Example of Box Girder Bridge Calculation

COMPREHENSIVE RETROFIT EXAMPLE 1 MULTI-SPAN CIP REINFORCED CONCRETE BOX GIRDER BRIDGE

1. Problem Statement Evaluate a six-span cast-in-place reinforced concrete highway overcrossing located in southern California for seismic retrofitting. The structure is supported on monolithic single column bents and has a single expansion joint hinge located in span 3. The bridge was constructed in the early 1960’s and has several obvious seismic deficiencies including substandard transverse column reinforcement and a minimal support length at the interior expansion joint hinge. Use the D2 method of evaluation. Once an evaluation has been completed and seismic deficiencies identified and quantified, develop a retrofit strategy that will result in the minimal performance criteria being met. Design the retrofit measures necessary to implement the selected strategy. 2. Description of As-Built Bridge The bridge, which is located in a seismically active region of southern California, is on a curved horizontal alignment of 600 ft radius and has variable span lengths. It passes over a freeway and parallel surface streets. The site class is Type D. The cross-section of the superstructure is of constant width and consists of five girder stems with an overhang on one side. A raised curb with emergency sidewalk is provided on the other side. The depth of the superstructure varies from 7’-0” to 3’-6” with the transition occurring in span 3. Abutments are seat type supported on 45-ton piles with approach retaining walls provided to contain approach roadway fills. They are oriented normal to the superstructure. The superstructure is supported on elastomeric bearings with concrete shear keys provided to restrain transverse movement. The bearing seat is 2’-6” in width. The internal expansion joint hinge located in span 3 consists of an 8 inch bearing seat with embedded steel angles for bearing. Transverse concrete shear keys are provided, but no longitudinal cable restrainers are in place. Internal bents are single columns of circular cross section supported on pile footings. Columns at Bents 2 and 3 are 6’-0” in diameter while the remaining

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columns are 5’-0”. The main reinforcing steel is lap spliced just above the footings, and the column transverse steel, consisting of #5 spirals with a 5” pitch, is lap spliced periodically. Pile footings vary in size depending on the size of the column, and lack upper layers of reinforcing steel to resist negative bending moments. Piles have a design capacity of 45 tons and are effectively “pinned” at the base of the footing. The reinforcing steel from the piles extends into the footing and can resist the seismic uplift capacity of the piles, which is assumed to be 50% of their ultimate compressive capacity (Cu = 2 x Cdesign). A field inspection of the bridge revealed no deterioration or modification of the structure. Because of the age of the concrete it is assumed to have an in-situ strength of 5500 psi. Reinforcing steel is Grade 60. The as-built plans for the bridge are shown in Figures E1-1 through E1-3. 3. Enhanced Procedure for Method D2 Seismic Evaluation The procedure described in the manual for Method D2 is enhanced to include components other than the columns. Step 1 – Strength and Deformation Capacities a. Hinge Force and Displacement Capacity The expansion joint hinge force and displacement capacities are calculated based on the details of the as-built structure. The transverse force capacity is based on shear friction in the shear keys. The total number of #5 bars crossing the shear plane is 16 and the bars are assumed to be Grade 60 with an expected strength of 66 ksi. The concrete crack surface over each of the two shear keys is 16 inches by 36 inches. Therefore, the shear capacity is given by

(

[

Vu = φVn = φ cA cv + μ A vf f y + Pc

])

= .85(.150(16 ⋅ 36 ⋅ 2) + 1.4[16 ⋅ 0.31⋅ 60 + 0]) = 502 kips The displacement capacity can be calculated as the seat width minus the expansion joint gap plus 100 mm (4 inches).

δ c = Ns − gej − 2c h = 8 − 1 − 4 = 3.0 inches

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Table E1-1 - Hinge Force and Displacement Capacities

Transverse Force Kips (KN) 502 (2232)

Hinge 1

Longitudinal Displacement - inches (mm) 3.0 (102)

b. Column and Foundation Shear Capacities In the case of column shear capacities, both the initial and final shear strength is considered. An example of the required calculation for Bent 2 follows.

0.25

⎡1.6ρ v A e ⎤ ⎡1.6ρ v 0.8 A g ⎤ =⎢ tan θ = ⎢ ⎥ ⎥ ⎢⎣ Λρ t A g ⎥⎦ ⎢⎣ 2ρ t A g ⎥⎦ A 32 ⋅ 1.27 ρ t = sl = = .01 Ac π(36) 2 ρv =

0.25

⎡ ρ ⎤ = ⎢0.64 v ⎥ ρt ⎦ ⎣

4 A ss 4(.31) = = 0.00368 sD′′ 5(72 − 4.63)

0.00368 ⎤ ⎡ ∴ tan θ = ⎢0.64 0.01 ⎥⎦ ⎣ 1 = 1.435 cot θ = tan θ

0.25

= [0.2355 ]

0.25

= 0.697

π π (72 − 4.63) D′′ (1.435 ) cot θ = (.31)(60) A h f yh 5 s 2 2 = 565 kips ⇒ 2514 KN Vs =

Λ 2 ⎛ .875(68.7) ⎞ P tan α = (1157 )⎜ ⎟ 240 2 2 ⎝ ⎠ = 290 kips ⇒ 1291 KN Vp =

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0.25

The initial and final contribution of the concrete (Vci and Vcf respective ly) is : 3.61 5500 ⋅ 0.8 ⋅ π ⋅ (36) 2 Vci = 3.61 = 1000 = 872 kips ⇒ 3881 KN ' fce Ae

' Vcf = 0.60 fce A e = 145 kips ⇒ 645 KN

Therefore, the initial and final ultimate shear capacity (Vui and Vuf ) is given by : Vui = 0.85(Vs + Vp + Vci ) = 0.85(565 + 290 + 872 )

= 1468 kips ⇒ 6532 KN Vuf = 0.85(Vs + Vp + Vcf ) = 0.85(565 + 290 + 145 ) = 850 kips ⇒ 3782 KN

The following table includes the shear capacities for all of the columns.

Table E1-2 - Column Shear Strength Capacity

Column 2 3 4 5 6

Column Length Feet (m) 20.0 (6.10) 24.5 (7.47) 17.0 (5.18) 19.4 (5.91) 21.7 (6.62)

Dead Load Axial Load Kips (KN) 1157 (5149) 1069 (4757) 448 (1994) 457 (2034) 545 (2425)

Initial Shear Strength Kips (KN) 1468 (6532) 1407 (6263) 1006 (4475) 996 (4431) 1001 (4455)

Final Shear Strength Kips (KN) 850 (3782) 789 (3512) 576 (2565) 567 (2521) 572 (2545)

Similarly, the foundation shear capacity is calculated based on the capacity of the piles in shear plus the capacity provided by passive pressure on the face of the pile cap. The ultimate lateral capacity of a single pile is assumed to be 40 kips (178 KN) based on physical testing of similar piles. The shear capacities for Bent 2 and 3 are calculated as follows: Hc (piles) = Np ⋅ 40 = 25(40 ) = 1000 kips ⇒ 4450 KN 2 ⋅ (4 + 2) 2 ⋅ h′ 4 ⋅ 15 dW = 3 3 = 240 kips ⇒ 1068 KN

Hc (cap) = Pp W =

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The total shear capacities of all pier foundations are summarized below Table E1-3 - Pier Foundation Capacities Pier Foundation

2 and 3 4, 5 and 6

Shear Capacity Kips (KN) Longit. Trans. 1240 1240 (5518) (5518) 832 832 (3702) (3702)

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c. Abutment Force and Displacement Capacities Abutment force capacities are governed either by the capacity of shear keys or the capacity of the piles and wingwalls. The shear key capacity is calculated in a manner similar to those for the hinge and is summarized below. i.

Shear Keys:

(

[

Vu = φVn = φ cA cv + μ A vf f y + Pc

])

= 0.85(.150(30 ⋅ 36 ⋅ 2) + 1.4[16 ⋅ 0.31⋅ 60]) = 630 kips ii. Piles and Wingwalls

In the case of the piles the calculation for Abutment 1 is performed as follows: Vp = Np ( 40 ) = 13 ⋅ 40 = 520 kips The wingwall capacity is equal to the capacity of one wingwall in shear. In this case the wingwall is 14 feet high and 12 inches thick (d=9”). Therefore: Vw = φHd ⋅ 2 fc' = 0.85 ⋅ 14 ⋅ 12 ⋅ 9 ⋅ 2 ⋅ 0.074 = 190 kips

Vabut = Vp + Vw = 520 + 190 = 710 kips The displacement capacity in the longitudinal direction depends on the geometry of the seat and the nominal amount of expansion (ge = 1”). In this case: δ abut = Ns − g e − 2c c = 30 − 1 − 4 = 25 inches

Similarly for Abutment 7: Vabut = 576 kips δ abut = 25 inches Table E1-4 - Abutment Force and Displacement Capacities

Abut

Transverse Force Kips (KN) Shear Piles and Keys Wingwalls

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Longitudinal Displacement inches (mm)

630 710 (2804) (3160) 630 576 7 (2804) (2563) Step 2 – Nonlinear Static Pushover Analysis 1

25.0 (635) 25.0 (635)

In a displacement-based approach, the first step in a nonlinear static pushover analysis is to assess the deformation capacity of various ductile elements such as columns. One method is to perform moment-curvature computer analyses based on allowable strains. For this problem, simplified methods presented in the retrofit guidelines for determining allowable plastic rotations of the columns are used. These depend on the limit state being investigated. In this bridge, the unconfined splices that are typical of bridge construction prior to 1971 must be considered. The transverse spiral reinforcing in the column is lap spliced (a substandard detail) and will be subject to failure as soon as the outer concrete cover spalls. Therefore, a compression failure in unconfined concrete should be investigated. Shear failure is another possibility that could limit ductile response. The following calculations are performed for Bent 2. φy =

2f y E sD′

=

2(60 ) 29000 (72 − 2(2) − 2(.69 ) − 1.44 )

= 0.00006348 rad/in L p = 0.08L + 4400ε y db

L p = 0.08(20(12)) + 4400(.00207 )(1.25 ) = 30.59 in (for transverse bending) L p = 0.08(10(12)) + 4400(.00207 )(1.25 ) = 20.99 in (for longitudinal bending) 0.725

f y ⎛ 1 − 2c D ⎞ ⎤ ⎡ Pe ⎟⎟ ⎥ + 0.5ρ t ' ⎜⎜ ⎢ ' fc ⎝ 1 − 2d′ D ⎠ ⎥ c 1 ⎢ fc A g = ⎥ D β⎢ 1.32α ⎢ ⎥ ⎢⎣ ⎥⎦ ⇒ 0.2216 by trial and error c = 0.2216D = 0.2216 (72 ) = 15.96 in

The allowable plastic rotation for each of the limit states can now be calculated.

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ε cu .005 − φy = − .00006348 c 15.96 = .0002498 rad/in θ p = φ pL p = .0002498 (30.59 ) φp =

= 0.00764 rad (transverse bending) θ p = φ pL p = .0002498 (20.99 ) = 0.00524 rad (longitudinal bending) The splice section is evaluated as follows: l s = 0.032

f ye ' fce

db = 0.032

66000 4225

1.25 = 41 in

L lap = 42 in

Therefore, this is a "long” splice and, by inspection, unconfined compression will control. Although the final shear capacity is sufficient to resist shear demands in the transverse direction, shear failure could occur in the longitudinal direction due to shear capacity degradation resulting from flexural yielding. The amount of plastic rotation that is allowed will be limited because of this. This is calculated as follows. The plastic overstrength moment at the dead load axial force is calculated first.

