1

Part 1

Introduction To Bridge Design

2

How Do Bridge Engineers Decide

On What Type Of Bridge To Build? Bridge Survey

• flood plain cross sections

• inspection reports

• existing bridge (scour, etc)

• water elevations

• photos

• existing roadway profile

Geotechnical Report

• soil / geological formations

• slopes and grading

• foundation problems

• soil prop.’s - phi angles etc

Factors affecting choice of superstructure

• location, city or rural

• span length

• vertical clearance

• maintainability

• environmental concerns

• transportation to site issues

• cost

Factors affecting choice of substructure

• location and geometry

• subsoil conditions

• height of column

3

Bridge Design Process

Preliminary Design Process

• Bridge Survey

• Geotechnical Report

1. Determine the most

economical type structure and

span arrangement

2. Hydraulic Analysis

3. Preliminary Cost Estimate

4. Foundation Borings

5. Determine Foundation Type

Final Design Process

• Top to Bottom Design (twice)

• Design methods per AASHTO and

MoDOT Bridge Manual

• Analysis via

•computations

•spreadsheets

•computer programs

• Detail plans are produced by technicians

(Micro-Station)

• Plans are checked

• Quantities computed

• Special Provisions written

• Plans are advertised for bidding

• Low Bid Contractor builds the bridge

4

Types of Superstructures

Bridges are often referred to by their superstructure types.

The superstructure system of members carry the roadway over a crossing

and transfer load to a substructure.

Superstructures are categorized by;

• Support type (simply supported or continuous)

• Design type (slab on stringer, slab, arch. Rigid frame, etc)

• Material type (steel, concrete, timber)

5

Slab on Stringer Bridges

• Most common type of bridge in Missouri.

• Consist of a deck, resting on the girders. The deck distributes the

loads transversely to the girders.

• The girders carry the loads longitudinally (down the length of the

bridge) to the supports, (abutments and intermediate bents).

• Concrete

• Deck Girder

• Prestressed I Girder

• Prestressed Double Tee

• Prestressed Box

• Steel

• Plate Girder

• Wide Flange

• Steel Box Girder

6

I I I I ---- GIRDERGIRDERGIRDERGIRDER

BULB TEEBULB TEEBULB TEEBULB TEE

Prestressed Girders

7

Prestressed Concrete I-Girder

8

Prestressed Concrete I-Girder Bridge

9

Prestressed Concrete Panels

10

Prestressed Double Tee Girders

11

Steel Plate Girder / Wide Flange Beam / Box Beam

12

Steel Plate Girder Bridge

13

Slab Bridges

In slab bridges the deck itself is the structural frame or the entire deck is a thin

beam acting entirely as one primary member. These types are used where

depth of structure is a critical factor.

Typical Slab Bridges : Concrete Box Culverts Solid Slabs Voided Slabs

14 Box Culvert

Triple Box Culvert

15

Voided Slab Bridge

16 Solid Slab

Voided Slab Bridge

17

Substructures

The substructure transfers the superstructure loads to the foundations.

End Abutments

• Integral Abutment - girders on beam supported by piles, girders “concreted” into the

diaphragm

• Non-Integral Abutment - diaphragms of steel cross-frames, uses expansion devices

• Semi-Deep Abutment - used when spanning divided highways to help shorten span

• Open C.C. Abutment - beam supported by columns and footings, rarely used

Intermediate bents

• Open Concrete Bent - beams supported by columns and footings (or drilled shafts)

either a concrete diaphragm (Pre-Stressed Girder) or steel diaphragm (Plate Girder)

This is the most common type of Pier MoDOT uses.

• Pile Cap Bent - beams supported by piling (HP or C.I.P.) and are used when the

column height is less than 15 feet and usually in rural areas.

• Hammer Head Bent - single oval or rectangular column and footing.

• Spread footings - are used when rock or soil can support the structure.

• Pile footings - rectangular c.c. supported by HP or Cast in Place piles

• Drilled Shafts - holes drilled into bedrock filled with concrete

18

Integral End Abutment

19

Semi-Deep End Abutment

20

Prestressed I-girder intermediate bent

21

Steel girders with open intermediate

bent diaphragms

22

Footing

Pile Cap Column Footing

23

Column Footing

24

Preliminary Design

• Bridge location

• Hydraulic design to determine required

bridge length and profile grade

• Bridge type selection

25

Stream Gage Data

26

Flood-Frequency Rating Curve

0

40000

80000

120000

160000

0 20 40 60 80 100

Return period (years)

Discharge (cfs)

27

Q = discharge (cfs or m3/s)

kc = constant (1.0 for English units or

0.00278 for metric units)

C = Runoff Coefficient

I = Rainfall Intensity (in/hr or mm/hr)

A = Drainage Area (acres or hectares)

