STRC15 Lateral Forces Bridges Seismic Considerations 0715

Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations) Structural Engineering Review Course

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Lesson Overview •

Development of Elastic Response  Spectra

•

AASHTO Analysis Methods

•

Basics of Structural Dynamics

•

Technologies in Bridge Response and  Engineering

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Learning Objectives You will learn •

how to determine the individual  variables for developing the design  response spectra

•

how to determine the period of  vibration for a structure from  fundamental dynamics

•

how to determine the seismic  coefficient for bridges according to  AASHTO 

•

the use and influence of isolators and  damping devices

•

how to explain basic terminology  related to the computer modeling of  bridges

•

how to determine seismic loads using  the AASHTO uniform load analysis  method and single mode elastic  analysis method

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Prerequisite Knowledge You should already be familiar with •

mechanics of dynamics

•

definitions of degrees of freedom

•

terminology of seismic loading

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Referenced Codes and Standards •

AASHTO LRFD Bridge Design Specifications (AASHTO, 2012)

•

International Building Code (IBC, 2012)

•

Minimum Design Loads for Buildings and Other Structures (ASCE/SEI7 2010)

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Bridge Behavior longitudinal direction parallel to direction of traffic; usually the  long dimension transverse direction perpendicular to direction of traffic bridge characteristics •

strong heavy superstructure (deck)

•

abutments for end support

•

flexible column(s) STRC ©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Bridge Behavior longitudinal movement •

Bearings at abutments and gap allow  bridge superstructure to move with  little resistance at abutment.

•

Entire resistance needs to be  provided by column(s).

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Bridge Behavior transverse movement •

Bearings at abutments prevent bridge  superstructure from moving at  abutment.

•

Flexible column(s) assist in resistance  to movement.

•

Sometimes the superstructure is  assumed to be rigid.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Bridge Design AASHTO design procedure 1. Identify seismic environment. 2. Prepare site response spectra. 3. Determine period of vibration of  structure. 4. Determine site response value for  associated period of vibration.

5. Adjust site response value for ductility  and expected performance of  structure. 6. Apply risk and damage mitigation  requirements based upon level of  seismic risk.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Bridge Design analysis methods •

methods with single degree of  freedom (manual calculation)

•

See AASHTO Sec. 4.7.4.3.1 and  Table 8.8.

• uniform load elastic

Table 8.8  Analysis Procedures

• single‐mode elastic •

methods with multiple degrees of  freedom (require computer for  calculation) • multimode elastic • time history STRC ©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Acceleration Estimate acceleration coefficients • PGA, S1, S2 • defined in AASHTO Sec. 3.10.4.2 • estimate of the site‐dependent design  ground acceleration expressed as a  percentage of the gravity constant, g • correspond to ground acceleration  values with a recurrence interval of  1000 yr (gives a 7% probability of being  exceeded in a 75 yr period)

nomenclature PGA peak seismic ground acceleration  coefficient on rock (site class B)  from AASHTO Sec. 3.10.2.1 S1

horizontal response spectral  acceleration coefficient at 1.0 sec  modified by long‐period site  factor from AASHTO Sec. 3.10.4.2

SS

horizontal response spectral  acceleration coefficient at 0.2 sec  period on rock (site class B) from  AASHTO Sec. 3.10.2.1

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Acceleration Estimate •

based upon geographic location  (latitude/longitude)

•

maps developed by United States  Geographic Service (USGS)

•

acceleration value expected in future  earthquake • based upon past seismic events • nationwide maps and local maps  for high seismic regions

•

Each map provides a different value  defined in AASHTO Sec. 3.10.4.2. • PGA: peak ground acceleration   (PGA) coefficient  on rock (site  class B)  • SS: horizontal response spectral  acceleration coefficient at 0.2 sec  period on rock (site class B) • S1: horizontal response spectral  acceleration coefficient at 1.0 sec  on rock (site class B)

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Seismic Coefficients Example 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Seismic Coefficients

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Importance Factor •

Some structures are more critical to  the transportation network.

