Design Procedure Manual For Bridges.pdf

Design Procedure Manual for Bridge Projects

Submitted by:

BLESILDA S. RAMOS OIC-Chief, Bridges Division

Recommending Approval:

Approved:

EDWIN C. MATANGUIHAN OIC-Assistant Director, BOD

LEA N. DELFINADO Officer-in-Charge, BOD

Design Procedure Manual for Bridges Page 2 of 56

TABLE OF CONTENTS 1

Design of Reinforced Concrete Deck Girder Superstructure .......................... 4 1.1

Main Design Steps ........................................................................................... 5

1.2

Deck Slab Design ............................................................................................. 6

1.3

Reinforced Concrete Girder Design ...................................................................11

2

Design of Prestressed Concrete Girder Superstructure ............................... 23 2.1

Main Design Steps ..........................................................................................24

2.2

Deck Slab Design ............................................................................................25

2.3

Prestressed Concrete Girder Design ..................................................................30

3

Design of Substructure ................................................................................ 42 3.1

Design of Pier Substructure..............................................................................43

Design Procedure Manual for Bridges Page 3 of 56

LIST OF TABLES Table 1-1 Traditional Minimum Depths for Constant Depth Superstructures (From Table 10.1.2.6-1).................. 6 Table 1-2 Dynamic Load Allowance, IM (from Table 10.8-1) ........................................................................... 7 Table 1-3 Multiple Presence Factors, m (from Table 10.7.2.2-1)...................................................................... 8 Table 1-4 Load Combination and Load Factors (from Table 10.3-1) ................................................................. 8 Table 1-5 Load Factors for Permanent Loads, γp (from Table 10.3-2) .............................................................. 9 Table 1-6 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1)......................................................... 9 Table 1-7 Traditional Minimum Depths for Constant Depth Superstructures (from Table 10.1.2.6-1) ................ 11 Table 1-8 Common Deck Structures covered in Articles of Distribution Factor Method for Moment and Shear, and Distribution Factor Method for Shear (from Table 11.3.2.2-2) ....................................................................... 12 Table 1-9 Distribution of Live Loads per Lane for Moment in Interior Beams (from Table 11.2.3.3-5) ............... 13 Table 1-10 Distribution of Live Load for Shear in Interior Beam (from Table 11.3.2.2-9) ................................. 15 Table 1-11 Load Combination and Load Factors (from Table 10.3-1) ............................................................. 16 Table 1-12 Load Factors for Permanent Loads, γp (from Table 10.3-2) .......................................................... 16 Table 1-13 Nominal Fatigue Resistance of Splices ........................................................................................ 17 Table 2-1 Traditional Minimum Depths for Constant Depth Superstructures (from Table 10.1.2.6-1) ................ 25 Table 2-2 Dynamic Load Allowance, IM (from Table 10.8-1) ......................................................................... 26 Table 2-3 Multiple Presence Factors, m (from Table 10.7.2.2-1).................................................................... 27 Table 2-4 Load Combination and Load Factors (from Table 10.3-1) ............................................................... 27 Table 2-5 Load Factors for Permanent Loads, γp (from Table 10.3-2)............................................................ 28 Table 2-6 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1)....................................................... 28 Table 2-7 Traditional Minimum Depths for Constant Depth Structures (from Table 10.1.2.6-1) ........................ 30 Table 2-8 Common Deck Structures covered in Articles of Distribution Factor Method for Moment and Shear, and Distribution Factor Method for Shear (from 11.3.2.2-2) ................................................................................ 31 Table 2-9 Distribution of Live Loads per Lane for Moment in Interior Beams (From Table 11.3.2.2-5)............... 33 Table 2-10 Distribution of Live Load for Shear in Interior Beam (from Table 11.3.2.2-9) ................................. 34 Table 2-11 Load Combination and Load Factors (from Table 10.3-1) ............................................................. 35 Table 2-12 Load Factors for Permanent Loads, γp (from Table 10.3-2) .......................................................... 35 Table 2-13 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1) ..................................................... 37 Table 3-1 Ground Types (Site Class) for Seismic Design ............................................................................... 44 Table 3-2 Values of Site Factor Fpga at Zero-Period on Acceleration Spectrum ................................................. 44 Table 3-3 Values of Site Factor Fa for Short-Period Range on Acceleration Spectrum....................................... 45 Table 3-4 Values of Site Factor Fv for Long-Period Range on Acceleration Spectrum ....................................... 45 Table 3-5 Response Modification Factors - Substructures ............................................................................. 47 LIST OF FIGURES Figure 1-1 Maximum Live Load Positive and Negative Moments (from Table A11-1).......................................... 7 Figure 1-2 Slab Reinforcement Details ........................................................................................................ 10 Figure 1-3 Design Truck and Tandem Loads ............................................................................................... 12 Figure 1-4 Section at midspan ................................................................................................................... 19 Figure 1-5 Camber Diagram ...................................................................................................................... 20 Figure 1-6 Design Procedure of Deck Slab .................................................................................................. 21 Figure 1-7 Design Procedure of Reinforced Concrete Girder .......................................................................... 22 Figure 2-1 Maximum Live Load Moments per Unit Width, N-mm/mm (from Table A11-1) ................................ 26 Figure 2-2 Slab Reinforcement Details ........................................................................................................ 29 Figure 2-3 Design Truck and Tandem Loads ............................................................................................... 31 Figure 2-4 Stress Limits for Prestressing Tendons (from Table 12.6.3-1) ........................................................ 36 Figure 2-5 Friction Coefficients for Post-Tensioning Tendons ........................................................................ 37 Figure 2-6 Design Procedure of Prestressed Concrete Girder ........................................................................ 41 Figure 3-1 Design Response Spectrum........................................................................................................ 46 Figure 3-2 Design Truck and Tandem Loads ............................................................................................... 47 Figure 3-3 Effective Length Factors, K ........................................................................................................ 48 Figure 3-4 Two-column pier section ........................................................................................................... 50 Figure 3-5 Seat length of girder ................................................................................................................. 52 Figure 3-6 Design Procedure of Pier Substructure ........................................................................................ 54 Figure 3-7 Design Procedure of Plastic (Inelastic) Hinging ............................................................................ 55 Figure 3-8 Design Procedure of Response Spectrum .................................................................................... 56

Design Procedure Manual for Bridges Page 4 of 56

1 Design of Reinforced Concrete Deck Girder Superstructure (LRFD) Part 1

Design Procedure Manual for Bridges Page 5 of 56

CHAPTER 1: DESIGN OF REINFORCED CONCRETE DECK GIRDER 1.1 Main Design Steps 1.1.1 Establish Design Criteria.  Material data  Span arrangement  Girder spacing  Bearing types  Substructure type and geometry  Foundation type based on subsurface investigation 1.1.2

Assume deck slab thickness based on girder spacing and anticipated girder top flange.

1.1.3

Design of deck slab.

1.1.4

Design of girder for flexure and shear.

Design Procedure Manual for Bridges Page 6 of 56

1.2 Deck Slab Design 1.2.1 Establish Design Criteria.  Design specification  Material data  Design live load 1.2.2

: : :

DGCS 2015 concrete and steel reinforcements HL 93 (Article 10.7.3)

Assume slab thickness (Article 14.4.1.1). Unless approved by the Owner, the depth of a concrete deck, excluding any provision for grinding, grooving and sacrificial surface, should not be less than 175 mm. Table 1-1 Traditional Minimum Depths for Constant Depth Superstructures (From Table 10.1.2.6-1) Superstructure

Minimum Depth (Including Deck) When variable depth members are used, values may be adjusted to account for changes in relative stiffness of positive and negative moment sections

Material Reinforced Concrete

Prestressed Concrete

Steel

1.2.3

Type

Simple Spans

Continuous Spans

1.20( 𝑆 + 3000) 30

𝑆 + 3000 ≥ 165𝑚𝑚 30

T-Beams

0.070L

0.065L

Box Beams

0.060L

0.055L

Pedestrian Structure Beams

0.035L

0.033L

0.030𝐿 ≥ 165𝑚𝑚.

0.027𝐿 ≥ 165𝑚𝑚..

CIP Box Beams

0.045L

0.040L

Precast I-Beams

0.045L

0.040L

Pedestrian Structure Beams

0.033L

0.030L

Adjacent Box Beams

0.030L

0.025L

Over-all Depth of Composite I-Beam

0.040L

0.032L

Depth of I-Beam Portion of Composite IBeam

0.033L

0.027L

Trusses

0.100L

0.100L

Slabs with reinforcement parallel to traffic

Slabs

Determine Dead Load Moments (assume per meter width).  Moment due to self-weight of slab 𝜔𝑠𝑙𝑎𝑏 𝑆 2 𝑀𝑠𝑙𝑎𝑏 = 10 where: ωslab = width X thickness of slab X γconcrete S = clear span length  Moment due to future wearing surface 𝜔𝑤𝑠 𝑆 2 𝑀𝑓𝑤𝑠 = 10 where: ωws = width of slab X thickness of wearing surface X γwearing surface S = clear span length 1.2.4 Determine the location of the critical section for negative moment based on the girder top flange width (Article 11.3.2.1.5).

Design Procedure Manual for Bridges Page 7 of 56

1.2.5

Determine Live Load Positive and Negative Moments using Table A11-1.

Figure 1-1 Maximum Live Load Positive and Negative Moments (from Table A11-1)

Note: Multiple presence factors and the dynamic load allowance are incorporated in the tabulated values. Interpolation between the listed values may be used for the distances other than those listed in Table A11-1. For methods of determining live load moments other than the use of Table A11-1, dynamic load allowance (Article 10.8) and multiple presence factors (Article 10.7.2.2) should be incorporated. The dynamic load allowance shall not be applied to pedestrian loads or to the design lane load. Table 1-2 Dynamic Load Allowance, IM (from Table 10.8-1) Component Deck Joints - All Limit States

IM 75%

All Other Components Fatigue and Fracture

15%

Limit State All Other Limit States

33%

Design Procedure Manual for Bridges Page 8 of 56 Table 1-3 Multiple Presence Factors, m (from Table 10.7.2.2-1)

1.2.6

Number of loaded lanes

Multiple Presence Factors

1

1.20

2

1.00

3

0.85

>3

0.65

Compute for factored moments. Using Load Combination (Table 10.3-1—Load Combinations and Load Factors)

Strength I Limit State: 1.0(dc * MDC + DW * MDW + LL* MLL1+IM)

Service I Limit State: 1.0(1.0 * MDC + 1.0 * MDW + 1.0* MLL1+IM) Table 1-4 Load Combination and Load Factors (from Table 10.3-1) Load Combination

Limit State

STRENGTH-I (Unless noted) STRENGTH-II STRENGTH-III STRENGTH-III STRENGTH-IV EH, EV,ES,DW, DC ONLY STRENGTH-V EXTREME EVENT - I EVENT - I EXTREME EVENT - II SERVICE - I SERVICE - II SERVICE - III SERVICE - IV FATIGUE – 1 LL, IM, & CE ONLY FATIGUE – II LL, IM, & CE ONLY