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2 ⎡ ⎛ P Pbcc ⎞ ⎤ e − ⎢ ⎜ ⎟ ⎥ ⎛ M ⎞ ⎢ ⎜ fc' A g fc' A g ⎟ ⎥ Mpo = ⎜ bo ⎟ ⎢1 − ⎜ ⎟ ⎥ fc' A gD ⎜⎝ fc' A gD ⎟⎠ ⎢ ⎜ Pto − Pbcc ⎟ ⎥ ⎢ ⎜⎝ fc' A g fc' A g ⎟⎠ ⎥ ⎣ ⎦ Where

fc' = 5.5 ksi Pe ' fc A g Pto fc' A g Pbcc fc' A g

=

1157 = 0.0517 5.5(28.27 )(144 )

= −ρ t

fsu fc'

= 0.5αβ

⎛ 1.5(66 ) ⎞ = −.01⎜ ⎟ = −0.180 ⎝ 5 .5 ⎠

A cc ⎛ 24.71 ⎞ = 0.5(0.85 )(0.85 )⎜ ⎟ = 0.316 Ag ⎝ 28.27 ⎠

⎛ f su D′ Pbcc 1 − κ o ⎞⎟ ⎜K = ρ + shape t ' fc' A gD ⎜⎝ fc D fc' A g 2 ⎟⎠ 1.5(66 ) 65.18 ⎛ 1 − 0 .6 ⎞ = 0.32(0.01) + 0.316⎜ ⎟ 5. 5 72 ⎝ 2 ⎠ = 0.1153 Therefore,

Mbo

Mpo

2 ⎡ ⎛ P Pbcc ⎞ ⎤ e − ⎢ ⎜ ⎟ ⎥ ⎛ M ⎞ ⎢ ⎜ fc' A g fc' A g ⎟ ⎥ ' = ⎜ ' bo ⎟ ⎢1 − ⎜ f A D ⎜ fc A gD ⎟ Pto Pbcc ⎟ ⎥ c g ⎟ ⎥ ⎝ ⎠⎢ ⎜ − ⎢ ⎜⎝ fc' A g fc' A g ⎟⎠ ⎥ ⎣ ⎦ ⎡ ⎛ 0.0517 − 0.316 ⎞ 2 ⎤ = 0.1153 ⎢1 − ⎜ ⎟ ⎥ (5.5 )(28.27 )(144 )(72) ÷ 12 ⎢⎣ ⎝ − 0.180 − 0.316 ⎠ ⎥⎦ = 11,091 kip ft

E1-12

Therefore, the limitations on flexural yielding based on shear strength for Bent 2 degradation is: Vm = Mp L = 11091 10 = 1109 kips ⎞ ⎛ ⎛ V − Vm ⎞ ⎛ ⎛ 1470 − 1109 ⎞ ⎞ ⎟⎟ + 2 ⎟φ y = ⎜⎜ 5⎜ φ p = ⎜⎜ 5⎜⎜ i ⎟ + 2 ⎟⎟(0.00006348 ) ⎟ ⎝ ⎝ 1470 − 852 ⎠ ⎠ ⎠ ⎝ ⎝ Vi − Vf ⎠ = 0.0003124 rad/in

θ p = φ pL p = 0.0003124 (20.99 ) = 0.00656 radians (Does not control)

The deformation capacity of all as-built columns is summarized below. Column Deformation Capacity (Longitudinal)

Column

2 3 4 5 6

Yield Ultimate Curvature Curvature radians/in radians/in (radians/m) (radians/m) .0000698 .000291 (.00275) (.01147) .0000698 .000300 (.00275) (.01182) .0000856 .000339 (.00337) (.01336) .0000856 .000378 (.00337) (.01489) .0000856 .000361 (.00337) (.01422)

Plastic Moment Kip ft (KN m) 11095 (15053) 10963 (14874) 7121 (9661) 7132 (9676) 7238 (9820)

Plastic Hinge Length inches (m) 22.1 (.561) 24.3 (.617) 20.7 (.526) 21.8 (.554) 22.9 (.582)

Plastic Rotation radians

.00643 .00729 .00786 .00825 .00828

Column Deformation Capacity (Transverse)

Column

2 3 4 5

Yield Ultimate Curvature Curvature radians/in radians/in (radians/m) (radians/m) .0000698 .000291 (.00275) (.01147) .0000698 .000300 (.00275) (.01182) .0000856 .000380 (.00337) (.01497) .0000856 .000378 (.00337) (.01489)

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Plastic Moment Kip ft (KN m) 11095 (15053) 10963 (14874) 7121 (9661) 7132 (9676)

Plastic Hinge Length inches (m) 31.7 (.805) 36.0 (.914) 28.8 (.732) 31.1 (.790)

Plastic Rotation radians

.00923 .01083 .01096 .01178

.0000856 .000361 7238 33.4 .01204 (.00337) (.01422) (9820) (.848) Once the deformation capacity of the potential plastic hinge has been determined, a longitudinal displacement capacity evaluation of the entire bridge is determined through a longitudinal “push-over” analysis. In this type of analysis the columns are modeled as non-linear elements. The frame, which is modeled in 2-dimensions, is incrementally displaced in the longitudinal direction until the maximum allowable plastic rotation is achieved in the plastic hinge zones. The displacement at which this occurs is identified as the displacement capacity, Δci. 6

The transverse displacement capacity is determined by a transverse “push-over” analysis of each bent. Both the longitudinal and transverse “push-over” models include non-linear foundation springs for both rotational and translational movement. 1. Longitudinal “Push-over” Analysis a. Computer Models The computer model used for the longitudinal “push-over” analysis is shown in Figure E1-4. This model was analyzed using the DRAIN2DX computer program that was originally developed at the University of California at Berkeley. The non-linear elements used to model the potential plastic hinges in the reinforced concrete column are based on a tri-linear interaction curve (i.e. Shape Code 3). This tri-linear curve is selected to match the actual interaction curve in the vicinity of the axial load. The actual interaction curve is calculated using the computer program YIELD, one of several that can be used for this purpose. The tri-linear curves used in this analysis are shown in Figures E1-5a and E1-5b.

Slaved Nodes at Hinge 101

301 203 302 303 310

201 102 202 210 Rigid Links (Typ) 220 230

320 330

305 401 304 306 307 402 410

420 430 Nonlinear Beam Element (Typ)

Nonlinear Foundation Element (Typ)

Figure E1-4 –DRAIN2DX Model

E1-14

501 403 502 510

601 503 602 610

520 530

620 630

Tri-linear curve fit for DRAIN2DX

35000 Tri-linear curve fit for DRAIN2DX

30000

9000 7000 5000 3000 1000 0 -1000 -3000 -5000

25000 20000 Axial Force - kips

Axial Force - kips

21000 19000 17000 15000 13000 11000 Interaction Diagram

15000

Interaction Diagram

10000 5000 0

10000

10000

20000

-5000 Nominal Moment - kip ft

Nominal Moment - kip ft

Figure E1-5a Interaction Diagram - 5 ft Column

Figure E1-5b Interaction Diagram - 6 ft Column

The foundations are modeled as non-linear elements for translation and rotation. With respect to rotation, this is done to simulate “rocking” of the footings when the pile axial capacities are exceeded. If “rocking” of the foundations occur prior to the limiting deformation in the column, the foundation will act as a fuse that may spare the columns significant damage. The foundation non-linear rotational springs are calculated as follows. Bent 2 & 3 Ultimate Compression Capacity of Pile = 2(90) = 180 kips Ultimate Tension Capacity of Pile = 0.5 Compression Capacity = 90 kips PDL( 2) = 1157 kips ⇒ 5149 KN PDL( 3 ) = 1069 kips ⇒ 4757 KN

Ultimate Moment Capacity (See Figure E1-6) N(1) = N(2) = 5(-90) = -450 kips => -2003 KN N(4) = N(5) = 5(180) = 900 kips => 4006 KN N(3)2 = 1157 + 2(450) – 2(900) = 257 kips => 1144 KN N(3)3 = 1069 + 2(450) – 2(900) = 169 kips => 752 KN

E1-15

Mc = N(1) ⋅ 6 + N(2) ⋅ 3 + N( 4) ⋅ 3 + N(5) ⋅ 6 = 450 ⋅ 6 + 450 ⋅ 3 + 900 ⋅ 3 + 900 ⋅ 6 Mc = 12,150 kip ⋅ ft ⇒ 16,484 KN ⋅ m For this example, the footing rotational response is modelled as perfectly elastic/plastic. Ultimate pile capacities are assumed to be reached at a vertical displaceme nt of 1". From this the initial rotational stiffness is calculated for input into the DRAIN2DX program. δ 1 φu = u = = 0.01389 rad l ex 2 ⋅ 3 ⋅ 12 kR =

Mc 12,150 = ≈ 875,000 kip ⋅ ft/rad φ u .01389

⇒ 1,187,000 KN ⋅ m/rad

P M

H

N(1)

N(2)

N(3)

N(4)

N(5)

Figure E1-6 – Pile Footing Free Body Diagram (Bent 2 & 3)

Ultimate Translational Capacity

E1-16

Hc (piles) = Np ⋅ 40 = 25(40 ) = 1000 kips ⇒ 4450 KN

2 ⋅ h′ 2 ⋅ (2 + 4 ) dW = 4 ⋅ 15 3 3 = 240 kips ⇒ 1068 KN Based on past testing, the pile ultimate capacity is reached at a displaceme nt of approximat ely 1". The initial translational stiffness is calculated for input to DRAIN2DX. Δ u = 1 inch ⇒ 25 mm Hc (cap) = Pp W =

kT =

Hc (piles) + Hc (cap) 1000 + 240 = ΔU 1

= 1240 kips/inch ⇒ 217 KN/mm

E1-17

Similarly for Bents 4 to 6: kR =

Mc 6,150 = ≈ 332,000 kip ⋅ ft/rad φ u 0.0185

⇒ 450,560 KN ⋅ m/rad (average) kT =

Hc 832 = = 832 kips/inch ⇒ 146 KN/mm Δu 1

Translational yielding of the piles in this case can mean destruction of the pile heads. This could potentially result in significant vertical settlements at the foundation although complete collapse is unlikely. Still it is advisable to avoid this failure mode. Rotational yielding will usually mean that piles will plunge and pull out of the soil if the pile to footing connection is sufficiently strong. Although this action can limit column forces, there are two issues to be considered. First, the response of the foundation is subject to some uncertainty, and the possibility of foundation over strength makes the “fusing” action unreliable unless there is a significant difference between the column and the foundation moment capacities. Therefore, columns should generally be retrofitted as a “fail safe” measure even if the pushover analysis indicates piles will yield first. Secondly, the amount of plastic rotation to be tolerated in the foundation before foundation retrofitting is mandated is subject to some judgment. Excessive plastic rotation can result in unacceptable foundation settlement as pointed out in Chapter 6. In this case, it is assumed that a plastic rotation of 0.03 radians can be tolerated. Member properties used for the “push-over” analysis are consistent with those used in the dynamic analysis described below. Appendix E1-1 includes the DRAIN2DX input files. b. Computer Results In the longitudinal direction the DRAIN2DX model is displaced incrementally until the allowable deformation is achieved at the potential plastic hinge zones. The controlling displacement is shown in bold face type. The following table summarizes the results of all of the non-linear “push-over” analyses.

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Table E1-7 - Displacement Capacity – inches (mm) Longitudinal Ultimate Ultimate (Bottom) (Top) 5.6 1 3.1 1 (142) (79) 7.1 1 4.1 1 (180) (104) 9.2 2 3.4 1 (234) (81) 9.2 2 3.1 1 (234) (79) 9.2 2 3.5 1 (234) (80)

Bent

2 3 4 5 6

Notes:

Transverse Ultimate Ultimate (Bottom) (Top) 7.0 1 N/A (178) 10.3 1 N/A (262) 10.8 2 N/A (274) 10.8 2 N/A (274) 10.8 2 N/A (274)

1. Controlled by column 2. Controlled by footing

Step 3 – Non-Seismic Demands Non-seismic loads to be considered in the Extreme Event 1 loading condition are assumed to be negligible for this example. Step 4 – Demand Analysis 1. Response Spectrum Parameters Based on the location of the bridge site, the following seismic loading parameters are determined from the maps developed by the United States Geologic Survey (USGS). Ss = 2.0 S1 = 1.0 Site factors (for Site Class D) are given in Table 1-4 of the retrofit manual. Fa = 1.0 Fv = 1.5 Therefore, SDS = FaSs = 1.0(2.0) = 2.0 SD1 = FvS1 = 1.5(1.0) = 1.5

E1-19

The resulting response spectrum to be used for the demand analysis is shown in Figure E1-7

Spectral Acceleration - g's

2.0

1.0

0 0

1.0

2.0

3.0

Period - Sec.

