Jordan University of Science and Technology
CE 536 Bridge Engineering
Pr epare pared d by by::
Dr. Ra Raj ai Al Alro usa Alrrous r ou ous san
Jordan University of Science and Technology
CE 536 Bridge Engineering
Policy and Outline
Pr epare pared d by by::
Dr. Ra Raj ai Al Alro usa Alrrous r ou ous san
Course Outline
Page 01
Connections with Other Classes
Page 02
Page 03
References – Design Code
Page 04
Topic
1.
Materials used for bridge construction
2. Theory of analysis of modern highway bridges. 3. Bridge loads and load distribution. distri bution. First Exam
4. Design of reinforced concrete bridge deck 5. Design of reinforced concrete bridge girder. Second Exam
6. Bearing 7. Substructures 8. Bridge management systems 9. Bridge inspection Final Exam
Grading Policy HW 10%
1st Exam
Final 40%
25%
2st Exam 25%
References - Textbooks
Page 05
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 01 Types of Bridges
Prepared by:
Dr. Rajai Alrousan
Components of Bridge
Page 001
Components of Bridge
Page 002
Components of Bridge
Page 003
Components of Bridge
Page 004
Components of Bridge
Page 005
Components of Bridge
Page 006
Types of Bridge by Traffic
Page 007
Types: Highway Bridge
Page 008
Types: Pedestrian Bridge
Page 009
Types: Railway Bridge
Page 010
Types: Transit Guideway
Page 011
Types: Others
Page 012
Types: Others
Page 013
Types: Others
Page 014
Types of Bridge by Traffic Position
Page 015
Types: Deck Type
Page 016
Types: Through Type
Page 017
Types: Through Type
Page 018
Types: Half -Through
Page 019
Types by Material & Fabrications
Page 020
Types by Material & Fabrications
Page 021
Types by Material & Fabrications
Page 022
Types by Material & Fabrications
Page 023
Types by Material & Fabrications
Page 024
Types by Material & Fabrications
Page 025
Types of Bridge by Structure
Page 026
Types: Arch Bridge
Page 027
Types: Arch Bridge
Page 028
Types: Concrete Arch Bridge
Page 029
Types: Prestressed Concrete Arch
Page 030
Types: Steel Arch Bridge
Page 031
Types: Beam/Girder Bridges
Page 032
Types: Beam/Girder Bridges
Page 033
Types: Beam/Girder Bridges
Page 034
Types: Beam/Girder Bridges
Page 035
Types: Beam/Girder Bridges
Page 036
Types: Beam/Girder Bridges
Page 037
Types: Beam/Girder Bridges
Page 038
Types: Beam/Girder Bridges
Page 039
Types: Beam/Girder Bridges
Page 040
Types: Beam/Girder Bridges
Page 041
Types: Beam/Girder Bridges
Page 042
Types: Beam/Girder Bridges
Page 043
Types: Beam/Girder Bridges
Page 044
Types: Cantilever Bridges
Page 045
Types: Cantilever Bridges
Page 046
Types: Cantilever Bridges
Page 047
Types: Cantilever Bridges
Page 48
Types: Cable-Stayed Bridge
Page 049
Types: Cable-Stayed Bridge
Page 050
Types: Cable-Stayed Bridge
Page 051
Types: Cable-Stayed Bridge
Page 052
Types: Cable-Stayed Bridge
Page 053
Types: Cable-Stayed Bridge
Page 054
Types: Cable-Stayed Bridge
Page 055
Types: Cable-Stayed Bridge
Page 056
Types: Cable-Stayed Bridge
Page 057
Types: Cable-Stayed Bridge
Page 058
Types: Cable-Stayed Bridge
Page 059
Types: Suspension Bridge
Page 060
Types: Suspension Bridge
Page 061
Types: Suspension Bridge
Page 062
Types: Suspension Bridge
Page 063
Types: Suspension Bridge
Page 064
Types: Suspension Bridge
Page 065
Types: Others
Page 066
Types: Others
Page 067
Types: Others
Page 068
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 02 Preliminary Design
Prepared by:
Dr Rajai Alrousan
Types of concrete bridges
Page 001
Which type should I use?