DC DD DW EH EV ES EL PS CR SH p p p p p 1.5

Use one of these at a time LL IM CE BR PL LS

WA

1.75 1.35 1.35 -

1.00 1.00 1.00 1.00 1.00

1.4 -

1.00 1.00 1.00 1.00 1.00

0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20

0.0 0.0 0.0 0.0 -

SE SE SE SE -

-

-

-

-

p p

1.35 EQ

1.00 1.00

0.40 -

1.00 1.00

0.50/1.20 -

0.0 -

SE -

1.00

-

-

-

p 1.00 1.00 1.00 1.00 -

0.5 1.00 1.3 0.8 1.50

1.00 1.00 1.00 1.00 1.00 -

0.30 0.70 -

1.00 1.00 1.00 1.00 1.00 -

1.00/1.20 1.00/1.20 1.00/1.20 1.00/1.20 -

0.0 0.0 -

SE SE 1.0 -

-

1.00 -

1.00 -

1.00 -

-

0.75

-

-

-

-

-

-

-

-

-

-

WS

FR

TU

TG

SE EQ

BL

CT

CV

Design Procedure Manual for Bridges Page 9 of 56 Table 1-5 Load Factors for Permanent Loads, γp (from Table 10.3-2) Load Factor Type of Load Max

Min

DC: Component and Attachments

1.25

0.90

DD: Downdrag

1.80

0.45

DW: Wearing Surfaces and Utilities

1.50

0.65

Active

1.50

0.90

At-Rest

1.35

0.90

EL: Locked-in Erection Stresses

1.00

1.00

Retaining Walls and Abutments

1.35

1.00

Rigid Buried Structure

1.30

0.90

Rigid Frames

1.35

0.90

Flexible Buried Structures other than Metal Box Culverts

1.95

0.90

Flexible Metal Box Culverts

1.50

0.90

ES: Earth Surcharge

1.50

0.75

EH: Horizontal Earth Pressure

EV: Vertical Earth Pressure

1.2.7 1.2.8

Calculate main reinforcement perpendicular to traffic (Article 12.4.3). Calculate factored flexural resistance, Mr at points of maximum moment (Article 12.4.3.2). 𝑀𝑟 = 𝛷𝑀𝑛 𝑎 𝑀𝑛 = 𝐴𝑠 𝑓𝑦 (𝑑𝑒 − ) 2 For conventional construction, resistance factor ɸ is tabulated below. Table 1-6 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1) Factor For tension-controlled reinforced concrete sections as defined in Article 11.3.4.2.1 For tension-controlled prestressed concrete sections as defined in Article 11.3.4.2.1 For shear and torsion: normal weight concrete lightweight concrete For compression-controlled sections with spirals or ties, as defined in Article 11.3.4.2.1,except as specified in Articles 11.3.7.11.3 and 11.3.7.11.4.1b for Seismic Zones 2, 3, and 4 at the extreme event limit state For bearing on concrete For compression in strut-and-tie model For compression in anchorage zones: normal weight concrete lightweight concrete For tension in steel in anchorage zones For resistance during pile driving

Value 0.90 1.00 0.90 0.80 0.75

0.70 0.70 0.80 0.65 1.00 1.00

For sections in which the net tensile strain in the extreme tension steel at nominal resistance, ɛt, is between the limits for compression-controlled (ɛt = 0.002) and tension-controlled (ɛt = 0.005), ɸ may be linearly increased from 0.75 to that for tension controlled sections as ɛt increases from the compression-controlled strain limit to 0.005.

Design Procedure Manual for Bridges Page 10 of 56

The variation ɸ may be computed for nonprestressed members such that: 𝑑𝑡 0.75 ≤ 𝜙 = 0.65 + 0.15 ( − 1) ≤ 0.9 𝑐 where: c = distance from the extreme compression fiber to the neutral axis (mm) dt = distance from the extreme compression fiber to the centroid of the extreme tension steel element (mm) 1.2.9 Compare factored flexural resistance versus maximum applied factored moment. 1.2.10 Calculate distribution reinforcement parallel to traffic (Article 14.4.3.1). Spacing of distribution bar shall be: 𝑆𝑟𝑒𝑞𝑑  𝑠𝑑𝑟 = % 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 where: Sreqd = spacing of main reinforcement

For primary reinforcement perpendicular to traffic: 3840 % distribution = 𝑆 ≤ 67% √

S = effective span length (in mm) 1.2.11 Calculate shrinkage and temperature bars (Article 12.7.8). The area of reinforcement per mm, on each face and in each direction shall be: 0.75 𝑏ℎ 𝐴𝑠 ≥ (Eq. 12.7.8-1) 2 (𝑏+ℎ)𝑓𝑦

0.233 ≤ 𝐴𝑠 ≤ 1.27 where: b = least width of component section (in mm) h = least thickness of component section (in mm) fy = specified yield strength of reinforcing bars Spacing shall not exceed:  30 times the component thickness, or  450 mm 1.2.12 Detail reinforcement. Shrinkage & Temp. Bars Main Top Bars

Distribution Bars Main Bottom Bars Figure 1-2 Slab Reinforcement Details

Design Procedure Manual for Bridges Page 11 of 56

1.3 Reinforced Concrete Girder Design 1.3.1 Establish Design Criteria.  Design specification : DGCS 2015  Superstructure data : Span length, bridge width, wearing surface thickness, sidewalk, post and railing dimensions  Material data : concrete and steel rebar  Design live load : HL 93 (Article 10.7.3) 1.3.2

Assume girder size based on span length and girder spacing (Table 10.1.2.6-1). Table 1-7 Traditional Minimum Depths for Constant Depth Superstructures (from Table 10.1.2.6-1) Superstructure

Minimum Depth (Including Deck) When variable depth members are used, values may be adjusted to account for changes in relative stiffness of positive and negative moment sections

Material Reinforced Concrete

Prestressed Concrete

Steel

1.3.3

Type

Simple Spans

Continuous Spans

1.20( 𝑆 + 3000) 30

𝑆 + 3000 ≥ 165𝑚𝑚 30

T-Beams

0.070L

0.065L

Box Beams

0.060L

0.055L

Pedestrian Structure Beams

0.035L

0.033L

0.030𝐿 ≥ 165𝑚𝑚.

0.027𝐿 ≥ 165𝑚𝑚..

CIP Box Beams

0.045L

0.040L

Precast I-Beams

0.045L

0.040L

Pedestrian Structure Beams

0.033L

0.030L

Adjacent Box Beams

0.030L

0.025L

Over-all Depth of Composite I-Beam

0.040L

0.032L

Depth of I-Beam Portion of Composite IBeam

0.033L

0.027L

Trusses

0.100L

0.100L

Slabs with reinforcement parallel to traffic

Slabs

Determine Dead Load Moments and Shear by STAAD Dead Load Analysis or manual calculation.  Component and Attachments - Slab, haunch, girder, diaphragm, post, railing, sidewalk 𝜔𝐷𝑊 𝐿2 𝑀𝐷𝑊 = (simply supported) 8

 Wearing Surface and Utilities 𝜔𝐷𝑊 𝐿2 𝑀𝐷𝑊 = (simply supported) 8 1.3.4 Determine Live Load Moments and Shear by STAAD Live Load Analysis or manual calculation. Vehicular live loading on the roadways of bridges or incidental structures, designated HL-93, and shall consist of combination of the:  Greater of Design Truck or Design Tandem, and

Design Procedure Manual for Bridges Page 12 of 56

or

Figure 1-3 Design Truck and Tandem Loads

 Design Lane Load (uniform load = 9.34 kN/m) 1.3.5

Determine Live Load Distribution Factors for Moments (Table 11.3.2.2-5) and for Shear (Table 11.3.2.2-9).  Determine the type of cross-section (Table 11.3.2.2-2)

Table 1-8 Common Deck Structures covered in Articles of Distribution Factor Method for Moment and Shear, and Distribution Factor Method for Shear (from Table 11.3.2.2-2) Supporting Components Steel Beam

Type of Deck Cast-in-place concrete slabs, precast concrete slab, steel grid, glued/spiked panels, stressed wood

Typical Cross Section

a.

Closed Steel or Precast Concrete Boxes

Cast-in-place concrete slab

b.

Open Steel or Precast Concrete Boxes

Cast-in-place concrete slab, precast concrete deck slab

c.

Cast-in-Place Concrete Multicell Box

Monolithic concrete

Cast-in-place Concrete Tee Beam

Monolithic concrete

d.

e.

Design Procedure Manual for Bridges Page 13 of 56 Supporting Components

Type of Deck

Precast Solid, Voided or Cellular Concrete Boxes with Shear Keys

Cast-in-place concrete overlay

Precast Solid, Voided, or Cellular Concrete Box with Shear Keys and with or without Transverse PostTensioning

Integral concrete

Precast Concrete Channel Sections with Shear Keys

Cast-in-place concrete overlay

Precast Concrete Double Tee Section with Shear Keys and with or without Transverse Post-Tensioning

Integral concrete

Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning

Integral concrete

Precast Concrete I or BulbTee Sections

Cast-in-place concrete, precast concrete

Typical Cross Section

f.

g. P /T

h.

i. P /T

j. P /T

k.

 Determine the Kg factor (Eq. 11.3.2.2-1) 𝐾𝑔 = 𝑛(𝐼 + 𝐴𝑒𝑔 2 ) 𝐸𝑏 𝑛= 𝐸𝑑 where: Eb = modulus of elasticity of beam material (MPa) Ed = modulus of elasticity of deck material (MPa) I = moment of inertia of beam (mm4) eg = distance between the centers of gravity of the basic beam and deck (mm)  Determine LL distribution factors for moment (Table 11.3.2.2-5) and for shear (Table 11.3.2.2-9) under single lane and multi-lane loading. Table 1-9 Distribution of Live Loads per Lane for Moment in Interior Beams (from Table 11.2.3.3-5)

Design Procedure Manual for Bridges Page 14 of 56 Applicable Crosssection from Table 11.3.2.2-2

Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double TSections

Cast-in-Place Concrete Multicell Box

a, e, k and also i, j if sufficiently connected to act as a unit

Distribution Factors

d

1100  S  4900

One Design Lane Loaded: 0.1

0. 4 0.3  S   S   K g  0.06       3  4300   L   Lt s  Two or More Design Lanes Loaded:

 S  0.075     2900 

0.6

S   L

0 .2

 Kg     Lt 3   s 

0.1

Nb = 3

One Design Lane Loaded:

2100  S  4000

 13   Nc

0.35

 1     Nc 

0.45

18000  L  73000

0.3

  S  1        430  L 

If N c  8 use N c  8

1800  S  5500

One Design Lane Loaded:  S     910 

0.35

 Sd   2  L 

 S     1900 

0.6

0.25

 Sd   2  L 

6000  L  43000 0.125

H g, i, j if connected only enough to prevent relative vertical displacement at the interface

S 5500

One Design Lane Loaded:  b  k   2.8 L 

g if sufficiently connected to act as a unit

0.5

I    J

0.25

where : k  2.5 N b   1.5 Two or More Design Lanes Loaded: 0.2

 b  k   7600 

0.6

b   L

0.2

I    J

0.06

Concrete Deck on Multiple Steel Box Girders

a

b, c

900  b  1500 6000  L  37000 5  N b  20

Regardless of Number of Loaded Lanes: S/D where: 𝐶 = 𝐾(𝑊⁄𝐿)𝐾 𝐷 = 300[11.5 − 𝑁𝐿 + 1.4𝑁𝐿 (1 − 0.2𝐶)2 ] when C  5 𝐷 = 300(11.5 − 𝑁𝐿 )when𝐶 > 5 𝐾= √

(1 + )𝐼 𝐽

for preliminary design, the following values of K may be used: Beam Type: K Non-voided rectangular beams 0.7 Rectangular beams with circular voids: 0.8 Box section beams 1.0 Channel beams 2.2 T-beam 2.0 Double T-beam 2.0 Open Steel Grid Deck on Steel Beams