Figure E1-7 – Design Spectra

2. Member Properties for Analysis The superstructure section properties were calculated using the “Section Wizard” computer program, which is part of STAAD III. Table E1-8 summarizes these results. Table E1-8 - Superstructure Section Properties – ft (Metric values shown in parentheses) Section Span 1 & 2 Bent 2 & 3 Span 3 – A Span 3 – B Spans 4-6 Bents 4-6

Depth

Ax

Izz

Iyy

Ixx

7.00 (2.13) 7.00 (2.13) 5.84 (1.78) 4.67 (1.42) 3.50 (1.07) 3.50 (1.07)

51.40 (4.78) 179.55 (16.69) 47.58 (4.42) 43.72 (4.06) 39.85 (3.70) 93.24 (8.67)

393.70 (3.40) 789.54 (6.82) 258.28 (2.23) 153.80 (1.33) 78.84 (0.68) 109.76 (0.95)

3855.05 (33.31) 9928.09 (85.78) 3578.65 (30.92) 3299.76 (28.51) 3020.71 (26.10) 5552.09 (47.96)

896.87 (7.75) 2279.85 (19.70) 624.55 (5.40) 394.65 (3.41) 213.71 (1.85) 318.47 (2.75)

E1-20

Gross column section properties are modified to reflect the cracking that is likely to occur during a seismic event. The modification factors are taken from Table 71 in the Bridge Retrofit Manual. In the as-built case, the structural details will not accommodate ductile behavior and thus preclude plastic hinging from taking place. Therefore: For Bents 2 and 3 (6’ φ Columns): A g = πr 2 = 3.1416 ⋅ (3)2 = 28.27 ft 2 ⇒ 2.63 m2

πr 4 3.1416 ⋅ (3 ) = = 63.61 ft 4 ⇒ 0.55 m4 4 4 A e = A g = 2.63 m2

Ig =

4

Mn = 9386(12) = 112,600 k - in (From YIELD computer program) D′ = 72 - 4 - 2(.69) - 1.44 = 65.2 in. E = 57000 fc' 1000 = 57000 5500 1000 = 4230 ksi M D′ 112600 ⋅ 65.2 Ie = n = = 419,000 in 4 ⇒ 20.2 ft 4 ⇒ 0.175 m 4 E2ε y 4230(2)(.00207 )

For Bents 4, 5 and 6 (5’ φ Columns): A g = πr 2 = 3.1416 ⋅ (2.5)2 = 19.64 ft 2 ⇒ 1.83 m2 πr 4 3.1416 ⋅ (2.5 ) Ig = = = 30.68 ft 4 ⇒ 0.27 m4 4 4 A e = A g = 1.83 m2 4

Mn = 5836(12) = 70,000 k - in D′ = 60 − 4 − 2(.69 ) − 1.44 = 53.2 in M D′ 70,000 ⋅ 53.2 Ie = n = = 213,000 in 4 ⇒ 10.26 ft 4 ⇒ 0.0886 m 4 E2ε y 4230(2)(.00207 )

3. Elastic Response Spectrum (Demand) Analysis a. Computer Models The SEISAB computer program was used to perform the elastic response spectrum (demand) analysis. SEISAB automatically models the structural elements of the bridge with “beam” elements. As a default, the superstructure spans are modeled using four “beam” elements, which result in lumped masses at the quarter points of the span. Columns are modeled using 3 “beam” elements. The pile foundations are modeled using SEISAB pile and footing data block capabilities.

E1-21

When using a linear elastic model to simulate the non-linear behavior of a bridge during a strong earthquake it is typical practice to use several computer models to envelope the actual bridge response. In this case, two “compression” models and one “tension” model was used. The first “compression” model assumed that the expansion joints at Abutment 1 and the hinge were locked up and able to transmit longitudinal forces. The second “compression” model assumed the hinge and Abutment 7 were locked up. The “tension” model assumed all expansion joints were free to move. The worst-case forces and displacements from each of these models were used to determine seismic demands. The behavior of the longitudinal expansion joints at the abutments depends not only on the expansion joint gap, but also on the non-linear behavior of the fill behind the abutment wall. In the compression models this behavior is usually “linearized” using a trial and error approach. This is demonstrated in Figure E18, which shows the non-linear force-displacement curve at Abutment 1 plus the linearized displacement actually used in the first “compression” model.

1200

1.0

800 k

Longituninal Force (kips)

1000

600 Linearized Stiffness

400 200

1.0

2.0 3.0 4.0 5.0 6.0 Longitudinal Displacement (inches)

Figure E1-8 Abutment 1 Longitudinal Response

In this figure the ultimate capacity of the abutment is given as the passive pressure behind the wall. The backwall is assumed to shear off at the level of the bearing seat and engage the fill behind the wall. The displacement at which the ultimate force is reached includes the displacement required to achieve full passive pressure (0.02H) plus the expansion joint gap, Dg. Therefore, at Abutment 1:

E1-22

2H2 W 2 ⋅ 7.5 2 ⋅ 28.78 = 3 3 = 1079 Kips ⇒ 4803 KN

HP = Pp W = p pHW =

Δ ult = 0.02H + D g = 0.02 ⋅ 7.5 ⋅ 12 + 1.0 = 2.80 in ⇒ 71 mm For Abutment 7: HP = Pp W = ppHW =

2H2 W 2 ⋅ 5.02 ⋅ 28.78 = = 480 Kips ⇒ 2135 KN 3 3

Δult = 0.02H + Dg = 0.02 ⋅ 5.0 ⋅ 12 + 1.0 = 2.20 in ⇒ 56 mm The actual stiffness used in the model must be adjusted until the computed abutment force demand is within 30% of Hp. b. Computer Input Files SEISAB computer input files for each of the three elastic models used are included in Appendix E1-2. c. Computer Results The following tables summarize the maximum results obtained from the SEISAB computer analyses. Table E1-9 Abutment Forces and Displacements

Location Abutment 1 Abutment 7

Forces – Kips (KN) Longitudinal Transverse 1109 920 (6884) (4250) 477 864 (6684) (3925)

E1-23

Displacements – inches (mm) Longitudinal Transverse 5.9 1.8 (149) (45) 5.7 1.7 (145) (42)

Table E1-10 Column Moments and Displacements

Bent

Location

Top 2

Bottom Top 3

Bottom Top 4

Bottom Top 5

Bottom Top 6

Bottom

Elastic Moment K ft (KN m) Longit. Trans. 34171 (46360) 21944 19987 (29772) (27116) 30288 (41092) 20863 34024 (28305) (46160) 17974 (24385) 10341 26691 (14030) (36212) 19486 (26437) 10758 15847 (14595) (21500) 16799 (22791) 10295 7298 (13967) (9901)

Displacement inches (mm) Longit. Trans.

5.8 (147)

7.3 (185)

6.1 (156)

13.9 (354)

5.0 (128)

15.2 (387)

5.4 (137)

10.7 (273)

5.6 (143)

6.1 (154)

Plastic shear demands on the columns and foundations are limited by yielding of the columns and/or the foundations and are calculated as follows for Bent 2 in the longitudinal direction: Vp =

∑ Mp Lc

=

2.0(11095 ) = 1110 kips 20

The remaining plastic shear demands are calculated in a similar fashion and are summarized below.

E1-24

Table E1-11 Column Plastic Shears

Bent

Plastic Shear Kips (KN) Longit. Trans.

2

1110 (4940)

555 (2470)

3

895 (3983)

448 (1994)

4

780 (3729)

362 (1885)

5

685 (3271)

317 (1638)

6

617 (2968)

283 (1486)

Hinge force and displacement demands are obtained from the worst case SEISAB model. Table E1-12 - Hinge Force and Displacement Demands

Hinge

Transverse Force Kips (KN) 1076 (4788)

Longitudinal Displacement inches (mm) 7.6 (193)

Step 5 - Summary of Capacity/Demand Ratios The adequacy of the current structure to resist earthquakes is given by the capacity/demand ratio for the various components of the bridge for different types of actions. These are summarized as follows with inadequate components indicated by bold type.

E1-25

Table E1-13 Capacity/Demand Ratios

Location Abutment 1

Abutment 7 Bent 2 Bent 3 Bent 4 Bent 5 Bent 6 Hinge 1 Footnotes:

Response Item Force – Keys Force - Piles Displacement Force – Keys Force - Piles Displacement Displacement Foundation Shear Displacement Foundation Shear Displacement Foundation Shear Displacement Foundation Shear Displacement Foundation Shear Displacement Force

Longitudinal N/A N/A 4.41 N/A N/A 4.56 0.53 1 1.12 0.67 1 1.39 0.68 1 1.07 0.57 1 1.21 0.63 1 1.35 0.53 N/A

Transverse 0.68 0.77 N/A 0.73 0.67 N/A 0.96 1 2.23 0.74 1 2.77 0.71 2 2.30 1.01 2 2.62 1.77 2 2.94 N/A 0.39

1. Controlled by failure of unconfined concrete in compression. 2. Controlled by plunging and uplift of foundation piles.

Figure E1-9 is a graphical presentation of the as-built seismic deficiencies of the bridge.

E1-26

4. Retrofit Strategy Evaluation a. Identification of Retrofit Strategy A retrofit strategy that addresses the global response of the bridge is shown in Figure E1-10. The strategy, which involves retrofitting of all five columns and both abutments, addresses each deficiency that was identified by the detailed seismic evaluation performed above. The hinge is also to be retrofitted with seat extenders and longitudinal cable restrainers to prevent unseating. It is also necessary to retrofit the foundations at Piers 2, 3, 5 and 6 to prevent failure of the pile cap in negative bending and Pier 4 to prevent excessive plastic rotation of the foundation. This strategy is evaluated in the following sections. A less obvious strategy, which relied on Piers 3 and 4 to carry all longitudinal forces, was also investigated. This strategy involved retrofitting these two columns with steel or fiber shells. Transverse forces would be carried by the two abutments, which were also to be retrofitted, and Piers 3 and 4, such that each frame could resist torsional response about the vertical axis. Piers 2, 5 and 6 would have been allowed to fail under lateral load, but would have been retrofitted with light steel shells to preserve axial load capacity at these locations. This strategy could have worked if it weren’t for the high ductility demands placed on the retrofitted columns. Short of replacing these columns, or strengthening them significantly, it was not possible to retrofit these columns to gain the ductility necessary to resist failure of the main reinforcement due to low cycle fatigue. Therefore, this trial strategy was ultimately rejected. b. Design of Retrofit Measures i.

