple, unified approach to shear
design that is applicable to both prestressed and nonprestressed
members. These rational methods give physical significance to the
parameters being calculated, unlike the previous empirical method.
The nominal resistance of a given section based on the section model
(MCFT) consists of the same three basic components as before. That
is,
Vn = Vc + Vs + Vp
where,
Vc = Shear resistance provided by the concrete
Vs = Shear resistance provided by shear reinforcement
Vp = Component of prestressing force acting in the
direction of the applied shear.
The major difference with MCFT is in the evaluation of Vc. Previously,
q (theta), the angle of inclination of diagonal compressive stresses,
was assumed to be 45o. Now, q is considered to be variable and must
be determined using a trial-and-error procedure. Overall, the amount
of calculation required to perform the procedure is comparable to
the previous method. Because the steps are entirely different, however,
you get the impression that there is more work involved when, in
fact, there really is not.
Table 1: Comparison of PCI BT72 Bulb Tee Girder Designed
in Accordance with Standard Specifications and in Accordance
with LRFD Specifications. |
Figure 2: Typical Section for Beam-Slab Example. |
Figure 3: Typical Section for Proposed AASHTO-PCI-ASBI Example
. |
How PB is Preparing for LRFD
Making the transition to LRFD is no less difficult a task than,
say, retooling for metric. Many areas of bridge practice are deeply
ensconced in the Standard Specifications. Design software,
training, design aids, standard drawings, etc. are all based largely
on the Standard Specifications. To convert to LRFD, a substantial
effort will be required.
PB has taken a leadership position in making the transition to LRFD
by funding two research and development projects through our Office
of Professional Practice:
- A training program that covers an overview of the LRFD Specifications
with respect to concrete bridge design
- A trial design of a precast segmental box girder bridge in
accordance with LRFD Specifications. This design incorporates
one of the newly-developed standard AASHTO-Precast/Prestressed
Concrete Institute – American Segmental Bridge Institute
(PCI-ASBI) box girder cross sections.
LRFD Training Course. There are outside courses
that are given periodically, but it is not practical to send all
of our engineers to such a course within the time necessary for
preparation. PB’s course was developed to be given internally
to make the educational process more uniform and timely.
The first phase of work is with respect to concrete bridges. Both
the superstructure and the substructure are addressed. The core
of this work is a complete bridge design (discussed below) that
has been designed in accordance with the LRFD Specifications.
Complete hand calculations are provided for each component of the
bridge: the deck, the girders, the substructure cap beam, the columns,
and the foundation. Each of these is presented as a stand-alone
example problem but relates to the bridge as a whole.
Work was completed on this phase in September, 1996. Eventually,
the course will be made available to individual PB offices to begin
company-wide training.
Trial Design. An opportunity arose recently for
our engineers to develop a trial design for one of the proposed
new family of AASHTO-PCI-ASBI box girder sections for precast segmental
bridges in accordance with LRFD Specifications. This opportunity
came as a result of PB’s involvement in the AASHTO-PCI-ASBI
Committee for Development of Standard Precast Segments for Segmental
Bridges. The main goal of the Joint Committee is to develop a set
of standard box sections in accordance with the LRFD Specifications
that would cover spans of up to 61 meters (200 feet). Several design
examples were proposed to test the viability of the proposed family
of sections. One was for a precast segmental bridge to be constructed
using the balanced cantilever method.
The draft-effort of the work has been completed. A summary of the
findings (see below) was presented to the Joint Committee at its
last meeting in Philadelphia on May 11, 1996. The next stage of
work, which will involve publishing the design example in final
form, is expected to be done later this year.
LRFD Glossary
Dynamic Load Allowance: An increase in
the applied static force effects to account for the dynamic
interaction between the bridge and moving vehicles. Essentially
equivalent to the impact factor of the Standard Specifications.
Extreme Event Limit State: Limit states relating
to events with return periods in excess of the design life
of the bridge, such as earthquakes, ice loads, vehicles and
vessel collision.
Fatigue Limit State: Load combination relating
to repetitive gravitational vehicular live load and dynamic
response under a single truck.
HL-93: LRFD vehicular live loading consisting
of a design truck or design tandem combined with a design
lane load.
