StructuralEngineeringReviewCourse
LateralForces:Bridges(SeismicDesign)
Lateral Forces: Bridges Structural Engineering Review Course
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StructuralEngineeringReviewCourse
LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Exam Specifications NCEES Specifications
Bridges Lateral Forces
6 questions (Bridge) / 4 questions (Building)
A. Lateral Forces (Wind) B. Columns C. Bridge Piers D. Footings
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Lesson Overview •
bridge wind loads
•
bridge columns
•
bridge piers
•
bridge footings
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Prerequisite Knowledge You should already be familiar with •
statics
•
dynamics
•
structural analysis
•
AASHTO seismic forces
4
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Referenced Codes and Standards •
AASHTO LRFD Bridge Design Specifications (AASHTO 2012)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Typical Bridge Components
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Types of Wind Loading •
•
wind on structure (WS) •
superstructure
•
substructure
wind on live (WL)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Load Combinations with Wind •
•
Strength III
•
Service I
•
1.4 wind on structure
•
0.3 wind on structure
•
0.0 wind on live
•
1.0 wind on live
Strength V
•
Service IV
•
0.4 wind on structure
•
0.7 wind on structure
•
1.0 wind on live
•
0.0 wind on live
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Height of Structure •
height above low ground or design water elevation of structure or component
•
if height ≤ 30 ft, use the simplified procedure (VDZ = VB and PD = PB)
•
if height > 30 ft, use the detailed procedure (calculate VDZ and PD)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Base Wind Velocity,VB •
100 mph
•
wind velocity for height above low ground or design water elevation ≤ 30 ft
•
if height ≤ 30 ft, use VDZ = VB •
skip equation (AASHTO Eq. 3.8.1.1-1) and use AASHTO Tables 3.8.1.2.1-1 and 3.8.1.2.2-1
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads For a truss bridge with a maximum height of 25 ft what is the design wind speed? (A) 50 mph (B) 75 mph (C) 100 mph (D) 125 mph
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads For a truss bridge with a maximum height
Solution
of 25 ft what is the design wind speed? (A) 50 mph
The simplified procedure can be used.
(B) 75 mph (C) 100 mph (D) 125 mph
Following the simplified procedure, the design wind speed is equal to the base wind speed of 100 mph. The answer is (C).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads For a truss bridge with a maximum height of 25 ft, what are the design wind pressures for wind loading perpendicular to the bridge? (A) 0.050 kips/ft2 (windward), 0.025 kips/ft2 (leeward) (B) 0.050 kips/ft2 (windward), NA (leeward) (C) 0.040 kips/ft2 (windward), NA (leeward) (D) 0.750 kips/ft2(windward), 0.000 kips/ft2 (leeward)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads For a truss bridge with a maximum height of
Solution
25 ft, what are the design wind pressures for wind loading perpendicular to the bridge?
According to AASHTO Table 3.8.1.2.1-1 for trusses, the windward design pressure for loading perpendicular to the bridge is 0.050 kips/ft 2. The leeward design pressure for loading perpendicular to the bridge is 0.025 kips/ft2.
(A) 0.050 kips/ft2 (windward), 0.025 kips/ft2 (leeward) (B) 0.050 kips/ft2 (windward), NA (leeward) (C) 0.040 kips/ft2 (windward), NA (leeward) (D) 0.750 kips/ft2(windward), 0.000 kips/ft2 (leeward)
The answer is (A).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Extra Simplified Procedure
If all of the following are true, apply 0.05 kips/ft2 transverse and 0.012 kips/ft2 longitudinal simultaneously. •
girder and slab bridge
•
no individual span length > 125 ft
•
maximum height ≤ 30 ft
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Wind Load Application •
•
•
•
•
Multiply design wind pressure, PD, by the exposed area.
Areas that do not contribute to extreme force effect may be neglected.