Page 002
Components of Bridge
Page 003
Span Length
Page 004
Span Length
Page 005
Span Length
Page 006
Cost vs. Span Length
Page 007
Cost vs. Span Length
Page 008
Access for Maintenance
Page 009
Beam Spacing
Page 010
Materials
Page 011
Speed of construction
Page 012
Site Requirement
Page 013
Site Requirement
Page 014
Site Requirement
Page 015
Aesthetics
Page 016
Preliminary Design
Page 017
Preliminary Design
Page 018
Preliminary Design
Page 019
Preliminary Design
Page 020
Preliminary Design
Page 021
Preliminary Design
Page 022
Preliminary Design
Page 023
Preliminary Design
Page 024
Preliminary Design
Page 025
Components of Bridge
Page 026
Page 027
Preliminary Design
Page 028
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 03 AASHTO LRFD Designs
Prepared by:
Dr. Rajai Alrousan
AASHTO LRFD Designs
Page 01
Design Criteria
Page 02
Load Multiplier
Page 03
Load Multiplier
Page 04
Load Multiplier
Page 05
Load Multiplier
Page 06
Load Factor & Load Combinations
Page 07
Limit States
Page 08
Permanent Loads
Page 09
Transient Loads
Page 10
Load Combinations
Page 11
Load Factors for DC, DW
Page 12
Load Combinations
Page 13
Load Combinations
Page 14
Load Combinations
Page 15
Load Combinations
Page 16
Load Combinations
Page 17
Notes on Load Combinations
Page 18
Resistance Factors
Page 19
Resistance Factors
Page 20
Resistance Factors
Page 21
LRFD Design Procedure
Page 22
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 04 Loads on Bridge
Prepared by:
Dr. Rajai Alrousan
Outline
Page 001
Loads on Bridge
Page 002
Typical Loads
Page 003
Dead Load: DC
Page 004
Dead Load of Wearing Surface: DW
Page 005
Tributary Area for Dead Loads
Page 006
Live Loads of Vehicles: LL
Page 007
Live Loads of Vehicles: LL
Page 008
Live Loads of Vehicles: LL
Page 009
Bridge LL vs. Building LL
Page 010
Analysis Strategy for LL
Page 011
Design Lane
Page 012
Design Lane
Page 013
Live Loads of Vehicles: LL
Page 014
1. Design Truck
Page 015
1. Design Truck
Page 016
-44
AASHTO HS 20-44 Truck (HS 20-44)
k 2 3
k 2 3
Varies (14’-30’)
k 8
14’
1. Design Truck
Page 017
2. Design Tandem
Page 018
Page 019
Analysis Strategy for LL
Page 020
AASHTO HS 25-44 Truck (HS 25-44)
k 0 1
k 0 4
k 0 4
Varies (14’-30’)
14’
3. Uniform Lane Loading
Live Load Combinations
Page 021
Live Load Placement -Transverse Page 023
Live Load Placement
Page 022
Live Load Placement -Longitudinal
Page 024
Influence Lines and Application of Live Loads Page 025
Influence Lines and Application of Live Loads Page 026
Influence Lines and Application of Live Loads Page 027
Influence Lines and Application of Live Loads Page 028
Influence Lines and Application of Live Loads Page 029
Influence Lines and Application of Live Loads Page 030
Influence Lines and Application of Live Loads Page 031
Influence Lines and Application of Live Loads Page 032
Influence Lines and Application of Live Loads Page 033
Influence Lines and Application of Live Loads Page 034
Influence Lines and Application of Live Loads Page 035
Influence Lines and Application of Live Loads Page 036
Influence Lines and Application of Live Loads Page 037
Influence Lines and Application of Live Loads Page 038
Influence Lines and Application of Live Loads Page 039
Influence Lines and Application of Live Loads Page 040
Influence Lines and Application of Live Loads Page 041
Influence Lines and Application of Live Loads Page 042
Influence Lines and Application of Live Loads Page 043
Influence Lines and Application of Live Loads Page 044
Influence Lines and Application of Live Loads Page 045
Influence Lines and Application of Live Loads Page 046
Influence Lines and Application of Live Loads Page 047
Influence Lines and Application of Live Loads Page 048
Influence Lines and Application of Live Loads
Page 049
Example 05 ::-
Influence Lines and Application of Live Loads
Page 050
Example 0505-Solution ::-
Calculate Calculate the the maximum maximum reaction reaction R100, R100, shear shear V100, V100, and moment M105 for the AASHTO vehicle loads (AASHTO). Use a simply supported beam of 35 -ft span. The influence lines for the actions required are shown in Figure s below. The critical actions for the design truck, design tandem, and the design lane loads are determined independently superimposed as necessary. necessary. The desig n truck is used first, independently and and are later superimposed followed followed by the design tandem, tandem, and finally, finally, the design design lane load .
Influence Lines and Application of Live Loads Page 051
Influence Lines and Application of Live Loads Page 052
Example 0505-Solution ::-
Example 0505-Solution ::-
Influence Lines and Application of Live Loads Page 053
Influence Lines and Application of Live Loads Page 054
