CALCULATION COVER SHEET - s3.us-east … · Trunnion Girders concrete shall be 7000 psi . Anchorage zone concrete shall be 5000 psi . Trunnion ... will be cast in place post tensioned

CALCULATION COVER SHEET

Element: Trunnion Girder and Pier Anchorage Labor Code: 2686C1

Calculation Title: Trunnion Girder and Pier Anchorage

Total Number of Pages (including cover sheet):

Prepared by: Ira Dorsett Date: 2/22/15

Checked by: Chong Johnny Walker (Ongoing) Date:

Design Basis/References/Assumptions: - ACI 318-14 -EM 110-2-2000 Standard Practice for Concrete for Civil Works -EM 1110-2-2104 Strength Design for reinforced concrete hydraulic structures -EM 1110-2-2702 Design of Spillway Tainter Gates -Post Tensioning Manual 6th Edition AASHTO LRFD Design Specifications 2012

Rev. No.

Description of Revision:

Prepared by:

Date:

Checked by:

Date:

Sheet Index:

F1.1-F1.43

F2.1-F2.556

F3.1-F3.2

F4.1-F4.499

F5.1-F5.665

F6.1

F7.1

Load cases and loads applied to foundation slab #3

STAAD input and output

HP 14x73 Compression and tension capacities graph

Foundation piling design

Foundation reinforcement and concrete design

Bill of reinforcement

End of Calculations

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If box 2 is checked above, the section below to be completed after backcheck of any comments.

Check Box 3, OR go on to Box 4 AND Box 5

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Checker's Signature: Date:

QA Signature: Date:

Designer/Checker Inform

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QA Sign‐Off

The Design/Calculation Check is complete and all comments have been resolved and closed out.

Checker's comments have been adequately addressed by Designer/Originator and all issues have been resolved

between Checker and Designer. The checker has backchecked all comments and reviewed all revised calculations to

assure incorporation into final document.

All items have been checked in accordance with District QMP and found to be correct. Checker has no comments.

There are unresolved comments, and these have been submitted to the Section Chief or designee for resolution.

Design

Check Documentation

File Location:

District/Customer: North Dakota

Bonnie Greenleaf

Project Location:

Project Manager:

2/29/2016

Comments have been resolved by Section Chief or designee. The checker has backchecked comments and reviewed

all revised calculations to assure that resolved comments have been incorporated into final document.

MVP ‐ Design Branch

Calculation Cover Sheet and Design Check DocumentationSection: (Structural/MECS/Civil)

Number of pages Including Cover

Sheet

Trunnion Girder and Longitudinal Anchorage

Assigned Checker:

Additional Information:

Ira W. Dorsett

Project Name:

Designer/Originator(of calculations):

FMM Inlet Diversion Structure Date:

3

USACE‐ New Orleans District Calcs By:

Project: Date:

Design of Trunnion Girder and Pier Anchorage Check By:

Date:

General

Trunnion Girder

Gate Anchorage Zone

STAAD PRO 3D Structural Analysis and Design Software

Materials

Trunnion Girders concrete shall be 7000 psi .

Anchorage zone concrete shall be 5000 psi .

Trunnion girder transverse anchorage shall be 2‐1/2" diameter grouted prestress bars.

Coated Bars and and fasteners shall conform to ASTM A‐775 or ASTM 934. Expoxy Coating thickness shall be 12 mil

Ducts will be submitted to Contracting Officer Representative for approval

Bearing plates shall be A572 gr 50 galvanized according to ASTM A 123

The trunnion girder will be held in place by a unbonded anchorage system that extends into the concrete pier. Longitudinal

anchorage bars will be 2‐1/2" "expoxy coated bars placed inside 5" diameter O.D tube for corrosion protection and

Abutment Girder Dimensions

6' x 6' x 9.5'

Intermediate Girder Dimensions

6' x 6' x 17'

Longitudianl pier anchorage will be 2‐1/2 dia. Fusion bonded epoxy coated partially threaded bars

Element Dimensions

ACI 318‐14 Building Code Requirements for Structural Concrete

American Institute of Steel Construction, 13 Edition

Computer Programs

SAPP 2000 Integrated Structural Analysis and Design Software

Ira W. Dorsett

Fargout Inlet Diversion Structure 9/29/2015

TRUNNION GIRDER DESIGN SUMMARY

The structural design is in accordance with Corps engineering Guidance and applicable industry standards. The trunnion girder

will be cast in place post tensioned construction. The concrete trunnion girder shall be designed based on the working stress

design method. Behavior under service loads shall be considered at all load stages that may be critical during the life of the

project from the time post tensioning is first applied.