Abutment Retrofit 1. CIDH Bolters

The existing abutment piles and wingwalls at the abutments do not have the capacity to resist transverse forces. It is necessary to provide additional capacity through large diameter cast-in-drilled hole (CIDH) bolsters. The shear capacity of this bolster must exceed the difference between the transverse force demands and the capacity of the existing abutment. Therefore, Vbolster = (Vd − Vabut ) For Abutment 1 this is calculated as follows Vbolster = 920 − 710 = 210 kips

E1-28

At Abutment 7: Vbolster = 864 − 576 = 288 kips Therefore, to simplify details, design both bolsters to resist the forces at Abutment 7. The minimum diameter of the CIDH bolster is determined based on the maximum shear capacity, which is determined by using the maximum allowable shear stress, which is 8 fc' . Therefore, A e (min) = A bolster =

Vbolster φ ⋅ 8 fc'

=

288 = 706 in 2 0.85 ⋅ 0.480

A e 706 = = 883 in 2 0. 8 .8

D bolster (min) =

4 ⋅ A bolster = π

4 ⋅ 883 = 33.5 in π

Use D bolster = 48 in

The top of the pile is detailed with a “pinned” connection at the level of the abutment footing. This eliminates the need for the bolster-to-abutment connection to resist large moments. Therefore, the connection need only resist the shear force of 288 kips. Dowels drilled and bonded into the side of the abutment wall are used for this purpose. According to Caltrans tests, a #7 dowel bonded into a 7” deep, drilled hole with magnesium phosphate grout can safely resist 20.3 kips in tension. Therefore, the number of dowels required to transfer the shear force eccentrically applied at the top of the bolster is: Ndowels =

1.5 Vbolster 1.5(288 ) = = 21.3 dowels ∴ use 21 dowels TC # 7 20.3

The 1.5 factor in the above equation accounts for the eccentricity of the load. Such dowels must be spaced at a minimum of 14 inches and must be a minimum of 4 inches away from the edge of any drilled concrete. The pinned connection at the top of the pile must also be capable of transferring the 288 kip shear force. The “pin” is designed using the principals of shear friction. Therefore, the minimum area of concrete is:

E1-30

A pin =

Vbolster φ(0.2)fc'

=

288 = 471 in 2 0.85(0.2)(3.6)

⇒ use a 25 in diameter circle The required area of reinforcing steel crossing the shear plane is: Vbolster

φ μf y

A vf =

− cA cv

288 =

− 0.1( 491) .85 = 4.83 in 2 1.0(60)

∴ use 7 - #8 dowels The moment in the CIDH bolster is calculated with the help of a computer program that models the CIDH pile as a series of beam-column elements and the subsurface lateral soil stiffness as p-y curves for each increment of soil depth along the length of the pile. Shear and moment diagrams along the pile can be developed using this technique, and from these the maximum moment demand can be determined. In this case the maximum moment demand is: Mbolster = 2155 k - ft Because plastic hinging in the CIDH bolsters will not be allowed, the bolster is designed for this moment. Based on an interaction analysis, this requires 20 #10’s as main reinforcement around the perimeter of the CIDH pile. This results in ρt of 0.0140. The final shear capacity provided by the concrete in the pile is determined as follows 0.6 3600 ⋅ 0.8π(24 ) Ae = = 52 kips 1000 2

Vcf = 0.6

fc'

Therefore, the shear capacity provided by the transverse reinforcement must be Vs =

Vbolster − φVcf 288 − 0.85(52) = = 287 kips φ 0.85

This requires hoop spacing as follows s = A v f yh

D′′ cot θ Vs

By assuming θ to be 35 degrees, and #6 hoops, the spacing is as follows

E1-31

π (0.44 )(60 ) 48 − 6.88 (1.43 ) = 8.50 inches 2 288 ∴ use # 6 hoops @ 8" oc

s=

This gives a volumetric ratio of ρv =

2A bh 2(0.44 ) = = 0.00268 sD′′ 8.0( 41.12)

Therefore, the assumption for θ can be checked ⎛ 1.6ρ v A e ⎞ ⎟ θ = a tan⎜ ⎜ Λρ t A g ⎟ ⎠ ⎝ = 35.1 degrees

0.25

⎛ 1.6(.00268 )(1448 ) ⎞ ⎟⎟ = a tan⎜⎜ ⎝ 1(.0140 )(1810 ) ⎠

0.25

Since this approximately equal to the assumed value for θ, the above shear reinforcement results are acceptable. 2. Pipe Restrainers The existing shear keys at the abutments are not capable of transferring the transverse shear forces from the superstructure to the abutments. The existing shear key capacity was previously calculated based on their shear friction capacity. Vkeys = 630 kips Therefore, additional shear capacity must be provided as follows based on Abutment 1: Vadd = Vd − Vkeys = 920 − 630 = 290 kips Pipe shear keys may be used to provide this extra capacity. An A36 pipe filled with concrete is capable of resisting 26 ksi in shear. Therefore a double extra strong 6” diameter pipe will provide 406 kips nominal capacity or 345 kips ultimate capacity after the application of a 0.85 capacity reduction factor. If one pipe is used, it will provide the required additional shear capacity. A cored hole will be required in the existing concrete in order to place the pipe. The pipe shear key may be placed vertically if provisions are made for longitudinal movement of the superstructure. This design has the advantage of eliminating excavation behind the abutment, but requires complicated details to

E1-32

provide for longitudinal movement. Alternately, the pipe may be oriented longitudinally. In this case one end of the pipe shear key will pass through the abutment backwall. Because this backwall is not thick enough to provide the necessary bearing area for the pipe, it must be reinforced from behind, which will require some excavation behind the abutment and potentially more disruption to traffic. The required bearing area in either case is calculated as follows:

Ag =

Vpipe

φ(0.85 )

fc'

=

290 = 105 in 2 0.9(0.85 )(3.6 )

The value of Ag may include as much as twice the actual contact area on the surface of the pipe if sufficient concrete surrounds the cored hole. Therefore, because the pipe will rotate and non-uniform (i.e. triangular) bearing during an earthquake, it is judged that the pipe must be embedded a minimum of 18” (i.e. approx. 105/2x6x1/2) to develop the required shear capacity. Pipe embedment can be reduced if supplemental steel bearing plates are provided to distribute concrete bearing stresses. Abutment retrofit details are shown in Figure E1-11. ii.

Column Retrofit 1. Carbon Fiber Jacket Retrofit

Carbon fiber jackets are chosen over steel shells because they add such a small increase in longitudinal strength and thus allow for a longer plastic hinge zone. This increases the amount of plastic rotation that can occur prior to a low cycle fatigue failure of the main reinforcing steel. If sufficient confinement is provided with a composite shell, the mode of column failure will always be low cycle fatigue of the main column reinforcement. For the 6 ft diameter columns the allowable plastic curvature for this mode of failure is calculated as follows: φp =

2ε ap

(d − d′)

where ε ap = 0.08(2N f )

− 0. 5

(

)

−0.333 −0.5

= 0.08 7(Tn )

(

)

−0.333 −0.5

= 0.08 7(0.77 )

= 0.0289 2(.0289 ) ∴ φp = = 0.0008868 (68.59 − 3.41) Therefore, the allowable pastic rotations for Bent 2 are as follows θ p = φpL p = .0008868 (22.1) = .01960 radians (longitudinal) θ p = φpL p = .0008868 (31.7 ) = .02811 radians (transverse)

Similarly, plastic rotations for the other columns can be determined

E1-33

These allowable plastic rotation capacities result in the following column displacement capacities assuming over strength and/or retrofitted footings at Bents 4 thru 6 do not yield.

E1-34

Table E1-14 – Retrofitted Displacement Capacity – inches (mm) Longitudinal

Transverse

6.2 (173) 8.2 (208) 6.1 (178) 6.4 (173) 6.8 (183)

12.5 (272) 17.6 (361) 13.7 (318) 14.2 (320) 15.0 (325)

Bent 2 3 4 5 6

Notice that all displacement capacities are sufficient with the exception of Bent 4 in the transverse direction. Because the displacement capacities listed in Table E1-15 are limited by low cycle fatigue failure, jacketing is not the solution at the bottom of Bent 4. In this case a replaceable hinge retrofit is required in order lengthen the plastic hinge and mitigate low cycle fatigue failure. The remaining columns may all be retrofitted with composite fiber shells. Another alternative may be steel shells or the use of replacement hinges on all columns. The thickness of the carbon fiber jackets should be sufficient to prevent the occurrence of a compression failure in the concrete or a shear failure of the column prior to the low cycle fatigue failure. As an example, consider Bent 3.

φ p = 0.0008868 radians/inch

(

)

∴ ε cu = φ p + φ y (c − d′′)

= (0.0008868 + 0.0000698 )(13.51 − 0) = .0129 ∴ use ε cu = .015 as the target concrete strain capacity Using the simplified method, the thickness of a passive carbon-fiber jacket for confinement is given by tp =

31D 31(72) = = 0.068 in Ej 33000

For lap splice performance:

E1-36

tp =

500Dfl 500(72)(.3 ) = = 0.327 in Ep 33000

For shear enhancement 2v sj 2(1110 − 850 ) / 0.85 tp = = πE p ε pD cot θ 3.1416(33000 )(.006 )(72)(1.43 ) = 0.01 in Therefore, use t = 0.375 inches at lap zone and t = 0.125 inches elsewhere Check εcu ε cu = 0.004 +

2.5ρ s fdu ε du ' fcc

where 4(t p ) 4(.125 ) ρs = = = 0.0069 D 72 f du = 600 ksi ε du = 0.02

' ' = 1.33fce = 1.33(5.5 ) = 7.315 ksi fcc

ε cu = 0.004 +

2.5(.0069 )(600 )(.02 ) = 0.0324 > 0.015 ∴ OK 7.315

Similar jackets can be used on the remaining columns. A 0.125 inch thick shell should be used at the upper plastic hinge zone of Bent 4. 2. Replaceable Plastic Hinge The plastic hinge length at the base of Pier 4 must be of sufficient length to accommodate the required plastic rotation. This can be accomplished by using the replaceable hinge detail discussed in Section 9.2.1.1(b). An example of this type of retrofit is shown in Figure 9-4. The first step is to determine the size of the fuse bar, which must provide the maximum strength but guarantee yielding before the existing main column steel. d f < db

2f y fsu

= 1.25

2(60 ) = 1.14 inches 144

∴ Use 1 - 1/8" diameter fuse bars

The length of the fuse bar is the length of the plastic hinge. Therefore, using a plastic rotation demand, θd, based on a transverse displacement demand of 15.2 E1-37

inches as required from Table E1-10 and a yield displacement of 6.7 inches obtained from the transverse DRAIN2DX output, the following minimum fuse bar length is obtained. du − d y du − d y 15.2 − 6.7 ≈ = = .0489 radians Lp 60 D 204 − L− L− 2 2 2 Therefore θp =

Lf =

θp

D′(2N f )

0.5

=

0.16 ∴ Use L f = 66 inches

.0489 (60 − 6.63 )(2(7.64 ))0.5 = 63.75 inches 0.16

The next step is to size the connector plate and welds. Assuming E70XX electrodes and 3/16” fillet welds: 2

L w = 0.56

d f fsu 1.125 2 144 = 0.56 = 12.2 inches s w fw .25 33.6

The minimum plate thickness based on AISC LRFD is 5/16 inches. Finally, the transverse reinforcement in terms of ½ inch diameter prestress strand must be determined for concrete confinement, anti-buckling and shear resistance. For concrete confinement 2 ⎡ fy ⎞ ⎛ A g fc' ⎢ ⎛⎜ Pe ⎟ ρ s = 0.008 + ρ t ' ⎜⎜ 12 Usf ⎢ ⎜⎝ fc' A g fc ⎟⎠ ⎝ A cc ⎣⎢

2 ⎤ ⎞ ⎟ − 1⎥ ⎟ ⎥ ⎠ ⎦⎥

2 2 ⎤ 4 ⎡ ⎛ 448 124 ⎞ ⎛ 2827 ⎞ ⎟⎟ ⎜ ρ s = 0.008 ⎢12⎜⎜ + .00984 ⎟ − 1⎥ 16 ⎢ ⎝ 4(2827 ) 4 ⎠ ⎝ 2402 ⎠ ⎥⎦ ⎣ ρ s = 0.00195

For anti-buckling the transverse reinforcement spacing is limited to 6 inches. For shear resistance ρ s = 2K shape Λ

ρ t fsu A g .00984 144 2827 53.37 (1.0) tan α tan θ = 2(0.32)(1.0 ) φ f yh A cc .9 216 2402 204

ρ s = 0.00144

E1-38

Therefore, confinement controls. Use ρs =0.00195 or ½” strand at 5-1/2” cc. iii.