Example 0505-Solution ::-
Example 0505-Solution ::-
Live Load Placement – Design Equation
Page 055
Live Load Placement - Longitudinal
Page 056
Live Load Placement – Design Chart
Page 057
Live Load Placement – Design Chart
Page 058
Live Load Placement – Design Chart
Page 059
Live Load Placement – Design Chart
Page 060
Pedestrian Live Load: PL
Page 061
Analysis Strategy for LL
Page 062
Dynamic Load Allowance: IM
Page 063
Dynamic Load Allowance: IM
Page 064
Analysis Strategy for LL
Page 065
Multiple Presence of LL
Page 066
Multiple Presence of LL
Page 067
Distribution of LL to Girders
Page 068
AASHTO Girder Distribution Factor (DF)
DF
Page 069
AASHTO Girder Distribution Factor (DF)
Page 070
AASHTO Girder Distribution Factor (DF)
Page 072
AASHTO Girder Distribution Factor (DF)
Page 073
AASHTO Girder Distribution Factor (DF)
Page 074
AASHTO Girder Distribution Factor (DF)
Page 075
AASHTO Girder Distribution Factor (DF)
Page 076
AASHTO Girder Distribution Factor (DF)
Page 077
AASHTO Girder Distribution Factor (DF)
Page 078
Example 06 ::Determine the AASHTO distribution factors for bridge shown in Figure below. below.A girder section is illustrated in Figure below. below. The system dimensions and properties are as follows: follows:
AASHTO Girder Distribution Factor (DF)
Page 079
Example 06 -Solution ::-
AASHTO Girder Distribution Factor (DF) Example 06 - Solution ::a. Interior Beams [A4.6.2.2.2b]
a. Interior Beams [A4.6.2.2.2b]
Page 080
One design lane loaded: (Moment)
b. Exterior Beams [A4.6.2.2.2d]
Two or more design lanes loaded: (Moment) (Moment)
One design lane loaded — loaded — lever lever rule: (Moment)
AASHTO Girder Distribution Factor (DF)
Page 081
Example 06 - Solution ::b. Exterior Beams [A4.6.2.2.2d]
AASHTO Girder Distribution Factor (DF)
Page 082
Example 06 - Solution ::
Two or more design lanes loaded: (Moment)
AASHTO Girder Distribution Factor (DF) Example 06 -Solution ::-
Page 083
LiveLive-Load Moments
AASHTO Girder Distribution Factor (DF) Example 06 - Solution ::-
a. Interior Beams [A4.6.2.2.2a]
One design lane loaded: (Shear)
a. Interior Beams [A4.6.2.2.2a]
Two design lanes loaded: (Shear)
b. Exterior Beams [A4.6.2.2.2b]
One design lane loaded: (Shear)
b. Exterior Beams [A4.6.2.2.2b]
Two design lanes loaded: (Shear)
LiveLive-Load Load Shears
Page 084
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 05 Other Loads on Bridge
Prepared by:
Dr. Rajai Alrousan
Other Loads
Page 01
Fatigue Load
Page 02
Page 03
Water Loads: WA-AASHTO 3.7
Page 04
Fatigue Wind Earthquake Vehicle/ Vessel Collision Centrifugal Forces Braking Force
Fatigue Load
Water Loads: WA-AASHTO 3.7
Page 05
3.7.3—Stream 3.7.3— Pressure Stream Pressur e
Water Loads: WA-AASHTO 3.7
Page 06
3.7.3—Stream 3.7.3— Pressure Stream Pressur e
3.7.3.1—Longitudinal 3.7.3.1—
3.7.3.2—Lateral 3.7.3.2—
The pressure of flowing water acting in the longitudinal directi on of substructures shall be taken as:
The lateral, uniformly distributed pressure on a substructure du e to water flowing at an angle, , to the longitudinal axis of the pier shall be taken as:
where: where: p = pressure of flowing water ( ksf ) CD = drag coefficient for piers as specified in Table 3.7.3.1 -1 V = design velocity of water for the design flood in strength and service limit states states and for the check flood in the extreme event limit state (ft/s)
where: where: p = lateral pressure ( ksf ) CL = lateral drag coefficient specified in Table 3.7.3.2 -1
Wind Load-AASHTO 3.8
Wind Load-AASHTO 3.8
Page 07
Page 08
Wind Load-AASHTO 3.8
Page 13
Earthquake Load: EQ
Page 14
Earthquake Load: EQ
Page 15
Earthquake Load: EQ
Page 16
Vehicular Collision Force: CT
Page 17
Vehicular Collision Force: CT
Page 18
Centrifugal Forces: CE
Page 19
Braking Force: BR
Page 20
3.6.3— 3.6.3—Centrifugal Forces: CE Centrifugal forces shall be applied horizontally at a distance 6 .0 ft above the roadway surface, C taken as: where: where: v = highway design speed (ft/s) f = 4/3 for load combinations other than fatigue and 1.0 for fat igue g = gravitational acceleration: acceleration: 32.2 32.2 (ft/s2) (ft/s2) R = radius of curvature of traffic lane (ft) Note: The multiple presence factors specified in Article 3.6.1.1.2 sha ll apply.
3.6.4— 3.6.4—Braking Force: BR The braking force shall be taken as the greater of:
25 % of
5% of
the axle weights of the design truck or design tandem or, the design truck plus lane load 5% of the design tandem plus lane load
Note: The multiple presence factors specified in Article 3.6.1.1.2 sha ll apply. These forces shall be assumed to act horizontally at a distance of 6.0 ft above the roadway surface in either longitudinal direction to cause extrem e force effects.