Rational Method

AICkQ c ⋅⋅⋅=

28

Drainage Area Delineation

29

n1 n2 n3

Left

Overbank

Right

Overbank

Channel

Stream Valley Cross-sections

30

Manning’s Equation

03

2486.1SRA

nQ ⋅⋅⋅=

n = Roughness Coefficient

A = Area

R = Hydraulic Radius = A / P

P = Wetted Perimeter

S = Hydraulic Gradient (channel slope)

31

n1 n2 n3

Left

Overbank

Right

Overbank

Channel

Stream Valley Cross-sections

32

Energy Equation

Elevation

1 2

Datum Elevation

Pressure

Pressure

Velocity

Velocity

Headloss EGL

HGL

z1

z2

y1

y2

V12/2g

V22/2g

hl

lhg

Vyz

g

Vyz +++=++

22

2

222

2

111

33

Constriction of Valley by Bridge

Opening Length

Bridge Deck/Roadway

34

Encroachment by Roadway Fill

Flood elevation

before encroachment

on floodplain

Fill Fill

Bridge Opening

Encroachment

Backwater

Encroachment

35

Backwater

Normal Water

Surface

Water Surface through Structure

Affect of Bridge on Flood

Elevations

Design High Water

Surface (DHW)

36

Part 2

Slab Design

37

Geometry & Loads

16k 16k

Deck Weight = Width x Thickness x Unit Weight

1 ft x (8.5in x12 in/ft) x 150 lb/cf = 106 lb/ft

38

39

40

Design Moment

• MDL1 = wS2/10 = 0.106 x 82 / 10 = 0.678

• MDL2 = wS2/10 = 0.035 x 82 / 10 = 0.224

• MLL = 0.8(S+2)P/32 = 0.8(8+2)(16)/32 = 4

• MImp = 30% x MLL = 1.2

• Mu = 1.3[0.678+0.224+1.67(4+1.2)] = 12.4

Design For 12.4 k-ft/ft

41

Statics, Moment, Shear, Stress?

42

Reinforced Concrete Design

• Basic Equations For Moment Utilize Whitney

Stress Block Concept

Design Moment = Capacity

12.4 k-ft/ft = φ As fy(d-a/2) φ = 0.90

Compression = Tension

0.85f’cba = As fy

Two Simultaneous Equations, Two Unknowns (a & As)

d

c

Comp.

Tens.

c = a / ββββ1

43

Reinforced Concrete Design

• (0.85)(4ksi)(12in)(a)=(As)(60ksi) a=1.47As

• 12.4k-ft=(0.9)(As)(60ksi)(6in-1.47As/2)/(12in/ft)

• 12.4=27As-3.31As2

• ax2+bx+c=0 a=3.31, b=-27, c=12.4, x=As

• As = [-b - (b2 - 4ac)1/2]/2a

• As = [-27 - ((-27)2-(4)(3.31)(12.4))1/2]/[(2)(3.31)]

• As = 0.49 in2/ft

• 5/8” rebar at 7.5 in centers

d

c

Comp.

Tens.

c = a / ββββ1

44

Part 3

Steel Beam Design

45

Simple Span Beam – 50 ft span

46

Dead Load = Beam Weight + Deck Weight

47

Live Load = HS20 Truck x Distribution Factor

Distribution Factor = S/5.5

48

Design Moment = 2358 kip-ft

49

Design Shear = 214 kips

50

Steel Girder Design • Design Moment = 2358 k-ft

• Design Shear = 214 kips

• Limit Bending Stress

Due To Moment

• Limit Shear Stress

Due to Shear

51

52

Girder Design

• Moment Of Inertia (I)

– 1/12bh3+Ad2

– Parallel Axis Theorem

• Section Modulus = S = I/c

• Stress = Moment/Section Modulus (M/S)

• For Strength Design – Limit Stress to Fy

• Find Shape With S > M/Fy • S > (2358k-ft)(12in/ft)/50ksi = 566 in3

• A W36x170 Provides 580 in3

53

Part 4

Intermediate Bent Design

54

Load Cases

• Permanent Loads:

– DD = Downdrag

– DC = Dead Load

Component

– DW = Dead Load

Wearing Surface

– EH = Horizontal Earth

– ES = Earth Surcharge

– EV = Vertical Earth

– EL = Locked In Forces

• Transient Loads:

– SE = Settlement

– BR = Braking

– CE = Centrifugal Force

– CT = Vehicular

Collision

– CV = Vessel Collision

– EQ = Earthquake

– IC = Ice Load

– FR = Friction

55

Load Cases (Cont.)