Wind pressure is uniformly distributed on exposed area. Exposed area includes area of sound barriers, regardless of pressure used to design the sound barrier itself. Exposed area is shown in elevation view perpendicular to wind direction.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Design Wind Velocity,VDZ •
design wind velocity at design elevation in mph, from AASHTO Table 3.8.1.1-1 V30 Z ln VB Z 0
•
VDZ 2.5V0
•
V0 , Z 0 surface condition coefficients
•
V30 wind velocity at 30 ft above low ground or design water elevation (mph) •
•
mph If not provided, assume V30 VB 100
VB 100 mph Z = height of component above low ground or design water
elevation (ft)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Design Wind Pressure, PD 2
•
•
PD PB VDZ VB
AASHTO Eq. 3.8.1.2.1-1
PB base wind pressure from AASHTO Table 3.8.1.2.1-1
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads A truss bridge in open country conditions has an average height of 50 ft. What are the design wind pressures for wind loading perpendicular to the bridge? Use average height for calculation of all wind loading. (A) 0.050 kips/ft2 (windward), 0.025 kips/ft2 (leeward) (B) 0.055 kips/ft2 (windward), 0.030 kips/ft2 (leeward) (C) 0.061 kips/ft2 (windward), 0.031 kips/ft2 (leeward) (D) 0.075 kips/ft2 (windward), 0.000 kips/ft2 (leeward)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Solution
Step 1: Use surface condition coefficients from AASHTO Table 3.8.1.1-1. For open country conditions, V0 = 8.23 mph and Z0 = 0.23 ft Step 2: Calculate design wind velocity using AASHTO Eq. 3.8.1.1-1. V Z VDZ 2.5V0 30 ln VB Z 0 VDZ 2.5 8.23mph
100 mph 50 ft ln mph 110.73 100 mph 0.23 ft
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Step 3: Calculate windward design wind pressures using AASHTO Equation 3.8.1.2.1-1. VDZ VB
PD PB
PD 0.050
2
kips 110.73 mph
2
2 0.061 kips/ft
ft 100 mph 2
Step 4: Calculate leeward design wind pressures using AASHTO Equation 3.8.1.2.1. VDZ VB
2
PD PB
PD 0.025
kips 110.73 mph
ft 100 mph 2
2
2 0.031 kips/ft
The answer is (C). STRC ©2016 Professional Publications, Inc.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Minimum Wind Load •
for truss and arch components, 0.30 kips/ft (windward) or 0.15 kips/ft (leeward)
•
for beam and girder spans, 0.30 kips/ft
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads A truss bridge in open country conditions has an average height of 50 ft. If the exposed height is 3 ft, what is2 the minimum wind loading on the bridge? (For windward, use 0.061 kips/ft ; for leeward use 0.031 0.031 kips/ft2.)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Solution
Step 1: Convert pressures from previous problem to line loads. 2 Windward: Using PD 0.061 kips/ft
LL PDh 0.061
kips (3 ft) 0.183 kips/ft ft2
2 Leeward: Using PD 0.031 kips/ft
LL PD h 0.031
kips (3 ft) 0.093 kips/ft ft 2
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Solution (continued)
Step 2: Compare calculated wind loading to minimum wind loading. Windward:
0.183 kips/ft 0.30 kips/ft
minimum governs
Leeward:
0.031 kips/ft 0.15 kips/ft minimum governs The minimum wind load governs.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Vertical Wind Pressure •
0.020 kips/ft2
•
upward on full width of deck, including parapets and sidewalks
•
acts as a line load at the quarter point of the deck width
•
acts in conjunction with horizontal wind load
•
only applies: •
in Strength III and Service IV load cases (no wind on live load (LL))
•
when wind loading is taken perpendicular to longitudinal axis of bridge
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Vertical Wind Pressure (continued)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Wind on Substructure •
0.040 kips/ft2
•
substructure = everything below the bearings
•
acts in conjunction with superstructure wind load
•
if applied at angle, break into parallel and perpendicular components
•
only applies: •
in Strength III and Service IV load cases (no wind on LL)
•
when wind loading is taken perpendicular to longitudinal axis of bridge
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Wind on Substructure
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Wind on Live Load •
loaded areas that do not contribute to extreme force effect may be neglected
•
acts 6 ft above roadway surface
•
only applies in Strength V and Service I load cases
•
if normal to structure, taken as 0.010 kips/ft line load
•
if taken at an angle, see AASHTO Table 3.8.1.3-1
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
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LateralForces:Bridges(SeismicDesign)
SEISMIC FROM HERE ON OUT !!!!