•

requires critical structures to be  designed for higher seismic loads  than nonessential structures 

•

AASHTO Sec. 3.10.5 assigns a  structure use to an importance  category. • critical bridges: must remain  functional immediately after a  2500 yr return period earthquake • essential bridges: must remain  functional immediately after the  design earthquake • other: nonessential bridges

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Importance Factor Example 8.32

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Importance Factor

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Class •

soil profile: vertical distribution of soil  from surface to bedrock

•

six soil profile types identified in  AASHTO Table 3.10.3.1‐1 and  Table 8.9

•

USGS maps based on assumed soil  profile above bedrock

•

site class adjusts USGS bedrock  acceleration to account for good or  bad soil conditions

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Class each site class given an alphabetic symbol •

A = hard rock, good soil conditions

•

F = peat, organic material, extremely  poor soil conditions

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Table 8.9 Site Classes

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Site Class Example 8.33

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Site Class

Table 8.9 Site Classes

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Factors •

amplification factors applied to ground accelerations (function of the site class)

•

USGS maps based on site class B (rock soil profile), which has a site factor  of 1.0

•

Site factors adjust map readings to other site class profiles.

•

value determined from tables, using site class and acceleration coefficients

•

three site factors listed in Table 8.10

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Site Factors Table 8.10 Site Factors (Fpga corresponding to Ss; Fv corresponding to S1)

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Site Factors Example 8.34

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Site Factors

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Site Factors Table 8.10 Site Factors (Fpga corresponding to Ss; Fv corresponding to S1)

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Adjusted Response Parameters •

design values determined from the  site factor and the acceleration  coefficients

•

ground motion parameters modified  by the site factors to allow for site  class effects (AASHTO Sec. 3.10.4.2)

•

adjusted response parameters are

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Adjusted Response Factors Example 8.35

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Adjusted Response Factors

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Design Response Spectra design response spectra seismic coefficient as a function of structure period seismic coefficient seismic design force/structure weight period of vibration is best predictor of response of structure to dynamic effects of earthquake elastic spectra used when loading expected to be less than failure strength of structure STRC ©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Design Response Spectra nomenclature peak seismic ground acceleration  AS coefficient modified by zero period  site factor from AASHTO 3.10.4.2 Csm seismic response coefficient specified  in AASHTO Sec. 3.10.4.2 SD1 horizontal response spectral  acceleration coefficient at 1.0 sec  modified by long‐period site factor  from AASHTO Sec. 3.10.4.2 SDS horizontal response spectral  acceleration coefficient at 0.2 sec  period modified by short‐period site  factor from AASHTO Sec. 3.10.4.2

T0

Tm TS

reference period used to define  shape of acceleration response  spectrum from AASHTO Sec. 3.10.4.2 fundamental period of vibration,  defined in AASHTO Sec. C4.7.4.3.2b corner period at which acceleration  response spectrum changes from  being independent of period to being  inversely proportional to period from  AASHTO Sec. 3.10.4.2

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

How to Construct Design Response Spectra •

given by AASHTO Fig. 3.10.4.1‐1 and  shown in Fig. 8.12

•

seismic coefficient functions  determined from adjusted response  parameters

•

critical points on period domain

Figure 8.12 Design Response Spectrum

• reference periods, T0 and TS • function changes at these periods

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

How to Use Design Response Spectra procedure

Figure 8.12 Design Response Spectrum

1. Determine Tm, the period of vibration  of the structure. 2. Read seismic coefficient from graph.

Csm

3. For multiple‐degree‐of‐freedom  systems, repeat for each mode shape.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Reference Periods Example 8.36

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Reference Periods

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Performance Zone •

based upon value of SD1

•

defined in AASHTO Sec. 3.10.6

•

divides structures according to the  likelihood of large seismic events

•

allows AASHTO to write specification  for higher levels of engineering,  construction, and inspection for  projects where seismic events may be  large

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Seismic Performance Zone •

categories (shown in Table 8.12)  determine necessary requirements  for design procedure, minimum  support lengths, substructure design  details

•

zone 1: very little earthquake activity  (Midwest)

•

zone 4: high levels of seismic activity  (California coast)

Table 8.12 Seismic Performance Zones

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Seismic Performance Zone Example 8.37

