STRC15 Lateral Forces Bridges Seismic Considerations 0715

Structural Engineering Exam Review Course

Lateral Forces: Bridges (Seismic Considerations)

Bridges (Seismic Considerations) Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.

©2015 Professional Publications, Inc.

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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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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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Prerequisite Knowledge You should already be familiar with •

mechanics of dynamics

•

definitions of degrees of freedom

•

terminology of seismic loading



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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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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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Seismic Bridge Behavior longitudinal movement •

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

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



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Seismic Bridge Behavior transverse movement •

Bearings at abutments prevent bridge superstructure from moving at abutment.

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Flexible column(s) assist in resistance to movement.

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Sometimes the superstructure is assumed to be rigid.



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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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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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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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Site Acceleration Estimate •

based upon geographic location (latitude/longitude)

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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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Example: Seismic Coefficients Example 8.31



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Example: Seismic Coefficients



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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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Example: Importance Factor Example 8.32

Problem Statement for Ex. 8.31



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Example: Importance Factor



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Site Class •

soil profile: vertical distribution of soil from surface to bedrock

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

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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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Site Class each site class given an alphabetic symbol •

A = hard rock, good soil conditions

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F = peat, organic material, extremely poor soil conditions



Table 8.9 Site Classes

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Example: Site Class Example 8.33




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Example: Site Class

Table 8.9 Site Classes



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Site Factors •

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

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

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



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Example: Site Factors Example 8.34




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Example: Site Factors



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



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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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Example: Adjusted Response Factors Example 8.35




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Example: Adjusted Response Factors



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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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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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How to Construct Design Response Spectra •

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

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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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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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Example: Reference Periods Example 8.36




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Example: Reference Periods



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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

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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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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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Example: Seismic Performance Zone Example 8.37




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Example: Seismic Performance Zone Table 8.12 Seismic Performance Zones



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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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Selection of Analysis Procedure •

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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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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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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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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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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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Example: Uniform Analysis Method Example 8.39




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Example: Uniform Analysis Method



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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

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

•

Structural model includes flexibility of superstructure and columns.



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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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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

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Draw deflected shape.

•

Determine integral (area under deflection curve.

•

Continue process as outlined.



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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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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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Example: Single‐Mode Elastic Method Example 8.40




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Example: Single‐Mode Elastic Method



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Structural Dynamics •

Some exam problems may require engineers to calculate dynamic characteristics.

•

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

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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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Columns, bearings, and so forth have component stiffness.

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

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springs in parallel K e  K1  K 2

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springs in series Ke 

K1 K 2 K1  K 2



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•

•

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

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mode: pattern of displacement of masses

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fundamental mode: mode with longest period of vibration

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



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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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Structural Dynamics mode pattern of displacement of masses fundamental mode •

mode with longest period of vibration

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corresponds to fundamental period

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usually dominates the vibration of the structure



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

all material: E = 29,000 ksi

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

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

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


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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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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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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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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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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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Response Modification Factor •

Use the reductions listed in Table 8.14 and Table 8.15.

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Reduction happens at the element level.

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Different portions of the same structure will have different reductions.

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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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Example: Response Modification Factor Example 8.41




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Example: Response Modification Factor

Table 8.14 Response Modification Factors for Substructures



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

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

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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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Example: Orthogonal Effects Example 8.42




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Example: Orthogonal Effects



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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

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increased damping systems • viscous oil dampers • hysteretic yielding dampers



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Technologies for Improved Seismic Performance passive system •

device responds to motion of ground or structure

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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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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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Isolation Bearings •

mechanical assembly to insert concentrated location of flexibility in structural system

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

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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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Rubber/Steel Plate Bearings •

cylindrical rubber bearing installed in column

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horizontal steel plates to resist lateral expansion due to vertical loads

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



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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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Friction Pendulum Bearings •

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

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Friction dissipates energy during movement.

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Curved surface returns building to original position after earthquake.

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

Friction slider is articulated to match curved surface. STRC ©2015 Professional Publications, Inc.


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Mechanical Damping •

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

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damper resists horizontal movement

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viscous damping = fluid movement

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energy loss related to velocity

floor framing above

shear wall below



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Mechanical Damping •

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

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tapered steel unit to yield when pushed horizontally

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hysteretic damping = yielding of steel

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energy loss related to displacement

Wall above

Wall below STRC ©2015 Professional Publications, Inc.


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Nonlinear Structural Analysis •

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

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requires input for the strength of elements

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

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

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



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Nonlinear Structural Analysis static analysis = pushover analysis •

represents the lateral collapse of a structure

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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

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requires engineer to input expected ground motion record

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shows progressive levels of damage to structure



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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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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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Soil‐Foundation‐Structure Interaction •

computationally complex models that allow flexibility of soils to be considered

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output shows development of bending and hinges in piles and foundation

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

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often results in lower superstructure accelerations but increased lateral displacements

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



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Soil‐Foundation‐Structure Interaction •

requires substantial • geotechnical information • engineering time • computational power

•

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

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can show resonance of soil vibration with structure vibration



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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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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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Example: Minimum Seat Size Example 8.43




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Example: Minimum Seat Size



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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

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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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Lesson Overview •

Development of Elastic Response Spectra

•

AASHTO Analysis Methods

•

Basics of Structural Dynamics

•

Technologies in Bridge Response and Engineering



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STRC15 Lateral Forces Bridges Seismic Considerations 0715

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