Limit States: A condition beyond which the
bridge or component ceases to satisfy the provisions for which
it was designed.
Load Factor: A factor accounting for the
variability of loads, the lack of accuracy in analysis, and
the probability of the simultaneous occurrence of different
loads.
Modified Compression Field Theory: A unified
rational method of shear and torsion design, applicable to
both reinforced and prestressed concrete, based on a simplified
variable-angle truss model.
Resistance Factor: A factor accounting for
the variability of material properties, structural dimensions,
and workmanship, and the uncertainty in the prediction of
resistance.
Service Limit States: Limit states relating
to stress, deformation, and cracking.
Strength Limit State: Limit states relating
to strength and stability.
Strut-and-Tie Model: A model used principally
in regions of concentrated forces and geometric discontinuities
to determine concrete proportions and reinforcement quantities
and patterns based on assumed compression struts in the concrete,
tensile ties in the reinforcement, and the geometry of nodes
at their points of intersection. |
LRFD vs. Standard Specifications
Relatively few designs have actually been completed under the LRFD
Specifications. It is difficult, therefore, to generalize about
the impact LRFD will have on the cost of bridges. In the meantime,
one can get a glimpse of the bottom-line effect from the examples
that were developed under the PB-funded research projects.
Case Study: Beam-Slab Bridge. This beam-slab type
example is of a typical three-span grade crossing with a superstructure
that incorporates PCI BT72 bulb tee girders. The spans were all
simple-spans, 36.5 m (105 feet) in length with the girders spaced
at 2.74 m (9 feet) (Figure 2). The 28-day strength of the girder
concrete is 41 MPa (6.0 KSI) and the strength of the deck concrete
is 31 MPa (4.5 KSI). A summary comparison of the girder design using
the LRFD Specifications as compared to the Standard
Specifications is given in Table 1.
Case Study: Concrete Segmental Bridges. The example
bridge, designed in metric and generally in accordance with the
LRFD Specifications, consists of five spans of 52 m, 61
m, 61 m, 61 m and 52 m (150 feet, 200 feet, 200 feet, 200 feet,
and 150 feet). The structure was assumed to be constructed using
the balanced canti-lever method Figure 3). The bridge is supported
on sliding bearings at all piers except for one. The 28-day concrete
strength is 41 MPa (6.0 KSI). Time-dependent effects were evaluated
using the CEB-FIB 1978 Model Code.
For transverse design at the strength limit states, the negative
moments are approximately 35 percent higher when compared to AASHTO
HS20-44 loading, and positive moments are approximately 25 percent
higher. Due to the minimum tendon spacing recommendation, however,
there is no net difference between the amount of transverse post-tensioning
that would be required under one specification as compared to the
other.
With regard to longitudinal design, the negative live load moments
are increased by approximately 30 percent while positive live load
moments are increased by approximately 50 percent when compared
to HS20 live load, accounting for the effects of impact and multiple
presence factors. Live load shears are increased by approximately
40 percent when compared to HS20 live load.
Both service and strength limit states were checked during the longitudinal
design. For the service limit states, net negative moments are approximately
5 percent higher than with HS20 loading, and the positive moments
are approximately 30 percent higher when checking tension in the
precompressed tensile zone (Service III), and 50 percent higher
elsewhere. For the strength limit states, the negative moments are
comparable to HS20 loading, and the positive moments are approximately
15 percent higher. The design shear at the strength limit state
is comparable to that of HS20 loading.
LRFD: Coming Soon to a State Near You?
The results of a survey of state departments of transportation dated
May 1, 1996—to which forty-seven states responded—show
that adoption of LRFD by individual state DOTs has been slow. Only
eight states (17 percent) indicated that they are ready to use LRFD,
although twelve states (26 percent) said that at least one bridge
in their state has been designed using LRFD. Meanwhile, LRFD training
within DOTs over the last twelve months in thirty-seven states (79
percent) is equal to or greater than that given in the previous
year.
One obstacle cited to general adoption of the LRFD Specifications
is the lack of design software. Until the tools are in place to
facilitate design in accordance with LRFD, some feel that “sunsetting”
of the Standard Specifications should be postponed. |