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Seismic Performance Zone Table 8.12 Seismic Performance Zones

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Regular and Irregular Bridges regular structures 

irregular bridges

•

less shaking during earthquakes

• everything else

•

uniform mass, uniform stiffness, short  overall length

• expected to have more higher mode  effect during vibration

regular bridges • fewer than seven spans • no abrupt change in weight, stiffness,  or geometry

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Selection of Analysis Procedure •

•

depends on seismic zone, importance  category, and regularity in accordance  with AASHTO Sec. 4.7.4.3 MM and TH acceptable, but  considered excessive when SM or UL  can be used Table 8.13 Selection of Analysis Procedure  for Multispan Bridges

•

seismic analysis not required for  bridges in seismic zone 1 • must still account for a seismic  force of either 15% or 25% of  the DL • values of 15% or 25% determined  based on the acceleration  coefficient, As

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Analysis Methods–MM and TH •

MM: multimode elastic method

•

TH: time history method

• response spectra for MM

•

require sophisticated structural  analysis software

• ground acceleration record for TH

•

require structural input 

•

require seismic input

• cross‐sectional properties • material properties (E) • element and nodal geometry • distribution of mass STRC ©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Uniform Load Elastic Method–UL •

suitable for regular bridges that respond principally in their fundamental mode

•

defined in AASHTO Sec. 4.7.4.3.2c

•

may be used for transverse or longitudinal earthquake motions

•

assumes bridge is a single‐degree‐of‐freedom structure

•

Assume abutment is pin support.

•

Structural model includes flexibility of superstructure and columns.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Uniform Load Elastic Method–UL procedure 1. Determine maximum lateral deflection,  vs,max due to uniform load along length  of bridge, po.

Figure 8.13 Transverse Displacement Due  to Unit Transverse Load

2. Determine bridge transverse stiffness. 3. Determine total weight of bridge. 4. Determine period of vibration.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Uniform Load Elastic Method–UL procedure (continued) 5.   Determine governing elastic seismic  response coefficient, Csm, from design  spectra based upon structure period  (AASHTO Sec. 3.10.4.2).

Figure 8.14 Equivalent Static Seismic Load  Applied to Bridge

6. The design force, pe, or uniform  equivalent static seismic load, is

7.   Apply pe to bridge as shown in  Fig. 8.14 and determine member  forces due to the seismic load. STRC ©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Uniform Analysis Method Example 8.39

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Uniform Analysis Method

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Uniform Analysis Method

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Uniform Analysis Method

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Uniform Analysis Method

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Single‐Mode Elastic Method–SM •

static analysis procedure

•

fundamental period and equivalent static force obtained from AASHTO  Sec. 4.7.4.3.2b

•

may be used for transverse or longitudinal earthquake motions 

•

assumes bridge is a single‐degree‐of‐freedom structure

•

assumes abutment is pin support for transverse, and roller for longitudinal

•

Structural model includes flexibility of superstructure and columns.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Single‐Mode Elastic Method–SM procedure 1. Calculate maximum lateral deflection,  vs(x) due to uniform unit load, po

Figure 8.15 Longitudinal Displacement Due  to Unit Longitudinal Load

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Single‐Mode Elastic Method–SM 2.   Integrate distribution of elastic  deflection terms (factors ߙ, ߚ, and ߛ).

•

Determine deflections at 1/10 points  along length of bridge for uniform  load

•

Draw deflected shape.

•

Determine integral (area under  deflection curve.

•

Continue process as outlined.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Single‐Mode Elastic Method–SM 3. Determine fundamental period of  vibration, Tm. Table 8.11 Elastic Seismic Response Coefficient Equations

4. Use governing elastic seismic  coefficient , Csm, to determine elastic  force in a member. (See AASHTO  Sec. 3.10.4.2 and Table 8.11).

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Single‐Mode Elastic Method–SM 5. The design force will be more  complex. Determine equivalent  seismic load.