Bridges: Lateral Forces
Bridge Seismic Loads For Seismic Zone 1 with SD1 < 0.1 •
design force per AASHTO Sec. 3.10.9.2 •
•
if As < 0.05, design superstructure to substructure connection for 15% of dead load + live load (DL+LL) if As ≥ 0.05, design superstructure to substructure connection for 25% of DL+LL
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads For Seismic Zone 1 with SD1 ≥ 0.1 •
design force per AASHTO Sec. 3.10.9.2 •
if As < 0.5, design superstructure to substructure connection for 15% of DL+LL
•
if As ≥ 0.5 design superstructure to substructure connection for 25% of DL+LL
•
transverse reinforcement detailing per AASHTO Sec. 5.10.11.4.1d
•
transverse reinforcement spacing per AASHTO Sec. 5.10.11.4.1e
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads A bridge is located in seismic zone 1 with a design spectral response acceleration at a period of 1.0 sec of 0.1. The dead load is 200 kips and the live load is 300 kips. The acceleration coefficient is 0.05 and the load factor is 0.5. What is the design seismic force?
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Solution
For a bridge in seismic zone 1 with SD1 = 0.1, design forces are per AASHTO Sec. 3.10.9.2. From AASHTO Sec. 3.10.9.2 forAs = 0.5, design superstructure to substructure connection for 25% of DL+LL
EQ 0.25 DL eq LL
0.25 200 kips 0.5 300 kips
87.5 kips The answer is 87.5 kips.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Spiral detailing per AASHTO Sec. 5.10.11.4.1d •
•
•
column core is confined in expected plastic hinge region. maximum yield strength on spiral reinforcement = yield strength of longitudinal reinforcement volumetric ratio of spirals, ρs, must satisfy both: strength design per AASHTO Sec. 5.7.4.6 fc ' AASHTO Eq. 5.10.11.4.1d-1 seismic design per s 0.12 y within hinge zones, all splices are made by full-welded splices or by full-mechanical connections •
•
•
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Hoop Detailing per AASHTO Sec. 5.10.11.4.1d •
•
•
column core shall be confined in expected plastic hinge region maximum yield strength on spiral reinforcement = yield strength of longitudinal reinforcement total gross sectional area of hoop reinforcement, Ash, must satisfy either f ' Ag AASHTO Eq. 5.10.11.4.1d-2 A0.30 shc c 1 sh f y Ac •
•
fc ' f y
Ash 0.12 shc
AASHTO Eq. 5.10.11.4.1d-3
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Hoop Detailing per AASHTO Eq. 5.10.11.4.1d •
s = vertical spacing of hoops, not exceeding 4.0 in
•
Ac = area of column core (in 2)
•
Ag = gross area of column (in 2)
•
Ash = total cross section area of tie reinforcement, including supplementary cross ties having a vertical spacing of s and crossing a section having a core dimension of hc (in2)
•
hc = core dimension of tied column in the direction under consideration (in)
•
Ash is determined for both principal axes
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Bridges: Lateral Forces
Bridge Wind Loads Confinement Transverse Reinforcement Spacing per AASHTO Sec. 5.10.11.4.1e provide at top and bottom of column over length not less than the greatest of
•
•
•
•
•
maximum cross-sectional column dimension
•
1/6 clear height of column
•
18 in
extend into top and bottom connections a distance not less than
•
15 in from face of column connection into adjoining member
spacing not to exceed •
¼ minimum dimension
•
4 in on center-to-center
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½ maximum column dimension
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Bridges: Lateral Forces
Bridge Wind Loads For Seismic Zone 2 •
same as seismic zones 3 and 4, except •
•
0.01Ag ≤ area of longitudinal reinforcement ≤ 0.06Ag column design based on modified design forces only (per AASHTO Sec. 3.10.9.3)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads For Seismic Zones 3 & 4 •
•
column requirements per AASHTO Sec. 5.10.11.4.1 longitudinal reinforcement 0.01Ag ≤ long. reinf. ≤ 0.04 Ag
•
flexural design requirements
•
shear design requirements
•
•
plastic hinging detailing requirements for confinement
•
transverse reinforcement spacing
•
splice requirements
•
wall pier requirements
•
column connection requirements
column shear and transverse reinforcement requirements
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Bridges: Lateral Forces
Bridge Wind Loads Column Requirements per AASHTO Sec. 5.10.11.4.1 •
•
•
A vertical support should be considered a column if the ratio of clear height to maximum plan dimension ≥ 2.5. Piers typically behave like columns in the weak axis but behave differently in the strong axis. For supports with ratios < 2.5, follow the provisions for piers in AASHTO Sec. 5.10.11.4.2.
