AASHTO LRFD Seismic Bridge

Design

Jingsong LiuJuly 20, 2017

History of AASHTO Seismic Specifications

• 1981: ATC-6, Seismic Design Guidelines for Highway Bridges.

• 1983: Guide Specifications for Seismic Design of Highway Bridges, 1st Edition.

• 1991: the guidelines were formally adopted into the Standard Specifications for Highway Bridges, then revised and reformatted as Division I-A.

• 1994: Division I-A became the basis for the seismic provisions included in the AASHTO LRFD Bridge Design Specifications. The latest version is 7th

edition with 2016 Interim.

• 2009: Guide Specifications for LRFD Seismic Bridge Design, 1st Edition. An alternate to the seismic provisions in the AASHTO LRFD Bridge Design Specifications

• 2011: Guide Specifications for LRFD Seismic Bridge Design, 2nd Edition, with 2012, 2014, and 2015 Interim Revisions.

• 2007 (4th Edition LRFD) and earlier: The seismic hazard maps have 10% probability of exceedance in 50 years (which is approximately equivalent to a 15% probability of exceedance in 75 years). This corresponds to a return period of approximately 475 years.

1 − (1 − 𝑃𝑃)50 = 0.10; 𝑃𝑃 = 0.0021 𝑝𝑝𝑝𝑝𝑝𝑝 𝑦𝑦𝑝𝑝𝑦𝑦𝑝𝑝

1/𝑃𝑃 = 475.06 𝑦𝑦𝑝𝑝𝑦𝑦𝑝𝑝

Seismic Hazard Map and Response Spectrum

PGA Seismic Map Before 2008

• 2008 Interims and later: The seismic hazard maps are revised and have 7% probability of exceedance in 75 years. This corresponds to a return period of approximately 1000 years.

• 3-Point Method.o The peak ground acceleration coefficient (PGA) at 0.0

sec and o The short-period spectral acceleration coefficient (SS)

at 0.2 sec o The long-period spectral acceleration coefficients (S1)

at 1.0 sec

The recurrence period from 475 to 1000 year does not double the demand.

PGA Seismic Map Since 2008

Site Effects: Table 3.10.3.1-1—Site Class Definitions

Sites shall be classified by their stiffness as determined by the shear wave velocity in the upper 100 ft.

o Site Class B (soft rock) is taken to be the reference site category for the USGS and NEHRP MCE ground shaking maps.

o Site class B rock is therefore the site condition for which the site factor is 1.0.

o Site classes A, C, D, and E have separate sets of site factors for zero-period (Fpga), the short-period range (Fa) and long-period range (Fv), as indicated in Tables 3.10.3.2-1, 3.10.3.2-2, and 3.10.3.2-3.

𝐴𝐴𝑆𝑆 = 𝐹𝐹𝑝𝑝𝑝𝑝𝑝𝑝 � 𝑃𝑃𝑃𝑃𝐴𝐴

𝑆𝑆𝐷𝐷𝑆𝑆 = 𝐹𝐹𝑝𝑝 � 𝑆𝑆𝑆𝑆

𝑆𝑆𝐷𝐷1 = 𝐹𝐹𝑣𝑣 � 𝑆𝑆1

Seismic Performance Zones

NC 1.0 Sec spectral acceleration coefficients (S1)

Pink Area: SD1>0.15 based on Site Class D.

NCDOT Structure Design Manual, FIGURE 2 – 1

SEISMIC ZONE, LRFD BRIDGE DESIGN SPECIFICATONS

https://earthquake.usgs.gov/designmaps/us/application.php

USGS website provides a tool to calculate the acceleration coefficients per AASHTO seismic hazard maps in US.Site Latitude and LongitudeStreet addressCity, State namesZipcode

For Seismic Performance Zones 2 and higher, Design Response Spectrum needs to be generated.

AASHTO LRFD Load Combinations

AASHTO Earthquake Load Case: Extreme Event I

Use load factors of 1.0 for all permanent loads γEQ is usually 0.0 For ordinary standard bridge, but it can be

other values as high as 0.5 on a project specific basis for operationally important structures.