• Transient Loads:

– LL = Live Load

– IM = Dynamic Load

– LS = Live Load

Surcharge

– PL = Pedestrian Load

– WL = Wind On Live

Load

– WS = Wind On

Structure

• Transient Loads:

– TG = Temperature

Gradient

– TU = Uniform

Temperature

– CR = Creep

– SH = Shrinkage

– WA = Water Load

56

Load Combinations

Load Combination

Limit State

DC

DD

DW

EH

EV

ES

EL

LL

IM

CE

BR

PL

LS WA WS WL FR

TU

CR

SH TG SE

Use One of These at a Time

EQ IC CT CV

STRENGTH I

(unless noted) γγγγ p

1.75 1.00 -- -- 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

STRENGTH II γγγγ p 1.35 1.00 -- -- 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

STRENGTH III γγγγ p -- 1.00 1.40 -- 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

STRENGTH IV γγγγ p -- 1.00 -- -- 1.00 0.50/1.20 -- -- -- -- -- --

STRENGTH V γγγγ p 1.35 1.00 0.40 1.0 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

EXTREME EVENT I γγγγ p γγγγEQ 1.00 -- -- 1.00 -- -- -- 1.00 -- -- --

EXTREME EVENT II γγγγ p 0.50 1.00 -- -- 1.00 -- -- -- -- 1.00 1.00 1.00

SERVICE I 1.00 1.00 1.00 0.30 1.0 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

SERVICE II 1.00 1.30 1.00 -- -- 1.00 0.50/1.20 -- -- -- -- -- --

SERVICE III 1.00 0.80 1.00 -- -- 1.00 0.50/1.20 γγγγTG γγγγ SE -- -- -- --

SERVIE IV 1.00 -- 1.00 0.70 -- 1.00 0.50/1.20 -- 1.0 -- -- -- --

FATIGUE – LL, IM &

CE ONLY -- 0.75 -- -- -- -- -- -- -- -- -- -- --

57

Water (WA) – Strength

M = (Pbh)(½h)

= ½ Pbh2

½ h

Resultant

P C

on

tra

ctio

n S

co

ur

10

0 y

ea

r P

ier

Sco

ur

10

0 y

ea

r

Q100

b

M

58

Water (WA) - Extreme Event

(Cont.)

( )(b)1000

0.7VForce2

=

Co

ntr

actio

n S

co

ur

50

0 y

ea

r P

ier

Sco

ur

50

0 y

ea

r

Q500

b

B

A ( )(B)

10000.5VForce

2

=

A = ½ Of Water Depth ≤ 10’

B = ½ Sum Of Adjacent Span Length ≤ 45’

Drift Mat

Pressure = CDV2/1000

CD=0.7

CD=0.5

59

Wind on Structure (WS)

P(WS)Vert.

W

¼W

P(WS)Trans. H ½

H

P(WS)Long.

PSub.

PVert. = (20psf)(W)(L)

PTrans. = (50psf)(H)(L)

PLong. = (12psf)(H)(LT)(%)

PSub. = (40psf)(b)

L = Tributary Length

LT = Total Bridge Length

% = Long. Distribution %

b = Column Or Cap Width

60

Wind on Live Load (WL) PTrans. = (100plf)(L)

PLong. = (40plf)(LT)(%)

L = Tributary Length

LT = Total Bridge Length

% = Long. Distribution %

P(WL)Trans.

P(WL)Long. 6’

61

Int. Bent Analysis

62

Cap Beam - Strength Limit State

• Basic Equations For Moment Utilize Whitney

Stress Block Concept

– φ Mn = φ As fy(d-a/2)

– φ = 0.90

de

c

Comp.

Tens.

c = a / ββββ1

63

Cap Beam – Service Limit State • Crack Control

–

– dc = Concrete Cover To Center Of Closest Bar

– fs = Service Tensile Stress In Reinforcement

– h = Overall Section Thickness

– γγγγe = 1.00 For Class 1 Exposure (Crack Width = 0.017”)

= 0.75 For Class 2 Exposure (Crack Width = 0.013”)

)d0.7(h

d1

c

cs

−−−−++++====ββββ2dc

700s

ss

e −−−−≥≥≥≥fββββ

γγγγ

64

Cap Beam Service Limit State

• Crack Control Is Based On A Physical Model

x

h

dc

fc1

fc2

fs/n

l l Crack Spacing

Primary Tension Reinforcement

fc1

fc2

fs/n

fc1

fc2

fs/n

l = =16.03”

s s

( )2 2 c 2

sd2 +

dc

65

Simplified Shear Design

• LRFD

– φ Vn = φ (Vc + Vs + Vp)(kips) φ = 0.90

–

– αααα Set At 90°

– Set: ββββ=2.0, θ θ θ θ =45°

–

– Results In:

vvcc d b ' 0.0316V fββββ====s

)sincot(cotdAV

vyv

s

ααααααααθθθθ ++++====

f

Lbs To Convert To 1000By Multiply V c

vvcc d b ' 2.00V f====s

dAV

vyv

s

f====

0.0

66

Simplifed Shear Design

Section A-A

5 -

#6

’s

(Ea

ch

Fa

ce

)

6 - #9’s

6 - #9’s

#5’s @ 12” or 6” A

A

-400

-200

0

200

400

67

Column Design

Column 42” Diameter

-1000

3500 P (kip)

(P max)

(P min)

1800

M (k-ft)

Controlling Point

Axial Load – Moment Interaction Diagram

18-#9 Bars