example of box girder bridge calculation

E1-1

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

E1-2

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

[ ]( )( ) [ ]( )

kips 502 06031.0164.123616150.85.

PfAcAVV cyvfcvnu

=+⋅⋅+⋅⋅=

+μ+φ=φ=

The displacement capacity can be calculated as the seat width minus the expansion joint gap plus 100 mm (4 inches).

inches 0.3418c2gN hejsc =−−=−−=δ

E1-6

Table E1-1 - Hinge Force and Displacement Capacities

Transverse Force Kips (KN)

Longitudinal Displacement - inches

(mm) Hinge

1 502

(2232) 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.

[ ]

KN 1291kips 290240

)7.68(875.)1157(22tanP

2V

KN 2514kips 565

)435.1(5

)63.472()60)(31(.2

cots

DfA2

V

435.1tan

1cot

697.02355.001.0

00368.064.0tan

00368.0)63.472(5

)31(.4DsA4

01.)36(27.132

AA

64.0A2

A8.06.1AA6.1

tan

p

yhhs

25.025.0

ssv

2c

slt

25.0

t

v25.0

gt

gv25.0

gt

ev

⇒=

⎟⎠⎞

⎜⎝⎛=α

Λ=

⇒=

−π=θ

′′π=

=θ

=θ

==⎥⎦⎤

⎢⎣⎡=θ∴

=−

=′′

=ρ

=π⋅

==ρ

⎥⎦

⎤⎢⎣

⎡ρρ

=⎥⎥⎦

⎤

⎢⎢⎣

⎡

ρ

ρ=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

ρΛρ

=θ

E1-7

( ) ( )

( ) ( )KN 7823kips 850

14529056585.0VVV85.0VKN 5326kips 1468

87229056585.0VVV85.0V:by given is ) Vand (Vcapacity shear ultimate final and initial the Therefore,

KN 456kips 145Af60.0V

KN 3881kips 872 1000

)36(8.0550061.3Af61.3V

:is ly)respective Vand (V concrete the of oncontributi final and initial The

cfpsuf

cipsui

ufui

e'cecf

2

e'ceci

cfci

⇒=

++=++=⇒=

++=++=

⇒==

⇒=

⋅π⋅⋅==

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

Table E1-2 - Column Shear Strength Capacity

Column Column Length

Feet (m)

Dead Load Axial Load Kips (KN)

Initial Shear Strength Kips (KN)

Final Shear Strength Kips (KN)

2 20.0 (6.10)

1157 (5149)

1468 (6532)

850 (3782)

3 24.5 (7.47)

1069 (4757)

1407 (6263)

789 (3512)

4 17.0 (5.18)

448 (1994)

1006 (4475)

576 (2565)

5 19.4 (5.91)

457 (2034)

996 (4431)

567 (2521)

6 21.7 (6.62)

545 (2425)

1001 (4455)

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:

( )( )

KN 1068kips 240

1543

242dW3h2WP)cap(H

KN 4450kips 1000402540N)piles(H

pc

pc

⇒=

⋅+⋅

=′⋅

==

⇒==⋅=

E1-8

The total shear capacities of all pier foundations are summarized below

Table E1-3 - Pier Foundation Capacities

Shear Capacity Kips (KN) Pier Foundation

Longit. Trans. 2 and 3 1240

(5518) 1240

(5518)

4, 5 and 6 832 (3702)

832 (3702)

E1-9

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:

[ ]( )( ) [ ]( )

kips 6306031.0164.123630150.85.0

PfAcAVV cyvfcvnu

=⋅⋅+⋅⋅=

+μ+φ=φ=

ii. Piles and Wingwalls In the case of the piles the calculation for Abutment 1 is performed as follows:

kips 5204013)40(NV pp =⋅== 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:

kips 190 074.029121485.0f2HdV '

cw

=

⋅⋅⋅⋅⋅=⋅φ=

kips 710190520VVV wpabut =+=+=

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:

inches 254130c2gN cesabut =−−=−−=δ Similarly for Abutment 7:

inches 25kips 576V

abut

abut

=δ

=

Table E1-4 - Abutment Force and Displacement Capacities


Abut

Shear Keys

Piles and Wingwalls

Longitudinal

Displacement - inches (mm)

E1-10

1 630 (2804)

710 (3160)

25.0 (635)

7 630 (2804)

576 (2563)

25.0 (635)

Step 2 – Nonlinear Static Pushover Analysis

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.

