Trial Design IL-2

AASHTO T-3 TRIAL DESIGN BRIDGE DESCRIPTION

State: Illinois Trial Design Designation: IL-2 Bridge Name: Superstructure Type: Simply supported steel wide flange with concrete deck Span Length(s): 62.0 ft. - 77.0 ft. - 62.0 ft. (total 201.0 ft.) Substructure Type: Drop cap supported on 4 reinforced concrete columns with monolithic connections at the column top and bottom Foundation: Steel piles at the abutments and bents Abutments: Seat type supported on steel piles Seismic Design Category (SDC): C Seismic Design Strategy (Type 1, 2 or 3): Type 1 Design Spectral Acceleration at 1-second Period (SD1): 0.487g Additional Description (Optional): Bridge simplified with an assumed zero degree skew.

Transverse Base Sh & Displ Pg. 1Bridge No.: 2 Template For Transverse Seismic CalculationsDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments

(Skew Simplified to 0 degrees)

Design Response Specturm

62 ft. 77 ft. 62 ft.62 ft. 77 ft. 62 ft.Varies

2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Transverse Base Sh & Displ Pg. 2

SDC and Other Pertinent Design Spectrum Information

SD1 = 0.487 g Seismic Design Category CSDS = 1.128 g 0.3g

Transverse Base Sh & Displ Pg. 3Simple Cross Section of Deck

Weight of Super and Sub Structure for Seismic Calculations

Beams W36 x 170No. Beams 7.00

Beam Spacing 6.00 ft.Wt. of 1 Beam 0.17 k/ft.

Wt. Tot. Beams 1.19 k/ft.

Th. of Slab 7.50 in.Th. of Surface 1.50 in.

Width 42.00 ft.Wt. of Slab 4.73 k/ft.

ParapetArea 1 1.12 ft^2Area 2 0.56 ft^2Area 3 0.83 ft^2

Total Area 2.51 ft^2Wt. of Parapet 0.38 k/ft.

Cross FramesAnd Bracing(est. as 5% 5.00 %

of Steel) 0.06 k/ft

Steel ParapetRail

(est. as 2% 2.00 %of Steel) 0.02 k/ft

Cap BeamLength 60.42 ft.Width 2.50 ft.

Height 4.00 ft.Wt. of 1 Beam 90.63 kips

Wt. of 2 Beams 181.26 kips

12

3

12

3

12

3

12

3

42 ft.

6 spaces @ 6 ft. = 36 ft.

7 in. 1 in. Added Surface 12

3

12

3

12

3

12

3

42 ft.

6 spaces @ 6 ft. = 36 ft.

7 in. 1 in. Added Surface

12

3

1.35 ft.

1.0 ft.

0.83 ft.

0.83 ft.

1.66 ft.

12

3

12

3

1.35 ft.

1.0 ft.

0.83 ft.

0.83 ft.

1.66 ft.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Transverse Base Sh & Displ Pg. 4Weight of Super and Sub Structure for Seismic Calculations (Cont.)

1/2 of ColumnsDiameter 2.17 ft.

Height 8.38 ft.Wt. of 1 Col. 4.65 kips

No. of Columns 8Wt. of 8 Col. 37.17 kips

Total Wt.for Seismic

CalculationsSuper Length 201 ft.Total Weight 1575 kips

Transverse Period Calculation

Pier StiffnessTransverse

Directionf'c 3500 psiEc 3372 ksicol 2.17 ft

Ic 22432 in4

IcEFF 15702 in4 cracked section (varies from 0.4 to 0.7 Ic)

No. columns 44 x IcEFF 62809 in4 cracked section (varies from 0.4 to 0.7 Ic)

hc 300 inches (clear column height)kc 24 k/in

kpier 94 k/in

I of Super-structure

Transverse

Es 29000 ksif'c 3000 psiEc 3122 ksi

n (mod. Ratio) 9.3 Transf. Area with 50% Shear LagI slab 80015040 in

4

AreaParapet 361.4 in2

Area 1 Beam 50 in2

AreaSteel Bm 232.2 in2 (Transformed)

3c

ccc h

IE12k

=1000

f57000E

'c

c =4

2I

4col

c

=

2AreanArea Beam Steel

=

Transverse Base Sh & Displ Pg. 5Transverse Period Calculation (Cont.)