450  d  1700 Nb  3

Use Lever Rule f

Nc  3

0.25

Two or More Design Lanes Loaded:

Concrete Beams used in Multibeam Decks

6000  L  73000 Nb  4

use lesser of the values obtained from the equation above with Nb= 3 or the lever rule S  300   1.75    1100  L  

b, c

110  t s  300

4  10 9  K g  3  1012

Two or More Design Lanes Loaded:

Concrete Deck on Concrete Spread BoxBeams

Range of Applicability

One Design Lane Loaded: S/2300 If tg<100mm S/3050 If tg P100 mm Two or More Design Lanes Loaded: S/2400 If tg< 100 mm S/3050 If tg ≥ 100mm Regardless of Number of Loaded Lanes:

0.425 N 0.05  0.85 L  Nb NL

Skew  45° NL 6

S ≤1800

S ≤3200

0 .5 

NL  1.5 Nb

Design Procedure Manual for Bridges Page 15 of 56

Table 1-10 Distribution of Live Load for Shear in Interior Beam (from Table 11.3.2.2-9) Applicable Cross Section from Table 11.3.2.2-2

Type of Superstructure

Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete TBeams, T- and Double TSections

a, e, k and also i, j if sufficiently connected to act as a unit

Cast-in-Place Concrete Multicell Box

D

One Design Lane Loaded

Two or More Design Lanes Loaded

S

0.36 

 S  0.2    3600  10700  S

7600

2.0

Range of Applicability

1100  S  4900 6000  L  73000 110  t s  300 Nb  4

Lever Rule

 S     2900 

Lever Rule

0.6

d    L

0.1

 S     2200 

Nb = 3

0. 9

d   L

0.1

1800  S  4000 6000  L  73000 890  d  2800 Nc  3

Concrete Deck on Concrete Spread Box Beams

b, c

 S     3050 

0.6

d   L

0.1

 S     2250 

0. 8

d    L

0. 1

1800  S  5500 6000  L  43000 450  d  1700 Nb  3

Lever Rule Concrete Box Beams Used in Multibeam Decks

f, g

Concrete Beams Other Than Box Beams Used in Multibeam Decks

H

Open Steel Grid Deck on Steel Beams Concrete Deck on Multiple Steel Box Beams

1.3.6

b 0.70  L

0.15

Lever Rule

I   J

0.06

0.4

𝑏 ( ) 4000

S>5500 0.1

0.05

𝑏 𝐼 𝑏 ( ) ( ) ( ) 𝐿 𝐽 1200 𝑏 ≥ 1.0 1200

900 ≤ b ≤ 1500 6000 ≤ L ≤ 37000 5 ≤ Nb ≤ 20 1.0 × 1010 ≤ J ≤ 2.5 × 1011 1.7 × 1010 ≤ I ≤ 2.5 × 1011

Lever Rule

Lever Rule

N/A

a

Lever Rule

Lever Rule

N/A

b, c

As specified in Table 11.3.2.2-5

i, j if connected only enough to prevent relative vertical displacement at the interface

Compute for factored moments. Using Load Combination (Table 10.3-1—Load Combinations and Load Factors)

Strength I Limit State: 1.0(dc * MDC + DW * MDW + LL* MLL1+IM) Service I Limit State: 1.0(1.0 * MDC + 1.0 * MDW + 1.0* MLL1+IM)

Design Procedure Manual for Bridges Page 16 of 56 Table 1-11 Load Combination and Load Factors (from Table 10.3-1) Load Combination

Limit State

STRENGTH-I (Unless noted) STRENGTH-II STRENGTH-III STRENGTH-III STRENGTH-IV EH, EV,ES,DW, DC ONLY STRENGTH-V EXTREME EVENT - I EVENT - I EXTREME EVENT - II EVENT - II SERVICE - I SERVICE - II SERVICE - III SERVICE - IV FATIGUE – 1 LL, IM, & CE ONLY FATIGUE – II LL, IM, & CE ONLY

DC DD DW EH EV ES EL PS CR SH p p p p p 1.5

Use one of these at a time LL IM CE BR PL LS

WA

1.75 1.35 1.35 -

1.00 1.00 1.00 1.00 1.00

1.4 -

1.00 1.00 1.00 1.00 1.00

0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20

0.0 0.0 0.0 0.0 -

SE SE SE SE -

-

-

-

-

p p

1.35 EQ

1.00 1.00

0.40 -

1.00 1.00

0.50/1.20 -

0.0 -

SE -

1.00

-

-

-

p

0.5

1.00

-

1.00

-

-

-

-

1.00

1.00

1.00

1.00 1.00 1.00 1.00 -

1.00 1.3 0.8 1.50

1.00 1.00 1.00 1.00 -

0.30 0.70 -

1.00 1.00 1.00 1.00 -

1.00/1.20 1.00/1.20 1.00/1.20 1.00/1.20 -

0.0 0.0 -

SE SE 1.0 -

-

-

-

-

-

0.75

-

-

-

-

-

-

-

-

-

-

WS

FR

TU

TG

SE EQ

BL

CT

CV

Table 1-12 Load Factors for Permanent Loads, γp (from Table 10.3-2) Load Factor Type of Load Max

Min

DC: Component and Attachments

1.25

0.90

DD: Downdrag

1.80

0.45

DW: Wearing Surfaces and Utilities

1.50

0.65

Active

1.50

0.90

At-Rest

1.35

0.90

EL: Locked-in Erection Stresses

1.00

1.00

Retaining Walls and Abutments

1.35

1.00

Rigid Buried Structure

1.30

0.90

Rigid Frames

1.35

0.90

Flexible Buried Structures other than Metal Box Culverts

1.95

0.90

Flexible Metal Box Culverts

1.50

0.90

ES: Earth Surcharge

1.50

0.75

EH: Horizontal Earth Pressure

EV: Vertical Earth Pressure

1.3.7

Design for flexure under Strength Limit State (Article 12.2.3).  Calculate main reinforcement of girder.  Calculate factored flexural resistance, Mr at points of maximum moment (Article 12.4.3.2). 𝑀𝑟 = 𝛷𝑀𝑛

Design Procedure Manual for Bridges Page 17 of 56 𝑎

𝑀𝑛 = 𝐴𝑠 𝑓𝑦 (𝑑𝑒 − 2 ) for rectangular section 𝑡

𝑀𝑛 = 0.85𝑓𝑐 ′𝑏𝑒 𝑡𝑠 (𝑑𝑒 − 2𝑠 ) for flanged section where: be = effective flange width ts = thickness of slab de = effective depth of girder

For conventional construction, resistance factor ɸ is tabulated below. Table 1-13 Nominal Fatigue Resistance of Splices Factor For tension-controlled reinforced concrete sections as defined in Article 11.3.4.2.1 For tension-controlled prestressed concrete sections as defined in Article 11.3.4.2.1 For shear and torsion: normal weight concrete lightweight concrete For compression-controlled sections with spirals or ties, as defined in Article 11.3.4.2.1,except as specified in Articles 11.3.7.11.3 and 11.3.7.11.4.1b for Seismic Zones 2, 3, and 4 at the extreme event limit state For bearing on concrete For compression in strut-and-tie model For compression in anchorage zones: normal weight concrete lightweight concrete For tension in steel in anchorage zones For resistance during pile driving

Value 0.90 1.00 0.90 0.80 0.75

0.70 0.70 0.80 0.65 1.00 1.00

For sections in which the net tensile strain in the extreme tension steel at nominal resistance, ɛt, is between the limits for compression-controlled (ɛt = 0.002) and tension-controlled (ɛt = 0.005), ɸ may be linearly increased from 0.75 to that for tension controlled sections as ɛt increases from the compression-controlled strain limit to 0.005. The variation ɸ may be computed for nonprestressed members such that: 𝑑𝑡 0.75 ≤ 𝜙 = 0.65 + 0.15 ( − 1) ≤ 0.9 𝑐 where: c = distance from the extreme compression fiber to the neutral axis (mm) dt = distance from the extreme compression fiber to the centroid of the extreme tension steel element (mm)  Compare factored flexural resistance versus maximum applied factored moment.  Check the maximum and minimum reinforcement (12.4.3.3). For maximum reinforcement: The current provisions of LRFD eliminate the maximum reinforcement limit. A reduction in the factored flexural resistance of the section is added instead. It states that below a net tensile strain in the extreme tension steel of 0.005, as the tension reinforcement quantity increases, the factored resistance of prestressed and nonprestressed sections is reduced to compensate for decreasing ductility with increasing overstrength. For minimum reinforcement: The amount of non-prestressed tensile reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equal to the lesser of:

Design Procedure Manual for Bridges Page 18 of 56

 1.33 times the factored moment required by the applicable strength load combination, and  𝑀𝑐𝑟 = 𝛾1 𝛾3 𝑓𝑟 𝑆𝑐 where: γ1 = flexural cracking variability factor = 1.2 for precast segmental structures = 1.6 for all other concrete structures γ3 = ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement = 0.67 for A615, 414 MPa reinforcement = 0.75 for A706, 414 MPa reinforcement fr = modulus of rupture of concrete specified in Article 12.1.1.6 Sc = section modulus for the extreme fiber of the composite section where tensile stress is caused by externally applied loads (mm3) 1.3.8

Design for flexure under Service Limit State (Article 12.2.1).  Control of cracking by distribution of reinforcement (Article 12.4.3.4) The spacing s of mild steel reinforcement in the layer closest to the tension face shall satisfy the following: s≤

123 000γe βs fss

− 2dc

in which: βs = 1 +

dc 0.7(h−dc )

where: γe

1.3.9

dc

= = = =

fss

=

h de

= =

exposure factor 1.00 for Class 1 exposure condition 0.75 for Class 2 exposure condition thickness of concrete cover measured from extreme tension fiber to center of the flexural reinforcement located closest thereto (mm) tensile stress in steel reinforcement at the service limit (MPa) overall thickness or depth of the component (mm) distance from the extreme compression fiber to the centroid of extreme tension steel element (mm)

Design for shear under Strength Limit State (Article 12.5).  Determine bv and dv bv = effective web width taken as the minimum web width (in mm) dv = effective shear depth 𝑀𝑛 𝑑𝑣 = ≥ 𝑚𝑎𝑥𝑖𝑚𝑢𝑚(0.90𝑑𝑒 , 0.72ℎ) 𝐴𝑠 𝑓𝑦  Calculate nominal shear resistance in concrete, Vc (Article 12.5.3.2). 𝑉𝑐 = 0.083𝛽𝑓𝑐 ′0.5 𝑏𝑣 𝑑𝑣  If Vu>0.5ɸ (Vc), transverse reinforcement shall be provided. where: Vu = factored shear force Vc = nominal shear resistance of the concrete ɸ = resistance factor

Design Procedure Manual for Bridges Page 19 of 56

The required spacing of transverse reinforcement, s, is equal to 𝑐𝑜𝑡𝛩 𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 (𝑉𝑢 ) ɸ