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Bridges: Lateral Forces
Bridge Wind Loads Longitudinal Reinforcement •
0.01Ag ≤ longitudinal reinforcement ≤ 0.04Ag
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Bridges: Lateral Forces
Bridge Wind Loads Flexural Design Force •
flexural resistance factor = 0.9 for either spiral or tie reinforcement
•
modified design forces = elastic seismic forces divided by R-factor •
calculate transverse (trans.) and longitudinal (long.)
•
combine trans. and long. using load combos per AASHTO Sec. 3.10.8 combination 1 = 100% long. + 30% trans. combination 2 = 30% long. + 100% trans.
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Bridges: Lateral Forces
Bridge Wind Loads Elastic Seismic Forces
Forces resulting from •
simplified seismic forces (15% or 25%)
•
single mode spectral analysis
•
uniform load method analysis
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Shear Design Force
Take the lesser of •
elastic seismic forces divided by R-factor
•
column plastic hinging forces
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Bridges: Lateral Forces
Bridge Wind Loads Plastic Hinging •
size column with modified design forces
•
Procedure •
Calculate Mn.
•
Multiply Mn by the overstrength factor. (Overstrength factors per AASHTO Sec. 3.10.9.4.3b taken as 1.3 for reinforced concrete columns or 1.25 for steel columns.)
•
Calculate shear force corresponding to plastic hinging moment.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads
Vp
T
MB LB
M T M B M n
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Bridges: Lateral Forces
Bridge Wind Loads Concrete Shear Capacity •
•
If Pu ≥ 0.1f’cAg, then Vc per AASHTO Sec. 5.8.3 (strength design) if Pu ≤ 0.1f’cAg, then Vc varies linearly from the AASHTO Sec. 5.8.3 value to 0 (at 0 compression force)
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Bridges: Lateral Forces
Bridge Wind Loads End Regions •
•
•
end regions at top and bottom of column must extend from face of cap/girder/footing into the column a distance equal to the greater of •
maximum cross-sectional column dimension
•
1/6 clear height of column
•
18 in
end region at top of pile bent must be the same as for columns (above) bottom of pile bent must extend three times the pile diameter below point of max moment but not less than 18 in above mud line
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Plastic Hinge Detailing Requirements for Confinement •
same requirements as discussed for seismic zone 1 per AASHTO Sec. 5.10.11.4.1d
Transverse Reinforcement Spacing •
same requirements as discussed for seismic zone 1 per AASHTO Sec. 5.10.11.4.1e
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Bridges: Lateral Forces
Bridge Wind Loads Splice Requirements (AASHTO Sec. 5.10.11.4.1f) •
follow AASHTO Sec. 5.11.5
•
lap splices not allowed
•
•
maximum transverse reinforcement spacing around splice is 4 in or ¼ the minimum member dimension full-welded and full-mechanical splices are allowed as long as •
•
adjacent longitudinal bars are not both spliced distance between splices of adjacent bars is greater than 24 in measured along the longitudinal axis
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Bridges: Lateral Forces
Bridge Wind Loads Wall Pier Requirements (AASHTO Sec. 5.10.11.4.2) •
•
pier weak direction designed as a column (following column provisions with column response modification factor to determine design forces) for strong axis: •
minimum reinforcement ratio horizontal, ρh, and vertical, ρV, must be ≥ 0.0025 and the vertical must not be less than the horizontal.