Momen of Inertia of Superstructure TableNo. I0 (In

4) A (in2) x bar (in) A (x bar)2 (in4) I (in4)

Parapet 2 ---- 361.44 240 20818944 41637888Slab 1 80015040 ---- ---- 80015040 80015040

Steel 1 2 ---- 232.2 72 1203836.526 2407673.05Steel 2 2 ---- 232.2 144 4815346.106 9630692.21Steel 3 2 ---- 232.2 216 10834528.74 21669057.5

ITotal 1.554E+08 in4

ATotal 6884 in2

Model the Bridge Transversely with Itotal of the Superstr. and Springs for the Abutment Piles and Pier Cols.

Estimate the Abutment Pile Transverse StiffnesskA 1000 k/in

Solve for the Displacement from Simple Model Above as Outlined Below for a 1 k/in Uniform Load

Find the Deflection at the Center of the Bridge Assuming No Piers and Infinitely Stiff Abutments

w 1 k/inL 2412 in

Ec 3122 ksiITotal 1.554E+08 in

4

c 0.909 in

Find the Deflection Along the Bridge Assuming an Infinitely Stiff Superstr., No Piers, and Abut. Springs

w 1 k/inL 2412 in

kA 1000 k/ine 1.206 in

0.909

1.206

Totalc

4

C IE384Lw5=

Ae k

2Lw

=

62 ft. = 744 in. 77 ft. = 924 in. 62 ft. = 744 in.

201 ft. = 2412 in.

kA kAkpier kpier

ITotal

62 ft. = 744 in. 77 ft. = 924 in. 62 ft. = 744 in.

201 ft. = 2412 in.

kA kAkpier kpier

ITotal


Find the Total Estimated Displacement Without the Piers

T = c + e 2.115 in

Find the Estimated Deflection at the Center of the Bridge for a Two Point Load at Piers with Infinitely Stiff Abuts.In Terms of an Applied Load "P".

L 2412 inx 744 ina 744 in


4

vc 0.0009740 P

Find the Estimated Deflection at the Pier of the Bridge for a Two Point Load at Piers with Infinitely Stiff Abuts.In Terms of an Applied Load "P".

L 2412 inx 744 ina 744 in


4

vp 0.0008103 P

a and x

L

a and xL 2a

P P

vc

a and x

L

a and xL 2a

P P

vc

( )22Totalc

v c a4L3IE24aP

=

a and x

L

a and xL 2a

P P

vp

a and x

L

a and xL 2a

P P

vp

( )22Totalc

v p xa3aL3IE6xP

=


Find the Estimated Uniform Deflection for a Two Point Load at Piers with Springs at Abuts.In Terms of an Applied Load "P".

kA 1000 k/inve 0.001 P

Find the Fraction of the Estimated Pier Deflection at the Piers Versus that at Center Span

vc 0.0009740 Pvp 0.0008103 Pve 0.001 P

fr 0.917

Find the Pier Reactions (V0) in Terms of max, the Actual Estimated Deflection of the Bridge

fr 0.917kpier 94 k/in

V0 86.3 max

Solve for max:

ve + vc = 0.001974 P

Set:P = V0 = 86.3 maxTherefore:ve + vc = 0.001974 x 86.3 x maxve + vc = 0.170408 maxAnd:

The Actual Estimated Delfection of the Bridge is the Deflection Without Piers Minus theContribution with the Piers

max = T - 0.170408 maxmax = 2.115 / 1.170408max = 1.807 in

Av e k

P=

v cve

v pv efr ++=

piermax0 kfrV =

P P

ve

P P

ve


Solve for the "Equivalent Stiffness" of the Bridge in the Transverse Direction

w 1 k/inL 2412 in

max 1.807 inkBridge 1335 k/in

Solve for the Period T

Tot. Weight (W) 1575 kipsg 386.4 in/sec2

kBridge 1335.016 k/inT 0.35 seconds

Transverse Seismic Force On Superstructure (Base Shear)

0.35 < 0.432 seconds

Therefore: 112.8% of the Mass is "Effective" and the Total Seismic Load in the Transverse Direction is:

1.128 x 1575 = 1777 kips (Base Shear)

or:1777 / 2412 = 0.74 k/in (Base Shear)

Transverse Seismic Force on Pier (Base Shear)

VBase Shear P = 0.74 / 1 x 1.807 x 86.3

VBase Shear P = 115 kips

Transverse Seismic Force on Abutments (Base Shear)