−𝑉𝑐

The spacing of the transverse reinforcement shall not exceed the maximum permitted spacing, smax, determined as: Case 1: If vu<0.125 f’c, smax is equal to lesser of 0.80 dv and 600 mm Case 2: If vu≥0.125 f’c, smax is equal to lesser of 0.40 dv and 300 mm where: vu = shear stress calculated |𝑉𝑢 − ɸ𝑉𝑝 | 𝑣𝑢 = ɸ𝑏𝑣 𝑑𝑣  Calculate factored shear resistance, Vr (Article 12.5.3.2). 𝑉𝑟 = ɸ𝑉𝑛 = ɸ(𝑉𝑐 + 𝑉𝑠 ) where: Vs = shear resistance provided by shear reinforcement 𝑐𝑜𝑡𝛩 𝑉𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 𝑠  Calculate longitudinal skin reinforcement (Article 12.4.3.4). The area of skin reinforcement Ask in mm2/m of height on each side face shall satisfy: 𝐴𝑠 𝐴𝑠𝑘 ≥ 0.001 (𝑑𝑒 − 760) ≤ 4 where: As = area of tensile reinforcement (mm2)

Figure 1-4 Section at midspan

1.3.10 Calculate immediate and long time deflection. 

Calculate gross (Ig), cracked (Icr) and effective (Ie) moments of inertia of superstructure 𝑀𝑐𝑟 3 𝑀𝑐𝑟 3 𝐼𝑒 = ( ) 𝐼𝑔 + [1 − ( ) ]𝐼𝑐𝑟 ≤ 𝐼𝑔 𝑀𝑎 𝑀𝑎 where: Ie = effective moment of inertia Ig = gross moment of inertia

Design Procedure Manual for Bridges Page 20 of 56

 

Icr = cracked moment of inertia 𝐼𝑔 𝑀𝑐𝑟 = 0.63√𝑓′𝑐 𝑦𝑡 Dg = depth of girder Yt = distance from neutral axis to the extreme tension fiber Ma = maximum moment in a component at the stage for which deformation is computed Obtain immediate deflection at quarter points from STAAD results or manual calculation Compute long time deflection Case 1: If IgIe, long time deflection = 3 - 1.2(As’/As)*(immediate deflection) As’ = area of compression reinforcement (mm2) As = area of tension reinforcement (mm2)

L/4

L/4

L/4

Figure 1-5 Camber Diagram

L/4

Design Procedure Manual for Bridges Page 21 of 56

Establish Design Criteria Assume slab thickness Article 14.4.1.1 Determine DL Moments Determine LL Positive and Negative Moments Table A11-1 Compute for factored moments Table 10.3-1 Calculate main reinforcement (perpendicular to traffic) Article 12.4.3

NO

Is the slab thickness adequate? YES Calculate distribution reinforcement (parallel to traffic) Article 14.4.3.1 Calculate shrinkage and temperature bars Article 12.7.8 Figure 1-6 Design Procedure of Deck Slab

Design Procedure Manual for Bridges Page 22 of 56

Establish Design Criteria

Assume girder size based on span length and girder spacing Table 10.1.2.6-1 Determine DL Moments and Shear by STAAD DL Analysis or manual calculation

Determine LL Moments and Shear by STAAD LL Analysis or manual calculation

Determine LL distribution factors for Moments (Table 11.3.2.2-5) and for Shear (Table 11.3.2.2-9) A Compute for factored moments and shear Table 10.3-1 Design for flexure under Strength Limit State Article 12.2.3 Design for flexure under Service Limit State Article 12.2.1 Design for shear under Strength Limit State Article 12.5

Calculate immediate and long time deflection

NO

Is the section adequate?

YES Detail reinforcement

Figure 1-7 Design Procedure of Reinforced Concrete Girder

Design Procedure Manual for Bridges Page 23 of 56

2 Design of Pre-stressed Concrete Girder Superstructure (LRFD) Part 2

Design Procedure Manual for Bridges Page 24 of 56

2.1 Main Design Steps 2.1.1 Establish Design Criteria.  Material data  Span arrangement  Girder spacing,  Bearing types  Substructure type and geometry  Foundation type based on soil investigation 2.1.2

Assume deck slab thickness based on girder spacing and anticipated girder top flange.

2.1.3

Analyze interior girder.

2.1.4

Design the deck slab.

2.1.5

Design the girder for flexure and shear.

Design Procedure Manual for Bridges Page 25 of 56

2.2 Deck Slab Design 2.2.1 Establish Design Criteria  Design specification  Material data  Design live load 2.2.2

: : :

DGCS 2015 concrete and steel reinforcements HL 93 (Article 10.7.3)

Assume slab thickness (Article 14.4.1.1). Unless approved by the Owner, the depth of a concrete deck, excluding any provisions for grinding, grooving and sacrificial surface, should not be less than 175 mm. Table 2-1 Traditional Minimum Depths for Constant Depth Superstructures (from Table 10.1.2.6-1) Superstructure

Minimum Depth (Including Deck) When variable depth members are used, values may be adjusted to account for changes in relative stiffness of positive and negative moment sections

Material

Type

Reinforced Concrete

Simple Spans

Continuous Spans

1.20( 𝑆 + 3000) 30

𝑆 + 3000 ≥ 165𝑚𝑚 30

T-Beams

0.070L

0.065L

Box Beams

0.060L

0.055L

Pedestrian Structure Beams

0.035L

0.033L

0.030𝐿 ≥ 165𝑚𝑚.

0.027𝐿 ≥ 165𝑚𝑚..

CIP Box Beams

0.045L

0.040L

Precast I-Beams

0.045L

0.040L

Pedestrian Structure Beams

0.033L

0.030L

Adjacent Box Beams

0.030L

0.025L

Over-all Depth of Composite I-Beam

0.040L

0.032L

Depth of I-Beam Portion of Composite IBeam

0.033L

0.027L

Trusses

0.100L

0.100L

Slabs with reinforcement parallel to traffic

Prestressed Concrete

Slabs

Steel

2.2.3

Determine the location of the critical section for negative moment based on the girder top flange width (11.3.2.1.5)

2.2.4

Determine Dead Load Moments.  Moment due to self-weight of slab 𝜔𝑠𝑙𝑎𝑏 𝑆 2 𝑀𝑠𝑙𝑎𝑏 = 10 where: ωslab = width x thickness of slab X γconcrete S = clear span length 

Moment due to future wearing surface 𝑀𝑓𝑤𝑠 =

𝜔𝑤𝑠 𝐿2 10

where: ωslab = width of slab X thickness of wearing surface X γwearing surface S = clear span length

Design Procedure Manual for Bridges Page 26 of 56

2.2.5

Determine Live Load Positive and Negative Moments using Table A11-1.

Figure 2-1 Maximum Live Load Moments per Unit Width, N-mm/mm (from Table A11-1)

Note: Multiple presence factors and the dynamic load allowance are incorporated in the tabulated values. Interpolation between the listed values may be used for the distances other than those listed in Table A11-1. For methods of determining live load moments other than the use of Table A11-1, dynamic load allowance (Article 10.8) and multiple presence factors (Article 10.7.2.2) should be incorporated. The dynamic load allowance shall not be applied to pedestrian loads or to the design lane load. Table 2-2 Dynamic Load Allowance, IM (from Table 10.8-1) Component Deck Joints - All Limit States

IM 75%

All Other Components Fatigue and Fracture

15%

Limit State All Other Limit States

33%

Design Procedure Manual for Bridges Page 27 of 56 Table 2-3 Multiple Presence Factors, m (from Table 10.7.2.2-1)

2.2.6

Number of loaded lanes

Multiple Presence Factors

1

1.20

2

1.00

3

0.85

>3

0.65

Compute for factored moments. Using Load Combination (Table 10.3-1—Load Combinations and Load Factors)

Strength I Limit State: 1.0(dc * MDC + DW * MDW + LL* MLL1+IM) Service I Limit State: 1.0(1.0 * MDC + 1.0 * MDW + 1.0*MLL+IM) Table 2-4 Load Combination and Load Factors (from Table 10.3-1) Load Combination

Limit State

STRENGTH-I (Unless noted) STRENGTH-II STRENGTH-III STRENGTH-III STRENGTH-IV EH, EV,ES,DW, DC ONLY STRENGTH-V EXTREME EVENT - I EVENT - I EXTREME EVENT - II EVENT - II SERVICE - I SERVICE - II SERVICE - III SERVICE - IV FATIGUE – 1 LL, IM, & CE ONLY FATIGUE – II LL, IM, & CE ONLY

DC DD DW EH EV ES EL PS CR SH p p p p p 1.5

Use one of these at a time LL IM CE BR PL LS

WA

1.75 1.35 1.35 -

1.00 1.00 1.00 1.00 1.00

1.4 -

1.00 1.00 1.00 1.00 1.00

0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20

0.0 0.0 0.0 0.0 -

SE SE SE SE -

-

-

-

-

p p

1.35 EQ

1.00 1.00

0.40 -

1.00 1.00

0.50/1.20 -

0.0 -

SE -

1.0 0

-

-

-

p

0.5

1.00

-

1.00

-

-

-

-

1.00

1.00

1.00

1.00 1.00 1.00 1.00 -

1.00 1.3 0.8 1.50

1.00 1.00 1.00 1.00 -

0.30 0.70 -

1.00 1.00 1.00 1.00 -

1.00/1.20 1.00/1.20 1.00/1.20 1.00/1.20 -

0.0 0.0 -

SE SE 1.0 -

-

-

-

-

-

0.75

-

-

-

-

-

-

-

-

-

-

WS

FR

TU

TG

SE EQ

BL

CT

CV

Design Procedure Manual for Bridges Page 28 of 56 Table 2-5 Load Factors for Permanent Loads, γp (from Table 10.3-2) Load Factor Type of Load Max

Min

DC: Component and Attachments

1.25

0.90

DD: Downdrag

1.80

0.45

DW: Wearing Surfaces and Utilities

1.50

0.65

Active

1.50

0.90

At-Rest

1.35

0.90

EL: Locked-in Erection Stresses

1.00

1.00

Retaining Walls and Abutments

1.35

1.00

Rigid Buried Structure

1.30

0.90

Rigid Frames

1.35

0.90

Flexible Buried Structures other than Metal Box Culverts

1.95

0.90

Flexible Metal Box Culverts

1.50

0.90

ES: Earth Surcharge

1.50

0.75

EH: Horizontal Earth Pressure

EV: Vertical Earth Pressure

2.2.7

Calculate main reinforcement perpendicular to traffic (Article 12.4.3).

2.2.8

Calculate factored flexural resistance, Mr at points of maximum moment (Article 12.4.3.2). 𝑀𝑟 = 𝛷𝑀𝑛 𝑎 𝑀𝑛 = 𝐴𝑠 𝑓𝑦 (𝑑𝑒 − ) 2 For conventional construction, resistance factor ɸ is tabulated in Table 2-6. Table 2-6 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1) Factor For tension-controlled reinforced concrete sections as defined in Article 11.3.4.2.1 For tension-controlled prestressed concrete sections as defined in Article 11.3.4.2.1 For shear and torsion: normal weight concrete lightweight concrete For compression-controlled sections with spirals or ties, as defined in Article 11.3.4.2.1,except as specified in Articles 11.3.7.11.3 and 11.3.7.11.4.1b for Seismic Zones 2, 3, and 4 at the extreme event limit state For bearing on concrete For compression in strut-and-tie model For compression in anchorage zones: normal weight concrete lightweight concrete For tension in steel in anchorage zones For resistance during pile driving

Value 0.90 1.00 0.90 0.80 0.75

0.70 0.70 0.80 0.65 1.00 1.00

For sections in which the net tensile strain in the extreme tension steel at nominal resistance, ɛt, is between the limits for compression-controlled (ɛt = 0.002) and tension-controlled (ɛt = 0.005), ɸ may be linearly increased from 0.75 to that for tension controlled sections as ɛt increases from the compression-controlled strain limit to 0.005.