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 06 Design of Slab for Bridge Deck
Prepared by:
Dr Rajai Alrousan
Outline
Page 01
Bridge Superstructure
Page 02
Bridge Superstructure –Girder Bridge
Page 03
Bridge Superstructure –Girder Bridge
Page 04
Components of Bridge
Page 05
Outline
Page 06
Table 4.6.2.2.14.6.2.2.1-1—Common Deck Superstructures
Page 07
Table 4.6.2.2.14.6.2.2.1-1—Common Deck Superstructures
Page 08
Table 4.6.2.2.14.6.2.2.1-1—Common Deck Superstructures
Page 09
Types of Deck
Page 10
Types of Slab Reinforcement
Page 11
Materials: Concrete
Page 12
5.4.2.4— 5.4.2.4—Modulus of Elasticity In the absence of measured data, the modulus of elasticity, Ec, for concretes with unit weights between 0.090 and 0.155 kcf and specified compressive strengths up to 15.0 ksi may be taken as:
Materials: Concrete
Page 13
5.4.2.4— 5.4.2.4—Modulus of Elasticity
Materials: Concrete
Page 14
5.4.2.6— 5.4.2.6—Modulus of Rupture Unless determined by physical tests, the modulus of rupture, f r in ksi, ksi, for specified concrete strengths up to 15.0 ksi, ksi, may be taken as:
Where: K1 = correction factor for source of aggregate to be taken as 1. 0 unless determined by physical test, and as approved by the authority of jurisdicti on wc = unit weight of concrete ( kcf ); ); refer to Table 3.5.1 -1 or Article C5.4.2.4 f c = specified compressive strength of concrete ( ksi) ksi) Note: For normal weight concrete with wc = 0.145 kcf , Ec may be taken as:
Materials: Reinforcing Steel Materials: Reinforcing Steel
Steel grade
E s ( ( ksi ) ( ksi ) ksi) ksi ) F y ( ksi ) Fu (ksi)
G40 (Table 2.3)
40
70
G60 (Table 2.3) 29,000
60
90
G80 (Table 2.3)
80
100
Page 15
Components of Bridge
Page 16
Outline
Page 17
Minimum Slab Thickness
Page 18
Minimum Slab Thickness
Page 19
Slab Span S
Page 20
Minimum Cover of Reinforcement
Page 21
Minimum Cover
Page 22
Analysis and Design Methods
Page 23
Empirical Method
Page 24
Outline
Page 25
Empirical Method
Page 26
Empirical Method
Page 27
Empirical Method
Page 28
Strip Method
Page 29
Outline
Page 30
Strip Method
Page 31
Strip Method
Page 32
Strip Method –Design Aid
Page 33
Strip Method –Design Aid
Page 34
Slab Design
Page 35
Slab Design
Page 36
Page 57
Example: Concrete Deck Design
s
Solution:Solution:-
Solution:Solution:-
Step 09: Control of Cracking —General Step 09 (a): Positive Moment Reinforcement
Step 09: Control of Cracking —General Step 09 (a): Positive Moment Reinforcement
M M DC M DW 1.33M LL 0.685 0.224 5.69 6.60 kip - ft/ft
I cr
The calculation of the transformed section properties is based o n a 1.01.0-ftft-wide doubly reinforced section as shown in Figure below
0.512 x 2 7.50.49 2.31 x 7.5 0.46 6.19 x
nAs/ d x nAs d x 2
3
2d c
12 1.72
2
3
7.50.49 2.31 1.72
2
2
ax bx c 0.0
and the tensile stress in the bottom steel becomes
where
My 6.60 126.19 1.72 7.5 f s n 90.60 I cr 29.31 ksi
a 0.5b 0.5 12 6
/ b n As As 7.50.49 0.46 7.125
3
s f x s
7.50.46 6.19 1.72 90.60 in 4 /ft
2
c n A d As d 7.50.49 2.31 0.46 6.19 / s
bx
700 e
3
0.5bx 2 nAs/ d x nAs d x
Page 58
Example: Concrete Deck Design
29.85 x
b b 2 4ac 2a
1.72 in.
Page 59
Example: Concrete Deck Design s
Solution:Solution:-
700 xe
Step 09: Control of Cracking —General Step 09 (a): Positive Moment Reinforcement
s 1
d c
1
0.7h d c
xs f x s
1.31 0.78.0 1.31
2d c
1.28
For class 2 exposure conditions, e = 0.75 so that
s 8.0 in. smax
700e s f s
2d c
7000.75 21.31 1.2829.31 11.40 in. OK
Use No. 5 at 9 in.
Example: Concrete Deck Design
Page 60
Solution:Solution:Step 09: Control of Cracking —General Step 09 (b): Negative Moment Reinfo rcement
M M DC M DW 1.33M LL 0.685 0.224 4.53 5.439 kip - ft/ft The calculation of the transformed section properties is based o n a 1.01.0-ftft-wide doubly reinforced section as shown in Figure below 0.5bx 2 n 1 As/ x d nAs d x 0.512 x 2 7.5 10.46 x 1.31 7.5 0.49 5.19 x 2 ax bx c 0.0
where a 0.5b 0.5 12 6
/ b n 1 As nAs 7.5 10.46 7.5 0.49 6.67
c n 1 As/ d nAs d 7.5 10.46 1.31 7.5 0.49 5.19
23.0 x
b b 2 4ac 2
1.48 in.
Page 61
Example: Concrete Deck Design s
Solution:Solution:Step 09: Control of Cracking —General Step 09 (b): Negative Moment Reinfo rcement
I cr
bx
3
3
700 e
2d c
s f x s
Step 09: Control of Cracking —General Step 09 (b): Negative Moment Reinfo rcement
s 1
12 1.48
2
3
3
s
Solution:Solution:-
n 1 As/ x d nAs d x 2
Page 62
Example: Concrete Deck Design
d c
0.7h d c
1
700 xe xs f x s
2.31 0.78.0 2.31
2d c
1.58
For class 1 exposure conditions, e = 1.0 so that
7.5 10.461.48 1.31
2
s 7.5 in. smax
7.50.495.19 1.48 63.64 in 4 /ft 2
700e s f s
2d c
7001.0 22.31 1.58 28.54 11.20 in. OK
and the tensile stress in the bottom steel becomes
My 5.439 125.19 1.48 7.5 f s n 63.64 I cr 28.54 ksi
Use No. 5 at 7.5 in. Step 10: Fatigue Lim it State Fatigue need not be investigated for concrete decks in multi-girder applications [A9.5.3].
