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Part 1
Introduction To Bridge Design
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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 problemssoil 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
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Bridge Design Process
Preliminary Design Process
Bridge Survey Geotechnical Report
1. Determine the most
economical type structure and
span arrangement
2. Hydraulic Analysis3. 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
spreadsheetscomputer 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
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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)
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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
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I - GIRDER
BULB TEE
Prestressed Girders
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Prestressed Concrete I-Girder
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Prestressed Concrete I-Girder Bridge
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Prestressed Concrete Panels
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Prestressed Double Tee Girders
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Steel Plate Girder / Wide Flange Beam / Box Beam
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Steel Plate Girder Bridge
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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 wheredepth of structure is a critical factor.
Typical Slab Bridges : Concrete Box Culverts Solid Slabs Voided Slabs
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Triple Box Culvert
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Voided Slab Bridge
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Solid Slab
Voided Slab Bridge
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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
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Integral End Abutment
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Semi-Deep End Abutment
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Prestressed I-girder intermediate bent
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Steel girders with open intermediate
bent diaphragms
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Footing
Pile Cap Column Footing
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Column Footing
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Preliminary Design
Bridge location
Hydraulic design to determine required
bridge length and profile grade
Bridge type selection
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Stream Gage Data
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Flood-Frequency Rating Curve
0
40000
80000
120000
160000
0 20 40 60 80 100
Return period (years)
Discharge(cfs)
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Q = discharge (cfs or m3/s)
kc = constant (1.0 for English units or0.00278 for metric units)
C= Runoff Coefficient
I= Rainfall Intensity (in/hr or mm/hr)
A = Drainage Area (acres or hectares)
Rational Method
AICkQc
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Drainage Area Delineation
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n1 n2 n3
LeftOverbank
RightOverbank
Channel
Stream Valley Cross-sections
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Mannings Equation
0
32486.1
SRAn
Q
n = Roughness Coefficient
A = Area
R = Hydraulic Radius = A / P
P = Wetted Perimeter
S = Hydraulic Gradient (channel slope)
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n1 n2 n3
LeftOverbank
RightOverbank
Channel
Stream Valley Cross-sections
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Energy Equation
Elevation
1 2
Datum
Elevation
Pressure
Pressure
Velocity
Velocity
HeadlossEGL
HGL
z1
z2
y1
y2
V12/2g
V22/2g
hl
lhg
Vyz
g
Vyz
22
2
2
22
2
1
11
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Constriction of Valley by Bridge
Opening Length
Bridge Deck/Roadway
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Encroachment by Roadway Fill
Flood elevationbefore encroachmenton floodplain
Fill Fill
Bridge Opening Encroachment
Backwater
Encroachment
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Backwater
Normal WaterSurface
Water Surface through Structure
Affect of Bridge on Flood
ElevationsDesign High WaterSurface (DHW)
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Part 2
Slab Design
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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
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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
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Statics, Moment, Shear, Stress?
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Reinforced Concrete Design
Basic Equations For Moment Utilize Whitney
Stress Block Concept
Design Moment = Capacity
12.4 k-ft/ft = fAsfy(d-a/2) f= 0.90
Compression = Tension
0.85fcba = Asfy
Two Simultaneous Equations, Two Unknowns (a & As)
d
c
Comp.
Tens.
c = a /b1
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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 centersd
c
Comp.
Tens.
c = a /b1
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Part 3
Steel Beam Design
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Simple Span Beam50 ft span
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Dead Load = Beam Weight + Deck Weight
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Live Load = HS20 Truck x Distribution Factor
Distribution Factor = S/5.5
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Design Moment = 2358 kip-ft
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Design Shear = 214 kips
S l Gi d D i
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Steel Girder Design Design Moment = 2358 k-ft
Design Shear = 214 kips
Limit Bending Stress
Due To Moment
Limit Shear Stress
Due to Shear
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Gi d D i
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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 DesignLimit Stress to Fy
Find Shape With S > M/Fy
S > (2358k-ft)(12in/ft)/50ksi = 566 in3
A W36x170 Provides 580 in3
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Part 4
Intermediate Bent Design
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Load Cases
Permanent Loads:
DD = Downdrag
DC = Dead LoadComponent
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
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Load Cases (Cont.)