( )( ) ( )( )

( )( ) ( )( )

( )( ) ( )( )

( ) in 96.15720.22160.2216Dcerror and trialby 2216.0

32.1

Dd21Dc21

f

f5.0

AfP

1Dc

bending) allongitudin (for in 99.20

25.100207.4400121008.0Lbending) transverse (for in 59.30

25.100207.4400122008.0L

d4400L08.0Lrad/in 00006348.0

44.169.2227229000602

DEf2

725.0

'c

yt

g'c

e

p

p

byp

s

yy

===⇒

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

α

⎟⎟⎠

⎞⎜⎜⎝

⎛′−

−ρ+

β=

=

+==

+=

ε+==

−−−=

′=φ

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

E1-11

( )

( )bending) nal(longitudi rad 00524.0

99.200002498.Lbending) e(transvers rad 00764.0

59.300002498.L rad/in 0002498.

00006348.96.15

005.c

ppp

ppp

ycu

p

=

=φ=θ=

=φ=θ=

−=φ−ε

=φ

The splice section is evaluated as follows:

in 42L

in 4125.14225

66000032.0df

f032.0l

lap

b'ce

yes

=

===

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.

E1-12

( )( )( )

( )( )

( ) ( )

( )( )( )( )

ft kip 091,11

127214427.285.5316.0180.0316.00517.011153.0

DAf

AfP

AfP

AfP

AfP

1DAf

MM

Therefore,1153.0

26.01316.0

7218.65

5.5665.101.032.0

21

AfP

DD

ffK

DAfM

316.027.2871.2485.085.05.0

AA5.0

AfP

180.05.5665.101.

ff

AfP

0517.014427.285.5

1157Af

Pksi 5.5f

Where

AfP

AfP

AfP

AfP

1DAf

MDAf

M

2

g'c

2

g'c

bcc

g'c

to

g'c

bcc

g'c

e

g'c

bopo

o

g'c

bcc'c

sutshape

g'c

bo

g

cc

g'c

bcc

'c

sut

g'c

to

g'c

e

'c

2

g'c

bcc

g'c

to

g'c

bcc

g'c

e

g'c

bo

g'c

po

=

÷⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

−−−

−=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−

−

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

=

⎟⎠⎞

⎜⎝⎛ −

+=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ κ−+′

ρ=

=⎟⎠⎞

⎜⎝⎛=αβ=

−=⎟⎠⎞

⎜⎝⎛−=ρ−=

==

=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−

−

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

E1-13

Therefore, the limitations on flexural yielding based on shear strength for Bent 2 degradation is:

( )

( ) control) not (Does radians 00656.099.200003124.0Lrad/in 0003124.0

00006348.028521470

1109147052VVVV5

kips 11091011091LMV

ppp

yfi

mip

pm

==φ=θ=

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛

−−

=φ⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

=φ

===

The deformation capacity of all as-built columns is summarized below.

Column Deformation Capacity (Longitudinal)

Column Yield

Curvature radians/in

(radians/m)

Ultimate Curvature radians/in

(radians/m)

Plastic Moment

Kip ft (KN m)

Plastic Hinge Length

inches (m)

Plastic Rotation radians

2 .0000698 (.00275)

.000291 (.01147)

11095 (15053)

22.1 (.561) .00643

3 .0000698 (.00275)

.000300 (.01182)

10963 (14874)

24.3 (.617) .00729

4 .0000856 (.00337)

.000339 (.01336)

7121 (9661)

20.7 (.526) .00786

5 .0000856 (.00337)

.000378 (.01489)

7132 (9676)

21.8 (.554) .00825

6 .0000856 (.00337)

.000361 (.01422)

7238 (9820)

22.9 (.582) .00828

Column Deformation Capacity (Transverse)

Column Yield

Curvature radians/in

(radians/m)

Ultimate Curvature radians/in

(radians/m)

Plastic Moment

Kip ft (KN m)

Plastic Hinge

Length inches (m)

Plastic Rotation radians

2 .0000698 (.00275)

.000291 (.01147)

11095 (15053)

31.7 (.805) .00923

3 .0000698 (.00275)

.000300 (.01182)

10963 (14874)

36.0 (.914) .01083

4 .0000856 (.00337)

.000380 (.01497)

7121 (9661)

28.8 (.732) .01096

5 .0000856 (.00337)

.000378 (.01489)

7132 (9676)

31.1 (.790) .01178

E1-14

6 .0000856 (.00337)

.000361 (.01422)

7238 (9820)

33.4 (.848) .01204

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. 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.