Example: Concrete Deck Design Solution:Solution:Step 11: The design sketch
Page 63
Example: Concrete Deck Design
Page 64
Solution:Solution:- Empirical Design o f Concrete Deck Slabs 1. Design Conditions [A9.7.2.4] Design depth subtracts the loss due to wear, h = 7.5 in. The following conditions must be satisfied:
Example: Concrete Deck Design Solution:Solution:- Empirical Design o f Concrete Deck Slabs 2. Reinforcement Requirements [A9.7.2.5]
Page 65
Example: Concrete Deck Design Solution:Solution:- Empirical Design o f Concrete Deck Slabs 3. The design ssketch ketch
Page 66
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 07 Design a RC T-beam bridge
Prepared by:
Dr. Rajai Alrousan
Example: Concrete T-Beam
Page 37
Example: Concrete T-Beam
Solution:Solution:-
Solution:Solution:-
Step 07: Shear Design
Step 07: Shear Design
7-(1) Determin e Vu and Mu at a distance d v from an support. [A5.8.2.7]. [A5.8.2.7]. d pos d e d s 35.625 in.
7-(1) Determin e Vu and Mu at a distance d v from an support. [A5.8.2.7].
a 1.36 in.
V Ta 250.9167 0.875 44.8 kips
1 32.08330.9167 9.4 kips 2 33 V LL IM 0.75 1.11546.81 9.4 70.863 kips 100 1 V DC 1.697 32.08330.9167 24.9 kips 2 1 V DW 0.254 32.08330.9167 3.7 kips V 100.833 160.7 kips 2 V Ln 0.64
Distance from support as a percentage of the span
d v
35.0 35.0 12
0.0833
Example: Concrete T-Beam
V Tr 320.9167 0.5167 80.1167
46.8 kips
d e a / 2 35.625 1.36 / 2 35.0 in. 0.9d e 0.9 35.625 32.1 in. d v max 0.72h 0.72 40 28.8 in.
L
Page 39
Example: Concrete T-Beam
Solution:Solution:-
Solution:Solution:-
Step 07: Shear Design
Step 07: Shear Design
7-(1) Determin e Vu and Mu at a distance d v from an support. [A5.8.2.7].
7-(2) Calculate the ultimate concr ete shear resist ance [A5.8.2.7]. concrete resistance
M Tr 322.674 1.507 80.340
136.5 k ft M Ta 252.674 2.3406 124.6 k ft
1 32.08332.674 29.94 k f 2 33 M LL IM 0.75 0.948136.51 29.94 150.4 k f 100 1 M DC 1.697 32.08332.674 79.41 k f 2 1 0 254 32 08332 674 11 9 k f 380 6 k f M Ln 0.64
Page 38
Page 40
/ vV C v 0.0632 f c bv d v 0.900.0632 4.5 1435 59.1 kips
vV C
29.55 kips 2 V @ d v V 100.833 1.25V DC 1.50V DW 1.75V LL IM 160.7 kips Assume No. 4 closed rect. stirrups ( Av 2 0.20 0.40 in 2 ) Zone#1 : V @ d v 160.7 kips V C 59.1 kips shear reinforcment is needed
vV S V @ d v vV C 160.7 59.1 101.6 k ips S req.
v Av f yv d v vV S
0.90.4 60 35 101.6
7.44 in.
Check for Smin : A
0 0316 f /
bv S
0 0316 4 5
147.44
0.116 in 2 A
0 40 in 2
Example: Concrete T-Beam
Page 41
Solution:Solution:-
Solution:Solution:-
Step 07: Shear Design
Step 07: Shear Design
7-(2) Design for Shear. Check for Smax :
7-(3) Check the adequacy of the longitudinal reinforcement.
vu
V @ d v
v bv d v
160.7 0.914 35
0.3644 ksi 0.125 f S max 0.8d v 24 in. / c
0.125 f c/ S max 0.4d v 12 in. vu 0.3644 ksi 0.125 f c/ 0.563 ksi S max 0.8d v 0.8 35 28in. 24 in.
S max 24 in. Sreq. 7.44 in. (Use #4@7 in.) Zone#2 : Smax needed when vV C V @ d v
vV C
Zone#3 : No shear reinforcment when V u
As f y 455.4 kips
V @ d 0.5V s 269.5 kips d v f v
M @ d v
v
As f y 7.59 60 455.4 kips
vV S
v Av f yv d v
0.90.4 6035 7
S req.
108 kips
V @ d 380.6 12 160.7 0.5V s 0.5 108 269.5 kips 35 0 . 9 0 . 9 d v f v
M @ d v
(Use #4@24 in.)
2 V C
v
Note: If this equation is not satisfied, 1. either the tensile reinforcement As must be increased 2. or the stirrups must be placed closer together to increases
2
Example: Concrete T-Beam
Page 43
Solution:Solution:-
Step 08: Calculate the deflection (General)
Step 08: Calculate the deflection (General)
ShortShort-Term (Instanteous) Deflection of Uncracked and Cracked Members:
8-(3) Live Load Deflection (
DL )
P P P Truck L LL max max all 800 25%Truck Lane 0.25 P P P Lane 1
P 1
DL
5w DL L4 384 E c I g
8-(2) Superimposed Load Deflection (
SD
SD)
w DL SD 384 E c I g w DL 5wSD L4
.