VBase Shear A = 1777 / 2 - 115

VBase Shear A = 774 kips

Transverse Seismic Displacement of Pier

PierT = 115 / 94 = 1.22 in.

maxBridge

Lwk =

BridgekgW2T =

Transverse Base Sh & Displ Pg. 9

Bridge No.: 2 Transverse SummaryDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Summary of Transverse Periods, Deflections and Base Shears for 16 Cases

Imbsen Fig. 5.4Transverse Transverse

Column Steel Fraction Trans. Trans. Base Shear Base ShearHeight Ratio of Ig Period Deflection Pier Abutments

(ft.) (Ast/Ag) (Sec.) (in) (kips) (kips)10 0.01 0.4 0.24 0.57 476 412

0.02 0.5 0.22 0.49 517 3710.03 0.6 0.21 0.44 549 3400.04 0.7 0.20 0.39 574 315

15 0.01 0.4 0.31 0.98 245 6430.02 0.5 0.30 0.91 284 6040.03 0.6 0.29 0.85 318 5700.04 0.7 0.28 0.80 348 540

20 0.01 0.4 0.34 1.20 126 7620.02 0.5 0.34 1.15 152 7370.03 0.6 0.33 1.11 175 7130.04 0.7 0.33 1.07 197 691

25 0.01 0.4 0.36 1.30 70 8190.02 0.5 0.35 1.27 86 8030.03 0.6 0.35 1.25 101 7880.04 0.7 0.35 1.22 115 774

62 ft. 77 ft. 62 ft.62 ft. 77 ft. 62 ft.Varies

2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Long. Base Sh & Displ Pg. 1Bridge No.: 2 Template For Longitudinal Seismic CalculationsDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Weight ofSuperstructure

Total Weight 1575 kips

Longitudinal Period Calculation

Pier StiffnessLongitudinal

Direction

Contribution from Columnf'c 3500 psiEc 3372 ksicol 2.17 ft

Ic 22570 in4

IcEFF 15799 in4 cracked section (Varies from 0.4 to 0.7 Ic)

No. columns 44 x IcEFF 63196.3288 in

4 cracked section (Varies from 0.4 to 0.7 Ic)hc 300 inches (clear column height)kc 6 k/in

kcols 24 k/in

62 ft. 77 ft. 62 ft.62 ft. 77 ft. 62 ft.

1000f57000

E'c

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

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cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

cc

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cc

cc

cc

cc

c

Pier Des. Forces Pg. 1Bridge No.: 2 Template For Seismic Pier Design Force CalculationsDescription3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Pier Forces

Dead

Dead Load Total 1575 kipsBridge Length 201 ft.Dead Load per ft. 7.84 k/ftDead Load per pier 605.5 kipsNo. of Columns 4Dead Ld. Per Col. 151.4 kipsPlus 1/2 1 Col. 4.65 kipsDesign Dead 156.0 kips

Transverse Overturning

62 ft. 77 ft. 62 ft.62 ft. 77 ft. 62 ft.

Sp

d d

PSTarm0.33PST

d

PST0.33PST

( )( )

dM

103P

dP2 dP2M

armSM

ST

21

ST31

23

ST

p

=

+==

Sp

d d

PSTarm0.33PST

d

PST0.33PST

( )( )

dM

103P

dP2 dP2M

armSM

ST

21

ST31

23

ST

p

=

+==

ft. per Load Deadw

L21L

85wpier per DL CenterSpanOuterSpan

=

+=

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Pier Des. Forces Pg. 2Transverse Overturning (Cont.)

SP (Pier Base Shear) 115 kipsarm 8 ft.d 14.67 ft.M 919.3 k-ft.PST 18.8 kips

Frame Action Transverse

SP (Pier Base Shear) 115 kipsNo. of Columns 4Column Height (h) 25.00 ftVST (Shear per col) 28.7 kipsMST (Mom. per col) 359.1 k-ft