101 102201

202 203301

302 303 304 306307401

402 403501

502 503601

602

210

220

310

320

410

420

510

520

610

630230 330

305

430 530620

Rigid Links (Typ)

Nonlinear Foundation Element (Typ)Nonlinear Beam Element (Typ)

Slaved Nodes at Hinge

Figure E1-4 –DRAIN2DX Model

E1-15

Interaction Diagram - 5 ft Column

10003000500070009000

110001300015000

0

5000

10000

15000

20000

25000

-500010000

0-1000-3000-5000

10000 20000

Nominal Moment - kip ftNominal Moment - kip ft

Axi

a l F

orce

- k i

ps

Axi

al F

orce

- ki

psInteraction Diagram Interaction Diagram

Tri-linear curve fit for DRAIN2DX

Tri-linear curve fit for DRAIN2DX

30000

35000

210001900017000

Figure E1-5aInteraction Diagram - 6 ft Column

Figure E1-5b

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

KN 4757 kips 1069P

KN 5149 kips 1157P

)3(DL

)2(DL

⇒=

⇒=

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

E1-16

m/radKN 1,187,000

ft/radkip 000,87501389.

150,12Mk

rad 01389.01232

1program. DRAIN2DX the into input for calculated is stiffness rotational initial the this From1". of ntdisplaceme vertical a at reached be to assumed are capacities pile Ultimate

astic.elastic/plperfectly as modelled is response rotational footing the example, this FormKN 16,484 ftkip 150,12M

6900390034506450 6)5(N3)4(N3)2(N6)1(NM

u

cR

ex

uu

c

c

⋅⇒

⋅≈=φ

=

=⋅⋅

=δ

=φ

⋅⇒⋅=⋅+⋅+⋅+⋅=

⋅+⋅+⋅+⋅=

l

P

HM

N(1) N(2) N(3) N(4) N(5)

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

Ultimate Translational Capacity

E1-17

( )

( )

KN/mm 217kips/inch 1240 1

2401000)cap(H)piles(Hk

mm 25inch 1DRAIN2DX.

to input for calculated is stiffness naltranslatio initial The 1".ely approximat ofntdisplaceme a at reached iscapacity ultimate pile the testing, past on Based

KN 1068kips 240

1543

422dW3h2WP)cap(H

KN 4450

kips 1000402540N)piles(H

U

ccT

u

pc

pc

⇒=

+=

Δ+

=

⇒=Δ

⇒=

⋅+⋅

=′⋅

==

⇒

==⋅=

E1-18

Similarly for Bents 4 to 6:

KN/mm 146 kips/inch 8321

832Hk

(average) m/radKN 560,450

ft/radkip 000,3320185.0150,6Mk

u

cT

u

cR

⇒==Δ

=

⋅⇒

⋅≈=φ

=

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.

E1-19

Table E1-7 - Displacement Capacity – inches (mm)

Longitudinal Transverse Bent Ultimate (Bottom)

Ultimate (Top)

Ultimate (Bottom)

Ultimate (Top)

2 5.6 1

(142) 3.1 1

(79) 7.0 1

(178) N/A

3 7.1 1

(180) 4.1 1

(104) 10.3 1

(262) N/A

4 9.2 2

(234) 3.4 1

(81) 10.8 2

(274) N/A

5 9.2 2

(234) 3.1 1

(79) 10.8 2

(274) N/A

6 9.2 2

(234) 3.5 1

(80) 10.8 2

(274) N/A

Notes: 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

E1-20

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

0 1.0 2.0 3.0

1.0

2.0

0

Period - Sec.

Spe

c tra

l Acc

eler

atio

n - g

's

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 Depth Ax Izz Iyy Ixx

Span 1 & 2 7.00 (2.13)

51.40 (4.78)

393.70 (3.40)

3855.05 (33.31)

896.87 (7.75)

Bent 2 & 3 7.00 (2.13)

179.55 (16.69)

789.54 (6.82)

9928.09 (85.78)

2279.85 (19.70)

Span 3 – A 5.84 (1.78)

47.58 (4.42)

258.28 (2.23)

3578.65 (30.92)

624.55 (5.40)

Span 3 – B 4.67 (1.42)

43.72 (4.06)

153.80 (1.33)

3299.76 (28.51)

394.65 (3.41)

Spans 4-6 3.50 (1.07)

39.85 (3.70)

78.84 (0.68)

3020.71 (26.10)

213.71 (1.85)

Bents 4-6 3.50 (1.07)

93.24 (8.67)

109.76 (0.95)

5552.09 (47.96)

318.47 (2.75)

E1-21

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 7-1 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):