Column Foundation Retrofit 1. Footing Overlay (Without Additional Piles)

Column Footings (pile caps) do not have a top mat of reinforcement. Therefore, they are structurally inadequate for resisting the uplift forces generated in the piles by column overturning. To prevent flexural failures of the footings these footings will be overlayed with 12 inches of concrete that contains horizontal reinforcement to resist negative bending moments. This overlay will be made to act compositely with the existing footing by drilling and bonding vertical reinforcement into the existing footing that will act in shear friction to resist horizontal shear stresses. The negative bending moment and shear generated by pile uplift at Bent 2 is given by:

d ⎛ M footing = Np Tp ⎜ x p1 − e + x p2 2 ⎝

⎛ ⎛ ⎞⎞ ⎜ ⎜ 6 .0 π ⎟ ⎟ d ⎞ ⎜ 4 ⎟⎟ − e ⎟ = 5 ⋅ 90 ⋅ ⎜ 6.0 + 3.0 − 2 ⋅ ⎜ ⎜ 2 ⎠ 2 ⎟⎟ ⎜⎜ ⎜ ⎟ ⎟⎟ ⎝ ⎠⎠ ⎝

= 1657 k ⋅ ft Vfooting = Np Tp = 5 ⋅ 90 = 450 kips

The ultimate moment resistance provided by 16 #6 reinforcing bars is given by: 16 ⋅ .44 ⋅ 60 ⎞ ⎛ ⎜ ⎟ a⎞ ⎛ Mu = φA s f y ⎜ d − ⎟ = 0.90 ⋅ 16 ⋅ .44 ⋅ 60⎜ 4.64 − 5.5 ⋅ 15 ⋅ 12 ⋅ 12 ⎟ 2⎠ ⎜ 2 ⎟ ⎝ ⎜ ⎟ ⎠ ⎝ = 1752 k ⋅ ft > 1657 OK

The shearing resistance at the interface of the existing footing and the overlay that is required to develop composite behavior is:

ν int erface =

Vfooting Q Ib

=

450(1.0 ⋅ 15 ⋅ 2.0 ) = 5.76 k/ft 2 1 5 3 ⋅ 15 ⋅ ⋅ 15 12

Therefore, the resistance provided by #5 dowels drilled and bonded in a 5 inch deep hole is: E1-39

ν u = φv dowel = 0.85 ⋅ 8.2 = 6.97 kips > 5.76 OK A pattern of #5 dowels at 12 inches on center in both directions will be sufficient to resist horizontal shear stresses. Similar overlays will be required on the remaining footings with the exception of Bent 4, which must have piles added for flexural strength.

E1-40

2. Footing Retrofit (With Additional Piles) Only at Bent 4 is the foundation rotational displacement capacity inadequate. In this case piles will either plunge or uplift an excessive amount. To prevent this, foundation flexural strength must be increased. This is accomplished by adding 8 - 16” diameter cast-in-drilled hole (CIDH) piles. Because piles must be installed under the existing superstructure, CIDH piles are used for constructability reasons. This results in more than enough additional flexural capacity, but is the minimum number of piles required to achieve a symmetric pile pattern. The additional piles will increase both the positive and negative moment demands on the footings.

M fpos

⎛ ⎛ π ⎞⎟ π ⎞⎟ ⎜ ⎜ 5 .0 5. 0 d ⎞ d ⎞ ⎛ ⎛ 4 ⎟ + 4 ⋅ 180⎜ 4.5 − 4⎟ = Np1C p ⎜ x 1 − e ⎟ + Np2 C p ⎜ x 2 − e ⎟ = 2 ⋅ 180⎜ 7.33 − ⎟ ⎜ ⎟ ⎜ 2 2 2 2 ⎝ ⎠ ⎝ ⎠ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ ⎠ ⎝ = 3482 k ⋅ ft

M fneg

⎛ ⎛ π ⎞⎟ π ⎞⎟ ⎜ ⎜ 5 .0 5 .0 d ⎞ d ⎞ ⎛ ⎛ 4 ⎟ + 4 ⋅ 90⎜ 4.5 − 4⎟ = Np1Tp ⎜ x 1 − e ⎟ + Np 2 Tp ⎜ x 2 − e ⎟ = 2 ⋅ 90⎜ 7.33 − ⎜ ⎟ ⎜ 2 ⎠ 2 ⎠ 2 2 ⎟ ⎝ ⎝ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ ⎠ ⎝ = 1741 k ⋅ ft

Positive moment will be resisted by the bottom reinforcement. Because additional footing width will be added to accommodate the 8 new piles, additional bottom bars can be added. Existing bottom bars can be extended into the widened portion of the footing by exposing the ends of these bars and welding or mechanically splicing an additional length of bar onto the ends of these existing bars. Therefore, check the capacity of the existing bottom bars.

Mcexist

12 ⋅ 1.0 ⋅ 60 ⎛ ⎞ ⎜ ⎟ a⎞ ⎛ 0 . 85 ⋅ 5 . 5 ⋅ 12 ⋅ 12 ⋅ 12 ⎜ ⎟ = 2783 k ⋅ ft = φA s f y ⎜ d − ⎟ = 0.9 ⋅ 12 ⋅ 1.0 ⋅ 60 4.34 − 2⎠ ⎜ 2 ⎟ ⎝ ⎜ ⎟ ⎝ ⎠

There is room to add 6 extra bottom bars in the widened portions of the footing. The capacity of these additional bars is:

E1-41

6 ⋅ 1.0 ⋅ 60 ⎛ ⎞ ⎜ ⎟ a⎞ ⎛ Mcnew = φA s f y ⎜ d − ⎟ = 0.9 ⋅ 6 ⋅ 1.0 ⋅ 60⎜ 4.34 − 0.85 ⋅ 3.5 ⋅ 5.67 ⋅ 12 ⋅ 12 ⎟ = 1382 k ⋅ ft 2⎠ 2 ⎜ ⎟ ⎝ ⎜ ⎟ ⎝ ⎠ ∴ Mctotal = Mcexist + Mcnew = 2783 + 1382 = 4165 k ⋅ ft > 3482 OK Negative moment can be resisted with an overlay similar to the one designed for the remaining footings. Therefore, use 8 new 16” diameter cast-in-drilled hole piles in a footing enlarged to 17’-8” square and 5’-0” deep. Use a 1’-0” overlay with 16 - #6 bars in each direction, # 5 drilled and bonded dowels at 12” on center in each direction, and 8 additional - #9 bars in each direction at the bottom of the footing. Details of the column and footing retrofits are shown in Figure E1-12.

iv.

Hinge Retrofit 1. Pipe Seat Extenders

The hinge seat is not wide enough to accommodate the longitudinal movement at the expansion joint hinge. In addition, the transverse shear keys are not strong enough to resist the transverse forces developed during the design earthquake. These problems can be overcome by using 8” xx strong pipe seat extenders that were developed by Caltrans after the 1989 Loma Prieta earthquake. These seat extenders will allow 8” of relative longitudinal displacement at the hinges, which is sufficient to accommodate the 7.6 inches of longitudinal displacement demand. In addition, these seat extenders will serve as supplemental transverse shear keys. Test performed by Caltrans have demonstrated that in addition to accommodating 8 inches of relative displacement, these devises are able to carry 180 kips of horizontal shear. Because it is assumed that the maximum transverse shear demand will not occur at the same time as the maximum relative longitudinal displacement, the existing concrete shear keys will participate in the resistance to transverse forces. Therefore, the additional shear capacity required from the seat extenders is given by:

(

)

Vdpipeextenders = L f Vd − Vkeys = 1.3(1076 − 536 ) = 702 kips Notice that a load factor of 1.3 was used to account for misalignment tolerances of the individual pipe extender units. The required number of seat extenders is determined as follows: Npipeextenders =

Vdpipeextenders 180

= 3.9 ∴Use 4 pipe extender units.

E1-42

Expansion joint hinge diaphragm bolsters are used to anchor the pipe seat extenders. 2. Longitudinal Cable Restrainers Some jurisdictions will use a minimum of two longitudinal cable restrainer units in conjunction with the seat extenders. These are optional unless it is necessary to restrain the relative longitudinal displacements at the hinges. In this example, restrainer units will not be specified. Figure E1-13 includes details of the expansion joint hinge retrofit.

E1-44

Appendix E1-1

E1-46

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER ! File : RETEX1 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Longitudinal direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn !-------------------------------------------------------------------*STARTXX retex1 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Longitudinal dir ! ----------------------------! Superstructure C 101 0.00 100.0 C 102 73.71 100.0 C 201 76.71 100.0 ! Bent 2 C 202 79.71 100.0 C 203 195.68 100.0 C 301 198.68 100.0 ! Bent 3 C 302 201.68 100.0 C 303 221.46 100.0 C 304 241.33 100.0 C 305 261.19 100.0 ! Hinge C 306 261.19 100.0 ! Hinge C 307 269.44 100.0 C 401 271.94 100.0 ! Bent 4 C 402 274.44 100.0 C 403 325.79 100.0 C 501 328.29 100.0 ! Bent 5 C 502 330.79 100.0 C 503 383.79 100.0 C 601 386.29 100.0 ! Bent 6 C 602 388.79 100.0 C 603 448.28 100.0 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74 C 530 328.29 80.74

! Bent 6 Column and Foundation C 610 386.29 97.75 C 620 386.29 80.74 C 630 386.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 010 101 ! ABUT 1 S 111 230 ! BENT 2 SPRINGS S 111 330 ! BENT 3 SPRINGS S 111 430 ! BENT 4 SPRINGS S 111 530 ! BENT 5 SPRINGS S 111 630 ! BENT 6 SPRINGS S 010 603 ! ABUT 7 !-------------------------------------------------------------------*SLAVING S 010 305 306 1 !-------------------------------------------------------------------!*MASSES !-------------------------------------------------------------------*ELEMENTGROUP ! ! GROUP 1: SUPERSTRUCTURE 2 0 0 .00 SUPERSTRUCTURE ! stiffness types 7 0 1 1 6.62E+05 0.00 51.40 393.70 4 4 2 2 6.62E+05 0.00 179.55 10000.0 4 4 2 3 6.62E+05 0.00 49.49 325.99 4 4 2 4 6.62E+05 0.00 44.69 206.04 4 4 2 5 6.62E+05 0.00 41.79 116.32 4 4 2 6 6.62E+05 0.00 39.85 78.84 4 4 2 7 6.62E+05 0.00 93.24 10000.0 4 4 2 1 1 10E09 -10E09 ! HIGH VALUE - NO YIELDING ASSUMED ! element generation 1 101 102 1 1 1 2 102 201 2 1 1 3 201 202 2 1 1 4 202 203 1 1 1 5 203 301 2 1 1 6 301 302 2 1 1 7 302 303 3 1 1 8 303 304 4 1 1 9 304 305 5 1 1 10 306 307 6 1 1 11 307 401 7 1 1 12 401 402 7 1 1 13 402 403 6 1 1 14 403 501 7 1 1 15 501 502 7 1 1 16 502 503 6 1 1 17 503 601 7 1 1 18 601 602 7 1 1 19 602 603 6 1 1 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 2: Bent 2 & 3 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2

1 6.62E+05 0.00 28.3 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 28.3 19.4 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 7895. -7895. 35000 -3625 3.17 .264 3.17 .264 ! element generation 1 201 210 1 1 1 1 2 210 220 1 2 2 2 3 301 310 1 1 1 1 4 310 320 1 2 2 2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 4 THRU 6 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 401 410 1 1 1 1 2 410 420 1 2 2 2 3 501 510 1 1 1 1 4 510 520 1 2 2 2 5 601 610 1 1 1 1 6 610 620 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 5 1 14880 0.00 1240 -1240 1 1 1 ! horizontal springs 2 9984 0.00 832 -832 1 1 1 3 875000 0.00 12150 -12150 1 3 1 ! rotational springs 4 332000 0.00 6150 -6150 1 3 1 5 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 220 230 1 ! horizontal springs 2 320 330 1 3 420 430 2 4 520 530 2 5 620 630 2 6 220 230 3 ! rotational springs 7 320 330 3 8 420 430 4 9 520 530 4 10 620 630 4 11 220 230 5 ! vertical springs 12 320 330 5 13 420 430 5 14 520 530 5 15 620 630 5 !----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 NSD 001 301 ! TOP OF PIER 3 NSD 001 401 ! TOP OF PIER 4