Design Procedure Manual for Bridges Page 29 of 56

The variation ɸ may be computed for prestressed members such that: 𝑑𝑡 0.75 ≤ 𝜙 = 0.583 + 0.25 ( − 1) ≤ 1.0 𝑐 where: c = distance from the extreme compression fiber to the neutral axis (mm) dt = distance from the extreme compression fiber to the centroid of the extreme tension steel element (mm) 2.2.9

Compare factored flexural resistance versus maximum applied factored moment.

2.2.10 Calculate distribution reinforcement parallel to traffic (Article 14.4.3.1). Spacing of distribution bar shall be: 𝑆𝑟𝑒𝑞𝑑  𝑠𝑑𝑟 = % 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 where: Sreqd = spacing of main reinforcement For primary reinforcement perpendicular to traffic: 3840 % distribution = 𝑆 ≤ 67% S

√

= effective span length (in mm)

2.2.11 Calculate shrinkage and temperature bars (Article 12.7.8). The area of reinforcement per mm, on each face and in each direction shall be: 0.75 𝑏ℎ 𝐴𝑠 ≥ 2 (𝑏+ℎ)𝑓 (Eq. 12.7.8-1) 𝑦

0.233 ≤ 𝐴𝑠 ≤ 1.27

where: b = least width of component section (mm) h = least thickness of component section (mm) fy = specified yield strength of reinforcing bars (MPa) 2.2.12 Detail reinforcement. Shrinkage & Temp. Bars Top Main Bars Bottom Main Bars Bottom Distribution Bars

Figure 2-2 Slab Reinforcement Details

Design Procedure Manual for Bridges Page 30 of 56

2.3

Prestressed Concrete Girder Design

2.3.1

Establish design criteria.  Design specification  Superstructure data  Material data  Design live load

2.3.2

: : : :

DGCS 2015 Span length, bridge width, girder type wearing surface thickness, sidewalk, post and railing dimensions concrete, steel rebar and prestressing tendons HL 93 (Article 10.7.3)

Assume girder size based on span length and girder spacing (Table 10.1.2.6-1). Table 2-7 Traditional Minimum Depths for Constant Depth Structures (from Table 10.1.2.6-1) Superstructure

Minimum Depth (Including Deck) When variable depth members are used, values may be adjusted to account for changes in relative stiffness of positive and negative moment sections

Material

Type

Reinforced Concrete

Prestressed Concrete

Continuous Spans 𝑆 + 3000 ≥ 165𝑚𝑚 30

T-Beams

0.070L

0.065L

Box Beams

0.060L

0.055L

Pedestrian Structure Beams

0.035L

0.033L

0.030𝐿 ≥ 165𝑚𝑚.

0.027𝐿 ≥ 165𝑚𝑚..

CIP Box Beams

0.045L

0.040L

Precast I-Beams

0.045L

0.040L

Pedestrian Structure Beams

0.033L

0.030L

Adjacent Box Beams

0.030L

0.025L

Over-all Depth of Composite I-Beam

0.040L

0.032L

Depth of I-Beam Portion of Composite IBeam

0.033L

0.027L

Trusses

0.100L

0.100L

Slabs

Steel

2.3.3

Simple Spans 1.20( 𝑆 + 3000) 30

Slabs with reinforcement parallel to traffic

Determine Dead Load Moments, Shear and Dead Load Analysis using STAAD software or by manual calculation.  Component and Attachments - Slab, haunch, girder, diaphragm, post, railing, sidewalk -

𝑀𝐷𝑊 =

𝜔𝐷𝑊 𝐿2 8

(simply supported)

 Wearing Surface and Utilities  2.3.4

𝑀𝐷𝑊 =

𝜔𝐷𝑊 𝐿2 8

(simply supported)

Determine Live Load Moments and Shear by STAAD Live Load Analysis or manual calculation. Vehicular live loading on the roadways of bridges or incidental structures, designated HL-93, and shall consist of combination of the:  Greater of Design Truck or Design Tandem, and

Design Procedure Manual for Bridges Page 31 of 56

or

Figure 2-3 Design Truck and Tandem Loads

 Design Lane Load (uniform load = 9.34 kN/m) 2.3.5

Determine Live Load Distribution Factors for Moments (Table 11.3.2.2-5) and for Shear (Table 11.3.2.2-9).  Determine the type of cross-section (Table 11.3.2.2-2)

Table 2-8 Common Deck Structures covered in Articles of Distribution Factor Method for Moment and Shear, and Distribution Factor Method for Shear (from 11.3.2.2-2) Supporting Components Steel Beam

Type of Deck Cast-in-place concrete slabs, precast concrete slab, steel grid, glued/spiked panels, stressed wood

Typical Cross Section

a.

Closed Steel or Precast Concrete Boxes

Cast-in-place concrete slab

b.

Open Steel or Precast Concrete Boxes

Cast-in-place concrete slab, precast concrete deck slab

c.

Cast-in-Place Concrete Multicell Box

Monolithic concrete

Cast-in-place Concrete Tee Beam

Monolithic concrete

d.

e.

Design Procedure Manual for Bridges Page 32 of 56 Supporting Components

Type of Deck

Precast Solid, Voided or Cellular Concrete Boxes with Shear Keys

Cast-in-place concrete overlay

Precast Solid, Voided, or Cellular Concrete Box with Shear Keys and with or without Transverse PostTensioning

Integral concrete

Precast Concrete Channel Sections with Shear Keys

Cast-in-place concrete overlay

Precast Concrete Double Tee Section with Shear Keys and with or without Transverse Post-Tensioning

Integral concrete

Precast Concrete Tee Section with Shear Keys and with or without Transverse Post-Tensioning

Integral concrete

Precast Concrete I or BulbTee Sections

Cast-in-place concrete, precast concrete

Typical Cross Section

f.

g. P /T

h.

i. P /T

j. P /T

k.

 Determine the Kg factor (Eq. 11.3.2.2-1) 𝐾𝑔 = 𝑛(𝐼 + 𝐴𝑒𝑔 2 ) 𝐸𝑏 𝑛= 𝐸𝑑 where: Eb = modulus of elasticity of beam material (MPa) Ed = modulus of elasticity of deck material (MPa) I = moment of inertia of beam (mm4) eg = distance between the centers of gravity of the basic beam and deck (mm)  Determine LL distribution factors for moment (Table 11.3.2.2-5) and shear (Table 11.3.2.2-9) under single lane and multi-lane loading.

Design Procedure Manual for Bridges Page 33 of 56 Table 2-9 Distribution of Live Loads per Lane for Moment in Interior Beams (From Table 11.3.2.2-5) Applicable Crosssection from Table 11.3.2.2-2

Type of Superstructure Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double TSections

a, e, k and also i, j if sufficiently connected to act as a unit

Distribution Factors

1100  S  4900

One Design Lane Loaded: 0.1

0. 4 0.3  S   S   K g  0.06       3  4300   L   Lt s  Two or More Design Lanes Loaded:

 S  0.075     2900 

0.6

S   L

0 .2

 Kg   Lt 3  s

   

0.1

d

0.35

 1     Nc 

0.45

0.3

Concrete Deck on Concrete Spread BoxBeams

b, c

0.35

 Sd   2  L 

If N c  8 use N c  8

1800  S  5500

0.25

6000  L  43000

Two or More Design Lanes Loaded:  S     1900 

0.6

 Sd   2  L 

0.125

f

h g, i, j if connected only enough to prevent relative vertical displacement at the interface

S 5500

One Design Lane Loaded:  b  k   2.8 L 

g if sufficiently connected to act as a unit

0.5

I    J

0.25

where : k  2.5 N b   1.5 Two or More Design Lanes Loaded: 0.2

 b  k   7600 

0.6

b   L

0.2

I    J

0.06

a

900  b  1500 6000  L  37000 5  N b  20

Regardless of Number of Loaded Lanes: S/D where: 𝐶 = 𝐾(𝑊⁄𝐿)𝐾 𝐷 = 300[11.5 − 𝑁𝐿 + 1.4𝑁𝐿 (1 − 0.2𝐶)2 ] when C  5 𝐷 = 300(11.5 − 𝑁𝐿 )when𝐶 > 5 𝐾= √

(1 + )𝐼 𝐽

for preliminary design, the following values of K may be used: Beam Type: K Non-voided rectangular beams 0.7 Rectangular beams with circular voids: 0.8 Box section beams 1.0 Channel beams 2.2 T-beam 2.0 Double T-beam 2.0 Open Steel Grid Deck on Steel Beams

450  d  1700 Nb  3

Use Lever Rule Concrete Beams used in Multibeam Decks

Nc  3

0.25

One Design Lane Loaded:  S     910 

Nb = 3

18000  L  73000

Two or More Design Lanes Loaded:  13   S  1        N c   430  L 

6000  L  73000 Nb  4

2100  S  4000

One Design Lane Loaded: S  300   1.75    1100  L  

110  t s  300

4  10 9  K g  3  1012

use lesser of the values obtained from the equation above with Nb= 3 or the lever rule Cast-in-Place Concrete Multicell Box

Range of Applicability

One Design Lane Loaded: S/2300 If tg<100mm S/3050 If tg P100 mm Two or More Design Lanes Loaded: S/2400 If tg< 100 mm S/3050 If tg ≥ 100mm

Skew  45° NL 6

S ≤1800

S ≤3200

Design Procedure Manual for Bridges Page 34 of 56 Applicable Crosssection from Table 11.3.2.2-2

Type of Superstructure Concrete Deck on Multiple Steel Box Girders

b, c

Range of Applicability

Distribution Factors Regardless of Number of Loaded Lanes:

0.05  0.85

0 .5 

N L 0.425  Nb NL

NL  1.5 Nb

Table 2-10 Distribution of Live Load for Shear in Interior Beam (from Table 11.3.2.2-9) Applicable Cross Section from Table 11.3.2.2-2

Type of Superstructure

Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete TBeams, T- and Double TSections

a, e, k and also i, j if sufficiently connected to act as a unit

Cast-in-Place Concrete Multicell Box

d

One Design Lane Loaded

Two or More Design Lanes Loaded

S

0.36 

 S  0.2    3600  10700  S

7600

2.0

Range of Applicability

1100  S  4900 6000  L  73000 110  t s  300 Nb  4

Lever Rule

 S     2900 

Lever Rule

0.6

d    L

0.1

 S     2200 

Nb = 3

0. 9

d   L

0.1

1800  S  4000 6000  L  73000 890  d  2800 Nc  3

Concrete Deck on Concrete Spread Box Beams

b, c

 S     3050 

0.6

d   L

0.1

 S     2250 

0. 8

d    L

0. 1

1800  S  5500 6000  L  43000 450  d  1700 Nb  3

Lever Rule Concrete Box Beams Used in Multibeam Decks

f, g

Concrete Beams Other Than Box Beams Used in Multibeam Decks

h

Open Steel Grid Deck on Steel Beams Concrete Deck on Multiple Steel Box Beams

2.3.6

b 0.70  L

0.15

Lever Rule

I   J

0.06

0.4

𝑏 ( ) 4000

S>5500 0.1

0.05

𝑏 𝐼 𝑏 ( ) ( ) ( ) 𝐿 𝐽 1200 𝑏 ≥ 1.0 1200

900 ≤ b ≤ 1500 6000 ≤ L ≤ 37000 5 ≤ Nb ≤ 20 1.0 × 1010 ≤ J ≤ 2.5 × 1011 1.7 × 1010 ≤ I ≤ 2.5 × 1011