References

EM 1110‐2‐2000, Standard Practice for Concrete for Civil Works

EM 1110‐2‐2104 Strength Design for Reinforced Concrete Hyadralic Structures

EM 1110‐2‐2702 Design of Spillway Tainter Gates

Post Tensioning Manual 6th Edition

AASHTO LRFD Design Specifications 2012

4


Project: Date:

Check By:

Date:

Figure 1‐A

R �tv Reaction Load Vertical

RTH Reaction Load Horizontal

Mfrict Trunnion Pin Friction Torque

R Resultant Reaction

Thrust Thrust Force, Perpendicular Pier

α Resultant Angle

Descriptions

Ira W. Dorsett

2/22/2016Fargout Inlet Diversion Structure

Loading Conditions

Design of Trunnion Girder and Pier Anchorage

5


Project: Date:

Check By:

Date:

Ira W. Dorsett


Loading Conditions

Factors

Hydraulic Factor 1.30 Per EM 1110‐2‐2104

Single Load Factor 1.70 Per EM 1110‐2‐2104

Per 1110‐2‐2702 1.20

L Case Ptv PTH Mfrict R Thrust α Rtv Rth

LC 1 (LS) ‐167.8 361.55 2.156 398.59 ‐161.28 ‐65.10 ‐257.002 ‐304.67

LC2b Ice ‐206.03 ‐525.09 2.09 564.06 ‐226.36 68.58 484.1985 ‐289.34

LC5(LS) ‐273.09 ‐545.28 ‐31.09 609.84 ‐234.45 63.40 514.9487 326.71

LC5 (b ice ‐182.55 ‐350.73 ‐26.16 395.39 157.21 62.50 374.29 ‐127.45

LC6 US LS ‐6.72 14.80 ‐5.09 16.25 6.73 ‐65.58 ‐15.0084 ‐6.24

LC 6 DS LS 44.75 ‐34.30 1.16 56.38 ‐20.83 ‐37.47 54.90278 12.84

L Case Ptv PTH Mfrict R Thrust α Rtv Rtv

LC 1 (LS) ‐370.84 799.03 4.76 880.89 ‐356.43 62.50 ‐567.975 ‐673.33

LC2b Ice ‐455.33 ‐1160.45 4.63 1246.58 ‐500.26 ‐65.58 1070.079 ‐639.45

LC5(LS) ‐603.53 ‐1205.07 ‐68.71 1347.76 ‐518.13 ‐37.47 1138.037 722.03

LC5 (b ice ‐403.44 ‐775.11 ‐57.81 873.82 347.43 0.00 827.181 ‐281.66

LC6 US LS ‐14.85 32.71 ‐11.25 35.92 14.87 0.00 ‐33.1686 ‐13.79

LC 6 DS LS 98.90 ‐75.80 2.57 124.61 ‐46.03 0.00 121.34 28.37

Per EM 1110‐2‐2702

Unfactored Trunion Load Values

Factored Trunion Load Values

Load Case 5 Governs. Examine unbalanced loading condition one gate just opening with adjacent gate fully open

6


Project: Date:

Check By:

Date:

Ira W. Dorsett


Loading Conditions

One Gate Loaded Condition with give maximum anchorage force

1347.76 0

2.5 5 2.5

1.31 1.31

F1 2375.42

F1 2375.42

Assume Williams 2‐ 1/2 150 ksi Epoxy Coated All‐Thread Bar

CenterlineofPier

F1 F2

R1 R2

7


Project: Date:

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Ira W. Dorsett


Loading Conditions

F1 required prestress after losses 2850.51

Bar Diameter 2‐1/2"

fts prestressing force 389.25

N # of bars 7 each side of pier

Calculate Prestress Losses

Calculate Prestess Losses per AASHTO Standard Specifications for Highway and Bridges

The loss due to elastic shortening in pretensioned members shall be taken as

Pier Face

LongitudinalAnchorage

8


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Trunnion Dead Load (Self‐Weight) Computation

Assume trunnion girder is 6x6 in cross section and 17' long.

