prev

next

out of 22

View

220Download

0

Embed Size (px)

DESCRIPTION

2

112.3.1

FLEXURAL DESIGN

z Service Limit State Transformed Section Compute Stresses Compare with Stress Limits

z Strength Limit Statez Moment - Curvature

12.3.2General Assumptions for Flexural Design

z Plane sections before bending remain plane after bending

z Equilibrium of external forces and internal stresses

z Compatibility of strains

12.3.3General Assumptions for Flexural Design of Prestressed Concrete Members

Service Load Design: Concrete is uncracked Stress in prestressing steel is linearly proportional to strain Iterate to determine strand pattern

- satisfy stress limits for concrete and prestressing steel

Check Strength at Critical Sections: Concrete

- inelastic in compressive regions- tensile strength neglected

Prestressing steel- inelastic

212.3.4Determine Strand Pattern

Add strands until stress limits at midspan are satisfied

Fill rows from bottom Minimum strand spacing

- LRFD Article 5.10.3.3.1 Minimum Cover Minimum Cover

- LRFD Article 5.12.3

Then check stresses at ends

12.3.5Typical Strand Pattern

12.3.65.10.3.3.1 Minimum Strand Spacing

Strand Size (in.) Spacing (in.)0 6000

Minimum clear distance between starnds at ends of pretensioned girders:

1.33 x maximum aggregate size 3db

0.60000.5625 Special

0.56252.00

0.50000.4375

0.50 Special1.75

0.3750 1.50

312.3.7Minimum Concrete CoverLRFD 5.12.3

12.3.8Minimum Concrete Cover

LRFD 5.12.3

Modification factors for W/C ratio

z For W/C 0.40 . . . . . . . . . . . 0.8

z For W/C 0.50 . . . . . . . . . . . 1.2

Minimum cover to main bars, including epoxy-coated bars = 1.0 IN.

Minimum cover to ties and stirrups may be 0.5 IN. less than the values specified in Table for main bars, but shall not be less than 1.0 IN.

12.3.9Design for Flexure at Service Limit State

Compute Section Properties Determine effective width of deck Transform deck to girder concrete Transform strand (optional)

Compute Stresses At release At Service Limit State

- Permanent loads only- Permanent and transient loads

Compare Stresses to Stress Limits Concrete Prestressing Steel

412.3.10Transform Composite Deck Concrete to Girder Concrete

Effective deck width - (LRFD 4.6.2.6.1)

Transformed effective deck width

Use same modular ratio for short- and long-term effects

12.3.11Transform Prestressing Steel to Girder Concrete

LRFD 5.9.1.4

Section properties may be based on either the gross or transformed section

Prestressing steel may be transformed using the same procedure used for mild reinforcement

12.3.12Assumptions for Service and Fatigue Limit States

LRFD 5.7.1

The following should apply to modular ratios between steel and concrete:

the modular ratio, n, is rounded to the nearest integer number,

the modular ratio is not less than 6.0, and

an effective modular ratio of 2n is applicable to permanent loads and prestress.- intended to apply to compression

reinforcement - see Std Specs Article 8.15.3.5

512.3.13Compute Stresses at Release

Non-Composite Section (Bare Girder)

Loads Girder dead load Initial prestress

Top of girder

Bottom of girder

b

gdl

b

iiRb

t

gdl

t

iiRt

SM

SeP

APf

SM

SeP

APf

+=

+=

12.3.14Compute Stresses at Release

12.3.15Compute Stresses at Service Limit State After Losses with Permanent Loads Only

Composite Section (Girder + Deck)

Loads on Non-Composite Section Girder, deck dead loads Other dead loads applied before placing deck

( di h )(e.g., diaphragms) Final prestress (after losses)

Loads on Composite Section Barrier and future wearing surface Other dead loads (utilities, etc.) Vehicular live load

612.3.16Compute Stresses at Service Limit State After Losses with Permanent Loads Only

Top of deck

tcd

cdlPtd S

Mf =

Top of girder

Bottom of girder

bcg

cdl

b

ncdlgdl

b

eePbg

tcg

cdl

t

ncdlgdl

t

eePtg

SM

SMM

SeP

APf

SM

SMM

SeP

APf

++=

+++=

12.3.17

Compute Stresses at Service Limit State After Losses with Permanent and Transient Loads

Top of deck

tcd

ILLcdlLPtd S

M Mf +++=

Top of girder

Bottom of girder

bcg

ILLcdl

b

ncdlgdl

b

eeLPbg

tcg

ILLcdl

t

ncdlgdl

t

eeLPtg

SM M

SM M

S

eP APf

SM M

SM M

S

eP APf

++

++

+++=

++++=

12.3.18

Compute Stresses at Service Limit State After Losses with Permanent and Transient Loads