2222g m 63.2ft 27.28)3(1416.3rA ⇒=⋅=π=

( ) 4444

g m 55.0ft 61.634

31416.34rI ⇒=

⋅=

π=

2ge m 63.2AA ==

ksi 423010005500570001000f57000E

in. 65.21.44-2(.69)-4-72Dprogram) computer YIELD(From in-k 600,112)12(9386M

'c

n

===

==′==

444

y

ne m 175.0ft 2.20in 000,419

)00207)(.2(42302.65112600

2EDMI ⇒⇒=

⋅=

ε′

=

For Bents 4, 5 and 6 (5’ φ Columns):

2222g m 83.1ft 64.19)5.2(1416.3rA ⇒=⋅=π=

( ) 4444

g m 27.0ft 68.304

5.21416.34rI ⇒=

⋅=

π=

2ge m 83.1AA ==

in-k 000,70)12(5836Mn == in 2.5344.1)69(.2460D =−−−=′

444

y

ne m 0886.0ft 26.10in 000,213

)00207)(.2(42302.53000,70

2EDMI ⇒⇒=

⋅=

ε′

=

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.

E1-22

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 E1-8, which shows the non-linear force-displacement curve at Abutment 1 plus the linearized displacement actually used in the first “compression” model.

Longitudinal Displacement (inches)1.0 2.0

200

400

800

600

1000

1200

6.03.0 4.0 5.0

Long

ituni

nal F

orce

(kip

s)

Linearized Stiffness

1.0

k

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:

E1-23

KN 4803Kips 1079 3

78.285.723

WH2HWpWPH22

ppP

⇒=

⋅⋅====

mm 71in 80.2

0.1125.702.0DH02.0 gult

⇒=

+⋅⋅=+=Δ

For Abutment 7:

KN 2135Kips 4803

78.280.523

WH2HWpWPH22

ppP ⇒=⋅⋅

====

mm 56in 20.20.1120.502.0DH02.0 gult ⇒=+⋅⋅=+=Δ

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

Forces – Kips (KN)

Displacements – inches (mm) Location

Longitudinal Transverse Longitudinal Transverse

Abutment 1 1109 (6884)

920 (4250)

5.9 (149)

1.8 (45)

Abutment 7 477 (6684)

864 (3925)

5.7 (145)

1.7 (42)

E1-24

Table E1-10 Column Moments and Displacements

Elastic Moment K ft (KN m)

Displacement inches (mm) Bent Location

Longit. Trans. Longit. Trans.

Top 34171 (46360) -

2 Bottom 21944

(29772)19987

(27116)

5.8 (147)

7.3 (185)

Top 30288 (41092) -

3 Bottom 20863

(28305)34024

(46160)

6.1 (156)

13.9 (354)

Top 17974 (24385) -

4 Bottom 10341

(14030)26691

(36212)

5.0 (128)

15.2 (387)

Top 19486 (26437) -

5 Bottom 10758

(14595)15847

(21500)

5.4 (137)

10.7 (273)

Top 16799 (22791) -

6 Bottom 10295

(13967)7298

(9901)

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:

kips 111020

)11095(0.2LM

Vc

pp ===

∑

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

E1-25

Table E1-11 Column Plastic Shears

Plastic Shear Kips (KN) Bent

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


Longitudinal Displacement inches

(mm) Hinge

1076 (4788)

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.

E1-26

Table E1-13 Capacity/Demand Ratios

Location Response Item Longitudinal Transverse

Force – Keys N/A 0.68 Force - Piles N/A 0.77 Abutment 1 Displacement 4.41 N/A Force – Keys N/A 0.73 Force - Piles N/A 0.67 Abutment 7 Displacement 4.56 N/A Displacement 0.53 1 0.96 1 Bent 2

Foundation Shear 1.12 2.23 Displacement 0.67 1 0.74 1 Bent 3




Foundation Shear 1.35 2.94 Displacement 0.53 N/A Hinge 1

Force N/A 0.39 Footnotes: 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.

E1-28

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,

( )abutdbolster VVV −= For Abutment 1 this is calculated as follows

kips 210710920Vbolster =−=

E1-30

At Abutment 7:

ipsk 288576864Vbolster =−= 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 '

cf8 . Therefore,

in 48 D Use

in 5.338834A4(min)D

in 8838.