d 14.67 ft.MST (Mom. per col) 359.1 k-ftPSB 40.9 kips

d

col.right far Comp. & & col.left far Tension P

dM67.1

d3

M2MP

VP ;MM

SB

ST

STST

SB

SBSBSTSB

=

=+=

==

VST VST VST

MST

h

MSB 2MSB/3

VSB

VSB

PSBd

Note: VST not shown for clarity

4SV PST =

VST

2MSB/3 MSB/3

0.4VSB

VSB

d

MST

0.6PSB

MSB/3

0.4VSB

d

col.right far Comp. & & col.left far Tension P

dM67.1

d3

M2MP

VP ;MM

SB

ST

STST

SB

SBSBSTSB

=

=+=

==

VST VST VST

MST

h

MSB 2MSB/3

VSB

VSB

PSBd

Note: VST not shown for clarity

4SV PST =

VST

2MSB/3 MSB/3

0.4VSB

VSB

d

MST

0.6PSB

MSB/3

0.4VSB

2hVM STST

=

VST

VST

MST

MST

2hVM STST

=

VST

VST

MST

MST

4SV PST =

2hVM STST

=

VST

VST

MST

MST

2hVM STST

=

VST

VST

MST

MST

2hVM STST

= 2hVM STST

=

VST

VST

MST

MST

2hVM STST

= 2hVM STST

=

VST

VST

MST

MST

4SV PST = 4SV PST =

Pier Des. Forces Pg. 3Longitudinal Shear and Moments (Simple Cantilever Statics)

SL (Pier Base Shear) 187 kipsNo. of Col. 4Cap arm 4 ft.Col arm (h) 25.00 ft.VSL 46.7 kipsMColTop (SLT) 186.9 k-ft.MColBot (SLB) 1354.8 k-ft.

P- Moment Amplification for Column DesignAssume = 1.05 for all casesR-Factor

Assume R = 3.5 for Transverse and Longitudinal Moments

Design Axial Forces and Moments For Columns (Orthogonally Combined)

2

alLongitudinSLB

2

TransverseST

DesignL

2

alLongitudinSLB

2

TransverseST

DesignT

SBST

SBSTMaxDeadDesignL

SBSTMaxDeadDesignT

RM

RM3.0M

Dom. Dir. alLongitudin - nsCombinatio Moment Reduced Factor-R and AmplifiedP

RM3.0

RMM

Dom. Dir. Transverse - nsCombinatio Moment Reduced Factor-R and AmplifiedP

column the on depending zero or negative positive either can P and P :Note

P3.0P3.0PPDominant Direction alLongitudin- nsCombinatio Force Axial

PPPPDominant Direction Transverse- nsCombinatio Force Axial

+

=

+

=

=

=

Pier Des. Forces Pg. 4Design Axial Forces and Moments For Columns (Orthogonally Combined) (Cont.)

Transverse Dominant (Load Case 1)

Column 1 2 3 4PDesignT 96.3 174.3 137.7 215.7 kipsMDesignT 162.7 162.7 162.7 162.7 k-ft.

Longitudinal Dominant (Load Case 2)

Column 1 2 3 4PDesignL 138.1 161.5 150.5 173.9 kipsMDesignL 407.7 407.7 407.7 407.7 k-ft.

Elastic (Not combined Orthogonal Shears)

TransverseVST 28.7 kips

LongitudinalVSL 46.7 kips

alLongitudinTransverseg RR

Pier Des. Forces Pg. 5Bridge No.: 2 Seismic Pier Design Force SummaryDescription3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Summary of Seismic Design Pier Forces for 16 Cases

Imbsen Fig. 5.4 Transverse Dominant (Load Case 1) Trans.Col 1 Col 2 Col 3 Col 4 Col 1 to 4 Elastic

Column Steel Fraction PDesignT PDesignT PDesignT PDesignT MDesignT ShearHeight Ratio of Ig Per Col.

(ft.) (Ast/Ag) (kips) (kips) (kips) (kips) (k-ft) (kips)10 0.01 0.4 10.3 171.0 141.1 301.7 236.4 119.1

0.02 0.5 -2.3 172.3 139.8 314.3 260.0 129.30.03 0.6 -11.9 173.2 138.8 323.9 279.8 137.20.04 0.7 -19.5 174.0 138.0 331.6 297.1 143.4

15 0.01 0.4 63.5 174.2 137.8 248.5 184.3 61.30.02 0.5 48.7 177.1 134.9 263.3 210.5 71.10.03 0.6 35.9 179.6 132.4 276.1 233.5 79.60.04 0.7 24.8 181.8 130.2 287.3 254.0 87.0

