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Revisions
5/23/13 - revisions per Delta comments
**Need to review AASHTO 2012 chap 11 for compliance before changing reference #1.
Design/Analysis References:
1.
2.
3.
4.
5.
6.
7.
717/13
7/24/13 found error in live load surcharge text.
4/8/14 - changed crack control calculation per Ron Thornton conversation.
2/2/15 - modified wall height in structural design to be taken as the design height instead of the wall height.
3/20/15 revised eccentricity calc to check eccentricity without footing AND with footing.
4/26/18 Updated LRFD factors per AASHTO
Assumptions:
1.
2.
3.
4.
5.
7.
9.
General Input:
Elevation of the Wingwall at its tallest point
Elevation of Wingwall at its tip.
Elevation of the Bottom of the Wall Footing
Thickness of Wall Footing
Height of Wall Footing
Short end of wall (less 1" for shim)
Tall end of wall (less 1" for shim)
Length of Wall Panel
Length of flat portion of wingwall before break in slope.
Thickness of Wall Panel
Thickness of Anchor Stem
Width of Anchor Flange
Angle of ww skew in plan view, measured from edge of roadway.
(to measure distance to traffic for each anchor)
Wall batter angle with horizontal
Anchor batter angle with horizontal
Backfill slope angle with horizontal, measured perpendicular to the wall.
Estimated minimum distance to traffic, measured from
backfill side of wall and perpendicular to the wall.
Assumed distance from face of guardrail to break-in-slope, meaured perpendicular to the wall.
Wall Material Properties
Concrete
Assumed unit weight of concrete panel.
Steel:
Soil:
Factored Bearing Resistance as specified in the contract (Sht 8)
Assumed soil unit weight for all soil
Surcharge Soil Pressure
Friction Angle of Soil below Wall Footing
Friction Angle of Backfill Soil
AASHTO C3.11.5.9-1 and HITEC p.D19
AASHTO C3.11.5.9-1 and HITEC p.D19
AASHTO 3.11.5.3
AASHTO 3.11.5.3
AASHTO 3.11.5.2-1
Determine Load Factors (Strength I) (AASHTO 1.3 and Table 3.4.1-1)
Load Modifiers
Ductility for a conventional design
Redundancy for conventional design
Importance for a conventional bridge
Load Factor
Max
Min
Service
Component Dead Loads
Horizontal Earth Loads
Vertical Earth Loads
Live Loads
Anchor Types, Layout and Backfill Geometry
To account for the connection of the wing to the bridge.
Anchor Type to be tied to the back face of the wall.
between Anchor Type B, C, D, and E as defined below.
Distance to each anchor is from culvert end of wing.
Note:
Tributary Width of Wall for each Anchor
Height of Wall at CL of Each Anchor
Height of wall at each anchor
Length of each Anchor Stem Extension
W is the additional anchor stem length beyond that of a "B" anchor.
Width of Soil Column above each Anchor
Bbot is the width of the soil column at the top of the anchor, measured from backfill side of wall to upper tip of each anchor.
Bbot.lower is the width of the soil column at the bottom of the anchor, measured from backfill side of wall to bottom tip of anchor.
Perpendicular Distance to Traffic at each Anchor
Height of backfill at CL of each anchor
Distance to break in slope, measured perpendicular to
The height of backfill is taken at the end of the reinforced soil mass.
Calculate Nominal Bearing Resistance
Per 11.11.4.3, Soil bearing resistance shall be evaluated according to 10.6.3.
Assumed Unit wt of foundation soil
Assumed internal friction angle of natural foundation soil.
Calculate Cohesion Term Ncm
Granular foundation soil.
Calculate Surcharge (Embedment) Term, Nqm
Depth of Footing
- Per HITEC, the vertical reaction will be supported on the horizontal portion of the anchor plus the footing.
Table 10.6.3.1.2a-1
Table 10.6.3.1.2a-3
Conservative estimate based on Table 10.6.3.1.2a-4
Per commentary on pg 10-63 regarding footings with modest embedment.
Eq 10.6.3.1.2a-3
Calculate Surcharge (Embedment) Term, Nγ
m
Table 10.6.3.1.2a-1
Table 10.6.3.1.2a-3
Per commentary on pg 10-63 regarding footings with modest embedment.