LL )
1
8-(1) Dead Load Deflectio n (
Vs
Example: Concrete T-Beam
Solution:Solution:-
Ti DL SD LL
Page 42
Example: Concrete T-Beam
P 3
P 2
P1bx
6 EI e L P3bx
6 EI e L 3
P2 L
48 EI e
L
b 2 x 2 ,
L
b 2 x 2
2
2
, Lane
5w Ln L4 384 E c I e
IM 100 IM P3 mg deflection 81 100 No. lanes P1 P2 mg deflection 321
2
2
3
3
Page 44
Example: Concrete T-Beam
Page 45
Solution:Solution:-
Solution:Solution:-
Step 08: Calculate the deflection (General)
Step 08: Calculate the deflection
8-(3) Live Load Deflection (
M M I e cr I g 1 cr M a M a 3
M cr
8-(1) Dead Load Deflectio n (
LL ) 3
I cr I g
DL
f r I g
4
5w DL L
384 E c I g
DL )
51.697 / 12 35 12
4
SD
M a ,105 M DC ,105 M DW ,105 mg deflection M Tr ,105 1 IM 8-(4) Longtime Deflections (
LT Ti 1
5wSD L4 384 E c I g
50.254 / 1235 12
3843860144,898 LL )
No. lanes 3 mg deflection m 0.85 0.425 No. beams 6
A / 3.0 1.2 s 1.6 for instantaneous deflection is based on I e As
Page 47
Solution:Solution:-
Step 08: Calculate the deflection
Step 08: Calculate the deflection
LL )
8-(3) Live Load Deflection (
M Tr 328.75 32 81.75 350 k- ft
260.0 32.2 0.425 3501
LL )
P P P Truck L LL max max all 0 . 25 800 P P P Lane 25%Truck Lane 1
M a ,105 M DC ,105 M DW ,105 mg deflection M Tr ,105 1 IM
33
490 k - ft
100 3 M 3 M I e cr I g 1 cr I cr I g M a M a 3 222 3 222 I e 144,898 1 57,263 490 490 13,475 51,938 65,413 in 4 144,898 in 4
Page 48
Example: Concrete T-Beam
Solution:Solution:8-(3) Live Load Deflection (
0.0153 in.
I g 144,898 0.509 M cr f r / 12 222 kip - ft yt 27.70
240 4.0 for instantaneous deflection is based on I g
Example: Concrete T-Beam
SD) 4
8-(3) Live Load Deflection (
LT )
L
0.102 in.
3843860144,898
8-(2) Superimposed Load Deflection (
yt
Page 46
Example: Concrete T-Beam
1
2
2
3
3
IM 33 0.425321 18.1 kips 100 100 IM 33 P3 mg deflection81 0.42581 4.52 kips 100 100 P1 P2 mg deflection321
P1bx
P
6 EI e L
1
2
b 2 x 2
18.13.5 1235 12 / 2 35 122 3.5 122 35 12 / 22 0.066 in. 63,86065,41335 12
P 3
L
P3bx
6 EI e L
L
2
b 2 x 2
4 523 5 1235 12 / 2
2
2
2
Example: Concrete T-Beam
Page 49
Example: Concrete T-Beam
Solution:Solution:-
Solution:Solution:-
Step 08: Calculate the deflection
Step 08: Calculate the deflection
8-(3) Live Load Deflection (
LL )
8-(3) Live Load Deflection (
P P P Truck L LL max max all 0 . 25 800 P P P Lane Truck Lane 25% P 0.066 in. 1
1
2
2
3
3
LL )
Ti DL SD LL 0.102 0.0153 0.1877 0.305 in. 8-(4) Longtime Deflections (
LT )
1
P 0.0165 in. 3
P 2
3
P2 L
48 EI e
Lane
18.135 12
3
483,86065,413
4
5w Ln L
384 E c I e
0.111 in.
50.64 / 1235 12
LT Ti 1 0.3051 3 1.22 in.
4
3843,860 65,413
0 3.0 1.2 3.0 1.6 7.59
0.0856 in.
0.066 0.01065 0.111 LL max 0.01065 0.111 0.0856 0 . 25 0 . 066 0.1877 35 12 L max 0.1877 in. all 0.525 in. 800 800 0.1325
L 240
35 12 240
1.75 in.
Page 50
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 08 Bearings
Prepared by:
Dr. Rajai Alrousan
Load Transfer
Page 01
Components of Bridge
Page 02
Bearing
Page 03
Bearing
Page 04
Forces and Movements on Bearing
Page 05
Types of Bearing
Page 06
Rocker/ Pin/ Roller Bearing
Page 07
Rocker/ Pin/ Roller Bearing
Page 08
Elastomeric Bearing
Page 09
Elastomeric Bearing with Slider
Page 10
Elastomeric Bearing
Page 11
Curved Bearing
Page 12
Curved Bearing
Page 13
Pot Bearing
Page 14
Pot Bearing
Page 15
Disk Bearing
Page 16
Which type of bearing should I use?
