Application of Displacement Based Design in Concrete Bridges

1) Msc. Aida Tasellari 2) Prof. Niko Pojani

1. Introduction 2. DBD-Fundamental considerations: Design process for longitudinal response of bridges Design process for transverse response of bridges

3. DDBD of single-degree-of-freedom: bridge structures

Numerical example

4. Conclusions

This article regards the newest approaches in the Seismic Engineering field, introduced under the

already known label “ Displacement Based Design – DBD ”

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A displacement-based seismic design procedure for SDOF structures has been presented, with example

design of a concrete bridge column


Force Based Design (FBD) - Displacement Based Design(DBD)

Conventional seismic design, as employed in codes of practice, is entirely force-based The reasons for this situation are more historical than scientific The primary input to the process is a set of forces In traditional FBD, the period of vibration of a structure is estimated, and a design acceleration response spectra is entered to determine the elastic force demand of the structure In the FBD procedures the displacement limit are checked at the end of the design process, or are considered in terms of ductility demands which are treated indirectly through the use of “behavior factors” that modify design forces


Why DBD? Under seismic action, displacements provide a more fundamental expression of structural response than forces, and the structural design process should be oriented accordingly Since damage of structures subjected to earthquakes is certainly expressed in deformations (strain at fibers, curvatures at sections, rotations at members and drift at story levels), DB approaches are conceptually more appealing Displacement-based design inverts the process. Here, the primary design quantity is a target displacement Furthermore, DBD offers the ability to explicitly control the displacement demand in each member rather than assigning a single, force-based behavior factor to entire structure.


Fundamental considerations

The seismic design methods for bridges involved in the current Design Codes are also entirely forced-based This concept and the design produced from it, in general does not guarantee that the bridge performance when subjected to the earthquake fulfills the expected design performance

Mostly used methods for the displacement based design of bridges are:

1) Methods based on the substitute structures

2) Methods based on the non-linear capacity of structures


Pier design displacement

While in buildings it is normal for the design displacement to be set by drift limits, this is rarely the case for bridge piers.

Occasionally there may be absolute design displacement limits: normally related to allowable relative displacements between

superstructure and abutments material strain limits will govern the design displacement P-Δ moments may also limit design displacement


1- the degree of fixity provided at the pier top and bottom 2- the pier height and 3- the section yield curvature

Pier yield displacement depends on:

Section yield curvature The form of the equations governing yield curvature for different section shapes are given below:

Possible fixity conditions for longitudinal response of bridge piers


In each case the yield displacement may be defined as:

where Lsp is the total strain penetration and C1 is a constant dependet on end fixity.


Displacement profile shape for tranverse response of bridges (strongly dependent on the degree of the restraint provided at the abutments)


* This design process is elaborated by Chopra (2001) * It is proposed for concrete bridges with superstructure constructed of simply-supported spans with rotational flexibility at the movement joints

* With the yield displacement and initial stiffness known, the yield force can be determined. * This method thereby designs the column to a target drift level and acceptable plastic rotation

The main issues: Determination of the design displacement and ductility of the piers Determination of an appropriate inelastic displacement response spectra, to

obtain the period and initial stiffness


* To implement the existing displacement-based design procedure the well-known constant-ductility spectra is needed

* A constant-ductility spectrum for an elastoplastic hysteretic system is a plot of pseudo-acceleration Ay, pseudo-velocity Vy and displacement Dy versus the initial elastic period Tn for selected values of μ

* It is established by dividing the elastic design spectrum by appropriate ductility-dependent factors depend on Tn

* An inelastic design spectrum, constructed by the procedure of Newmark and Hall is plotted in Figure below.

Inelastic displacement spectra


Construction of inelastic design spectrum by Newmark-Hall procedure


2.DETERMINE: -Design displacement: um = uy + θH -Design ductility: μ = um / uy

3.DETERMINE: Tn from deformation design spectrum

4.DETERMINE: Lateral stiffness k

5.DETERMINE: The required yield strength Fy =k uy

6. SELECT member sizes and detailing to provide the strength determined from in step 5 -CALCULATE initial elastic stiffness k and yield deformation uy=fyk

7.Uy computed

in step 6, complies with uy

determined in step 1

?

Repeat steps 2 through 6

NO

YES

A satisfactory design has been produced

1.ESTIMATE: -Yield displacement uy

-DETERMINE -Acceptable plastic rotation θp at the

column base

Iterations are necessary

Bridge Description * The bridge is a continuous concrete box girder bridge with 3 spans 30 m in

length, simply-supported with rotational flexibility at the movement joints. It is straight in plan with a total length of 90 m.


* The box superstructure is supported by 2 identical bents. Each bent consists

of a singular column 1.5 m in diameter and 9 m in height

* The columns are supported on strong soil, and a value of peak ground accelerations ag equal to 0.5g is assumed

The proposed design procedure is evaluated by applying it in the design of a concrete bridge pier


Bridge pier column

Superstructure cross-section

The single-column bent is simply modeled as a SDOF system in the transverse direction


The step-by-step procedure described earlier is now implemented for the column design. The results are summarized in Table 1


The predicted maximum

deformation

The deformation

demand


The procedure converged after five iterations giving a column design with ρt = 5.5%. This column has an initial stiffness kcr =238.6 kN/cm and lateral yield strength fy =1907 kN.

CLEARLY the proposed procedure has produced a satisfactory design.

The predicted maximum deformation of 7.99 cm is equal to the deformation demand.

Furthermore, the plastic rotation demand is identical to the acceptable value of 0.02 radians that was imposed on the design.


In the article fundamental concepts of the DBD for structures in genaral, and bridgs in particular were given

A displacement-based seismic design procedure for SDOF structures, with example design of a concrete bridge column has been presented

With the aid of example, it has been demonstrated that DDBD method (1) is very simple to be used for SDOF structures design (2) provides a structural design that fulfills the expected design performance

THANK YOU!


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Application of Displacement Based Design in Concrete Bridges