Eq 10.6.3.1.2a-4
Calculate Nominal Bearing Resistance
Table 10.6.3.1.2a-2, conservatively assuming a depth of water at 0.0 ft
Table 10.6.3.1.2a-2, conservatively assuming a depth of water at 0.0 ft
Eq. (10.6.3.1.2a-1)
Table 10.5.5.2.2-1
Eq. 10.6.3.1.1-1, compared to factored bearing resistance given in contract
Check Pullout Capacity of Bolts at Connection Plates and Plate Bending
Connection plates connected to the culvert wall provide stability for half the distance of the wall from the culvert to Anchor 1.
Number of plates
Overall height of wall at plates
The plate closest to the ground.
Height is from bottom of wall to bolt line in Plate 1
If n_plates is 2, this is the top plate.
Height is from bottom of wall to bolt line in Plate 2
If n_plate is 3, this is the top plate.
Height is from bottom of wall to bolt line in Plate 3
Plate height.
Plate thickness
Distance from corner of plate to CL of bolt
Yield strength of plates (A36 steel)
AISC F1.(1)
Diameter of Coil Insert.
Number of bolts per side per plate
Tensile Strength of a A307 bolt (AASHTO 6.4.3.1)
Resistance factor for an A307 bolt in tension (AASHTO 6.5.4.2)
Factored Pullout capacity (SF = 3) of a Meadow Burke Double Wingwall Anchor (1-8NC 6x8) Ferrule Insert with 1" diameter bolt. 8500lbs tension, 4500lbs shear
Calculate Bolt Reaction at Plate 3
Calculate Bolt Reaction at Plate 2
Calculate Bolt Reaction at Plate 1
Check Bolt Capacity
Nominal Tensile Resistance of a bolt (AASHTO 6.13.2.10)
Controlling tensile capacity, per bolt.
Check Plate Bending
Sum moments about the corner of the plate.
External Stability Analysis at Anchor 1
Calculate Vertical Loads and Associated Lever Arms
(See Anchor Geometry Drawing)
Used in bearing calcs only
Note: This moment arm is measured from the front toe of the ftg since it is only used in bearing calculations.
Calculate Lateral Loads and Associated Lever Arms
(Assumed for ease of calculation)
Check Sliding
Per AASHTO 11.11.4.2, Sliding shall be evaluated according to 10.6.3.4.
Resisting Forces
AASHTO Table 10.5.5.2.2-1, "Precast on Sand" or "Soil on Soil"
AASHTO 10.6.3.4
Driving Forces
Check Overturning and Eccentricity
Per AASHTO 11.11.4.4, Overturning shall be evaluated according to 11.6.3.3.
Resisting Forces
Driving Forces
Case 1:
(Distance to resultant from face of wall)
(Within Middle Half per AASHTO 11.6.3.3)
Case 2:
(Distance to resultant
from face of ftg)
(Within Middle Half of ftg per AASHTO 11.6.3.3)
Check Bearing Pressure
Per 11.11.4.3 Evaluate bearing pressure with respect to resistance calculated in 10.6.3.
(Distance to resultant
from face of ftg)
Eq. 11.6.3.2-1, Rectangular Distibution for
Foundations on soil
External Stability Analysis at Anchor 2
Calculate Vertical Loads and Associated Lever Arms
(See Anchor Geometry Drawing)
Used in bearing calcs only
Note: This moment arm is measured from the front toe of the ftg since it is only used in bearing calculations.
Calculate Lateral Loads and Associated Lever Arms
(Assumed for ease of calculation)
Check Sliding
Per AASHTO 11.11.4.2, Sliding shall be evaluated according to 10.6.3.4.
Resisting Forces
AASHTO Table 10.5.5.2.2-1, "Precast on Sand" or "Soil on Soil"
AASHTO 10.6.3.4
Driving Forces
Check Overturning and Eccentricity
Per AASHTO 11.11.4.4, Overturning shall be evaluated according to 11.6.3.3.
Resisting Forces
Driving Forces
Case 1:
(Distance to resultant from face of wall)
(Within Middle Half per AASHTO 11.6.3.3)
Case 2:
(Distance to resultant
from face of ftg)
(Within Middle Half of ftg per
AASHTO 11.6.3.3)
Check Bearing Pressure
Per 11.11.4.3 Evaluate bearing pressure with respect to resistance calculated in 10.6.3.