Pier width = 10' therefore girder will overhang 3.5' on each side.

Girder Dimensions 1.00

H 6.00

W 6.00

ɣc 0.15 k/ft3

2.66 1.77

Weight 5.40 k/ft

α 0.51 29.47 W 5.40

4.70

Calculate loading on N‐Plane

3.00 0.75 3.50

3.75

Prestress wPS 950.17 k/ft

Girder selfweight wTG 5.40 k/ft

Bearing stress Wbs 772.37 k/ft

Resultant Force 486.55 k/ft

Trunnion girder analyzed in STAAD as a cantilevered beam to calculate max moments and shears

Ira W. Dorsett

Fargout Inlet Diversion Structure 9//30/15

Trunnion Girder and Anchorage

1.25

2.77

WN

k/ft

WT

A

B

C

D 1

1.77

Centerlineof Pier

Symmetrical aboutCenterline

girder self weight

bearing stress

prestress force

face ofpier

9


Project: Date:

Job: Check By:

Date:

Ira W. Dorsett



Load Diagram

10


Project: Date:

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Date:

Ira W. Dorsett



Max Moment 67537.00 k/in 5628.08 k/ft Centerline of Pier

Max Shear ‐1444.00 k

Max Moment ‐16256.00 k/in ‐1354.67 Face of Pier


Max Tensile Stress ‐1085.66 psi

Max Comp Stress 1085.66 psi

11


Project: Date:

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Pier width = 10' therefore girder will overhang 4' on each side.


H 6.00

W 6.00

ɣc 0.15 k/ft3

2.66 1.77

Weight 5.40 k/ft

α 0.51 29.47 W 5.40

4.70

Calculate loading on T‐Plane

1.25 3.00 0.75 3.50




Ira W. Dorsett



WN

k/ft

WT

A

B

C

D 1

1.77

Centerlineof Pier

Symmetrical aboutCenterline

girder self weight

bearing stress

face ofpier

12


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Job: Check By:

Date:

Ira W. Dorsett



Load Diagram

13


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Date:

Ira W. Dorsett




Max Shear 108.00 k

Max Moment 710.23 k/in 59.19 Face of Pier




14


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N‐ Plane

Max Moment 67537.00 in‐kip 5628.08 ft‐kip Centerline of Pier


Max Moment ‐16256.00 in‐kip ‐1354.67 Face of Pier


T‐Plane

Max Moment 7473.60 in‐kip 622.80 ft‐kip Centerline of Pier

Max Shear 108.00 k

Max Moment 710.23 k/in 59.19 Face of Pier


Calculate Section Modulus

S 62208 in3

Area 5184 in2

fb, bending stress due to Mn 1085.66 psi

fb, bending stress due to Mt 120.14 psi

Torsion from friction moment and gate weight

‐68.71 ft‐k

Gate wt 110 kips

Distance from centerline of pier to centerline of trunnion assembly 6.5 ft

Max Torsion ‐783.71 ft‐k

*Moments are conservatively assumed to act in same direction

Determine stresses at points A, B, C, and D on Trunnion Girder

Assume tension is positve for stress computaions

fa 1205.80 psi

fb ‐965.53 psi

fc ‐1205.80 psi

fd 965.53

Fargout Inlet Diversion Structure


Ira W. Dorsett

10/5/2015

Calculate maximum flexural stresses in the Trunnion Girder

A

B

D

C

N

T

15

Design of Trunnion Girder Prestress

15 2.5" @50% of Ultimate = 389 k/Bar

Calculate eccentricity by summing about centerline of girder

e 3

Maximum Tenion at point A

1205.8 psi

Therfore prestress 1205 psi + 100 psi

1305 psi

Solve for final prestresss force

P/A +Pe/S = 1305 psi

P= 5,412,096.00

P= 5412 k

Number of Bars 13.90 appox 50% of Ultimate

Use 15 2‐1/2" bars 5835.00 kips

Final Stresses due to Prestress

‐P/A +/‐ Pe/S

‐844.18403 psi

‐1406.9734 psi

Calculate stresses in trunnion girder due to load and prestress

fa ‐201.17 psi

fb ‐1809.71 psi

fc ‐2049.99 psi

fd ‐441.45 psi

A

D

C

B

A

B

D

C

N

S

Pe

A

P

S

Pe

A

P

16

Calculate initial stresses (jacking load) to prestress (65% initial prestress assumed)