7068.0

AA

in 706480.085.0

288

f8

V(min)A

bolster

bolsterbolster

2ebolster

2'c

bolstere

=

=π⋅

=π

⋅=

===

=⋅

=⋅φ

=

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:

( ) dowels 21 use dowels 3.213.20

2885.1TV5.1N

7#C

bolsterdowels ∴===

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:

E1-31

circle diameter in 25 a use

in 471)6.3)(2.0(85.0

288f)2.0(

VA 2'c

bolsterpin

⇒

==φ

=

The required area of reinforcing steel crossing the shear plane is:

dowels #8- 7 use

in 83.4)60(0.1

)491(1.085.288

f

cAVA 2

y

cvbolster

vf

∴

=−

=μ

−φ=

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:

ft-k 2155Mbolster = 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

( ) kips 521000

248.036006.0Af6.0V2

e'ccf =

π⋅==

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

( ) kips 28785.0

5285.0288VVV cfbolster

s =−

=φ

φ−=

This requires hoop spacing as follows

θ′′

= cotVDfAs

syhv

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

E1-32

( )( ) ( )

oc 8" @ hoops 6# use

inches 50.843.1288

88.6486044.02

s

∴

=−π

=

This gives a volumetric ratio of

00268.0)12.41(0.8

)44.0(2DsA2 bh

v ==′′

=ρ

Therefore, the assumption for θ can be checked

( )( )( )( )

degrees 1.35

18100140.1144800268.6.1tana

AA6.1tana

25.025.0

gt

ev

=

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛

ρΛρ

=θ

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.

kips 630Vkeys = Therefore, additional shear capacity must be provided as follows based on Abutment 1:

kips 290630920VVV keysdadd =−=−= 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

E1-33

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:

( ) ( )( ) in 1056.385.09.0

290f85.0

VA 2

'c

pipeg ==

φ=

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:

( )

( ) ( )( ) ( )( )

( )( )

( )( ) e)(transvers radians 02811.7.310008868.L

nal)(longitudi radians 01960.1.220008868.Lfollows as are 2 Bent for rotationspastic allowable the Therefore,

0008868.041.359.68

0289.20289.0

77.0708.0T708.0N208.0

wheredd

2

ppp

ppp

p

5.0333.05.0333.0n

5.0fap

app

==φ=θ

==φ=θ

=−

=φ∴

=

===ε

′−

ε=φ

−−−−−

Similarly, plastic rotations for the other columns can be determined

E1-34

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.

E1-36

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

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.

( )( )( )

capacity strain concrete target the as 015. use 0129.)051.13(0000698.00008868.0

dc

chradians/in 0008868.0

cu

ypcu

p

=ε∴=−+=

′′−φ+φ=ε∴

=φ

Using the simplified method, the thickness of a passive carbon-fiber jacket for confinement is given by

( ) in 068.033000

7231E

D31tj

p ===

For lap splice performance:

Bent Longitudinal Transverse

2 6.2

(173) 12.5

(272)

3 8.2

(208) 17.6

(361)

4 6.1

(178) 13.7

(318)

5 6.4

(173) 14.2

(320)

6 6.8

(183) 15.0

(325)

E1-37

( )( ) in 327.033000

3.72500E

Df500tp

p === l

For shear enhancement

( )( )( )( )( )

in 01.0

43.172006.330001416.385.0/85011102

cotDEv2

tpp

sjp

=

−=

θεπ=

Therefore, use t = 0.375 inches at lap zone and t = 0.125 inches elsewhere Check εcu

( ) ( )

( )( )( )( ) OK 015.00324.0

315.702.6000069.5.2004.0

ksi 315.75.533.1f33.1f

02.0ksi 600f

0069.072125.4

Dt4

whereff5.2004.0

cu

'ce

'cc

du

du

ps

'cc

duduscu

∴>=+=ε

===

=ε

=

===ρ

ερ+=ε

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.

( )

bars fuse diameter 1/8"-1 Use

inches 14.1144

60225.1ff2

ddsu

ybf

∴

==<

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

E1-38

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.

( ) ( ) ( )( )

inches 66L Use

inches 75.6364.7263.66016.0

0489.N2D16.0

L

Therefore

radians 0489.

260204

7.62.15

2DL

dd

2L

L

dd

f

5.05.0f

pf

yu

p

yup

=∴

=−=′θ

=

=−

−=

−

−≈

−

−=θ

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

inches 2.126.33

14425.

125.156.0ff

sd56.0L

2

w

su

w

2f

w ===

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

( )00195.0

124022827

412400984.