NSD 001 501 ! TOP OF PIER 5 NSD 001 601 ! TOP OF PIER 6 ! E 001 2 2 ! TOP OF COLUMN 2 ! E 001 2 4 ! TOP OF COLUMN 3 ! E 001 3 2 ! TOP OF COLUMN 4 ! E 001 3 4 ! TOP OF COLUMN 5 ! E 001 3 6 ! TOP OF COLUMN 6 ! E 001 4 1 10 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S 1.0 0.0 201 !-------------------------------------------------------------------*NODALOAD PUS2 FRAME 2 PUSHOVER PATTERN S 1.0 0.0 401 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !-------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS1 D 201 1 0.01 0.500 !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 401 1 0.01 0.500 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER ! File : RETEXA ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Longitudinal direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/15/2004 revised by rvn !-------------------------------------------------------------------*STARTXX retexa 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Longitudinal dir ! ----------------------------! Superstructure C 101 0.00 100.0 C 102 73.71 100.0 C 201 76.71 100.0 ! Bent 2 C 202 79.71 100.0 C 203 195.68 100.0 C 301 198.68 100.0 ! Bent 3 C 302 201.68 100.0 C 303 221.46 100.0 C 304 241.33 100.0 C 305 261.19 100.0 ! Hinge C 306 261.19 100.0 ! Hinge C 307 269.44 100.0 C 401 271.94 100.0 ! Bent 4 C 402 274.44 100.0 C 403 325.79 100.0 C 501 328.29 100.0 ! Bent 5 C 502 330.79 100.0 C 503 383.79 100.0 C 601 386.29 100.0 ! Bent 6 C 602 388.79 100.0 C 603 448.28 100.0 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74

C 530 328.29 80.74 ! Bent 6 Column and Foundation C 610 386.29 97.75 C 620 386.29 80.74 C 630 386.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 010 101 ! ABUT 1 S 111 230 ! BENT 2 SPRINGS S 111 330 ! BENT 3 SPRINGS S 111 430 ! BENT 4 SPRINGS S 111 530 ! BENT 5 SPRINGS S 111 630 ! BENT 6 SPRINGS S 010 603 ! ABUT 7 !-------------------------------------------------------------------*SLAVING S 010 305 306 1 !-------------------------------------------------------------------*MASSES S 010 1157.0 201 32.2 S 010 1069.0 301 S 010 448.0 401 S 010 457.0 501 S 010 545.0 601 !-------------------------------------------------------------------*ELEMENTGROUP ! ! GROUP 1: SUPERSTRUCTURE 2 0 0 .00 SUPERSTRUCTURE ! stiffness types 7 0 1 1 6.62E+05 0.00 51.40 393.70 4 4 2 2 6.62E+05 0.00 179.55 10000.0 4 4 2 3 6.62E+05 0.00 49.49 325.99 4 4 2 4 6.62E+05 0.00 44.69 206.04 4 4 2 5 6.62E+05 0.00 41.79 116.32 4 4 2 6 6.62E+05 0.00 39.85 78.84 4 4 2 7 6.62E+05 0.00 93.24 10000.0 4 4 2 1 1 10E09 -10E09 ! HIGH VALUE - NO YIELDING ASSUMED ! element generation 1 101 102 1 1 1 2 102 201 2 1 1 3 201 202 2 1 1 4 202 203 1 1 1 5 203 301 2 1 1 6 301 302 2 1 1 7 302 303 3 1 1 8 303 304 4 1 1 9 304 305 5 1 1 10 306 307 6 1 1 11 307 401 7 1 1 12 401 402 7 1 1 13 402 403 6 1 1 14 403 501 7 1 1 15 501 502 7 1 1 16 502 503 6 1 1 17 503 601 7 1 1 18 601 602 7 1 1 19 602 603 6 1 1

!-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 2: Bent 2 & 3 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 28.3 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 28.3 19.4 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 7895. -7895. 35000 -3625 3.17 .264 3.17 .264 ! element generation 1 201 210 1 1 1 1 2 210 220 1 2 2 2 3 301 310 1 1 1 1 4 310 320 1 2 2 2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 4 THRU 6 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 401 410 1 1 1 1 2 410 420 1 2 2 2 3 501 510 1 1 1 1 4 510 520 1 2 2 2 5 601 610 1 1 1 1 6 610 620 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 5 1 14880 0.00 1240 -1240 1 1 1 ! horizontal springs 2 9984 0.00 832 -832 1 1 1 3 875000 0.00 12150 -12150 1 3 1 ! rotational springs 4 332000 0.00 6150 -6150 1 3 1 5 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 220 230 1 ! horizontal springs 2 320 330 1 3 420 430 2 4 520 530 2 5 620 630 2 6 220 230 3 ! rotational springs 7 320 330 3 8 420 430 4 9 520 530 4 10 620 630 4 11 220 230 5 ! vertical springs 12 320 330 5 13 420 430 5 14 520 530 5

15 620 630 5 !----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 NSD 001 301 ! TOP OF PIER 3 NSD 001 401 ! TOP OF PIER 4 NSD 001 501 ! TOP OF PIER 5 NSD 001 601 ! TOP OF PIER 6 ! E 001 2 2 ! TOP OF COLUMN 2 ! E 001 2 4 ! TOP OF COLUMN 3 ! E 001 3 2 ! TOP OF COLUMN 4 ! E 001 3 4 ! TOP OF COLUMN 5 ! E 001 3 6 ! TOP OF COLUMN 6 ! E 001 4 1 10 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S 1.0 0.0 201 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !-------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS1 D 201 1 0.01 0.750 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER ! File : RETEXB ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Longitudinal direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn !-------------------------------------------------------------------*STARTXX retexb 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Longitudinal dir ! ----------------------------! Superstructure C 101 0.00 100.0 C 102 73.71 100.0 C 201 76.71 100.0 ! Bent 2 C 202 79.71 100.0 C 203 195.68 100.0 C 301 198.68 100.0 ! Bent 3 C 302 201.68 100.0 C 303 221.46 100.0 C 304 241.33 100.0 C 305 261.19 100.0 ! Hinge C 306 261.19 100.0 ! Hinge C 307 269.44 100.0 C 401 271.94 100.0 ! Bent 4 C 402 274.44 100.0 C 403 325.79 100.0 C 501 328.29 100.0 ! Bent 5 C 502 330.79 100.0 C 503 383.79 100.0 C 601 386.29 100.0 ! Bent 6 C 602 388.79 100.0 C 603 448.28 100.0 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74 C 530 328.29 80.74

! Bent 6 Column and Foundation C 610 386.29 97.75 C 620 386.29 80.74 C 630 386.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 010 101 ! ABUT 1 S 111 230 ! BENT 2 SPRINGS S 111 330 ! BENT 3 SPRINGS S 111 430 ! BENT 4 SPRINGS S 111 530 ! BENT 5 SPRINGS S 111 630 ! BENT 6 SPRINGS S 010 603 ! ABUT 7 !-------------------------------------------------------------------*SLAVING S 010 305 306 1 !-------------------------------------------------------------------*MASSES S 010 1157.0 201 32.2 S 010 1069.0 301 S 010 448.0 401 S 010 457.0 501 S 010 545.0 601 !-------------------------------------------------------------------*ELEMENTGROUP ! ! GROUP 1: SUPERSTRUCTURE 2 0 0 .00 SUPERSTRUCTURE ! stiffness types 7 0 1 1 6.62E+05 0.00 51.40 393.70 4 4 2 2 6.62E+05 0.00 179.55 10000.0 4 4 2 3 6.62E+05 0.00 49.49 325.99 4 4 2 4 6.62E+05 0.00 44.69 206.04 4 4 2 5 6.62E+05 0.00 41.79 116.32 4 4 2 6 6.62E+05 0.00 39.85 78.84 4 4 2 7 6.62E+05 0.00 93.24 10000.0 4 4 2 1 1 10E09 -10E09 ! HIGH VALUE - NO YIELDING ASSUMED ! element generation 1 101 102 1 1 1 2 102 201 2 1 1 3 201 202 2 1 1 4 202 203 1 1 1 5 203 301 2 1 1 6 301 302 2 1 1 7 302 303 3 1 1 8 303 304 4 1 1 9 304 305 5 1 1 10 306 307 6 1 1 11 307 401 7 1 1 12 401 402 7 1 1 13 402 403 6 1 1 14 403 501 7 1 1 15 501 502 7 1 1 16 502 503 6 1 1 17 503 601 7 1 1 18 601 602 7 1 1 19 602 603 6 1 1 !--------------------------------------------------------------------

*ELEMENTGROUP ! GROUP 2: Bent 2 & 3 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 28.3 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 28.3 19.4 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 7895. -7895. 35000 -3625 3.17 .264 3.17 .264 ! element generation 1 201 210 1 1 1 1 2 210 220 1 2 2 2 3 301 310 1 1 1 1 4 310 320 1 2 2 2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 4 THRU 6 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 401 410 1 1 1 1 2 410 420 1 2 2 2 3 501 510 1 1 1 1 4 510 520 1 2 2 2 5 601 610 1 1 1 1 6 610 620 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 5 1 14880 0.00 1240 -1240 1 1 1 ! horizontal springs 2 9984 0.00 832 -832 1 1 1 3 875000 0.00 12150 -12150 1 3 1 ! rotational springs 4 332000 0.00 6150 -6150 1 3 1 5 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 220 230 1 ! horizontal springs 2 320 330 1 3 420 430 2 4 520 530 2 5 620 630 2 6 220 230 3 ! rotational springs 7 320 330 3 8 420 430 4 9 520 530 4 10 620 630 4 11 220 230 5 ! vertical springs 12 320 330 5 13 420 430 5 14 520 530 5 15 620 630 5

!----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 NSD 001 301 ! TOP OF PIER 3 NSD 001 401 ! TOP OF PIER 4 NSD 001 501 ! TOP OF PIER 5 NSD 001 601 ! TOP OF PIER 6 ! E 001 2 2 ! TOP OF COLUMN 2 ! E 001 2 4 ! TOP OF COLUMN 3 ! E 001 3 2 ! TOP OF COLUMN 4 ! E 001 3 4 ! TOP OF COLUMN 5 ! E 001 3 6 ! TOP OF COLUMN 6 ! E 001 4 1 10 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS2 FRAME 2 PUSHOVER PATTERN S 1.0 0.0 401 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 401 1 0.01 0.750 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE BENT 2 PUSHOVER ! File : RETBT2 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push column at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/14/2004 rvn !-------------------------------------------------------------------*STARTXX retBT2 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE B2 !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse B2 dir ! ----------------------------! Superstructure C 201 76.71 100.0 ! Bent 2 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 !-------------------------------------------------------------------*RESTRAINTS ! S 111 230 ! BENT 2 SPRINGS !-------------------------------------------------------------------!*MASSES !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 2: Bent 2 Column 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 28.3 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 28.3 19.4 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 7895. -7895. 35000 -3625 3.17 .264 3.17 .264 ! element generation 1 201 210 1 1 1 1 2 210 220 1 2 2 2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 14880 0.00 1240 -1240 1 1 1 ! horizontal springs 2 875000 0.00 12150 -12150 1 3 1 ! rotational springs 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation

1 220 230 1 ! horizontal springs 2 220 230 2 ! rotational springs 3 220 230 3 ! vertical springs !----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 ! E 001 1 2 ! TOP OF COLUMN 2 ! E 001 2 1 3 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S 1.0 0.0 201 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !-------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS1 D 201 1 0.01 1.500 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE BENT 3 PUSHOVER ! File : RETBT3 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/14/2004 rvn !-------------------------------------------------------------------*STARTXX retbt3 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 301 198.68 100.0 ! Bent 3 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 !-------------------------------------------------------------------*RESTRAINTS ! S 111 330 ! BENT 3 SPRINGS !-------------------------------------------------------------------*MASSES S 010 33.2 301 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 2: Bent 2 & 3 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 28.3 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 28.3 19.4 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 7895. -7895. 35000 -3625 3.17 .264 3.17 .264 ! element generation 1 301 310 1 1 1 1 2 310 320 1 2 2 2 *ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 14880 0.00 1240 -1240 1 1 1 ! horizontal springs 2 875000 0.00 12150 -12150 1 3 1 ! rotational springs 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation

1 320 330 1 ! horizontal springs 2 320 330 2 ! rotational springs 3 320 330 3 ! vertical springs !----------------------------------------------------------------------------*RESULTS NSD 001 301 ! TOP OF PIER 3 ! E 001 1 2 ! BOTTOM OF COLUMN 3 ! E 001 2 1 3 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS1 BENT 3 PUSHOVER PATTERN S 1.0 0.0 301 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !-------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS1 D 301 1 0.01 2.000 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER - BT 4 ! File : RETBT4 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/15/2004 rvn !-------------------------------------------------------------------*STARTXX retbt4 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 401 271.94 100.0 ! Bent 4 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 430 ! BENT 4 SPRINGS !-------------------------------------------------------------------*MASSES S 010 448.0 401 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 4 THRU 6 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 401 410 1 1 1 1 2 410 420 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 832 -832 1 1 1 2 332000 0.00 6150 -6150 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 420 430 1

2 420 430 2 3 420 430 3 !----------------------------------------------------------------------------*RESULTS NSD 001 401 ! TOP OF PIER 4 ! E 001 1 2 ! BOTTOM OF COLUMN 4 ! E 001 2 1 3 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS2 BENT 4 PUSHOVER PATTERN S 1.0 0.0 401 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 401 1 0.01 2.000 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER ! File : RETBT5 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/19/2004 revised by rvn !-------------------------------------------------------------------*STARTXX retbt5 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 501 328.29 100.0 ! Bent 5 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74 C 530 328.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 530 ! BENT 5 SPRINGS !-------------------------------------------------------------------*MASSES S 010 457.0 501 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 5 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 501 510 1 1 1 1 2 510 520 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 832 -832 1 1 1 2 332000 0.00 6150 -6150 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 520 530 1

2 520 530 2 3 520 530 3 !----------------------------------------------------------------------------*RESULTS NSD 001 501 ! TOP OF PIER 5 ! E 001 1 2 ! TOP OF COLUMN 5 E 001 2 1 3 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS2 FRAME 2 PUSHOVER PATTERN S 1.0 0.0 501 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 501 1 0.01 1.500 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER ! File : RETBT6 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Bent at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/19/04 revised by rvn !-------------------------------------------------------------------*STARTXX retbt6 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 601 386.29 100.0 ! Bent 6 ! Bent 6 Column and Foundation C 610 386.29 97.75 C 620 386.29 80.74 C 630 386.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 630 ! BENT 6 SPRINGS !-------------------------------------------------------------------*MASSES S 010 545.0 601 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 6 Column 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 601 610 1 1 1 1 2 610 620 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 832 -832 1 1 1 2 332000 0.00 6150 -6150 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 620 630 1


!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER - STRATEGY EVALUATION ! File : SETEXA ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Longitudinal direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/15/2004 revised by rvn !-------------------------------------------------------------------*STARTXX setexa 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Longitudinal dir ! ----------------------------! Superstructure C 101 0.00 100.0 C 102 73.71 100.0 C 201 76.71 100.0 ! Bent 2 C 202 79.71 100.0 C 203 195.68 100.0 C 301 198.68 100.0 ! Bent 3 C 302 201.68 100.0 C 303 221.46 100.0 C 304 241.33 100.0 C 305 261.19 100.0 ! Hinge C 306 261.19 100.0 ! Hinge C 307 269.44 100.0 C 401 271.94 100.0 ! Bent 4 C 402 274.44 100.0 C 403 325.79 100.0 C 501 328.29 100.0 ! Bent 5 C 502 330.79 100.0 C 503 383.79 100.0 C 601 386.29 100.0 ! Bent 6 C 602 388.79 100.0 C 603 448.28 100.0 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74



15 620 630 5 !----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 NSD 001 301 ! TOP OF PIER 3 NSD 001 401 ! TOP OF PIER 4 NSD 001 501 ! TOP OF PIER 5 NSD 001 601 ! TOP OF PIER 6 ! E 001 2 2 ! TOP OF COLUMN 2 ! E 001 2 4 ! TOP OF COLUMN 3 ! E 001 3 2 ! TOP OF COLUMN 4 ! E 001 3 4 ! TOP OF COLUMN 5 ! E 001 3 6 ! TOP OF COLUMN 6 ! E 001 4 1 10 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS1 FRAME 1 PUSHOVER PATTERN S 1.0 0.0 201 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !-------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS1 D 201 1 0.01 1.000 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER - STRATEGY EVALUATION ! File : SETEXB ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Longitudinal direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/21/2004 rvn !-------------------------------------------------------------------*STARTXX setexb 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Longitudinal dir ! ----------------------------! Superstructure C 101 0.00 100.0 C 102 73.71 100.0 C 201 76.71 100.0 ! Bent 2 C 202 79.71 100.0 C 203 195.68 100.0 C 301 198.68 100.0 ! Bent 3 C 302 201.68 100.0 C 303 221.46 100.0 C 304 241.33 100.0 C 305 261.19 100.0 ! Hinge C 306 261.19 100.0 ! Hinge C 307 269.44 100.0 C 401 271.94 100.0 ! Bent 4 C 402 274.44 100.0 C 403 325.79 100.0 C 501 328.29 100.0 ! Bent 5 C 502 330.79 100.0 C 503 383.79 100.0 C 601 386.29 100.0 ! Bent 6 C 602 388.79 100.0 C 603 448.28 100.0 ! Bent 2 Column and Foundation C 210 76.71 95.79 C 220 76.71 75.79 C 230 76.71 75.79 ! Bent 3 Column and Foundation C 310 198.68 95.79 C 320 198.68 71.29 C 330 198.68 71.29 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74



15 620 630 5 !----------------------------------------------------------------------------*RESULTS NSD 001 201 ! TOP OF PIER 2 NSD 001 301 ! TOP OF PIER 3 NSD 001 401 ! TOP OF PIER 4 NSD 001 501 ! TOP OF PIER 5 NSD 001 601 ! TOP OF PIER 6 ! E 001 2 2 ! TOP OF COLUMN 2 ! E 001 2 4 ! TOP OF COLUMN 3 ! E 001 3 2 ! TOP OF COLUMN 4 ! E 001 3 4 ! TOP OF COLUMN 5 ! E 001 3 6 ! TOP OF COLUMN 6 ! E 001 4 1 10 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS2 FRAME 2 PUSHOVER PATTERN S 1.0 0.0 401 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 401 1 0.01 1.000 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER - BT 4 ! File : SETBT4 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/15/2004 rvn !-------------------------------------------------------------------*STARTXX setbt4 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 401 271.94 100.0 ! Bent 4 ! Bent 4 Column and Foundation C 410 271.94 97.75 C 420 271.94 80.74 C 430 271.94 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 430 ! BENT 4 SPRINGS !-------------------------------------------------------------------*MASSES S 010 448.0 401 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 4 THRU 6 Columns 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 401 410 1 1 1 1 2 410 420 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 1248 -1248 1 1 1 2 332000 0.00 9225 -9225 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 420 430 1


!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER ! File : SETBT5 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Each frame at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/19/2004 revised by rvn !-------------------------------------------------------------------*STARTXX setbt5 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 501 328.29 100.0 ! Bent 5 ! Bent 5 Column and Foundation C 510 328.29 97.75 C 520 328.29 80.74 C 530 328.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 530 ! BENT 5 SPRINGS !-------------------------------------------------------------------*MASSES S 010 457.0 501 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 5 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 501 510 1 1 1 1 2 510 520 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 1248 -1248 1 1 1 2 332000 0.00 9225 -9225 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 520 530 1

2 520 530 2 3 520 530 3 !----------------------------------------------------------------------------*RESULTS NSD 001 501 ! TOP OF PIER 5 ! E 001 1 2 ! TOP OF COLUMN 5 E 001 2 1 3 ! FOUNDATION SPRINGS !-------------------------------------------------------------------*NODALOAD PUS2 FRAME 2 PUSHOVER PATTERN S 1.0 0.0 501 !-------------------------------------------------------------------*PARAMETERS OS 1 0 -1 0 !-------------------------------------------------------------------*GRAV Gravity Load Analysis I 32.2 0 -1 ! Gravity !--------------------------------------------------------------------*STAT Nonlinear pushover analysis N PUS2 D 501 1 0.01 1.500 !--------------------------------------------------------------------*STOP

!-------------------------------------------------------------------! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER ! File : SETBT6 ! FOUNDATION SPRINGS, ! 1. rotation and horiz. translation ==> elastic perfectly plastic ! 2. vert. dir. ==> Fixed ! Transverse direction, ! Push Bent at superstructure level ! Units: kips, ft ! ! ! NOTE : ! 1. 2/3/2004 rvn ! 2. 9/19/04 revised by rvn !-------------------------------------------------------------------*STARTXX setbt6 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE !-------------------------------------------------------------------*NODECOORDS ! ----------------------------! NODES ! for Transverse dir ! ----------------------------! Superstructure C 601 386.29 100.0 ! Bent 6 ! Bent 6 Column and Foundation C 610 386.29 97.75 C 620 386.29 80.74 C 630 386.29 80.74 !-------------------------------------------------------------------*RESTRAINTS ! S 111 630 ! BENT 6 SPRINGS !-------------------------------------------------------------------*MASSES S 010 545.0 601 32.2 !-------------------------------------------------------------------*ELEMENTGROUP ! GROUP 3: Bent 6 Column 2 0 1 .00 COLUMNS ! stiffness types 2 0 2 1 6.62E+05 0.00 19.6 100000.00 4 4 2 ! rigid links 2 6.62E+05 0.00 19.6 9.9 4 4 2 ! columns 1 1 10E09 -10E09 ! RIGID LINK 2 3 5556. -5556. 21000. -3522. 4.54 .333 4.54 .333 ! element generation 1 601 610 1 1 1 1 2 610 620 1 2 2 2 !------------------------------------------------------------------*ELEMENTGROUP ! GROUP 4: Bent foundation Springs 4 0 0 .00 PILE SPRINGS ! stiffness types 3 1 9984 0.00 1248 -1248 1 1 1 2 332000 0.00 9225 -9225 1 3 1 3 1000000 0.00 1000000 -1000000 1 2 1 ! vertical ! element generation 1 620 630 1


Appendix E1-2

E1-47

SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" STATIC ANALYSIS OUTPUT LEVEL 2 C AS-BUILT ANALYSIS C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680.