712.3.19Stress Limits for Prestressing Tendons

LRFD 5.9.3

For Pretensioned Construction:

Low relaxation strand ( fpy = 0.90 fpu ):0 75f Immediately prior to transfer0.75fpu Immediately prior to transfer 0.80fpy At Service Limit State, after

losses

Stress Relieved strand ( fpy = 0.85 fpu ):0.70fpu Immediately prior to transfer 0.80fpy At Service Limit State, after

losses

12.3.20Stress Limits for Concrete

LRFD 5.9.4.1.1 and 5.9.4.1.2

For Temporary Stresses Before Losses (Fully Prestressed Components):

Compression: Pretensioned components

Tension (non-segmental bridges):Precompressed tensile zone without bonded

reinforcement 0.200 KSI Other than precompressed tensile

zone, and without bonded reinforcementIn areas with bonded reinforcement sufficient to

resist concrete tensile force (fs = 0.50fy)

cif0948.0 A/N

cif 60.0

cif24.0

12.3.21

LRFD 5.9.4.2.1

For Stresses At Service Limit State After Losses (Fully Prestressed Components):

Compression (non-segmental bridges):

Stress Limits for Concrete

Compression (non-segmental bridges):

c

c

c

f 40.0

f 60.0f 45.0

Permanent loads

Permanent and transient loads, and during shipping and handlingLive load and 0.5 the sum of effective prestress and permanent loads

812.3.22Stress Limits for Concrete

LRFD 5.9.4.2.2

For Stresses At Service Limit State After Losses (Fully Prestressed Components):

Tension in precompressed tensile zone (other th t l b id )than segmental bridges):

Components with bonded prestressing tendons other than piles

Components subjected to severe corrosive conditions

Components with unbonded prestressing tendons

tension no

f0948.0

f190.0

c

c

12.3.23

LRFD 5.9.4.2.2

For Stresses At Service Limit State After Losses (Fully Prestressed Components):

Tension in other areas (segmental only):

Stress Limits for Concrete

Note other tensile stress limits for segmentally constructed bridges.

cf190.0 If bonded reinforcement is provided which is sufficient to carry the tensile force in the concrete at a stress of 0.5fsy

12.3.24Control of Stresses at Ends of Pretensioned Members

The following methods can be used individually or in combination with other methods

1. Draping, Harping or Deflecting Reduce eccentricity at ends Raise center group of strands until stressRaise center group of strands until stress

limits are satisfied

912.3.25Control of Stresses at Ends of Pretensioned Members

2. Debonding, Blanketing or Shielding Reduce prestress force at ends by preventing

bond of selected strands with concrete Increase number of debonded strands until

stress limits are satisfied

12.3.26Special Provisions for Debonded Strands

Std Specs 9.27.3 requires: Development length for debonded strands is

doubled

LRFD 5.11.4.3 further requires: Number of strands debonded 25% of totalNumber of strands debonded 25% of total

strands Number of strands debonded in any row 40%

of total strands in that row Exterior strands in each row must be fully

bonded All limit states must be satisfied

12.3.27Control of Stresses at Ends of Pretensioned Members

3. Adding Mild Reinforcement If tensile stress > , but not more

than , add mild reinforcement to resist 120% of the tensile force

cif0948.0 cif22.0

( )( )s

toptopcis f

bx2f2.1A =

where fs = 0.5 fsy = 30 KSI

10

12.3.28Control of Stresses at Ends of Pretensioned Members

4. Adding Top Strands Reduce moment at ends by adding

strands at the top of the girder Can debond top strands in center

portion of the girderportion of the girder- Must provide access hole for cutting

strand

12.3.29

5. Increasing Compressive Strength of Concrete at Release,

Increase until stress limits are satisfied

Control of Stresses at Ends of Pretensioned Members

cif

cif

Use reasonable value for that can be achieved economically by local producers

Maintain reasonable balance between cci fand f

cif

12.3.30Fatigue Limit State Stress Range Requirements

LRFD 5.5.3.3

Prestressing Tendons

18.0 KSI for radii of curvature in excess of 30.0 FT 10 0 KSI for radii of curvature not exceeding 12 0 FT 10.0 KSI for radii of curvature not exceeding 12.0 FT Linear interpolation may be used between the limits

Fatigue loading is a design truck (no lane load) with constant axle spacing of 30.0 FT.

11

12.3.31Basic Assumptions for Design at Streng