2827444812

164008.0

1AA

f

f

AfP12

Uf008.0

s

22

s

2

cc

g2

'c

yt

g'c

e

sf

'c

s

=ρ

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+=ρ

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ρ+=ρ

For anti-buckling the transverse reinforcement spacing is limited to 6 inches. For shear resistance

( )( ) ( )

00144.0

0.1204

37.5324022827

216144

9.00984.0.132.02tantan

AA

ffK2

s

cc

g

yh

sutshapes

=ρ

=θαφρ

Λ=ρ

E1-39

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:

kips 450905TNV

ftk 1657

24

0.620.30.6905

2dx

2dxTNM

ppfooting

e2p

e1pppfooting

=⋅==

⋅=

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ π

⋅−+⋅⋅=⎟⎠

⎞⎜⎝

⎛ −+−=

The ultimate moment resistance provided by 16 #6 reinforcing bars is given by:

OK 1657 ftk 1752

21212155.5

6044.16

64.46044.1690.02adfAM ysu

>⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛⋅⋅⋅

⋅⋅

−⋅⋅⋅=⎟⎠⎞

⎜⎝⎛ −φ=

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

( ) 2

3

footingerfaceint k/ft 76.5

15121155

0.2150.1450Ib

QV=

⋅⋅⋅

⋅⋅==ν

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

E1-40

OK 5.76 kips 97.62.885.0vdowelu >=⋅=φ=ν

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.

E1-41

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.

ftk 1741

24

0.55.4904

24

0.533.7902

2d

xTN2

dxTNM

ftk 3482

24

0.55.41804

24

0.533.71802

2dxCN

2dxCNM

e2p2p

e1p1pfneg

e2p2p

e1p1pfpos

⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ π

−⋅+⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ π

−⋅=⎟⎠

⎞⎜⎝

⎛ −+⎟⎠

⎞⎜⎝

⎛ −=

⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ π

−⋅+⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛ π

−⋅=⎟⎠

⎞⎜⎝

⎛ −+⎟⎠

⎞⎜⎝

⎛ −=

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.

ftk 27832

1212125.585.0600.112

34.4600.1129.02adfAM yscexist ⋅=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛⋅⋅⋅⋅

⋅⋅

−⋅⋅⋅=⎟⎠⎞

⎜⎝⎛ −φ=

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

E1-42

OK 3482 ftk 416513822783MMM

ftk 13822

121267.55.385.0600.16

34.4600.169.02adfAM

cnewcexistctotal

yscnew

>⋅=+=+=∴

⋅=⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛⋅⋅⋅⋅

⋅⋅

−⋅⋅⋅=⎟⎠⎞

⎜⎝⎛ −φ=

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:

( ) ( ) kips 70253610763.1VVLV keysdfdersdpipeexten =−=−= 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:

units. extender pipe 4 Use 9.3180

VN dersdpipeexten

erspipeextend ∴==

E1-44

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.

E1-46

Appendix E1-1

!--------------------------------------------------------------------

! 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


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74


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 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


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


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


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





! E 001 2 2 ! TOP OF COLUMN 2





! E 001 4 1 10 ! FOUNDATION SPRINGS

!--------------------------------------------------------------------

*NODALOAD

PUS1 FRAME 1 PUSHOVER PATTERN

S 1.0 0.0 201

!--------------------------------------------------------------------

*NODALOAD


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

!---------------------------------------------------------------------


N PUS2

D 401 1 0.01 0.500

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------


! File : RETEXA






! 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


! -----------------------------

! 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


C 210 76.71 95.79

C 220 76.71 75.79

C 230 76.71 75.79


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74


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 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



! 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



1 101 102 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


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


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


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


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



! 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



2 320 330 1

3 420 430 2

4 520 530 2

5 620 630 2


7 320 330 3

8 420 430 4

9 520 530 4

10 620 630 4


12 320 330 5

13 420 430 5

14 520 530 5

15 620 630 5

!-----------------------------------------------------------------------------

*RESULTS












!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 201

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!--------------------------------------------------------------------


N PUS1

D 201 1 0.01 0.750

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------


! File : RETEXB






! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn

!--------------------------------------------------------------------

*STARTXX

retexb 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! 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


C 210 76.71 95.79

C 220 76.71 75.79

C 230 76.71 75.79


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74


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 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



! 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



1 101 102 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


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


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


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


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



! 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



2 320 330 1

3 420 430 2

4 520 530 2

5 620 630 2


7 320 330 3

8 420 430 4

9 520 530 4

10 620 630 4


12 320 330 5

13 420 430 5

14 520 530 5

15 620 630 5

!-----------------------------------------------------------------------------

*RESULTS












!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 401

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 401 1 0.01 0.750

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - TRANSVERSE BENT 2 PUSHOVER

! File : RETBT2




! 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


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


1 201 210 1 1 1 1

2 210 220 1 2 2 2

!--------------------------------------------------------------------

*ELEMENTGROUP



! 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





!-----------------------------------------------------------------------------

*RESULTS




!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 201

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!--------------------------------------------------------------------


N PUS1

D 201 1 0.01 1.500

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - TRANSVERSE BENT 3 PUSHOVER