Lever Rule

Lever Rule

N/A

a

Lever Rule

Lever Rule

N/A

b, c

As specified in Table 11.3.2.2-5

i, j if connected only enough to prevent relative vertical displacement at the interface

Compute for factored moments (Table 10.3-1). Using Load Combination (Table 3.4.1-1—Load Combinations and Load Factors)

Strength I Limit State: 1.0(dc * MDC + DW * MDW + LL* MLL1+IM) Service I Limit State: 1.0( 1.0 * MDC + 1.0 * MDW + 1.0*MLL+IM)

Design Procedure Manual for Bridges Page 35 of 56 Table 2-11 Load Combination and Load Factors (from Table 10.3-1) Load Combination

Limit State

STRENGTH-I (Unless noted) STRENGTH-II STRENGTH-III STRENGTH-III STRENGTH-IV EH, EV,ES,DW, DC ONLY STRENGTH-V EXTREME EVENT - I EVENT - I EXTREME EVENT - II EVENT - II SERVICE - I SERVICE - II SERVICE - III SERVICE - IV FATIGUE – 1 LL, IM, & CE ONLY FATIGUE – II LL, IM, & CE ONLY

DC DD DW EH EV ES EL PS CR SH p p p p p 1.5

Use one of these at a time LL IM CE BR PL LS

WA

1.75 1.35 1.35 -

1.00 1.00 1.00 1.00 1.00

1.4 -

1.00 1.00 1.00 1.00 1.00

0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20 0.50/1.20

0.0 0.0 0.0 0.0 -

SE SE SE SE -

-

-

-

-

p p

1.35 EQ

1.00 1.00

0.40 -

1.00 1.00

0.50/1.20 -

0.0 -

SE -

1.00

-

-

-

p

0.5

1.00

-

1.00

-

-

-

-

1.00

1.00

1.00

1.00 1.00 1.00 1.00 -

1.00 1.3 0.8 1.50

1.00 1.00 1.00 1.00 -

0.30 0.70 -

1.00 1.00 1.00 1.00 -

1.00/1.20 1.00/1.20 1.00/1.20 1.00/1.20 -

0.0 0.0 -

SE SE 1.0 -

-

-

-

-

-

0.75

-

-

-

-

-

-

-

-

-

-

WS

FR

TU

TG

SE EQ

BL

CT

CV

Table 2-12 Load Factors for Permanent Loads, γp (from Table 10.3-2) Load Factor Type of Load Max

Min

DC: Component and Attachments

1.25

0.90

DD: Downdrag

1.80

0.45

DW: Wearing Surfaces and Utilities

1.50

0.65

Active

1.50

0.90

At-Rest

1.35

0.90

EL: Locked-in Erection Stresses

1.00

1.00

Retaining Walls and Abutments

1.35

1.00

Rigid Buried Structure

1.30

0.90

Rigid Frames

1.35

0.90

Flexible Buried Structures other than Metal Box Culverts

1.95

0.90

Flexible Metal Box Culverts

1.50

0.90

ES: Earth Surcharge

1.50

0.75

EH: Horizontal Earth Pressure

EV: Vertical Earth Pressure

2.3.7

Determine the stress limit immediately prior to transfer in the prestressing strands for the prestressing steel used (12.6.3)

Design Procedure Manual for Bridges Page 36 of 56

Figure 2-4 Stress Limits for Prestressing Tendons (from Table 12.6.3-1)

2.3.8

Determine Instantaneous Losses (12.6.5.2) for post-tensioned members  Anchorage Set The magnitude of the anchorage set shall be the greater of that required to control the stress in the prestressing steel at transfer or that recommended by the manufacturer of the anchorage. The magnitude of the set assumed for the design and used to calculate set loss shall be shown in the contract documents and verified during construction.  Friction Losses due to friction between the prestressing tendons and the duct wall may be taken as: 𝛥𝑓𝑝𝐹 = 𝑓𝑝𝑗(1 − 𝑒 −(𝐾𝑥+𝑢𝛼) ) Losses due to friction between the external tendons across a single deviator pipe may be taken as: 𝛥𝑓𝑝𝐹 = 𝑓𝑝𝑗(1 − 𝑒 −𝑢(𝛼+0.04) ) where: fpj = stress in the prestressing steel at jacking x = length of a prestressing tendon from the jacking end to any point under consideration K = wobble friction coefficient u = coefficient of friction α = sum of the absolute values of angular change of prestressing steel path from jacking end, or from the nearest jacking end if tensioning is done equally at both ends, to the point under investigation (rad) e = base of Napierian logarithms

Design Procedure Manual for Bridges Page 37 of 56

Figure 2-5 Friction Coefficients for Post-Tensioning Tendons

 Elastic Shortening 𝛥𝑓𝑝𝐸𝑆 = 2.3.9

𝑁 − 1 𝐸𝑝 𝑓𝑐𝑔𝑝 2𝑁 𝐸𝑐𝑖

Determine the approximate estimate of time dependent losses (12.6.5.3) 𝛥𝑓𝑝𝐿𝑇 = 10.0

𝑓𝑝𝑖 𝐴𝑝𝑠 𝛾ℎ 𝐴𝑔

𝛾𝑠𝑡 + 12.0 𝛾ℎ 𝛾𝑠𝑡 + 𝛥𝑓𝑝R

2.3.10 Determine stress in strands immediately after transfer as the stress prior to transfer minus instantaneous losses 2.3.11 Determine final stress in strands as stress immediately prior to transfer minus sum of instantaneous loss and time dependent losses after transfer 2.3.12 Determine compression and tension stress limits at transfer 2.3.13 Determine final compression and tension stress limits at service 2.3.14 Calculate initial service moment stress in the top and bottom of the prestressed girder 2.3.15 Calculate final service moment stress in the top and bottom of the prestressed girder 2.3.16 Design for flexure under Service Limit State (Article 12.2.1). 2.3.17 Design for flexure under Strength Limit State (Article 12.2.3).  Calculate main reinforcement of girder.  Calculate factored flexural resistance, Mr at points of maximum moment (Article 12.4.3.2). 𝑀𝑟 = 𝛷𝑀𝑛 𝑎 𝑀𝑛 = 𝐴𝑠 𝑓𝑦 (𝑑𝑒 − ) 2 For conventional construction, resistance factor ɸ is tabulated below. Table 2-13 Nominal Fatigue Resistance of Splices (from Table 12.2.3.1-1) Factor For tension-controlled reinforced concrete sections as defined in Article 11.3.4.2.1 For tension-controlled prestressed concrete sections as defined in Article 11.3.4.2.1 For shear and torsion: normal weight concrete lightweight concrete For compression-controlled sections with spirals or ties, as defined in Article 11.3.4.2.1,except as specified in Articles 11.3.7.11.3 and 11.3.7.11.4.1b for Seismic Zones 2, 3, and 4 at the extreme event limit state For bearing on concrete For compression in strut-and-tie model For compression in anchorage zones: normal weight concrete lightweight concrete For tension in steel in anchorage zones For resistance during pile driving

Value 0.90 1.00 0.90 0.80 0.75

0.70 0.70 0.80 0.65 1.00 1.00

Design Procedure Manual for Bridges Page 38 of 56

For sections in which the net tensile strain in the extreme tension steel at nominal resistance, ɛt, is between the limits for compression-controlled (ɛt = 0.002) and tension-controlled (ɛt = 0.005), ɸ may be linearly increased from 0.75 to that for tension controlled sections as ɛt increases from the compression-controlled strain limit to 0.005. The variation ɸ may be computed for prestressed members such that: 𝑑𝑡 0.75 ≤ 𝜙 = 0.583 + 0.25 ( − 1) ≤ 1.0 𝑐 where: c = distance from the extreme compression fiber to the neutral axis (mm) dt = distance from the extreme compression fiber to the centroid of the extreme tension steel element (mm)  Compare factored flexural resistance versus maximum applied factored moment.  Check the maximum and minimum reinforcement (12.4.3.3). For maximum reinforcement: The current provisions of LRFD eliminate the maximum reinforcement limit. A reduction in the factored flexural resistance of the section is added instead. It states that below a net tensile strain in the extreme tension steel of 0.005, as the tension reinforcement quantity increases, the factored resistance of prestressed and nonprestressed sections is reduced to compensate for decreasing ductility with increasing overstrength. For minimum reinforcement: The amount of non-prestressed tensile reinforcement shall be adequate to develop a factored flexural resistance, Mr, at least equal to the lesser of:  1.33 times the factored moment required by the applicable strength load combination, or  1.2𝑀𝑐𝑟 = 𝛾1 𝛾3 𝑓𝑟 𝑆𝑐 where: γ1 = flexural cracking variability factor = 1.2 for precast segmental structures = 1.6 for all other concrete structures γ3 = ratio of specified minimum yield strength to ultimate tensile strength of the reinforcement = 0.67 for A615, 414 MPa reinforcement = 0.75 for A706, 414 MPa reinforcement = 1.00 for prestressed concrete structures fr = modulus of rupture of concrete specified in Article 12.1.1.6 Sc = section modulus for the extreme fiber of the composite section where tensile stress is caused by externally applied loads (mm3) 2.3.18 Design for shear under Strength Limit State (Article 12.5).  Determine bv and dv bv = effective web width taken as the minimum web width (in mm) dv = effective shear depth 𝑀𝑛 𝑑𝑣 = ≥ 𝑚𝑎𝑥𝑖𝑚𝑢𝑚(0.90𝑑𝑒 , 0.72ℎ) 𝐴𝑠 𝑓𝑦

Design Procedure Manual for Bridges Page 39 of 56

 Calculate nominal shear resistance in concrete, Vc (Article 12.5.3.2). 𝑉𝑐 = 0.083𝛽𝑓𝑐 ′0.5 𝑏𝑣 𝑑𝑣  If Vu>0.5ɸ (Vc), transverse reinforcement shall be provided. where: Vu = factored shear force Vc = nominal shear resistance of the concrete ɸ = resistance factor The required spacing of transverse reinforcement, s, is equal to 𝑐𝑜𝑡𝛩 𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 (𝑉𝑢 ) ɸ

−𝑉𝑐

The spacing of the transverse reinforcement shall not exceed the maximum permitted spacing, smax, determined as: Case 1: If vu<0.125 f’c, smax is equal to lesser of 0.80 dv and 600 mm Case 2: If vu≥0.125 f’c, smax is equal to lesser of 0.40 dv and 300 mm where: vu = shear stress calculated |𝑉𝑢 − ɸ𝑉𝑝 | 𝑣𝑢 = ɸ𝑏𝑣 𝑑𝑣  Calculate factored shear resistance, Vr (Article 12.5.3.2). 𝑉𝑟 = ɸ𝑉𝑛 = ɸ(𝑉𝑐 + 𝑉𝑠 ) where: Vs = shear resistance provided by shear reinforcement 𝑐𝑜𝑡𝛩 𝑉𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 𝑠  Calculate longitudinal skin reinforcement (Article 12.4.3.4). The area of skin reinforcement Ask in mm2/m of height on each side face shall satisfy: 𝐴𝑠 𝐴𝑠𝑘 ≥ 0.001 (𝑑𝑒 − 760) ≤ 4 where: As = area of tensile reinforcement (mm2) 2.3.19 Calculate immediate and long time deflection. 