•
minimum reinforcement spacing (horizontal and vertical) = 18 in
•
shear reinforcement continuous and distributed uniformly
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Bridges: Lateral Forces
Bridge Wind Loads Wall Pier Requirements (AASHTO Sec. 5.10.11.4.2) (continued) •
Factored shear resistance in pier,Vr, is lesser of •
•
Vr 0.253 f bd' c Vr Vn •
•
AASHTO Eq. 5.10.11.4.2-1 AASHTO Eq. 5.10.11.4.2-2
Vn 0.063 c yfh' f
bd
AASHTO Eq. 5.10.11.4.2-3
0.9
•
Horizontal and vertical layers of reinforcement are provided on each face.
•
Splices in horizontal reinforcement must be staggered.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Column Connection Requirements (AASHTO Sec. 5.10.11.4.3) •
•
•
design forces per AASHTO Sec. 3.10.9.4.3 (same design forces as footing) development strength of longitudinal steel = (1.25)(full yield strength) per AASHTO Sec. 5.11 end region transverse reinforcement extend from the column into the adjoining member a distance not less than •
half the maximum column dimension
•
15 in
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Bridge Wind Loads Column Connection Requirements (AASHTO Sec. 5.10.11.4.3) (continued) •
Nominal shear resistance, Vn, of joint must satisfy •
•
Vn 0.380 bd f
' c
[for normal weight concrete (AASHTO Eq. 5.10.11.4.3-1)]
Vn 0.285 bd f
' c
[for lightweight concrete (AASHTO Eq. 5.10.11.4.3-2)]
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Which seismic zones require the calculation of plastic hinging forces for column design? (A) 1 and 2 (B) 2, 3, and 4 (C) 3 and 4 only (D) 4 only
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Bridge Wind Loads Which seismic zones require the calculation
Solution
of plastic hinging forces for column design? (A) 1 and 2
Columns in seismic zone 1 are designated for a percent of the dead load.
(B) 2, 3, and 4
Columns in seismic zone 2 are designated for the modified design forces only.
(C) 3 and 4 (D) 4 only
Columns in zones 3 and 4 are designed for the lesser shear force of the modified design forces or plastic hinging. The answer is (C).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Weak Axis
Modified and plastic hinging force calculated in the same manner as columns (per AASHTO Sec. 3.10.9.4.3b). Strong Axis
Use plastic hinging forces, calculated through an iterative procedure (per AASHTO Sec. 3.10.9.4.3c).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Typically, the weak axis of a bridge pier corresponds with which bridge axis? (A) longitudinal (B) lateral (C) vertical (D) diagonal
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Typically, the weak axis of a bridge pier
Solution
corresponds with which bridge axis? (A) longitudinal
On a typical bridge without skew, the weak axis of the pier corresponds with the longitudinal bridge axis.
(B) lateral (C) vertical (D) diagonal
The strong axis of the pier will typically correspond with the lateral bridge axis. If a bridge is skewed, then the weak and strong axis of the pier will not correspond with either the longitudinal or the lateral bridge axis. The answer is (A). STRC ©2016 Professional Publications, Inc.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Strong Axis (hinging forces) per AASHTO Sec. 3.10.9.4.3c
Step 1 •
•
Determine column overstrength moment resistances. Determine initial axial load using extreme event load combination with EQ = 0. (This is typically DL only.)
Step 2 •
Calculate shear forces corresponding to overstrength moments.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Strong Axis (hinging forces) per AASHTO Sec. 3.10.9.4.3c
Step 3 •
Sum column plastic shear forces and reapply to CG of superstructure.