20 0.01 0.4 99.5 170.7 141.3 212.6 140.7 31.50.02 0.5 88.1 173.7 138.3 224.0 162.7 37.90.03 0.6 77.5 176.5 135.6 234.6 183.1 43.80.04 0.7 67.7 179.0 133.0 244.4 202.0 49.3

25 0.01 0.4 119.6 167.2 144.8 192.4 113.2 17.50.02 0.5 111.5 169.7 142.4 200.5 130.6 21.40.03 0.6 103.8 172.1 140.0 208.3 147.1 25.10.04 0.7 96.3 174.3 137.7 215.7 162.7 28.7

Imbsen Fig. 5.4 Longitudinal Dominant (Load Case 2) Long.Col 1 Col 2 Col 3 Col 4 Col 1 to 4 Elastic

Column Steel Fraction PDesignL PDesignL PDesignL PDesignL MDesignL ShearHeight Ratio of Ig Per Col.

(ft.) (Ast/Ag) (kips) (kips) (kips) (kips) (k-ft) (kips)10 0.01 0.4 112.3 160.5 151.5 199.7 518.9 122.9

0.02 0.5 108.5 160.9 151.1 203.5 580.0 137.40.03 0.6 105.6 161.2 150.8 206.4 635.1 150.50.04 0.7 103.4 161.4 150.6 208.7 685.8 162.6

15 0.01 0.4 128.3 161.5 150.6 183.8 409.7 71.50.02 0.5 123.8 162.3 149.7 188.2 458.2 79.90.03 0.6 120.0 163.1 148.9 192.0 502.1 87.60.04 0.7 116.6 163.8 148.3 195.4 542.4 94.6

20 0.01 0.4 139.1 160.4 151.6 173.0 348.2 48.20.02 0.5 135.6 161.3 150.7 176.4 389.5 53.90.03 0.6 132.5 162.2 149.9 179.6 426.9 59.00.04 0.7 129.5 162.9 149.1 182.5 461.2 63.8

25 0.01 0.4 145.1 159.4 152.7 166.9 307.9 35.30.02 0.5 142.7 160.1 151.9 169.4 344.3 39.50.03 0.6 140.3 160.8 151.2 171.7 377.3 43.30.04 0.7 138.1 161.5 150.5 173.9 407.7 46.7

Pier Col Vert Reinf. Des. Pg. 1Bridge No.: 2 Force Based Pier Vertical Reinforcment Design for 4 Col. HeightsDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments

(Skew Simplified to 0 degrees) ( = 1.0 for Design)

Col. Height 10 ft. Ast 12.7 in2

Assumed Columns are Ag 530.9 in2

"Half Cracked" for Design 0.5 Ic Ast/Ag 2.4 %

Computer Program Design Dialog Box

Computer Program Column Design Envelope

Pier Col Vert Reinf. Des. Pg. 2

Bridge No.: 2 Force Based Pier Vertical Reinforcment Design for 4 Col. HeightsDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Col. Height 15 ft. Ast 10.0 in2

Assumed Columns are Ag 530.9 in2

"Half Cracked" for Design 0.5 Ic Ast/Ag 1.9 %






Col. Height 20 ft. Ast 8.0 in2 Vert. Bar SpacingAssumed Columns are Ag 530.9 in2 Just Larger than 8 in."Half Cracked" for Design 0.5 Ic Ast/Ag 1.5 % Say OK






Col. Height 25 ft. Ast 6.3 in2 Vert. Bar SpacingAssumed Columns are Ag 530.9 in2 Just Larger than 8 in."Half Cracked" for Design 0.5 Ic Ast/Ag 1.2 % Say OK



Pier Displ Check Pg. 1Bridge No.: 2 Imbsen Displ. Checks for 16 Cases (& Force Based Design Comparisons)Description: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Scratch Calculation Table

Imbsen Section 4.8Column Column H/100 x Delta Delta H/100 x Delta DeltaHeight Diameter Fixed- Calc. Allow. Fixed- Calc. Allow.

Fixed Fixed - Fixed - Pinned Fixed - Fixed -Fixed Fixed Pinned Pinned

(ft) (ft) (in) (in) (in) (in) (in) (in)10 2.17 1.20 0.43 0.86 1.20 1.20 0.22 2.79 2.7915 2.17 1.80 0.29 2.99 2.99 1.80 0.14 5.88 5.8820 2.17 2.40 0.22 5.59 5.59 2.40 0.11 9.45 9.4525 2.17 3.00 0.17 8.54 8.54 3.00 0.09 13.36 13.36

62 ft. 77 ft. 62 ft.62 ft. 77 ft. 62 ft. Varies 2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Varies2 ft. 2 in.