(Distance to resultant
from face of ftg)
Eq. 11.6.3.2-1, Rectangular Distibution for
Foundations on soil
External Stability Analysis at Anchor 3
Calculate Vertical Loads and Associated Lever Arms
(See Anchor Geometry Drawing)
Used in bearing calcs only
Note: This moment arm is measured from the front toe of the ftg since it is only used in bearing calculations.
Calculate Lateral Loads and Associated Lever Arms
(Assumed for ease of calculation)
Check Sliding
Per AASHTO 11.11.4.2, Sliding shall be evaluated according to 10.6.3.4.
Resisting Forces
AASHTO Table 10.5.5.2.2-1, "Precast on Sand" or "Soil on Soil"
AASHTO 10.6.3.4
Driving Forces
Check Overturning and Eccentricity
Per AASHTO 11.11.4.4, Overturning shall be evaluated according to 11.6.3.3.
Resisting Forces
Driving Forces
Case 1:
(Distance to resultant from face of wall)
(Within Middle Half per AASHTO 11.6.3.3)
Case 2:
(Distance to resultant
from face of ftg)
(Within Middle Half of ftg per
AASHTO 11.6.3.3)
Check Bearing Pressure
Per 11.11.4.3 Evaluate bearing pressure with respect to resistance calculated in 10.6.3.
(Distance to resultant
from face of ftg)
Eq. 11.6.3.2-1, Rectangular Distibution for
Foundations on soil
Check Wall Reinforcement
Assume the wall stem is cantilevered above the anchor.
Calculate Horizontal Loads and resp. Lever Arms at top of Anchor
Check Moment Capacity
Per AASHTO 5.5.4.2.1
Per AASHTO 5.5.4.2.1
Verify that
Simplified equation 5.7.3.1.2-4
This is less than 0.60 therefore
Check Minimum Flexural Reinforcement (5.7.3.3.2)
AASHTO 5.4.2.6
Distance from centroid to extreme tension fibers.
0.67 = Factor for Grade 60 ASTM A615 rebar
1.2 = Factor for precast segmental structures
Simplified AASHTO Eq 5.7.3.3.2-1
Shear Resistance at Bottom of Wall (Section 5.8.3.4.2)
The section contains less than the minimum transverse reinforcement specified in 5.8.2.5, therefore use equation 5.8.3.4.2-2 to determine the longitudinal strain effect factor (β) at the location of maximum shear.
In the eqtn below Mu shall not be less than
(5.8.3.4.2-4)
(5.8.3.4.2-5)
(5.8.3.4.2-2)
(5.8.3.4.2-3)
(5.8.3.3)
Check Crack Control in Section 5.7.3.4
Stress in reinforcement calculated per MacGregor "Reinforced Concrete Mechanics and Design" 4th Ed
Stress in Reinforcement at Service Limit State
exposure factor
Check Minimum Bar Spacing in Section 5.10.3.1.2:
Check Maximum Bar Spacing in Section 5.10.3.2:
Check Anchor Attachment to Wall
Check Moment Capacity of Connection Bars
Conservatively assume the entire wall is cantilevered about the footing, therefore consider only driving moments.
size of bar
Number of bars in tension
thickness of anchor stem
height of anchor stem
distance from centroid of tension reinforcement extreme compression fiber.
Verify that
Simplified equation 5.7.3.1.2-4
This is less than 0.60 therefore
Check Minimum Flexural Reinforcement (5.7.3.3.2)
AASHTO 5.4.2.6
Distance from centroid to extreme tension fibers.
0.67 = Factor for Grade 60 ASTM A615 rebar
1.2 = Factor for precast segmental structures
Simplified AASHTO Eq 5.7.3.3.2-1
Check Minimum Steel for Temperature and Shrinkage (11.6.1.5.1 & 5.10.8)
Account for extra two bars in compression face
Check Hook Development of Connection Steel in Wall
Per 5.10.2, A standard hook with a 180 degree bend shall have a 4*db extension, but not less than 2.5 inches.
Basic development length for a Grade 60 bar with a standard hook (AASHTO 5.11.2.4.1)
Modification Factors to be applied to the Basic Development Length (AASHTO 5.11.2.4.2)
Increase by fy/60 for yield strength greater than 60ksi
0.7 if side cover normal to plane of hook is at least 2.5 inches AND Cover beyond hook is at least 2.0in
0.8 if hook is enclose in with ties or stirrups as specified in 5.11.2.4.2
Conservatively assume entire area of steel provided is required.
1.3 if lightweight concrete is used.
1.2 if epoxy rebar is used.