Figure 8.16 Equivalent Static Seimic Load Applied to Bridge

6. Apply pe(x) to bridge as shown in  Fig. 8.16 and determine member  forces due to the seismic load.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Single‐Mode Elastic Method Example 8.40

Problem Statement for Ex. 8.31

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Single‐Mode Elastic Method

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Single‐Mode Elastic Method

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Single‐Mode Elastic Method

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Single‐Mode Elastic Method

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Structural Dynamics •

Some exam problems may require  engineers to calculate dynamic  characteristics.

•

for single‐degree‐of‐freedom system  (one mass vibrating in one direction)

•

period of vibration determined from  mass and stiffness of structure Tm  2

W gK

AASHTO Eq. C4.7.4.3.2C‐3

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Structural Dynamics •

Columns, bearings, and so forth have component stiffness.

•

For multiple springs, reduce to a single equivalent spring stiffness.

•

springs in parallel K e  K1  K 2

•

springs in series Ke 

K1 K 2 K1  K 2

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Structural Dynamics •

•

•

multiple‐degree‐of‐freedom systems:  more than one mass or one mass  vibrating in more than one direction Each degree of freedom will generate  one equation relating a mass to  multiple stiffness terms. usually solved though modal  decomposition: one period of  vibration and one mode for each  degree of freedom

•

mode: pattern of displacement of  masses 

•

fundamental mode: mode with  longest period of vibration

•

Fundamental mode corresponds to  fundamental period and usually  dominates the vibration of the  structure.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Structural Dynamics multiple‐degree‐of‐freedom systems •

more than one mass or one mass vibrating in more than one direction

•

Each degree of freedom generates one equation relating a mass to multiple stiffness  terms.

•

usually solved though modal decomposition (one period of vibration and one mode  for each degree of freedom)

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Structural Dynamics mode pattern of displacement of masses  fundamental mode •

mode with longest period of vibration

•

corresponds to fundamental period

•

usually dominates the vibration of the structure

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Poll: Design Response Spectra For typical design spectra, which of the  following is FALSE? (A) The seismic design load for each mode  of a multiple‐degree‐of‐freedom system  will not be equal. (B) Two modes of a structure cannot have  the same design coefficient. (C) For higher numbered modes of the  structure, the elastic seismic coefficient  will usually get larger. (D) It is conservative to use a seismic  coefficient of SDS for all modes of a  structure. STRC ©2015 Professional Publications, Inc.

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Bridges (Seismic Considerations)

Poll: Design Response Spectra For typical design spectra, which of the  following is FALSE? (A) The seismic design load for each mode  of a multiple‐degree‐of‐freedom system  will not be equal. (B) Two modes of a structure cannot have  the same design coefficient. (C) For higher numbered modes of the  structure, the elastic seismic coefficient  will usually get larger. (D) It is conservative to use a seismic  coefficient of SDS for all modes of a  structure.

Solution If two modes have corresponding periods  between T0 and TS, they will have the same  coefficient. The answer is (B).

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Bridges (Seismic Considerations)

Example: Structural Dynamics For the single‐degree‐of‐freedom system  shown, determine the period of  vibration. criteria •

all material: E = 29,000 ksi

•

post – A = 20 in2, I = 2000 in4,  L = 15 ft

•

truss – A = 4 in2, I = 400 in4, L = 10 ft

•

weight = 2000 kips STRC ©2015 Professional Publications, Inc.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Structural Dynamics Solution Determine the stiffness of a single post. For a cantilever, PL3  3EI

So, K post 

P 3EI  3   L

 3  29, 000

kips   2000 in 4  2  in   3  in     15 ft  12 ft     

 29.84 kips in STRC ©2015 Professional Publications, Inc.

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Bridges (Seismic Considerations)

Example: Structural Dynamics Determine the stiffness of the truss. For a truss, 

PL EA

Therefore, kips   29, 000 4 in 2    2  P EA  in  K tr    in L  10 ft  12  ft    966.67 kips in STRC ©2015 Professional Publications, Inc.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Structural Dynamics Combine the right post and truss into a  single spring. kips    29.84    966.67 K post K tr in  Kr   kips K post  K tr  966.67 29.84 in  28.95 kips in

kips   in  kips in

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Structural Dynamics Combine the left post, which is in parallel  with the right end. K e  K post  K r  29.84  58.79

kips kips  28.95 in in

kips in

Determine the period of vibration. W 2000 kips  2 in   kips  gK  58.79  386    sec 2   in    1.9 sec

T  2

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Response Modification Factor •

The analysis output is an expected  load if the structure remains elastic,  which is not expected in a major  earthquake.