1. Simple span bridges:

o Seismic analysis is not required for single-span bridges, regardless of seismic zone.

o Connections between the bridge superstructure and the abutments shall be designed for the minimum force requirements as specified in Article 3.10.9.

o Minimum support length requirements shall be satisfied at each abutment as specified in Article 4.7.4.4.

The empirical support length shall be taken as:

𝑁𝑁 = (8 + 0.02 � L + 0.08 � L )(1+ 0.000125 � 𝑆𝑆2 )

2. Seismic Zone 1

o As<0.05, the horizontal design connection force in the restrained directions shall not be less than 0.15 times the vertical reaction due to the tributary permanent load and the tributary live loads assumed to exist during an earthquake.

o For other As, the horizontal design connection force in the restrained directions shall not be less than 0.25 times the vertical reaction due to the tributary permanent load and the tributary live loads assumed to exist during an earthquake.

2016 Interim drops the requirement: The horizontal design connection force shall be addressed from the point of application through the substructure and into the foundation elements.

3. Seismic Zones 2 and up

Analysis for Earthquake Loads (LRFD 4.7.4) for Multispan Bridges

* = no seismic analysis required

UL = uniform load elastic method

SM = single-mode elastic method

MM = multimode elastic method

TH = time history method

Effective Flexural Stiffness of Cracked Reinforced Concrete Sections

Generally two global dynamic analyses should be developed to approximate the nonlinear response of a bridge with expansion joints because it possesses different characteristics in tension and compression (AASHTO Guide Spec 5.1.2): o In the tension model, the superstructure joints are permitted

to move independently of one another in the longitudinal direction. Appropriate elements connecting the joints may be used to model the effects of earthquake restrainers.

o In the compression model, all of the restrainer elements are inactivated and the superstructure elements are locked longitudinally to capture structural response modes where the joints close up, mobilizing the abutments when applicable.

Actual/Ductile Response

1 – Onset of cracking2 – Pseudo-yielding point3 – Maximum plastic deformations4 – Collapse

Maximum displacements of elastic systems and similar period ductile systems are roughly equal.

Idealized Elasto-Plastic Response

Ductility Factor – µ

Strength and Ductility Relationship

Force Based Design

Determination of Modified Design Force

Table 3.10.7.1-1—Response Modification Factors—Substructures

Substructure

Operational Category

Critical Essential Other

Wall-type piers—larger dimension 1.5 1.5 2.0

Reinforced concrete pile bents

Vertical piles only 1.5 2.0 3.0

With batter piles 1.5 1.5 2.0

Single columns 1.5 2.0 3.0

Steel or composite steel and concrete pile bents

Vertical pile only 1.5 3.5 5.0

With batter piles 1.5 2.0 3.0

Multiple column bents 1.5 3.5 5.0

If an inelastic time history method of analysis is used, the response modification factor, R, shall be taken as 1.0 for all substructure and connections.

Combination of Seismic Force Effects

The elastic seismic force effects on each of the principal axes of a component resulting from analyses in the two perpendicular directions shall be combined to form two load cases as follows: o 100 percent of the absolute value of the force effects in one

of the perpendicular directions combined with 30 percent of the absolute value of the force effects in the second perpendicular direction, and

o 100 percent of the absolute value of the force effects in the second perpendicular direction combined with 30 percent of the absolute value of the force effects in the first perpendicular direction.

Capacity Protection Design:

Reaching the elastic capacity (yield) of one member protects adjacent members from excessive force.

Member Strengths• Nominal strength, Sn• Design strength, Sd = φ Sn

• Overstrength, So = φo SnAASHTO LRFD APPENDIX B3—OVERSTRENGTH RESISTANCE

φ: strength reduction factor < 1.0

φo: overstrength factor > 1.0,1.3 for reinforced concrete columns and 1.25 for structural steel columns

𝑀𝑀𝑜𝑜 = 1.3𝑀𝑀𝑛𝑛

𝑉𝑉𝑜𝑜 =∑𝑀𝑀𝑜𝑜∑𝐿𝐿𝑖𝑖

For reinforced concrete columns

1. Seismic Zone 2Except for foundations, seismic design forces for all components, including pile bents and retaining walls, shall be determined by dividing the elastic seismic forces, obtained from Article 3.10.8, by the appropriate response modification factor, R, specified in Table 3.10.7.1-1.