60 ft. 5 in.

4 ft.

4 ft.2 ft. 3 in.

Pier Displ Check Pg. 2Transverse Direction

Imbsen Fig. 5.4 Imbsen Sec. 4.3.3 Uncombined Req. SeismicShort Trans Ast/Ag

Column Steel Fraction Trans. Trans. Period Trans Allow. Force Height Ratio of Ig Period Deflection Ampl. Des. Defl. Des. Defl. Based

(ft.) (Ast/Ag) (Sec.) (in) (in) (in) Design10 0.01 0.4 0.24 0.57 1.86 1.06 1.20

0.02 0.5 0.22 0.49 2.00 0.98 1.20 0.0240.03 0.6 0.21 0.44 2.08 0.91 1.200.04 0.7 0.20 0.39 2.17 0.85 1.20

15 0.01 0.4 0.31 0.98 1.52 1.49 2.990.02 0.5 0.30 0.91 1.56 1.42 2.99 0.0190.03 0.6 0.29 0.85 1.60 1.36 2.990.04 0.7 0.28 0.80 1.64 1.31 2.99

20 0.01 0.4 0.34 1.20 1.41 1.69 5.590.02 0.5 0.34 1.15 1.41 1.62 5.59 0.0150.03 0.6 0.33 1.11 1.44 1.60 5.590.04 0.7 0.33 1.07 1.44 1.55 5.59

25 0.01 0.4 0.36 1.30 1.35 1.76 8.540.02 0.5 0.35 1.27 1.38 1.75 8.54 0.0120.03 0.6 0.35 1.25 1.38 1.73 8.540.04 0.7 0.35 1.22 1.38 1.68 8.54

Longitudinal Direction

Imbsen Fig. 5.4 Uncombined Req. SeismicLongitudinal Ast/Ag

Column Steel Fraction Long. Long. Allowable Force Height Ratio of Ig Period Deflection Deflection Based

(ft.) (Ast/Ag) (Sec.) (in) (in) Design10 0.01 0.4 0.78 3.72 2.79

0.02 0.5 0.70 3.33 2.79 0.0240.03 0.6 0.64 3.04 2.790.04 0.7 0.59 2.81 2.79

15 0.01 0.4 1.34 6.39 5.880.02 0.5 1.20 5.72 5.88 0.0190.03 0.6 1.10 5.22 5.880.04 0.7 1.01 4.83 5.88

20 0.01 0.4 1.99 9.48 9.450.02 0.5 1.78 8.48 9.45 0.0150.03 0.6 1.62 7.74 9.450.04 0.7 1.50 7.17 9.45

25 0.01 0.4 2.72 12.95 13.360.02 0.5 2.43 11.58 13.36 0.0120.03 0.6 2.22 10.57 13.360.04 0.7 2.05 9.79 13.36

Pier Displ Check Pg. 3Orthongonally Combined

Imbsen Fig. 5.4 Ld. Case 1 Ld. Case 1 Ld. Case 2 Ld. Case 2 RequiredTrans. Trans. Long. Long. Seismic

Dominant Dominant Dominant Dominant Ast/AgColumn Steel Fraction Combined Combined Combined Combined Force Height Ratio of Ig Allowable Allowable Based

(ft.) (Ast/Ag) (in) (in) (in) (in) Design10 0.01 0.4 1.54 1.46 3.73 2.82

0.02 0.5 1.40 1.46 3.34 2.82 0.0240.03 0.6 1.29 1.46 3.05 2.820.04 0.7 1.19 1.46 2.82 2.82

15 0.01 0.4 2.43 3.47 6.41 5.950.02 0.5 2.22 3.47 5.74 5.95 0.0190.03 0.6 2.07 3.47 5.24 5.950.04 0.7 1.96 3.47 4.85 5.95

20 0.01 0.4 3.31 6.27 9.49 9.590.02 0.5 3.02 6.27 8.49 9.59 0.0150.03 0.6 2.82 6.27 7.75 9.590.04 0.7 2.65 6.27 7.18 9.59

25 0.01 0.4 4.26 9.43 12.96 13.610.02 0.5 3.89 9.43 11.59 13.61 0.0120.03 0.6 3.61 9.43 10.58 13.610.04 0.7 3.39 9.43 9.80 13.61