! File : RETBT3






! 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


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*MASSES

S 010 33.2 301

!--------------------------------------------------------------------

*ELEMENTGROUP


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


1 301 310 1 1 1 1

2 310 320 1 2 2 2

*ELEMENTGROUP



! 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





!-----------------------------------------------------------------------------

*RESULTS


! E 001 1 2 ! BOTTOM OF COLUMN 3


!--------------------------------------------------------------------

*NODALOAD

PUS1 BENT 3 PUSHOVER PATTERN

S 1.0 0.0 301

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!--------------------------------------------------------------------


N PUS1

D 301 1 0.01 2.000

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER - BT 4

! File : RETBT4






! 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


! -----------------------------

! Superstructure

C 401 271.94 100.0 ! Bent 4


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*MASSES

S 010 448.0 401 32.2

!--------------------------------------------------------------------

*ELEMENTGROUP


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


1 401 410 1 1 1 1

2 410 420 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 420 430 1

2 420 430 2

3 420 430 3

!-----------------------------------------------------------------------------

*RESULTS




!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 401

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 401 1 0.01 2.000

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER

! File : RETBT5






! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn


!--------------------------------------------------------------------

*STARTXX

retbt5 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! Superstructure

C 501 328.29 100.0 ! Bent 5


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*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


1 501 510 1 1 1 1

2 510 520 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 520 530 1

2 520 530 2

3 520 530 3

!-----------------------------------------------------------------------------

*RESULTS



E 001 2 1 3 ! FOUNDATION SPRINGS

!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 501

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 501 1 0.01 1.500

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------


! File : RETBT6





! Push Bent at superstructure level

! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn


!--------------------------------------------------------------------

*STARTXX

retbt6 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! Superstructure

C 601 386.29 100.0 ! Bent 6


C 610 386.29 97.75

C 620 386.29 80.74

C 630 386.29 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*MASSES

S 010 545.0 601 32.2

!--------------------------------------------------------------------

*ELEMENTGROUP


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


1 601 610 1 1 1 1

2 610 620 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 620 630 1

2 620 630 2

3 620 630 3

!-----------------------------------------------------------------------------

*RESULTS




!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 601

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 601 1 0.01 1.500

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER - STRATEGY EVALUATION

! File : SETEXA






! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn


!--------------------------------------------------------------------

*STARTXX

setexa 0 1 1 0 F EXAMPLE PROBLEM LONGITUDINAL

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! 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


C 210 76.71 95.79

C 220 76.71 75.79

C 230 76.71 75.79


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74


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 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



! 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



1 101 102 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


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


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


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


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



! 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 9225 -9225 1 3 1

5 1000000 0.00 1000000 -1000000 1 2 1 ! vertical



2 320 330 1

3 420 430 2

4 520 530 2

5 620 630 2


7 320 330 3

8 420 430 4

9 520 530 4

10 620 630 4


12 320 330 5

13 420 430 5

14 520 530 5

15 620 630 5

!-----------------------------------------------------------------------------

*RESULTS












!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 201

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!--------------------------------------------------------------------


N PUS1

D 201 1 0.01 1.000

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - LONGITUDINAL PUSHOVER - STRATEGY EVALUATION

! File : SETEXB






! 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


! -----------------------------

! 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


C 210 76.71 95.79

C 220 76.71 75.79

C 230 76.71 75.79


C 310 198.68 95.79

C 320 198.68 71.29

C 330 198.68 71.29


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74


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 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



! 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



1 101 102 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


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


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


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


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



! stiffness types

5

1 14880 0.00 1240 -1240 1 1 1 ! horizontal

springs

2 9984 0.00 1248 -1248 1 1 1

3 875000 0.00 12150 -12150 1 3 1 ! rotational

springs

4 332000 0.00 9225 -9225 1 3 1

5 1000000 0.00 1000000 -1000000 1 2 1 ! vertical



2 320 330 1

3 420 430 2

4 520 530 2

5 620 630 2


7 320 330 3

8 420 430 4

9 520 530 4

10 620 630 4


12 320 330 5

13 420 430 5

14 520 530 5

15 620 630 5

!-----------------------------------------------------------------------------

*RESULTS












!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 401

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 401 1 0.01 1.000

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------

! RETROFIT EXAMPLE 1 - TRANSVERSE PUSHOVER - BT 4

! File : SETBT4






! 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


! -----------------------------

! Superstructure

C 401 271.94 100.0 ! Bent 4


C 410 271.94 97.75

C 420 271.94 80.74

C 430 271.94 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*MASSES

S 010 448.0 401 32.2

!--------------------------------------------------------------------

*ELEMENTGROUP


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


1 401 410 1 1 1 1

2 410 420 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 420 430 1

2 420 430 2

3 420 430 3

!-----------------------------------------------------------------------------

*RESULTS




!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 401

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 401 1 0.01 2.000

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------


! File : SETBT5






! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn


!--------------------------------------------------------------------

*STARTXX

setbt5 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! Superstructure

C 501 328.29 100.0 ! Bent 5


C 510 328.29 97.75

C 520 328.29 80.74

C 530 328.29 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*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