•

Based on expected ductility, the load  can be divided by the response  modification factor.

•

Structural systems and response  modification factors listed in AASHTO  Tables 3.10.7.1‐1 and 3.10.7.1‐2.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Response Modification Factor •

Use the reductions listed in Table 8.14  and Table 8.15.

•

Reduction happens at the element  level.

•

Different portions of the same  structure will have different  reductions.

•

Table 8.14 Response Modification Factors  for Substructures

Table 8.15 Response Modification Factors  for Connections

Superstructure to abutment is an  amplifier, not a reduction.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Response Modification Factor Example 8.41

Problem Statement for Ex. 8.31

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Response Modification Factor

Table 8.14 Response Modification Factors  for Substructures

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Orthogonal Effects AASHTO Sec. 3.10.8 requires combination  of orthogonal seismic forces to account  for the •

•

directional uncertainty of earthquake  motions (i.e., earthquake loading may  come from any direction)

•

Two load combinations are specified.  Choose maximum value of • 100% of longitudinal result plus  30% of transverse result • 100% of transverse result plus  30% of longitudinal result

simultaneous occurrence of  earthquake forces in two  perpendicular horizontal directions

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Orthogonal Effects Example 8.42

Problem Statement for Ex. 8.31

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Orthogonal Effects

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Technologies for Improved Seismic Performance •

Technologies developed since the 1980s have become standard in the design of  bridges and the retrofit of older bridges in some parts of the U.S.

•

isolation systems • rubber isolators • friction pendulum isolators

•

increased damping systems • viscous oil dampers • hysteretic yielding dampers

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Technologies for Improved Seismic Performance passive system •

device responds to motion of ground or structure

•

most systems in use are passive

active systems •

sensors detect movement or acceleration and adjust the structure stiffness or  system to decrease expected response

•

show much superior response but require maintenance and continuous monitoring

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Technologies for Improved Seismic Performance advanced engineering usually required to  design and optimize these systems •

nonlinear structural analysis (stress  not a linear relationship with strain)

•

soil‐foundation‐structure interaction 

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Isolation Bearings •

mechanical assembly to insert concentrated location of flexibility in structural system

•

disconnects the rigidity of the structure from the ground/foundation (large  movement of ground does not immediately shake structure)

•

equivalent stiffness of system = combination of structure stiffness and isolator  stiffness • Springs in series results in stiffness that is less than the stiffness of either  component. • Multiple isolators under abutments or columns are springs in parallel (sum  stiffness of individual components)

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Rubber/Steel Plate Bearings •

cylindrical rubber bearing installed in  column

•

horizontal steel plates to resist lateral  expansion due to vertical loads

•

Top and bottom plates connect to  column and/or foundation.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Rubber/Steel Plate Bearings SEIS Fig. 14.1 Base Isolation  (Foothill Center, San Bernadino County, California)

SEIS Fig. 14.2 One Type of Isolation Bearing

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Friction Pendulum Bearings •

Curved surface creates pendulum  action. • Horizontal movement of building  causes vertical motion due to  curve.

•

Friction dissipates energy during  movement.

•

Curved surface returns building to  original position after earthquake.