Pier Col Sh Reinf Design Pg. 1Bridge No.: 2 Pier Shear Reinforcement DesignDescription: 3-Span Wide Flange with Cicrular Pier Columns and Steel Piles at Piers and Abutments


Pier Column Shear Reinforcement Design

For simplicity, use the elastic seismic design forcesPerform basic desgin in plastic hinging region only (reinf. for confinement)For all columns, take the shear strength of the concrete as zero (0) = 1.0 for Design InitiallyEquations and Methods (LRFD and Imbsen - Both are Similar for Simple Design)

LRFD 5.10.11.4.1e Max. Spacing of Spirals = 4 in.

LRFD 5.10.11.4.1d Minimum Reinforcment #1

f'c = 3500 psify = 60000 psis min = 0.0070

LRFD 5.7.4.6 Minimum Reinfocement #2

f'c = 3500 psifyh = 60000 psiAg = 530.9 in2

Ac = 415.5 in2

s min = 0.0073

Imbsen 8.6.6 Minimum Reinfocement #2

s min = 0.0040

LRFD 5.8.3.4.1 Simplified Shear Procedure for Non-Prestressed Sections

Av = 0.62 in2 (#5 bars)fy = 60 ksidv = 18.72 in (0.72h LRFD 5.8.2.9)s = 4 in Vs = 174 kips

y

'c

s ff

12.0

y h

'c

c

gs f

f1A

A45.0

sdfA

V vyvs =

004.0s

Imbsen 8.6.3 Shear Strength of Steel Pier Col Sh Reinf Design Pg. 2

Av = 0.31 in2 (#5 bars according to Imbsen 8.26)fyh = 60 ksiD = 26 in (Imbsen means full col dia.?)s = 4 inVs = 190 kips

LRFD s Provided

Asp = 0.31 in2

s = 4 inDcore = 23 ins prov = 0.0135 OK

Imbsen s Provided

Asp = 0.31 in2

s = 4 inD = 26 in (Imbsen means full col dia.?)s prov = 0.0119 OK

Summary of Shear Reinforcement Designs (LRFD and Imbsen) for 16 Cases

Using #5 Spirals at Max. Spacing of 4 in. = 1.0 = 0.85 = 1.0 = 0.9

Imbsen Fig. 5.4 Trans. Long. Ld. Cse 2 Imbsen Imbsen LRFD LRFDElastic Elastic Governs Strength Strength Strength Strength

Column Steel Fraction Shear Shear (Long. #5's #5's #5's #5'sHeight Ratio of Ig Per Col. Per Col. Dom.) at 4 in. at 4 in. at 4 in. at 4 in.

(ft.) (Ast/Ag) (kips) (kips) (kips) (kips) (kips) (kips) (kips)10 0.01 0.4 119.1 122.9 128.0 190.0 161.5

0.02 0.5 129.3 137.4 142.8 190.0 161.5 174.0 156.60.03 0.6 137.2 150.5 156.0 190.0 161.50.04 0.7 143.4 162.6 168.2 190.0 161.5

15 0.01 0.4 61.3 71.5 73.8 190.0 161.50.02 0.5 71.1 79.9 82.7 190.0 161.5 174.0 156.60.03 0.6 79.6 87.6 90.8 190.0 161.50.04 0.7 87.0 94.6 98.1 190.0 161.5

20 0.01 0.4 31.5 48.2 49.1 190.0 161.50.02 0.5 37.9 53.9 55.1 190.0 161.5 174.0 156.60.03 0.6 43.8 59.0 60.5 190.0 161.50.04 0.7 49.3 63.8 65.5 190.0 161.5

25 0.01 0.4 17.5 35.3 35.7 190.0 161.50.02 0.5 21.4 39.5 40.0 190.0 161.5 174.0 156.60.03 0.6 25.1 43.3 43.9 190.0 161.50.04 0.7 28.7 46.7 47.5 190.0 161.5

=

sDfA

2V y hvs

core

sps sD

A4=

sDA4 sp

s =

Bridge_Example_No. 2-1.pdfBridge_Example_No. 2-2.pdfBridge_Example_No. 2-3.pdfBridge_Example_No. 2-4.pdfBridge_Example_No. 2-5.pdfBridge_Example_No. 2-6.pdf

Trial Design IL-2

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