Transient Loads:
LL = Live Load
IM = Dynamic Load LS = Live Load
Surcharge
PL = Pedestrian Load
WL = Wind On LiveLoad
WS = Wind On
Structure
Transient Loads:
TG = Temperature
Gradient
TU = Uniform
Temperature
CR = Creep
SH = Shrinkage WA = Water Load
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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)gp 1.75 1.00 -- -- 1.00 0.50/1.20 gTG gSE -- -- -- --
STRENGTH II gp 1.35 1.00 -- -- 1.00 0.50/1.20 gTG gSE -- -- -- --STRENGTH III gp -- 1.00 1.40 -- 1.00 0.50/1.20 gTG gSE -- -- -- --STRENGTH IV gp -- 1.00 -- -- 1.00 0.50/1.20 -- -- -- -- -- --STRENGTH V gp 1.35 1.00 0.40 1.0 1.00 0.50/1.20 gTG gSE -- -- -- --EXTREME EVENT I gp gEQ 1.00 -- -- 1.00 -- -- -- 1.00 -- -- --EXTREME EVENT II gp 0.50 1.00 -- -- 1.00 -- -- -- -- 1.00 1.00 1.00SERVICE I 1.00 1.00 1.00 0.30 1.0 1.00 0.50/1.20 gTG gSE -- -- -- --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 gTG gSE -- -- -- --SERVIE IV 1.00 -- 1.00 0.70 -- 1.00 0.50/1.20 -- 1.0 -- -- -- --
FATIGUELL, IM &
CE ONLY-- 0.75 -- -- -- -- -- -- -- -- -- -- --
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Water (WA)Strength
M = (Pbh)(h)= Pbh2
h
Resultant
P
ContractionS
cour
100year
PierSco
ur
100yea
r
Q100
b
M
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Water (WA) - Extreme Event
(Cont.)
(b)1000
0.7VForce2
ContractionScou
r
500year
PierScour
500year
Q500
b
B
A (B)1000
0.5VForce2
A = Of Water Depth 10
B = Sum Of Adjacent Span Length 45
Drift Mat
Pressure = CDV2/1000
CD=0.7
CD=0.5
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Wind on Structure (WS)
P(WS)Vert.
W
W
P(WS)Trans. HH
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
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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
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Int. Bent Analysis
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Cap Beam - Strength Limit State
Basic Equations For Moment Utilize Whitney
Stress Block Concept
fMn
= fAs
fy
(d-a/2)
f= 0.90
de
c
Comp.
Tens.
c = a /b1
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Cap BeamService Limit State Crack Control
dc = Concrete Cover To Center Of Closest Bar fs = Service Tensile Stress In Reinforcement
h = Overall Section Thickness
ge= 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
2dc700sss
e f
g
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Cap Beam Service Limit State
Crack Control Is Based On A Physical Model
x
h dc
fc1
fc2
fs/n
l lCrackSpacing
Primary TensionReinforcement
fc1
fc2
fs/n
fc1
fc2
fs/n
l= =16.03
s s
22c2
sd2
dc
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Simplified Shear Design
LRFD
fVn = f(Vc + Vs + Vp)(kips) f= 0.90
a Set At 90 Set: b=2.0, q =45
Results In:
vvcc db'0.0316V f s
)sincot(cotdA
Vvyv
s
a
f
LbsToConvertTo1000ByMultiply V c
vvcc db'2.00V fs
dAV
vyv
s
f
0.0
Si lif d Sh i
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Simplifed Shear Design
Section A-A
5-#6s
(E
achFace)
6 - #9s
6 - #9s
#5s @
12 or 6A
A
-400
-200
0
200
400
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Column Design
Column42 Diameter
-1000
3500P (kip)
(P max)
(P min)
1800
M (k-ft)
Controlling Point
Axial Load Moment Interaction Diagram
18-#9 Bars