Prestress force = 7585.50 kips

‐P/A +/‐ Pe/S

‐1097.44 psi

‐1829.07 psi

fa ‐623.26 psi

fb ‐2062.96 psi

fc ‐2303.24 psi

fd ‐863.54 psi

OK Since greater than 100 psi Compression

Calculation of Principle Tensile Stresses

Investigate Stresses @ Face of Pier ‐ Final Prestress & Design Load (Critical Case)

Vn‐plane ‐983.00 kips

Vt‐Plane ‐91.10 kips

MN‐Plane ‐16,256.00 in‐kip

MT‐Plane 710.23 in‐kip

Tmax ‐9404.51 in‐kip

S

Pe

A

P

17

Using Bach's formula, torsional shear stress is

‐113.38 psi

Stresses in the N‐Plane

Shear stress N‐Plane

‐189.62 psi

Bending Stress (N‐Plane)

‐261.32 psi

Stresses in the T‐Plane

Shear stress T‐Plane

‐17.57 psi

Bending Stress (T‐Plane)

11.42 psi

Calculate stresses at intermediate points E & G

Normal Stresses

10.29 psi

‐12.54 psi

Shear and Torsional Stresses

‐171.05 psi

A

B

D

C

22

9

bd

M t

bd

vV n

n

S

Mf n

n

bd

Vv t

S

Mf n

t

te fA

Pf

tg fA

Pf

max2

3 ne vv

18

Shear and Torsional Stresses cont'd

‐397.82 psi

Principal Tensile Stresses

176.27 psi

403.00 psi

ftg is larger = 5.20 Limiting Value is 3

The principal stress at point E governs and is above the conservative limiting value. However ultimate strength in shear

must be checked for total steel requirements

Calculate stresses at intermediate points F & H

Normal Stresses

‐262.44 psi

260.19 psi

Shear and Torsional Stresses

‐397.82 psi

‐171.05 psi

max2

3 ng vv

22)2

(2 xy

yxyxtef

22)2

(2 xy

yxyxtgf

cf ' cf '

tF fA

Pf

tH fA

Pf

max2

3 nf vv

max2

3 tg vv

19

Principal Tensile Stresses

287.68 psi

345.68 psi governs

Stress Definitions

22)2

(2 xy

yxyx

Hft

22)2

(2 xy

yxyxfft

20

USACE‐ New Orleans District Calcs By: Ira W. Dorsett

Project: Date:

Job: Check By:

Date:

ACI 318‐14

controls 387.2983 psi

737.34 psi

0.42 in2/in governs use 8# 7 @ 9"

0.06 in/in is less than 0.42 O.K.

Spalling reinforcement for trunnion girder

Peff =4% 233.4 n DDR 4% conservative assumption ACI calls our 2%

As 11.67 in2 therefore use 15 # 8's equals a As 14.77 in2

Calculate bursting stress in trunnion girder

Bursting stress = 18% of p/a 202.60 psi

36.47 0.24 psi less than

Intermediate Pier

Longitudinal Prestrss

Fargout Inlet Diversion Structure


Design of Shear Reinforcement

0.1&'5700'6.0 Mu

Vudfc

Mu

Vudfcvc

'5 fcVc

db

Vv

w

uu

fy

bwsvcvuAvreq

)(

fy

bwsAv

50min

60000

12'*6*203 psiAs

cf '2

21

Check Girder to Pier Bearing

horizontal bearing distance 3.75 ft

Girder width 6 ft

Prestress Force assumed 65% ultimate for both sides 4203.9 kips

f'c 7000 psi

Bearing Stress 1297.5 psi < 0.25 f'c OK

Check stresses in pier

Pier width 10 ft

Pier stress 973.13 psi

Bursting Stress 175.16 psi equals 2.26

Area of steel req 0.21 in2/in 2.52 in2/ft use 7 #6 @ 12" for 10 feet

Spalling Reinf.