C *********************************** C PILE SUB BLOCK * C *********************************** PILE 'PILE' "TYPICAL PILE" STIFFNESS KF1F1 480. KF1M3 0. KF2F2 4040. KF3F3 480. KF3M1 0.0 KM1M1 0.0 KM2M2 0.0 KM3M3 0.0 C *********************************** C FOOTING DATA BLOCK * C *********************************** FOOTING PILE '23' "PIERS 2 & 3" TOP LAYOUT 1 'PILE' AT -6.0 0.0 -6.0 2 'PILE' AT -6.0 0.0 -3.0 3 'PILE' AT -6.0 0.0 -0.0 4 'PILE' AT -6.0 0.0 3.0 5 'PILE' AT -6.0 0.0 6.0 6 'PILE' AT -3.0 0.0 -6.0 7 'PILE' AT -3.0 0.0 -3.0 8 'PILE' AT -3.0 0.0 -0.0 9 'PILE' AT -3.0 0.0 3.0 10 'PILE' AT -3.0 0.0 6.0 11 'PILE' AT 0.0 0.0 -6.0 12 'PILE' AT 0.0 0.0 -3.0 13 'PILE' AT 0.0 0.0 -0.0 14 'PILE' AT 0.0 0.0 3.0 15 'PILE' AT 0.0 0.0 6.0 16 'PILE' AT 3.0 0.0 -6.0 17 'PILE' AT 3.0 0.0 -3.0 18 'PILE' AT 3.0 0.0 -0.0 19 'PILE' AT 3.0 0.0 3.0 20 'PILE' AT 3.0 0.0 6.0 21 'PILE' AT 6.0 0.0 -6.0 22 'PILE' AT 6.0 0.0 -3.0 23 'PILE' AT 6.0 0.0 -0.0 24 'PILE' AT 6.0 0.0 3.0 25 'PILE' AT 6.0 0.0 6.0 PILE '456' "PIERS 4,5 & 6" TOP LAYOUT 1 'PILE' AT -4.5 0.0 -4.5 2 'PILE' AT -4.5 0.0 -1.5 3 'PILE' AT -4.5 0.0 1.5 4 'PILE' AT -4.5 0.0 4.5 5 'PILE' AT -1.5 0.0 -4.5 6 'PILE' AT -1.5 0.0 -1.5 7 'PILE' AT -1.5 0.0 1.5 8 'PILE' AT -1.5 0.0 4.5 9 'PILE' AT 1.5 0.0 -4.5 10 'PILE' AT 1.5 0.0 -1.5 11 'PILE' AT 1.5 0.0 1.5 12 'PILE' AT 1.5 0.0 4.5 13 'PILE' AT 4.5 0.0 -4.5 14 'PILE' AT 4.5 0.0 -1.5

15 'PILE' AT 4.5 0.0 1.5 16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 16330. KF2F2 100000. KF3F3 100. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 5. KF2F2 100000. KF3F3 100. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C ********************************* LOADS STATICS ANALYSIS C RESPONSE SPECTRUM C MODE SHAPES 20 C DIRECTION FACTORS C X 1.0 Y 0.0 Z 0.0 "LONGIT" C X 0.0 Y 0.0 Z 1.0 "TRANS" C X 1.0 Y 0.0 Z 0.4 "CASE I" C X 0.4 Y 0.0 Z 1.0 "CASE II"

C ARBITRARY CURVE C PERIOD .000 .150 .75 .80 .90 1.0 1.1 1.2 1.3 1.4 C 1.5 1.6 1.7 1.8 1.9 2.0 2.25 2.50 3.0 C VALUE .800 2.00 2.00 1.875 1.667 1.5 1.364 1.25 1.154 1.07 C 1.00 0.938 0.882 0.833 0.789 0.75 0.667 0.600 0.500 C GRAVITY 32.2 FINISH

SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C AS-BUILT ANALYSIS - TENSION C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************

C PILE SUB BLOCK * C *********************************** PILE 'PILE' "TYPICAL PILE" STIFFNESS KF1F1 480. KF1M3 0. KF2F2 4040. KF3F3 480. KF3M1 0.0 KM1M1 0.0 KM2M2 0.0 KM3M3 0.0 C *********************************** C FOOTING DATA BLOCK * C *********************************** FOOTING PILE '23' "PIERS 2 & 3" TOP LAYOUT 1 'PILE' AT -6.0 0.0 -6.0 2 'PILE' AT -6.0 0.0 -3.0 3 'PILE' AT -6.0 0.0 -0.0 4 'PILE' AT -6.0 0.0 3.0 5 'PILE' AT -6.0 0.0 6.0 6 'PILE' AT -3.0 0.0 -6.0 7 'PILE' AT -3.0 0.0 -3.0 8 'PILE' AT -3.0 0.0 -0.0 9 'PILE' AT -3.0 0.0 3.0 10 'PILE' AT -3.0 0.0 6.0 11 'PILE' AT 0.0 0.0 -6.0 12 'PILE' AT 0.0 0.0 -3.0 13 'PILE' AT 0.0 0.0 -0.0 14 'PILE' AT 0.0 0.0 3.0 15 'PILE' AT 0.0 0.0 6.0 16 'PILE' AT 3.0 0.0 -6.0 17 'PILE' AT 3.0 0.0 -3.0 18 'PILE' AT 3.0 0.0 -0.0 19 'PILE' AT 3.0 0.0 3.0 20 'PILE' AT 3.0 0.0 6.0 21 'PILE' AT 6.0 0.0 -6.0 22 'PILE' AT 6.0 0.0 -3.0 23 'PILE' AT 6.0 0.0 -0.0 24 'PILE' AT 6.0 0.0 3.0 25 'PILE' AT 6.0 0.0 6.0 PILE '456' "PIERS 4,5 & 6" TOP LAYOUT 1 'PILE' AT -4.5 0.0 -4.5 2 'PILE' AT -4.5 0.0 -1.5 3 'PILE' AT -4.5 0.0 1.5 4 'PILE' AT -4.5 0.0 4.5 5 'PILE' AT -1.5 0.0 -4.5 6 'PILE' AT -1.5 0.0 -1.5 7 'PILE' AT -1.5 0.0 1.5 8 'PILE' AT -1.5 0.0 4.5 9 'PILE' AT 1.5 0.0 -4.5 10 'PILE' AT 1.5 0.0 -1.5 11 'PILE' AT 1.5 0.0 1.5 12 'PILE' AT 1.5 0.0 4.5 13 'PILE' AT 4.5 0.0 -4.5 14 'PILE' AT 4.5 0.0 -1.5 15 'PILE' AT 4.5 0.0 1.5

16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG FREE TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 1750. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 1750. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C ********************************* LOADS

RESPONSE SPECTRUM MODE SHAPES 20 DIRECTION FACTORS C X 1.0 Y 0.0 Z 0.0 "LONGIT" C X 0.0 Y 0.0 Z 1.0 "TRANS" C X 1.0 Y 0.0 Z 0.4 "CASE I" C X 0.4 Y 0.0 Z 1.0 "CASE II" ARBITRARY CURVE PERIOD .000 .150 .75 .80 .90 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.25 2.50 3.0 VALUE .800 2.00 2.00 1.875 1.667 1.5 1.364 1.25 1.154 1.07 1.00 0.938 0.882 0.833 0.789 0.75 0.667 0.600 0.500 GRAVITY 32.2 FINISH

SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C AS-BUILT ANALYSIS - COMPRESSION ABUT 1 C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************


16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG PIN TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 2500. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 5. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C ********************************* LOADS


SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C AS-BUILT ANALYSIS - COMPRESSION ABUT 7 C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************


16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG PIN TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 5. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 1000. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C ********************************* LOADS


SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C STRATAGY 1 ANALYSIS - TENSION C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************


16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG FREE TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP FREE AT BENT 2,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 1000. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 1000. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C *********************************

LOADS RESPONSE SPECTRUM MODE SHAPES 20 DIRECTION FACTORS C X 1.0 Y 0.0 Z 0.0 "LONGIT" C X 0.0 Y 0.0 Z 1.0 "TRANS" C X 1.0 Y 0.0 Z 0.4 "CASE I" C X 0.4 Y 0.0 Z 1.0 "CASE II" ARBITRARY CURVE PERIOD .000 .150 .75 .80 .90 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.25 2.50 3.0 VALUE .800 2.00 2.00 1.875 1.667 1.5 1.364 1.25 1.154 1.07 1.00 0.938 0.882 0.833 0.789 0.75 0.667 0.600 0.500 GRAVITY 32.2 FINISH

SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C STRATAGY 1 ANALYSIS - COMPRESSION ABUT 1 C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************


16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG PIN TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLIMN TOP FREE AT BENT 2,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 1100. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 5. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C *********************************


SEISAB "EXAMPLE 1 - WEST COAST BRIDGE" RESPONSE SPECTRUM ANALYSIS C STRATAGY 1 ANALYSIS - COMPRESSION ABUT 7 C ************************************ C ALIGNMENT DATA BLOCK * C ************************************ ALIGNMENT OFFSET L 15.5 STATION 18 + 00.00 COORDINATES N 10000.00 E 10000.00 BEARING N 56 44 15 W BC 18 + 85.15 RADIUS R 600.0 BEARING N 28 08 04 W BC 21 + 84.68 RADIUS R 590.0 BEARING N 07 02 34 W C ************************************ C SPAN DATA BLOCK * C ************************************ SPANS LENGTHS /1.0,74.6,3.0/,/3.0,118.97,3.0/, /3.0,20.34,20.35,20.35,8.52,2.5/,/2.5,52.73,2.5/, /2.5,54.43,2.5/,/2.5,60.01,1.0/ AREA /179.6,51.4,179.6/,/179.6,51.4,179.6/, /179.6,49.5,45.7,41.8,39.9,93.2/, /93.2,39.9,93.2/,/93.2,39.9,93.2/,/93.2,39.9,93.2/ I11 /2280,897,2280/,/2280,897,2280/, /2280,761,510,304,214,318/, /318,214,318/,/318,214,318/,/318,214,318/ I22 /9928,3855,9928/,/9928,3855,9928/, /9928,3717,3440,3161,3021,5552/, /5552,3021,5552/,/5552,3021,5552/,/5552,3021,5552/ I33 /790,394,790/,/790,394,790/, /790,326,206,116,79,110/, /110,79,110/,/110,79,110/,/110,79,110/ DENSITY .150 WEIGHT 1.50 E 609000. C *********************************** C DESCRIBE DATA BLOCK * C *********************************** DESCRIBE C *********************************** C COLUMN SUB BLOCK * C *********************************** COLUMN 'SIX' "SIX FT ROUND COL" AREA 28.3 I11 25.4 I22 19.4 I33 19.4 DENSITY .150 E 661680. COLUMN 'FIVE' "FIVE FT ROUND COL" AREA 19.6 I11 12.3 I22 9.9 I33 9.9 DENSITY .150 E 661680. C ***********************************


16 'PILE' AT 4.5 0.0 4.5 C ********************************** C ABUTMENT DATA BLOCK * C ********************************** ABUTMENT STATION 18 + 65.99 CONNECTION PIN AT ABUTMENT 1 7 C ********************************** C HINGE DATA BLOCK * C ********************************** HINGE AT 3 62.5 WEIGHT 17.5 TRANS PIN LONG PIN TORSION FREE C ********************************** C BENT DATA BLOCK * C ********************************** BENT HEIGHT 24.21,28.71,19.26,21.65,23.95 COLUMN 'SIX' AT BENT 2,3 COLUMN 'FIVE' AT BENT 4,5,6 COLUMN TOP FREE AT BENTS 2,5,6 COLUMN TOP END JOINT SIZE 4.21 AT BENT 2,3 COLUMN TOP END JOINT SIZE 2.25 AT BENT 4,5,6 C ********************************** C FOUNDATION DATA BLOCK * C ********************************** FOUNDATION AT BENT 2,3 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '23' WEIGHT 27.0 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT BENT 4,5,6 SPRING CONSTANTS KF1F1 3600 KF3F3 3600 PILE FOOTING '456' WEIGHT 17.3 $ EFFECTIVE PILE CAP WEIGHT -(GAMMA(CONC)-GAMMA(SOIL)) AT ABUTMENT 1 SPRING CONSTANTS KF1F1 5. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. AT ABUTMENT 7 SPRING CONSTANTS KF1F1 550. KF2F2 100000. KF3F3 6240. KM1M1 1000000. KM2M2 1000000. KM3M3 1000000. C ********************************* C LOADS DATA BLOCK * C *********************************


Example of Box Girder Bridge Calculation

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