Calculate gross (Ig), cracked (Icr) and effective (Ie) moments of inertia of superstructure 𝑀𝑐𝑟 3 𝑀𝑐𝑟 3 𝐼𝑒 = ( ) 𝐼 + [1 − ( ) ]𝐼𝑐𝑟 ≤ 𝐼𝑔 𝑀𝑎 𝑔 𝑀𝑎 where: Ie = effective moment of inertia Ig = gross moment of inertia Icr = cracked moment of inertia 𝐼𝑔 𝑀𝑐𝑟 = 0.63√𝑓′𝑐 𝑦𝑡

Design Procedure Manual for Bridges Page 40 of 56

Dg = depth of girder Yt = distance from neutral axis to the extreme tension fiber Ma = maximum moment in a component at the stage for which deformation is computed  

Obtain immediate deflection at quarter points from STAAD results or manual calculation Compute long time deflection Case 1: If IgIe, long time deflection = 3 - 1.2(As’/As)*(immediate deflection) As’ = area of compression reinforcement (mm2) As = area of tension reinforcement (mm2)

Design Procedure Manual for Bridges Page 41 of 56

Establish design criteria

Assume girder size based on span length and girder spacing Table 10.1.2.6-1 Determine DL Moments and Shear by STAAD DL Analysis or manual calculation

Determine LL Moments and Shear by STAAD LL Analysis or manual calculation

Determine LL distribution factors for Moments (Table 11.3.2.2-5) and for Shear (Table 11.3.2.2-9) A Compute for factored moments Table 10.3-1 Determine long-term and short term prestressing losses

Design for flexure under Service Limit State Article 12.2.1 Design for flexure under Strength Limit State Article 12.2.3 Design for shear under Strength Limit State Article 12.5

NO

Is the section adequate?

YES Go to Figure 1-6. Design Procedure of Deck Slab Figure 2-6 Design Procedure of Prestressed Concrete Girder

Design Procedure Manual for Bridges Page 42 of 56

3 Design of Substructure (LRFD) PART 3

Design Procedure Manual for Bridges Page 43 of 56

3.1

Design of Pier Substructure

3.1.1. Establish design criteria. Design Specifications : Material Specifications : Design Loads : Seismic Specifications : 3.1.2.

DPWH DGCS 2015 Reinforced concrete, Steel reinforcement HL 93 (Article 10.7.3), Response Spectrum (BSDS 2013) DPWH BSDS 2013, Bridge Operational Classification

Assume column and coping dimensions.

3.1.3. Calculate geometric properties of the superstructure. a. Area of the superstructure Compute the total area of the slab, haunch and girder: 𝐴𝑥 = (𝑊𝑠 × 𝑡𝑠 ) + (𝑊ℎ × 𝑡ℎ × 𝑁𝑔 ) + (𝑁𝑔 × 𝐴𝑔 ) b. Moment of inertia of the superstructure Compute the total moment of inertia of the dead loads about the 3 axes:  Moment of inertia about the z-axis 𝐼𝑧 = ∑ 𝐼𝑧𝑜 + ∑(𝐴 × 𝑦𝑏𝑜 2 )



Moment of inertia about the y-axis 𝐼𝑌 = ∑ 𝐼𝑦𝑜 + ∑(𝐴 × 𝑧 2 )



Moment of inertia about the x-axis 𝐼𝑥 = ∑ 𝐼𝑥𝑜

3.1.4. Determine the site-specific Design Response Spectrum for Level 2 earthquake using the mapped peak ground acceleration and spectral acceleration coefficients (BSDS Article 3) a. Determine the following: i. Bridge Operational Classification (Article 3.2) ii. Seismic Performance Requirements (Article 3.3) b. Determine the Seismic Hazard at the bridge site. (Article 3.4) i. Determine location of bridge site. ii. Identify applicable regional acceleration coefficient maps to be used (Appendix 3B). For the general procedure, acceleration coefficients taken from the maps are for rock (AASHTO Site Class B) and shall be adjusted further on for site effects.   

Horizontal peak ground acceleration (PGA) coefficient Horizontal short-period spectral acceleration (Ss) coefficient Horizontal long-period spectral acceleration (S1) coefficient

c. Adjust the values of the horizontal acceleration coefficients depending on the site effects.

Design Procedure Manual for Bridges Page 44 of 56

d. Determine the Ground Characteristic Value, TG, for the project site (Article 3.5.1) 𝑛

𝑇𝐺 = 4 ∑ 𝑖=1

𝐻𝑖 𝑉𝑠𝑖

In case there is no available data of the average shear elastic wave velocity, Vsi, of the ith soil layer from wave propagation method or PS logging, Vsi may be estimated using the following equations based on their N-values: For cohesive soil layer (1≤ Ni ≤ 25), 1/3 𝑉𝑠𝑖 = 100𝑁𝑖 For sandy/cohesionless soil layer (1≤ Ni ≤ 50), 1/3 𝑉𝑠𝑖 = 80𝑁𝑖 e. Determine the Ground Type (Site Class) for Seismic Design (Table 3.5.1-1) Table 3-1 Ground Types (Site Class) for Seismic Design

f.

Ground Type

Soil Profile Description

Characteristic Value of Ground, TG (s)

Type I

Hard (Good diluvial ground and rock)

TG < 0.2

Type II

Medium (Diluvial and alluvial ground not belonging to Types I and III)

0.2 ≤ TG < 0.6

Type III

Soft (Soft ground and alluvial ground)

0.6 ≤ TG

Determine the Site Factors to be used based on the Peak Ground Acceleration Coefficient and Ground Type (Article 3.5.3) i.

Values of Site Factor, Fpga, at Zero-Period on Acceleration Spectrum Table 3-2 Values of Site Factor Fpga at Zero-Period on Acceleration Spectrum

Peak Ground Acceleration (PGA) Coefficient (Table 3.5.3-1)

Ground Type (Site Class)

≤ 0.10

0.20

0.30

0.40

0.50

≥ 0.80

I

1.2

1.2

1.1

1.0

1.0

1.0

II

1.6

1.4

1.2

1.0

0.9

0.85

III

2.5

1.7

1.2

0.9

0.8

0.75

Design Procedure Manual for Bridges Page 45 of 56

ii. Values of Site Factor, Fa, for Short-Period Range on Acceleration Spectrum Table 3-3 Values of Site Factor Fa for Short-Period Range on Acceleration Spectrum

Ground Type (Site Class)

Spectral Acceleration Coefficient at Period 0.2sec (Ss) (Table 3.5.3-2)

≤ 0.10

0.20

0.30

0.40

0.50

≥ 0.80

I

1.2

1.2

1.1

1.0

1.0

1.0

II

1.6

1.4

1.2

1.0

0.9

0.85

III

2.5

1.7

1.2

0.9

0.8

0.75

iii. Values of Site Factor, Fv, for Long-Period Range on Acceleration Spectrum Table 3-4 Values of Site Factor Fv for Long-Period Range on Acceleration Spectrum

Ground Type (Site Class)

Spectral Acceleration Coefficient at Period 1.0sec (S1) (Table 3.5.3-3)

≤ 0.10

0.20

0.30

0.40

0.50

≥ 0.80

I

1.7

1.6

1.5

1.4

1.4

1.4

II

2.4

2.0

1.8

1.6

1.5

1.5

III

3.5

3.2

2.8

2.4

2.4

2.0

g. Determine the effective acceleration coefficients by applying the site factors on the acceleration coefficients to be used on the Design Response Spectrum (Article 3.6.1) i.

Effective Horizontal Peak Ground Acceleration (PGA) Coefficient 𝐴𝑆 = 𝐹𝑝𝑔𝑎 𝑃𝐺𝐴

ii.

Effective Horizontal Short-Period Spectral Acceleration (Ss) Coefficient 𝑆𝐷𝑆 = 𝐹𝑎 𝑆𝑆

iii.

Effective Horizontal Long-Period Spectral Acceleration (S1) Coefficient 𝑆𝐷1 = 𝐹𝑣 𝑆1

h. Determine the reference periods that define the spectral shape (Article 3.6.1) i.

Corner Period, TS, at which spectrum changes from being independent of period to being inversely proportional to period, 𝑇𝑆 =

ii.

𝑆𝐷1 𝑆𝐷𝑆

Reference Period, T0, used to define spectral shape, 𝑇0 = 0.2𝑇𝑆

Design Procedure Manual for Bridges Page 46 of 56

i.

Determine the Elastic Seismic Response Coefficients for different modes of vibration (Article 3.6.2) i.

For periods less than or equal to T0, 𝑇𝑚 𝐶𝑠𝑚 = 𝐴𝑆 + (𝑆𝐷𝑆 − 𝐴𝑆 ) ( ) 𝑇0

ii.

For periods greater than T0 and less than or equal to Ts, 𝐶𝑠𝑚 = 𝑆𝐷𝑆

iii.

For periods greater than Ts, 𝐶𝑠𝑚 =

j.

𝑆𝐷1 𝑇𝑚

Plot the five-percent-damped-design response spectrum (Elastic Seismic Response Coefficient versus Period) up to at least 5.0 sec period. (Figure 3.6.1-1)

Figure 3-1 Design Response Spectrum

3.1.5. Create Mathematical (Stick) Model and input design data using structural analysis and design software (STAAD Pro v8i, MIDAS Civil, SAP2000, etc.). a. Dead Loads – girders, slab, haunch, diaphragm b. Superimposed Dead Loads – post, railings, sidewalk, utilities, future wearing surface c. Vehicular Live Loads – HL-93 design truck, tandem and lane loads

Design Procedure Manual for Bridges Page 47 of 56

or

Figure 3-2 Design Truck and Tandem Loads

d. Seismic Loads – Design Response Spectrum for Level 2 Earthquake (BSDS Article 3) 3.1.6. Run Seismic Analysis. 3.1.7. Determine Elastic Seismic Design Forces at critical locations. 3.1.8. Combine Seismic Force Effects (BSDS Article 5.2). a. Load Case 1: 1.0 Longitudinal Eq. + 0.3 Transverse Eq. b. Load Case 2: 0.3 Longitudinal Eq. + 1.0 Transverse Eq. 3.1.9. Determine Dead Load and Live Load Forces. 3.1.10. Combine Design Forces using Extreme Event Limit State I the applicable Load Combinations for Reinforced Concrete Column Design (Table 10.3-1)

Strength I Limit State: Service I Limit State: Extreme Event I Limit State:

dc DC + dw DW + LL [LLTL(1 + IM) + LLDL] dc DC + dw DW + LL [LLTL(1 + IM) + LLDL] dc DL + LL [LLTL(1 + IM) + LLDL] + eq 0EQ

3.1.11. Determine Response Modification Factor (BSDS Table 3.8.1-1) and apply to Design Moments.

Table 3-5 Response Modification Factors - Substructures

Operational Category (BSDS) Type of pier Response Modification Factor (R)

SingleColumn bents MultipleColumn bents

OC-I (Critical)

OC-II (Essential)

OC-III (Others)

1.5

2.0

3.0

1.5

3.5

5.0

Design Procedure Manual for Bridges Page 48 of 56

3.1.12. Compute for the Modified Design Forces a. Axial and Shear: b. Moment:

(DL + 0.5LL + EQ) (DL + 0.5LL + EQ) / R

3.1.13. Identify the governing elastic design forces    

Design Moment Design Shear Maximum Axial Force (greater of LC1 and LC2 + PDL + PLL/2) Minimum Axial Force (greater of LC1 and LC2 - PDL - PLL/2)

Buckled shape of column is shown by dashed line

3.1.14. Determine effective length factor of column (AASHTO Table C.4.6.2.5.1).

0.65

0.80

End condition code

k - value

1.20

1.00

2.10

2.00

- Rotation fixed and translation fixed - Rotation free and translation fixed - Rotation fixed and translation free - Rotation free and translation free

Figure 3-3 Effective Length Factors, K

3.1.15. Check slenderness provisions for concrete columns (Article 12.4.4.2) a.

𝐿𝑢 𝑟

b.