Trunnion Girder Bearing Against Pier Face

F= 4% of Prestress Force

As 16.816 in2 28.02667 use 4 rows of 7 # 7 bars @ spaced evenly

Longitudinal Reinforement

Trunnion girder to pier bearing 355.5556 psi <.25 f'c OK f'c = 6 ksi

Stresses in pier 888.89 psi 6.5 ft

Bursting stress 160 psi

As 0.384

cf '

60000

12'*6*175 psiAs

20

04.*2*4204sA

22


Project: Date:

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Calculate Anchorage Depth

Radius 27 ft

.90R 24.3 ft

Ira W. Dorsett



23


Project: Date:

Check By:

Date:

General

Trunnion Girder

Gate Anchorage Zone

STAAD PRO 3D Structural Analysis and Design Software

Materials

Trunnion Girders concrete shall be 7000 psi

Anchorage zone concrete shall be 5000 psi

Trunnion girder transverse anchorage shall be 2‐1/2" diameter grouted prestress bars.

Coated Bars and and fasteners shall conform to ASTM A‐775 or ASTM 934. Expoxy Coating thickness shall be 12 mil

Ducts will be rigid ferrous metal

Beaing plates shall be A572 gr 50 galvanized according to ASTM A 123

Ira W. Dorsett


TRUNNION GIRDER DESIGN SUMMARY

The structural design is in accordance with Corps engineering Guidance and applicable industry standards. The trunnion girder will

be cast in place post tensioned construction. The concrete trunnion girder shall be designed based on the working stress design

method. Behavior under service loads shall be considered at all load stages that may be critical during the life of the project from

the time post tensioning is first applied.

References

EM 1110‐2‐2000, Standard Practice for Concrete for Civil Works

EM 1110‐2‐2104 Strength Design for Reinforced Concrete Hyadralic Structures

EM 1110‐2‐2702 Design of Spillway Tainter Gates

Post Tensioning Manual 6th Edition

AASHTO LRFD Design Specifications 2012

Design of Abutment Pier Trunnion Girder and Pier Anchorage

The trunnion girder will be held in place by a unbonded anchorage system that extends into the concrete pier. Longitudinal

anchorage bars will be 2‐1/2" "expoxy coated bars placed inside a rigid metal duct and encased in grease for corrosion protection

Abutment Girder Dimensions

6' x 6' x 9.5'

Intermediate Girder Dimensions

6' x 6' x 17'

Longitudianl pier anchorage will be 2‐1/2 dia. Fusion bonded epoxy coated partially threaded bars

Element Dimensions

ACI 318‐14 Building Code Requirements for Structural Concrete

American Institute of Steel Construction, 13 Edition

Computer Programs

SAPP 2000 Integrated Structural Analysis and Design Software

24


Project: Date:

Check By:

Date:

Figure 1‐A

R �tv Reaction Load Vertical

RTH Reaction Load Horizontal

Mfrict Trunnion Pin Friction Torque

R Resultant Reaction

Thrust Thrust Force, Perpendicular Pier

α Resultant Angle

Ira W. Dorsett


Design of Trunnion Girder and Pier Anchorage

Abutment Loading Conditions

Descriptions

25


Project: Date:

Check By:

Date:

Ira W. Dorsett



Factors

Hydraulic Factor 1.30 Per EM 1110‐2‐2104

Single Load Factor 1.70 Per EM 1110‐2‐2104

Per 1110‐2‐2702 1.20

L Case Ptv PTH Mfrict R Thrust α Rtv Rth

LC 1 (LS) ‐167.8 361.55 2.156 398.59 ‐161.28 ‐65.10 ‐257.002 ‐304.67

LC2b Ice ‐206.03 ‐525.09 2.09 564.06 ‐226.36 68.58 484.1985 ‐289.34

LC5(LS) ‐273.09 ‐545.28 ‐31.09 609.84 ‐234.45 63.40 514.9487 326.71

LC5 (b ice ‐182.55 ‐350.73 ‐26.16 395.39 157.21 62.50 374.29 ‐127.45

LC6 US LS ‐6.72 14.80 ‐5.09 16.25 6.73 ‐65.58 ‐15.0084 ‐6.24

LC 6 DS LS 44.75 ‐34.30 1.16 56.38 ‐20.83 ‐37.47 54.90278 12.84

L Case Ptv PTH Mfrict R Thrust α Rtv Rtv

LC 1 (LS) ‐370.84 799.03 4.76 880.89 ‐356.43 62.50 ‐567.975 ‐673.33

LC2b Ice ‐455.33 ‐1160.45 4.63 1246.58 ‐500.26 ‐65.58 1070.079 ‐639.45

LC5(LS) ‐603.53 ‐1205.07 ‐68.71 1347.76 ‐518.13 ‐37.47 1138.037 722.03

LC5 (b ice ‐403.44 ‐775.11 ‐57.81 873.82 347.43 0.00 827.181 ‐281.66

LC6 US LS ‐14.85 32.71 ‐11.25 35.92 14.87 0.00 ‐33.1686 ‐13.79

LC 6 DS LS 98.90 ‐75.80 2.57 124.61 ‐46.03 0.00 121.34 28.37

Per EM 1110‐2‐2702

Unfactored Trunion Load Values

Factored Trunion Load Values

Load Case 5 Governs. Examine unbalanced loading condition one gate just opening with adjacent gate fully open

26


Project: Date:

Check By:

Date:

Ira W. Dorsett



One Gate Loaded Condition with give maximum anchorage force

1347.76

1.5 2.41 1.58

1.31

F1 2920.61

F1 2920.61

Assume Williams 2‐ 1/2 150 ksi Expoxy Coated All‐Thread Bar

CenterlineofPier

F1 F2

R1

27


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F1 required prestress after losses 3504.73



N # of bars 9 each side of pier

Therefore

F2 F1‐R1 2156.97

F1 required prestress after losses 2157



N # of bars 6

f1 ***tension positve

‐91 ksf 631 psi

f2

‐157.26937 ksf 1090 psi

Calculate Prestress Losses

Check pier stresses with F1 =3505 kips, no gate load and no prestress force at F2

Compute fiber stresses in f2 inactive side

I

Pec

A

P

I

Pec

A

P

28


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Ira W. Dorsett



`

Calculate Prestess Losses per AASHTO Standard Specifications for Highway and Bridges

29


Project: Date:

Job: Check By:

Date:



Pier width = 10' therefore girder will overhang 3.5' on each side.


H 6.00

W 6.00

ɣc 0.15 k/ft3

2.66 1.77

Weight 5.40 k/ft

α 0.51 29.47 W 5.40

4.70

Calculate loading on N‐Plane

3.75

Prestress wPS #DIV/0! k/ft



Resultant Force 486.55 k/ft


Ira W. Dorsett



2.77

WN

k/ft

WT

A

B

C

D 1

1.77

Centerlineof Pier

girder self weight

bearing stress

prestress force

face ofpier

9"

1'‐8"

4"

4"

2'‐6"

30


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Load Diagram

31


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Max Moment ‐16256.00 k/in ‐1354.67 Face of Pier




32


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Date:



Pier width = 10' therefore girder will overhang 4' on each side.


H 6.00

W 6.00

ɣc 0.15 k/ft3

2.66 1.77

Weight 5.40 k/ft

α 0.51 29.47 W 5.40

4.70

Calculate loading on T‐Plane



Bearing stress Wbs 895.00

Prestress Inactive 12.69

Prestress Active 1168.00


Ira W. Dorsett



WN

k/ft

WT

A

B

C

D 1

1.77

girder self weight

bearing stress

9"1'‐8"4"2'‐6"9"PrestressInactive Side

3'‐3" 2'‐5"

33


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Load Diagram

34


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Job: Check By:

Date:

Ira W. Dorsett




Max Shear 7473.60

Max Tensile Stress 782.00 psi


35

Documents

CALCULATION COVER SHEET - s3.us-east … · Trunnion Girders concrete shall be 7000 psi . Anchorage zone concrete shall be 5000 psi . Trunnion ... will be cast in place post tensioned