1 501 510 1 1 1 1

2 510 520 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 520 530 1

2 520 530 2

3 520 530 3

!-----------------------------------------------------------------------------

*RESULTS



E 001 2 1 3 ! FOUNDATION SPRINGS

!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 501

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 501 1 0.01 1.500

!---------------------------------------------------------------------

*STOP

!--------------------------------------------------------------------


! File : SETBT6





! Push Bent at superstructure level

! Units: kips, ft

!

! ! NOTE :

! 1. 2/3/2004 rvn


!--------------------------------------------------------------------

*STARTXX

setbt6 0 1 1 0 F EXAMPLE PROBLEM TRANSVERSE

!--------------------------------------------------------------------

*NODECOORDS

! -----------------------------

! NODES


! -----------------------------

! Superstructure

C 601 386.29 100.0 ! Bent 6


C 610 386.29 97.75

C 620 386.29 80.74

C 630 386.29 80.74

!--------------------------------------------------------------------

*RESTRAINTS


!--------------------------------------------------------------------

*MASSES

S 010 545.0 601 32.2

!--------------------------------------------------------------------

*ELEMENTGROUP


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


1 601 610 1 1 1 1

2 610 620 1 2 2 2

!-------------------------------------------------------------------

*ELEMENTGROUP



! 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


1 620 630 1

2 620 630 2

3 620 630 3

!-----------------------------------------------------------------------------

*RESULTS




!--------------------------------------------------------------------

*NODALOAD


S 1.0 0.0 601

!--------------------------------------------------------------------

*PARAMETERS

OS 1 0 -1 0

!--------------------------------------------------------------------


I 32.2 0 -1 ! Gravity

!---------------------------------------------------------------------


N PUS2

D 601 1 0.01 1.500

!---------------------------------------------------------------------

*STOP

E1-47

Appendix E1-2

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


BC 21 + 84.68

RADIUS R 590.0


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'


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


RESPONSE SPECTRUM ANALYSIS

C AS-BUILT ANALYSIS - TENSION

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



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





C **********************************


C **********************************

FOUNDATION

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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



C AS-BUILT ANALYSIS - COMPRESSION ABUT 1

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



C **********************************


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





C **********************************


C **********************************

FOUNDATION

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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



C AS-BUILT ANALYSIS - COMPRESSION ABUT 7

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



C **********************************


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





C **********************************


C **********************************

FOUNDATION

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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



C STRATAGY 1 ANALYSIS - TENSION

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



C **********************************


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 TOP FREE AT BENT 2,5,6



C **********************************


C **********************************

FOUNDATION

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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



C STRATAGY 1 ANALYSIS - COMPRESSION ABUT 1

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



C **********************************


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



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

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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



C STRATAGY 1 ANALYSIS - COMPRESSION ABUT 7

C ************************************


C ************************************


STATION 18 + 00.00

COORDINATES N 10000.00 E 10000.00


BC 18 + 85.15

RADIUS R 600.0


BC 21 + 84.68

RADIUS R 590.0


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

C ***********************************


C ***********************************


AREA 28.3

I11 25.4

I22 19.4

I33 19.4

DENSITY .150

E 661680.


AREA 19.6

I11 12.3

I22 9.9

I33 9.9

DENSITY .150

E 661680.

C ***********************************

C PILE SUB BLOCK *

C ***********************************


STIFFNESS

KF1F1 480.

KF1M3 0.

KF2F2 4040.

KF3F3 480.

KF3M1 0.0

KM1M1 0.0

KM2M2 0.0

KM3M3 0.0

C ***********************************


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 **********************************



C **********************************


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 TOP FREE AT BENTS 2,5,6



C **********************************


C **********************************

FOUNDATION

AT BENT 2,3

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '23'


AT BENT 4,5,6

SPRING CONSTANTS

KF1F1 3600

KF3F3 3600

PILE FOOTING '456'


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

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

example of box girder bridge calculation

Documents

column transverse steel

main reinforcing steel

span cast

method d2 seismic evaluation

transverse concrete

single expansion joint

seismic retrofitting

seismic uplift capacity