Page 17
Which type of bearing should I use? TABLE 1:
Summery of Bearing Capacities
Page 18
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 09 Substructures
Prepared by:
Dr. Dr Rajai Alrousan
Types of Substructures
Page 01
Types of Substructures
Page 02
Loads on Substructures
Page 03
Loads from Superstructure
Page 04
Loads from Superstructure
Page 05
Wind Loads (WS, WL)
Page 06
Vehicle Collision Forces (CT)
Page 07
Load Combinations
Page 08
Load Combinations
Page 09
Design of Abutment and Retaining Substructures
Page 10
Roles and Types
Page 11
Types of Abutment
Page 12
Types of Abutment
Page 13
Types of Abutment
Page 14
Types of Abutment
Page 15
Failure Limit States
Page 16
Failure Limit States
Page 17
Loads on Abutment from Superstructure
Page 18
Loads on Abutment
Page 19
Loads on Abutment
Page 20
Pressures generated by the Live Load and Dead Load Surcharges:
Loads on Abutment
Page 21
Defined the other loads
Loads on Abutment Soil Pressure Distribution
Loads on Abutment
Page 22
Dead load of the abutment
Page 23
Loads on Abutment Soil Pressure Distribution
Page 24
Loads on Abutment
Page 25
TABLE 1: Abutment Design Design Loads (Service (Service Load Design)
Page 26
TABLE 1: Abutment Design Design Loads (Service (Service Load Design)
Soil Pressure Distribution
Configuration of abutment design load and load combinations
Configuration of abutment design load and load combinations
Page 27
Configuration of abutment design load and load combinations Table 11.5.611.5.6-1 —Resistance Factors for Permanent Retaining Walls
Page 28
Configuration of abutment design load and load combinations
Page 29
Miscellaneous Design Considerations
Page 30
Table 11.5.611.5.6-1 —Resistance Factors for Permanent Retaining Walls
Miscellaneous Design Consi derations deration s Abutment Wingwall Abutment Drainage Abutment Slope Protection
Miscellaneous Design Considerations (1) Abutm ent Wingwall
Page 31
Miscellaneous Design Considerations (1) Abutm ent Wingwall
Page 32
Design loading for cantilever wingwall cantilever wingwall
Miscellaneous Design Considerations
Page 33
(2) Abutm ent Drainage
Miscellaneous Design Considerations (3) Abutm ent Slope Protection Protecti on
Miscellaneous Design Considerations
Page 34
(3) Abutm ent Slope Protection
Page 35
Reinforced Concrete Abutment
Page 36
Design of Abutment Step 1: Select Preliminary Proportions of the Wall. Step 2: Determine Loads and Earth Pressures. Step 3: Calculate Magnitude of Reaction Forces on Base Step 4: Check Stability and Safety Criteria a. Location of normal component of reactions. b. Adequacy of bearing pressure. c. Safety against sliding. Step 5: Revise Proportions of Wall and Repeat Steps 2-4 Until Stability Criteria is Satisfied and Then Check a. b.
Settlement within tolerable limits. Safety against deep-seated foundation failure.
Step 6: If Proportions Become Unreasonable, Consider a Foundation Supported on Driven Piles or Drilled Shafts.
Typical Abutment Design Sketch
Page 37
Typical Wingwall Design Sketch
Page 38
Design of Retaining Substructures
Page 39
Types of Retaining Structures
Page 40
Types of Retaining Structures
Page 41
Types of Retaining Structures
Page 42
Types of Retaining Structures
Page 43
Typical loads on retaining wall
Page 44
Lateral Load
Page 45
Lateral Load
Page 46
Typical Retaining wall Design Sketch
Page 47
Design of Piers
Page 48
Piers
Page 49
Piers
Page 50
Piers
Page 51
Piers
Page 52
Pier Shpes
Page 53
Pier Types-Steel Bridges
Page 55
Pier Shpes
Pier TypesTypes- river and waterway crossings
Page 54
Page 56
Figure Figure 1: Typical pier types for steel bridges.
Figure 2: Typical pier types and configurations for river and waterway cr ossings. cr ossings. .
Pier Types-Concrete Bridges
Page 57
Pier Selection
Page 58
Page 59
Strength Limit States
Page 60
Figure 3: Typical pier types for Concrete bridges.
Pier Selection Guidelines
Loads on Piers from Superstructure
Page 61
Loads on Piers Itself
Page 62
Pier Load Analysis for Wind Loads
Page 63
Reinforced Concrete Short Columns
Page 64
Reinforced Concrete Short Columns
Page 65
Reinforced Concrete Short Columns
Page 66
Reinforced Concrete Short Columns
Page 67
Reinforced Concrete Short Columns
Page 68
Reinforced Concrete Slender Columns
Page 69
Slenderness Effects
Page 70
Unsupported Length, l u
The degree of slenderness in a column is expressed in terms of "slenderness ratio," defined below:
Reinforced Concrete Slender Columns
The unsupported length (l u) of a column is measured as the clear distance between the underside of the beam, slab, or column capital above, and the top of the beam or slab below.
Slenderness ratio
klu /r k = effective length factor (reflecting the end restraint and lateral bracing conditions of a column) l = unsupported column length u r = radius of gyration (reflecting the size and shape of a column cross-section)
Reinforced Concrete Slender Columns Effective Length Factor, k
Page 71
Reinforced Concrete Slender Columns
Page 72
Effective Length Factor, k
0.82
For compression members in a nonsway frame, an upper bound to the effective length factor may be taken as the smaller of the values given by the following two expressions (ACI R10.12.1. ) k 0.7 0.05( A B ) 1.0 k 0.85 0.05( min ) 1.0
i
EI / l EI / l
c Columns B Beams
at end i of column
Reinforced Concrete Slender Columns
Page 73
Radius of Gyration, r The radius of gyration introduces the effects of cross-sectional size and shape to slenderness. For the same cross-sectional area, a section with higher moment of inertia produces a more stable column with a lower slenderness ratio. The radius of gyration r is defined below.
r
Reinforced Concrete Slender Columns
Page 74
Slenderness effects may be neglected for columns in non-sway frames if the following inequality is satisfied:
klu r
Where
34 12 M 1 / M 2 40
M1/M2 is the ratio of smaller to larger end moments.
I A
M1/M2 is negative value when the column is bent in double curvature M1/M2 is positive when it is bent in single curvature.