𝐿𝑢 𝑟

<

<

𝑘 × 𝐿𝑢 𝑟

< 100

35 𝑃𝑢

√𝑓′ ×𝐴 𝑐 𝑔

3.1.16. Apply Moment Magnification Factor 

Determine Flexural Stiffness of column (Article 12.4.4.2) 𝐸𝑐 𝐼𝑔 𝐸𝐼 = 2.5 1 + 𝛽𝑑 𝑀 where, 𝛽𝑑 = 𝑀 𝐷𝐿 𝑚𝑎𝑥

Design Procedure Manual for Bridges Page 49 of 56



Determine buckling load (Article 11.2.2.2) 𝜋 2 𝐸𝐼 𝑃𝑐 = 𝑘𝐿𝑢 2



Compute for the Moment Magnification Factor (not braced against sidesway) (Article 11.2.2.2) 1 𝛿𝑠 = ∑ 𝑃𝑢 1− ∅ ∑ 𝑃𝑐 where:



𝛿𝑠 > 1.0

Compute for the Magnified Design Moment, Mc 𝑀𝑐 = 𝛿𝑠 𝑀𝑚𝑎𝑥

3.1.17. Check P-Δ requirements (BSDS Article 4.7). a. Displacement verification ΔPu < 0.25∅Mn

Nominal Flexural strength, Mn, is taken from the interaction diagram in SPcolumn based on the elastic axial load on column

b. Design Displacement P-Δ requirement: Δd = 12R d Δe where: 



𝛥 > 𝛥𝑑 Δe = displacement of joint (taken from STAAD output)

If T < 1.25Ts If T ≥ 1.25Ts

1 1.25𝑇𝑠 1 𝑅𝑑 = (1 − ) + 𝑅 𝑇 𝑅 𝑅𝑑 = 1

3.1.18. Determine Plastic Forces (Inelastic Hinging Analysis) (Article 10.18.13). a. Determine the Strength Moment Resistance, Mn, which is taken from the interaction diagram in SPcolumn based on the elastic column axial load. b. Compute for the Column Overstrength Moment Resistance Mp = ∅Mr where:

∅ = 1.30 ∅ = 1.25

for reinforced concrete columns for steel columns

Design Procedure Manual for Bridges Page 50 of 56

Lu

a Figure 3-4 Two-column pier section

c.

Compute for the lateral shear force on the column due to Mp Shear Force: where:

d.

Vp =

ℎ

h = clear height of the column

Compute for the Column Axial Force due to Vp 

Apply the shear force to the center of mass of the superstructure and determine the axial force in the columns due to overturning when the column overstrength moment resistances are developed. Increase in Axial Force due to Mp: Maximum Plastic Axial Force: Minimum Plastic Axial Force:

where: e.

∑ 𝑀p

∑ 𝑉 𝐿 −∑ 𝑀

𝑝 ∆p = 𝑝 𝑢 𝑎 Pp1 = P𝐷𝐿 + P𝐿𝐿/2 + ∆p Pp2 = P𝐷𝐿 + P𝐿𝐿/2 − ∆p

Lu = unsupported length a = distance from the centerline of columns

Check percent difference of total shear force  Difference in total shear force of succeeding steps must be within 10% 𝑉𝑇1 − 𝑉𝑇2 %= 𝑉𝑇1 

If the difference in total shear is not within 10%, repeat the process using the computed column axial forces to determine the column overstrength moment resistance and total shear force until 10% difference in total shear force is reached.

3.1.19. Design column using the identified governing forces as modified a.

Design column with the Magnified Elastic Forces

Design Procedure Manual for Bridges Page 51 of 56

b.

Check the steel reinforcement ratio (Article 12.7.11.2) 0.01 < As / Ag < 0.04

3.1.20. Determine the required column lateral reinforcements. 

Design for shear under Strength Limit State (Article 12.5) 

Determine effective shear depth, dv 𝐷 𝐷𝑐 𝑑𝑣 = 0.90𝑑𝑒 = 0.90 ( + ) 2 𝜋



Calculate nominal shear resistance in concrete, Vc (Article 12.5.3.2). 0.5 𝑉𝑐 = 0.083𝛽𝑓′𝑐 𝑏𝑣 𝑑𝑣 where:

For simplified procedure of non-prestressed sections, β = factor indicating ability of diagonally cracked concrete to transmit tension = 2 θ = angle of inclination of diagonal compressive stresses = 45.0° bv = diameter of column = D



If the Plastic shear force, Vu > 0.5ɸs(Vc), provide transverse reinforcement. where: Vu = Vplastic



The required spacing of transverse reinforcement, s, is equal to 𝑐𝑜𝑡𝛩 𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 (𝑉𝑢 ) ɸ𝑠





−𝑉𝑐

The spacing of the spiral reinforcement shall not exceed the maximum permitted spacing, smax, determined as the lesser of: smax = 6.0db or 150mm

Calculate factored shear resistance, Vr (Article 12.5.3.2). 𝑉𝑟 = ɸ𝑉𝑛 = ɸ(𝑉𝑐 + 𝑉𝑠 ) where:

Vs = shear resistance provided by shear reinforcement 𝑐𝑜𝑡𝛩 𝑉𝑠 = 𝐴𝑣 𝑓𝑦 𝑑𝑣 𝑠 c.

Determine the transverse reinforcement at Plastic Hinges (Article 12.7.10.2) i.

Determine the ratio of spiral reinforcement to total volume of concrete core, ρ, shall be taken as the larger of:

Design Procedure Manual for Bridges Page 52 of 56 𝑓′ 𝑐

𝐴



𝜌 = 0.45 ( 𝐴𝑔 − 1) 𝑓



𝜌 = 0.12 𝑓

𝑐

𝑦ℎ

𝑓′ 𝑐 𝑦ℎ

(Article 12.4.4.5) (Article 12.7.10.2)

ii. The required spacing of the spiral reinforcement, s, is equal to 4𝐴𝑣 𝑠= 𝜌𝐷𝑐 iii. The spacing of the spiral reinforcement shall not exceed the maximum permitted spacing, smax, determined as the lesser of: smax = 0.25D or 100mm d.

Determine the column end region, length shall be taken as the larger of the following (Article 12.7.10.2): i. Maximum cross-sectional dimension of column ii. 1/6 of the clear height of column iii. 450mm

e.

Determine the lateral reinforcements (Article 12.7.11.2) for the following locations:  Outside end region  End region  Hinge requirement  Adjoining member

3.1.21. Design coping for flexural and shear resistance. 

Determine seat length of girder, SE, at the support (BSDS Article 7.2) 𝑆𝐸 = 𝜇𝑅 + 𝜇𝐺

Figure 3-5 Seat length of girder

where:

μR= maximum relative displacement between the superstructure and the edge of the top of the substructure due to Level 2 Earthquake μG= relative ground displacement caused by seismic ground strain 𝜇𝐺 = 𝜀𝐺 𝐿 εG = seismic ground strain

Design Procedure Manual for Bridges Page 53 of 56

εG 0.0025 0.00375 0.005

Ground Type I II III

L = superstructure span length 

Determine minimum bridge seat length of girder, SEM SEM = 0.70 + 0.005 L



Determine design forces  Reaction dead load  Reaction live load  Column plastic hinging forces



Design flexural resistance (Article 12.2.1)



Design for shear resistance (Article 12.5.2)

Design Procedure Manual for Bridges Page 54 of 56 Establish Design Criteria Design Specifications DPWH DGCS 2015, DPWH BSDS 2013 Material Specifications: Reinforced Concrete, Steel Reinforcement Design Loads: HL-93 truck loading

Assume dimensions for column and coping

Calculate geometric properties of superstructure

Determine site-specific Design Response Spectrum using mapped peak ground acceleration and spectral acceleration coefficients

BSDS Figure 3.4.1-1 to 3.4.1-6 (Refer to Figure 5.)

Create Mathematical (Stick) Model and input data using structural analysis software (STAAD Pro v8i)

Run Seismic Analysis and determine Elastic Seismic Design Forces at critical locations

Combine Seismic Force Effects and determine Dead Load and Live Load Forces

Combine Design Forces using Extreme Event Limit State I

Determine Response Modification Factor and apply to the Design Moments

Determine the governing Elastic Design Forces

NO

Are the slenderness provisions for concrete columns satisfied?

YES Apply Moment Magnification Factor and compute for the Magnified Design Moment

NO

Is the P-Δ requirement satisfied? YES Design Column

Determine Plastic Forces (refer to Figure 6)

Design Column Transverse Reinforcements (DGCS Art. 12.5 – 12.7)

Design Coping for flexure (DGCS Art. 12.2.1), shear (DGCS Art. 12.5.2) and seat length (BSDS Art. 7.2)

Figure 3-6 Design Procedure of Pier Substructure

Design Procedure Manual for Bridges Page 55 of 56

Determine Strength Moment Resistance of column taken from interaction diagram (PCACOL or SPColumn) of the column based on the elastic axial load

Compute for the Overstrength Moment Resistance, Mp = ∅Mr, where ∅=1.3 for reinforced concrete columns

Compute the lateral Shear Force, Vp = ΣMp /h

Compute for the increase in axial force due to Mp, ∑ Vp Lu − ∑ Mp ∆p = a and the maximum and minimum axial forces, Pp1 = P𝐷𝐿 + P𝐿𝐿/2 + ∆p Pp2 = PDL + PLL/2 − ∆p

Check the difference in total shear force, % =

NO

VT1 −VT2 VT1

Is the % difference less than 10%? YES

Determine the Design Forces located at the Plastic Hinge

Figure 3-7 Design Procedure of Plastic (Inelastic) Hinging

Design Procedure Manual for Bridges Page 56 of 56 Establish Design Criteria Seismic Specifications DPWH BSDS 2013 Design Earthquake: Level 2 (App. 1000-year return period) Design Loads: HL-93 truck loading

Determine the Bridge Operational Classifications and Seismic Performance Requirements

Determine the Seismic Hazard at the bridge site (BSDS Art. 3.4)

Determine the horizontal peak ground acceleration (PGA), shortperiod spectral (Ss) and long-period spectral (S1) acceleration coefficients from the regional acceleration coefficient maps (Appendix 3B) based on the location of the bridge site.

Adjust the values of the horizontal acceleration coefficients based on the site effects. (BSDS Art. 3.5)

Determine the effective horizontal acceleration coefficients by applying the site factors (BSDS Art. 3.6.1)

Determine the reference periods that define the spectral shape (BSDS Art. 3.6.1)

Determine the Elastic Seismic Response Coefficients for different modes of vibration (BSDS Art. 3.6.2)

Plot the five-percent-damped design response spectrum (Elastic Seismic Response Coefficient vs. Period) (BSDS Fig. 3.6.1-1)

Figure 3-8 Design Procedure of Response Spectrum