Step 4 •
Calculate axial forces in the columns due to overturning with overstrength plastic moments developed.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Strong Axis (Hinging forces) per AASHTO Sec. 3.10.9.4.3c
Step 5 •
Compare step 4 axial forces to step 1 axial forces. •
•
If they are within 10%, stop iterating. If not, recalculate column hinging forces with new axial forces and repeat steps 2–5.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Determine the design plastic hinging forces at the base of the columns for the following multicolumn pier given the following information. All dead load: DL 1250 k eq
0
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Solution
Calculate the factored dead load corresponding to the extreme event seismic limit state. P
1.25
p DL
[from AASHTO Table 3.4.1-2]
1.2 5 1250 k 1563 k
Determine the overstrength moment. w 2200 k -ft Mn ΦM n 1.3 2 200 kft-
2860 -k ft
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Solution (continued)
Determine the plastic shear. Vp
ΦM n ,top ΦM n,bottom 2860 -ft k 2860 -ft k
hc
15 ft
381 k
Calculate the change in axial load due to applied plastic shear. ΔP
(20 ft)(1143 k ) (3)(2860 k ) 30 ft
476 k
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Solution (continued)
Check within 10%. (10%)(1563 k ) 156 k 476 k
therefore, iterate
Repeat this process
P Po P 1563 k 476 k
2039 k
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Design Process •
determine design forces
•
size footing (based on bearing resistance) (AASHTO Sec. 10.6)
•
•
determine thickness based on shear (typically punching shear) (AASHTO Sec. 5.13.3.6) design reinforcement (AASHTO Sec. 5.13.3)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Design Forces for Footings
Seismic Zone 1 •
Seismic Zones 3 & 4
same forces as columns
•
Seismic Zone 2 •
elastic seismic forces divided by half of the R-factor from AASHTO Table 3.10.7.1-1 for the substructure component to which it is attached
lesser of •
elastic seismic forces
•
column plastic hinging forces
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers What dead load + live load (DL+LL) forces are columns in seismic zone 1 designed for? (A) 15% of DL+LL (B) 20% of DL+LL (C) 25% of DL+LL (D) either 15% of DL+LL or 25% of DL+LL
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers What dead load + live load (DL+LL) forces
Solution
are columns in seismic zone 1 designed for? (A) 15% of DL+LL
Column design forces in seismic zone 1 vary based on the peak seismic ground acceleration coefficient, As.
(B) 20% of DL+LL
For As < 0.05, 15% DL+LL.
(C) 25% of DL+LL (D) either 15% of DL+LL or 25% of DL+LL
For As ≥ 0.05, 25% DL+LL. The answer is (D).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Elastic Seismic Forces •
•
Use R = 1 for foundations per AASHTO Sec. 3.10.9.4.2. If taking modified forces used for column design, remember to remove the column design R-factor.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Elastic Seismic Forces (continued)
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Column Plastic Hinging Forces •
Use overstrength hinging forces from base of columns.
•
Use iterative approach for multicolumn pier in strong axis direction.
Phi Factors •
For extreme event limit state use phi factor of 1, except for uplift resistance of piles and shafts which should be taken as 0.8.
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Size Footing Based on Bearing Resistance •
•
Take design forces and resolve into an axial load with an eccentricity. Using equations from foundation design lectures determines the footing size that works for allowable bearing pressure (which will be provided in the problem statement).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Equivalent Square Column Width (AASHTO Sec. 5.13.3.1) •
•
Circular columns may be treated as square columns with the same area, where h = 0.886D. Used for •
location of critical sections for moment
•
shear
•
development of reinforcement in footings
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Most nearly, what is the equivalent diameter of a square column for a 24 in diameter circular column? (A) 21 in (B) 23 in (C) 24 in (D) 26 in
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Example – Multicolumn Bridge Piers Most nearly, what is the equivalent
Solution
diameter of a square column for a 24 in diameter circular column?
h 0.886 D 0.886 24 in
(A) 21 in (B) 23 in
21.26 in (21 in) The answer is (A).
(C) 24 in (D) 26 in
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Determine Thickness (Based on Shear) •
Check both flexural and punching shear.
•
Typically, punching shear governs the footing thickness.
•
Critical section is the same as in AASHTO concrete lectures (AASHTO Sec. 5.13.3.6).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Multicolumn Bridge Piers Design Reinforcing Steel (Based on M oment) •
Check moment in both directions.
•
Critical section is the same as in AASHTO concrete lecture (AASHTO Sec. 5.13.3.6).
•
Minimum Reinforcement is the same as in AASHTO concrete lecture.
•
Temperature and shrinkage reinforcement minimums apply as well (per AASHTO Sec. 5.10.8).
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LateralForces:Bridges(SeismicDesign)
Bridges: Lateral Forces
Lesson Overview •
bridge wind loads
•
bridge columns
•
bridge piers
•
bridge footings
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