Reinforced Concrete Slender Columns
Page 75
Design of Slender Columns
Reinforced Concrete Slender Columns
Page 76
Design of Slender Columns
Slender columns in sway frames are designed for factored axial force P u and amplified moment M c. The amplified moment is obtained by
Where the moment of inertia of reinforcement about the cross-sectional centroid (I se) equal
M c b M 2 b s M 2 s Where moment magnification factor (ns) in is obtained by
b
1
C m Pu
1.0
s
1
P 1 0.75 P (Euler buckling load) is; u
0.75Pc
The critical column load, P c
1.0 I se 0.25 t bh 3
2
3 2 I se 0.18 t bh
c
Pc
3 2 I se 0.17 t bh 3 bars per face 3 2 I se 0.12 t bh 6 bars per face
2 EI
klu 2
EI is computed either with 1
EI
0.2 E c I g E s I se 1 d
2
EI
0.4 E c I g 1 d
I se 0.10 t h 4
I se 0.22 t bh 3 2
2
I se 0.13 t bh 3 2
Reinforced Concrete Slender Columns
Page 77
Design of Slender Columns
Reinforced Concrete Slender Columns
Page 78
Design of Slender Columns An outline of the separate steps in the analysis/design procedure procedure for sway frames follows along these lines:
Coefficient Cm is equal to
M 1 0.40 M 2
C m 0.6 0.4
Step 1:
Determine factored design forces: Note: M1 is the lower and M 2 is the higher end moment. Step 2:
Calculate slenderness ratio klu /r i) Find unsupported column length, lu ii) Find the radius of gyration, r iii) Find effective length factor "k." This requires the calculation of stiffness ratios at the ends. First find beam and column stiffness.
Figure 1
Step 3: Check if slenderness can be neglected
Figure 2
Reinforced Concrete Slender Columns
Page 79
Design of Slender Columns An outline of the separate steps steps in in the analysis/design procedure procedure for sway frames follows along these lines: Step 4: Compute moment magnification factor ( b) and (s)
i) Compute critical load Pc ii) Compute Cm iii) Moment magnification factor (b) and (s) Step 5:
Compute amplified moment M c Step 6:
Select reinforcement ratio and design the column section A) Compute K n
Pu / f c/ Ag
B) Compute Rn
M u / /
f c Ag h
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 10 Bridge Management Systems
Prepared by:
Dr. Rajai Alrousan
Jordan University of Science and Technology
CE 536 Bridge Engineering
Chapter 11 Inspection
Prepared by:
Dr. Dr Rajai Alrousan
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 05
11.3.1.1 Inspection of concrete decks and slabs 11.3.1.1.1 Cracking:
Page 07
Page 06
11.3.1.1 Inspection of concrete decks and slabs 11.3.1.1.1 Cracking:
Concrete cracks due to tensile forces from
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Shrinkage Temperature changes Bending loading Shear loading Freezing and thawing Corrosion of reinforcement Sulfate or aggregate reactions.
In particular, a basic horizontal and vertical pattern with some branching that surrounds the larger aggregate particles could indicate a chemic al attack. If this is suspected, a petrographic examination should be carried out to establish its presence or otherwise.
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures 11.3.1.1.1 Cracking:
Page 08
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 09
11.3.1.1.1 Cracking:
Shrinkage Cracks
Page 10
11.3.1.1.1 Cracking:
Temperature changes
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures 11.3.1.1.1 Cracking:
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 11
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures 11.3.1.1.1 Cracking:
Page 12
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 13
11.3.1.1.1 Cracking:
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 14
11.3.1.1.1 Cracking: Concrete Crack with Guidlines Type of Crack Hairline (HL)
Width (mm) w
0.1
Narrow (Fine) (N)
0.1< w 0.3
Mediu m (M)
0.3< w 0.7
Wide (W)
w > 0.7
Crack width measuring rule
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 15
11.3.1.1 Inspection of concrete decks and slabs 11.3.1.1.2 Spalling
11.3 WHAT TO LOOK FOR 11.3.1 Superstructures
Page 16
11.3.1.1 Inspection of concrete decks and slabs 11.3.1.1.3 Corrosion of reinforcement
Under pressure (for example, due to freeze -thaw action) bits of concrete can fall away from the deck leaving a crater, which defines the fracture surface.
In its early stages this can be detected by surface discoloratio n and rust stains, and later (when it has advanced) by spalling.
The cause is often due to to corrosion of reinforcement where the v olume of the corrosion products is much greater than the virgin steel and the resulting pressure causes local fracture of the concrete
The location and extent of any discoloration are recorded and a cover meter survey is carried out
11.8 PLANNING AN INSPECTION 11.8.1 Condition Ratings
Page 41
Page 42
The following general condition ratings shall be used as a guide in evaluating Items:
Page 43
Page 44
Page 45
Page 46 Page 47
Page 48
Page 49
Jordan University of Science and Technology
CE 536 Bridge Engineering
Appendix
Prepared by:
Dr Rajai Alrousan
Page 02
Chapter 02: Preliminary Design
Page 01
Page 03
Page 04
Live Load Placement – Design Equation
Chapter 04: Loads on Bridge
Page 05
Page 06
Live Load Placement – Design Chart
Live Load Placement – Design Chart
Page 07
Page 08
Live Load Placement – Design Chart
Page 09
Page 10
AASHTO Girder Distribution Factor (DF)
Page 11
Page 12
Chapter 06: Design of Slab for Bridge Deck
Page 13
Page 14
Page 15
Page 16
Page 17
Page 18