• Building kinetic energy is  absorbed by necessity to  overcome potential energy from  gravity load. •

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Bridges (Seismic Considerations)

Mechanical Damping •

addition of device to increase the  dissipation of kinetic energy of  structure

•

damper resists horizontal  movement

•

viscous damping = fluid movement 

•

energy loss related to velocity

floor framing above

shear wall below

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Mechanical Damping •

addition of device to increase the  dissipation of kinetic energy of  structure

•

tapered steel unit to yield when  pushed horizontally

•

hysteretic damping = yielding of steel

•

energy loss related to displacement

Wall above

Wall below STRC ©2015 Professional Publications, Inc.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Nonlinear Structural Analysis •

structural model represents yielding of material (hysteretic dissipation of energy)

•

requires input for the strength of elements

•

may include only a few nonlinear elements, such as for isolators

•

does not allow for superposition (cannot analyze loads independently and then  combine results)

•

usually done by step‐by‐step integration process (predicts next step by extrapolating  from the last calculated value)

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Bridges (Seismic Considerations)

Nonlinear Structural Analysis static analysis = pushover analysis •

represents the lateral collapse of a  structure

•

shows sequence of hinge formation  and plastic collapse mechanism

dynamic analysis = time history analysis •

expected to make best representation  of how structure will respond during  an earthquake

•

requires engineer to input expected  ground motion record 

•

shows progressive levels of damage  to structure

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Poll: Analysis Methods An engineer is working on a single‐ degree‐of‐freedom bridge structure.  Which of the AASHTO analysis methods  will help the engineer determine how  many times the bridge will deflect more  than 1.0 in during an earthquake? (A) uniform load elastic (UL) (B) single‐mode elastic (SM) (C) multimode elastic (MM) (D) time history (TH)

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Poll: Analysis Methods An engineer is working on a single‐ degree‐of‐freedom bridge structure.  Which of the AASHTO analysis methods  will help the engineer determine how  many times the bridge will deflect more  than 1.0 in during an earthquake?

Solution

(A) uniform load elastic (UL)

The output from TH analysis is a graph of  the expected displacement vs. the  duration of the shaking. From this graph,  the engineer can determine the number  of times a certain displacement threshold  is exceeded.

(B) single‐mode elastic (SM)

The answer is (D).

(C) multimode elastic (MM) (D) time history (TH)

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Bridges (Seismic Considerations)

Soil‐Foundation‐Structure Interaction •

computationally complex models that  allow flexibility of soils to be  considered

•

output shows development of  bending and hinges in piles and  foundation

•

replaces conventional assumption  that foundation is either perfect pin  or absolute rigid

•

often results in lower superstructure  accelerations but increased lateral  displacements

•

common method is to represent  layers of soil as horizontal nonlinear  springs

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Bridges (Seismic Considerations)

Soil‐Foundation‐Structure Interaction •

requires substantial • geotechnical information • engineering time  • computational power

•

can show influence of soil mass being  accelerated with piles or basements

•

can show resonance of soil vibration  with structure vibration

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Minimum Seat‐Width Requirements •

•

•

common detail has one portion of  bridge sitting on seated connection  for gravity support Displacement of superstructure  during earthquake must not exceed  seated connections.

nomenclature H average height of columns ft L length of bridge between  ft expansion joints in N length of seat S angle of skew of bridge

degrees

AASHTO Sec. 4.7.4.4 requires  minimum support lengths at  expansion ends of all girders.

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Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Minimum Seat‐Width Requirements For seismic zone 1, with As ൒ 0.05,  minimum support length, N, in inches, is Figure 8.17 Minimum Seat‐Width Requirements

For seismic zone 1, with As ൏ 0.05,

From AASHTO Sec. 4.7.4.4, for seismic  zones 2, 3, and 4, the minimum support  length is

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Minimum Seat Size Example 8.43

Problem Statement for Ex. 8.31

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Example: Minimum Seat Size

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Bridges (Seismic Considerations)

Learning Objectives You have learned •

how to determine the individual  variables for developing the design  response spectra

•

how to determine the seismic  coefficient for bridges according to  AASHTO 

•

how to determine seismic loads using  the AASHTO uniform load analysis  method and single mode elastic  analysis method

•

how to determine seismic loads using  the AASHTO how to determine the  period of vibration for a structure  from fundamental dynamics

•

the use and influence of isolators and  damping devices

•

how to explain basic terminology  related to the computer modeling of  bridges

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©2015 Professional Publications, Inc.

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Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations)

Lesson Overview •

Development of Elastic Response  Spectra

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AASHTO Analysis Methods

•

Basics of Structural Dynamics

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Technologies in Bridge Response and  Engineering

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©2015 Professional Publications, Inc.

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