Table Of ContentRevisions
to the
California Amendments to the AASHTO LRFD
Bridge Design Specifications (Fourth Edition)
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 4-2A
4.2 DEFINITIONS:
Add the following definitions:
Central Angle—The angle included between two points along the centerline of a curved bridge measured from the
center of the curve as shown in Figure 4.6.1.2.3-1.
Spine Beam Model—An analytical model of a bridge in which the superstructure is represented by a single beam
element or series of straight, chorded beam elements located along the centerline of the bridge.
November 2011
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 4-17A
4.6.1.1 Plan Aspect Ratio: C4.6.1.1
Revise paragraph 2 as follows: Add the following after paragraph 2:
This The length-to-width restriction specified Asymmetrical sections need to consider the
above does not apply to cast-in-place multicell box relative location of the shear center and center of
girders concrete box girder bridges. gravity.
4.6.1.2 Structures Curved in Plan
4.6.1.2.1 General
Add the following to the end of paragraph 1:
Analysis of sections with no axis of symmetry should
consider the relative locations of the center of gravity
and the shear center. The substructure shall also be
considered in the case of integral abutments, piers, or
bents.
November 2011
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 4-18A
In Article 4.6.1.2.2, revise paragraph 1:
Except for concrete box girder bridges, a A
horizontally curved, torsionally stiff single-girder
superstructure meeting the requirements of Article
4.6.1.1 may be analyzed for global force effects as a
curved spine beam.
Modify Article 4.6.1.2.3 as follows: C4.6.1.2.3
4.6.1.2.3—Multicell Concrete Box Girders Bridges Modify as follows:
Horizontally curved cast-in-place multicell Concrete box girders generally behave as a single-
concrete box girders may be designed as single-spine girder multi-web torsionally stiff superstructure. A
beams with straight segments, for central angles up to parameter study conducted by Song, Chai, and Hida
34 12 degrees within one span, unless concerns about (2003) indicated that the distribution factors from the
other force effects dictate otherwise. LRFD formulae compared well with the distribution
Horizontally curved nonsegmental concrete box factors from grillage analyses when using straight
girder bridge superstructures may be analyzed and segments on spans with central angles up to 34 degrees
designed for global force effects as single-spine beams in one span.
with straight segments, for central angles up to 34 Nutt, Redfield and Valentine (2008) studied the
degrees within one span as shown in Figure 4.6.1.2.3-1, limits of applicability for various methods of analyzing
unless concerns about local force effects dictate horizontally curved concrete box girder bridges. The
otherwise. The location of the centerline of such a beam focus of this study was on local as well as global force
shall be taken at the center of gravity of the cross- effects, and provided the basis for revisions in 2010.
section, and the eccentricity of dead loads shall be They identified three approaches for the analysis of
established by volumetric consideration. Where the concrete box girder bridges as follows:
substructure is integral with the superstructure, the
substructure elements shall be included in the model 1. The first method allows bridges with a central
and allowance made for prestress friction loss due to angle within one span of less than 12 degrees
horizontal curvature or tendon deviation. to be analyzed as if it were straight because
curvature has a minor effect on response. This
is typically done with a plane frame analysis.
2. The second method involves a spine beam
analysis which the superstructure is idealized
as a series of straight beam chorded segments
of limited central angle located along the
bridge centerline. Where the substructure is
integral with the superstructure, a space frame
analysis is required. Whole-width design as
described in Article 4.6.2.2.1 was found to
yield conservative results when space frame
analysis was used. It is acceptable to reduce
the number of live load lanes applied to the
whole-width model to those that can fit on the
bridge when global response such as torsion or
transverse bending is being considered.
3. Bridges with high curvatures or unusual plan
Figure 4.6.1.2.3-1—Definition of Central Angle geometry require a third method of analysis
that utilizes sophisticated three-dimensional
computer models. Unusual plan geometry
includes, but is not limited to bridges with
variable widths, or unconventional orientation
of skewed supports.
November 2011
SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 4-18B
Horizontally curved segmental concrete box girder The range of applicability using approximate methods
superstructures meeting the requirements of Article herein is expected to yield results within 5 percent of
4.6.1.1 and whose central angle within one span is the most detailed type of analysis. Analysis of force
between 12 degrees and 34 degrees may be analyzed as effects in curved tendons is also addressed in Article
a single-spine beam comprised of straight segments 5.10.4.3.
provided no segment has a central angle greater than
3.5 degrees as shown in Figure 4.6.1.2.3-2. For integral
substructures an appropriate three-dimensional model
of the structure shall be used. Redistribution of forces
due to the time-dependant properties of concrete shall
be accounted for.
Figure 4.6.1.2.3-2—Three-Dimensional Spine Model
of Curved Concrete Box Girder Bridge
For both segmental and nonsegmental box girder
bridges with central angles exceeding 34 degrees within
any one span, or for bridges with a maximum central
angle in excess of 12 degrees with unusual plan
geometry, the bridge shall be analyzed using 6 degrees
of freedom in a proven three-dimensional analysis
method.