Seismic design forces for foundations, other than pile bents and retaining walls, shall be determined by dividing elastic seismic forces, obtained from Article 3.10.8, by half of the response modification factor, R, from Table 3.10.7.1-1, for the substructure component to which it is attached. The value of R/2 shall not be taken as less than 1.0.

The design forces of each component shall be taken as the lesser of those determined using: • Modified design forces shall be determined as specified in

Article 3.10.9.3, except that for foundations the R-factor shall be taken as 1.0; or

• Inelastic Hinging Forces resulting from plastic hinging at the top and/or bottom of the column

for all components of a column, column bent and its foundation and connections.

2. Seismic Zones 3 and 4

Overstrength Forces for Zones 2, 3 & 4

• For SDCs B and C, ASTM A 706 Grade 60 reinforcing steel shall be used in members where plastic hinging is expected. ASTM A 615 Grade 60 reinforcing steel may be used in members where plastic hinging is expected, with the Owner’s approval.

• For SDC D, ASTM A 706 Grade 60 reinforcing steel shall be used in members where plastic hinging is expected.

• Transverse reinforcement shall be butt-welded hoops. Spiral reinforcement is not allowed in cast-in-place concrete columns and drilled shafts.

• Where ductility is to be assured or where welding is required, steel conforming to the requirements of ASTM A706, “Low Alloy Steel Deformed Bars for Concrete Reinforcement,” should be specified.

A706 versus A615• low-alloy, welding steel• tighter strength limits with yield strength not to

exceed 18 ksi above minimum fy tensile strength must be at least 1.25 of the

actual yield strength• used where greater ductility is required• generally available -- a small premium of compared to

A615 bars

APPENDIX A3—SEISMIC DESIGN FLOWCHARTS

Figure A3-1—Seismic Design Procedure Flow Chart

Figure A3-2—Seismic Detailing and Foundation Design Flow Chart

Displacement Based Method

• In forced based method, elastic demand force is applied with prescribed ductility factors “R” for anticipated Deformation. Ductile response is assumed to be adequate but without verification.

• In displacement based method, displacement demands are compared with displacement capacity. Ductile response is assured for each seismic design category.

Table 3.5-1—Partitions for Seismic Design Categories A, B, C, and D

1. Design Requirements For Seismic Design Category A • The same as AASHTO LRFD

2. Design Requirements For Seismic Design Category B• SDC B structures are designed and detailed to achieve

a displacement ductility, µD, of around 2.• Use formula to perform displacement capacity

verification• Capacity Design Required for column shear & footing

3. Design Requirements For Seismic Design Category C• SDC C structures are designed and detailed to

achieve a displacement ductility, µD, of around 3.• Use formula to perform displacement capacity

verification• Capacity Design Required for column shear &

footing

4. Design Requirements For Seismic Design Category D• SDC D structures are designed and detailed to

achieve a displacement ductility, µD, of at most 6.• The Nonlinear Static Procedure (NSP), commonly

referred to as “pushover” analysis, shall be used to perform displacement capacity verification

• Capacity Design Required for column shear & footing

Capacity Design Principles

𝑀𝑀𝑝𝑝𝑜𝑜 = 𝜆𝜆𝑚𝑚𝑜𝑜𝑀𝑀𝑛𝑛

• For steel members:

where: Mn = nominal moment strength for which expected steelstrengths for steel members are usedλmo = overstrength factor taken as 1.2

• For concrete members:Guide Specs 8.5

𝑀𝑀𝑝𝑝𝑜𝑜 = 𝜆𝜆𝑚𝑚𝑜𝑜𝑀𝑀𝑝𝑝

where:Mne: the expected nominal moment capacity based on the expected concrete and reinforcing steelstrengths when either the concrete strain reaches amagnitude of 0.003 or the reinforcing steel strain reaches the reduced ultimate tensile strain as defined in Table 8.4.2-1.Mp = idealized plastic moment capacity of reinforced concrete member based on expected material properties Mpo = overstrength plastic moment capacity λmo = overstrength magnifier

= 1.2 for ASTM A 706 reinforcement = 1.4 for ASTM A 615 Grade 60 reinforcement

QUESTIONS?