November 2011
SECTION 5: CONCRETE STRUCTURES
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 5-25A
5.5.4.2.1 Conventional Construction
Insert the following under the first bullet:
For tension-controlled cast-in-place
prestressed concrete sections and spliced
precast girder sections as defined in Article
5.7.2.1………………….…..0.95
Modify the 2nd bullet as follows:
For tension-controlled precast prestressed
concrete section as defined in Article
5.7.2.1………………….…..1.00
November 2011
SECTION 5: CONCRETE STRUCTURES
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 5-26A
C5.5.4.2.1
Delete Fig. C5.5.4.2.1-1 and replace with the following:
Precast Prestressed Members φ = 0.75 + 83.33(ε – 0.002)
t
Cast-In-Place or Spliced Post
0.95 Tensioned Prestressed Members
φ=0.75+66.67(ε −0.002)
t
Non Prestressed Members
φ=0.75+50.00(ε −0.002)
t
Figure C5.5.4.2.1-1 – Variation of φ with net tensile strain ε for Grade 60 reinforcement and for
t
prestresseding members steel.
November 2011
SECTION 5: CONCRETE STRUCTURES
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 5-44A
5.7.3.3.2 Minimum Reinforcement C5.7.3.3.2
Revise as follows: Add the following:
Unless otherwise specified, at any section of a Minimum reinforcement provisions are intended to
noncompression-controlled flexural component, the reduce the probability of brittle failure by providing
amount of prestressed and nonprestressed tensile flexural capacity greater than the cracking moment.
reinforcement shall be adequate to develop a factored Testing of a large number of lightly reinforced and
flexural resistance, M , at least equal to the lesser of: prestressed concrete members at the University of
r
Illinois demonstrated that significant inelastic
• 1.2 times the cracking moment, Mer displacements can be achieved, and none of the beams
determined on the basis of elastic stress
tested failed without large warning deflections
distribution and the modulus of rupture, f r, of (Freyermuth and Alami, 1997). If these experiments
the concrete as specified in Article 5.4.2.6, were conducted in load control, a number of specimens
where Mer may be taken as: would have failed without warning because the ultimate
• 1.33 times the factored moment required by strength (including the effects of strain hardening) was
the applicable strength load combination less than the cracking strength. Based on this
specified in Table 3.4.1-1; and observation, the ultimate strength should be used
instead of the nominal strength as a true measure of
brittle response. γ sufficiently approximates the ratio
3
M = S (f + f )−M Sc −1 ≤S f of the nominal yield strength to ultimate strength for
cr c r cpe dncS c r lightly reinforced concrete members.
nc
The sources of variability in computing the
(5.7.3.3.2-1)
cracking moment and resistance are based on Holombo
and Tadros, 2009. The factor applied to the modulus of
• M =γ(γf +γ f )S −M Sc −1 rupture γis greater than the factor applied to the
cr 3 1 r 2 cpe c dncSnc amount of1 prestress γ to account for greater variability.
2
where:
For precast segmental construction, cracking
generally starts at the segment joints. Research at the
f = modulus of rupture of concrete specified in
r University of California, San Diego, has shown that
Article 5.4.2.6 flexure cracks occur adjacent to the epoxy-bonded
match-cast face, where the accumulation of fines
reduces the tensile strength (Megally et al, 2003). Based
f = compressive stress in concrete due to effective
cpe on this observation, a reduced γfactor of 1.2 is
prestress forces only (after allowance for all 1
justified.
prestress losses) at extreme fiber of section
where tensile stress is caused by externally
applied loads (ksi)
November 2011
SECTION 5: CONCRETE STRUCTURES
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 5-45A
M = total unfactored dead load moment acting on
dnc
the monolithic or noncomposite section
(kip-in.)
S = section modulus for the extreme fiber of the
c
composite section where tensile stress is
caused by externally applied loads (in3.)
S = section modulus for the extreme fiber of the
nc
monolithic or noncomposite section where
tensile stress is caused by externally applied
loads (in3.)
Appropriate values for M and S shall be used
dnc nc
for any intermediate composite sections. Where the
beams are designed for the monolithic or noncomposite
section to resist all loads, substitute S shall be
nc
substituted forS in the above equation for the
c
calculation of M .
cr
• 1.33 times the factored moment required by
the applicable strength load combinations
specified in Table 3.4.1.1.
The following factors shall be used to account for
variability in the flexural cracking strength of concrete,
variability of prestress, and the ratio of nominal yield
strength of reinforcement to ultimate:
γ = flexural cracking variability factor
1
= 1.2 for precast segmental structures
= 1.6 for all other concrete structures
γ = prestress variability factor
2
= 1.1 for bonded tendons
= 1.0 for unbounded tendons
γ = ratio of specified minimum yield strength to
3
ultimate tensile strength of the reinforcement
= 0.67 for A615, Grade 60 reinforcement
= 0.75 for A706, Grade 60 reinforcement
= 1.00 for prestressed concrete structures
The provisions of Article 5.10.8 shall apply.
November 2011
SECTION 5: CONCRETE STRUCTURES
CALIFORNIA AMENDMENTS TO AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS – FOURTH EDITION 5-47A
5.7.3.4 Control of Cracking by Distribution of
Reinforcement
Revise the 3rd Paragraph as follows:
Class 1 exposure condition applies when cracks
can be tolerated due to reduced concerns of appearance
and/or corrosion. Class 2 exposure condition applies to
transverse design of segmental concrete box girders for
any loads applied prior to attaining full nominal
concrete strength and when there is increased concern
of appearance and/or corrosion.
Add a new paragraph after the 3rd Paragraph:
Class 2 exposure condition applies to all bridge
decks. The clear concrete cover to the top
reinforcement shall be taken as 2-1/2 in to determine d
c
for use in Eq.1 when verifying reinforcement spacing in
bridge decks.
November 2011
Description:SECTION 4: STRUCTURAL ANALYSIS AND EVALUATION Central Angle—The angle included between two points along the centerline of a curved bridge measured from concrete box girders may be designed as single-spine.
