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Design of Cantilevered Design of Cantilevered Retaining WallsRetaining Walls
CE A433 – RC DesignCE A433 – RC Design
T. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.
Spring 2009Spring 2009
IntroductionIntroduction
A cantilever retaining wall is a A cantilever retaining wall is a system of cantilever slabs (i.e. system of cantilever slabs (i.e. beams) that retain soil.beams) that retain soil.
The key is to draw the appropriate The key is to draw the appropriate FBDs so that you can determine the FBDs so that you can determine the internal forces.internal forces.
Cantilever Retaining WallCantilever Retaining Wall
Shear Key
Toe
Stem
Heel
Forces ACTING ON the WallForces ACTING ON the Wall
Wall
FootingShear Key
Soil on Toe
Soil on Heel
Active Lateral Soil Pressure
ReactionsReactions
Passive Lateral Soil Pressure
Vertical Reaction
Friction
ACTUAL FRICTION is not the same as
FRICTION CAPACITY!
Computing Soil Bearing Computing Soil Bearing StressStress
Resolve applied Resolve applied forces into a forces into a concentric vertical concentric vertical force and moment on force and moment on the contact area.the contact area.
IIxx = bL = bL33/12/12 A = bLA = bL c = L/2c = L/2 maxmax = P/A + Mc/I = P/A + Mc/Ixx
minmin = P/A – Mc/I = P/A – Mc/Ixx
P
M
SlidingSliding
Driving Force
Resisting Capacity
Vslide = Driving Force = Demand
Vresist = sum(Resisting Forces) = Capacity
FS = Vresist / Vslide
Design for FS > 1.5
Friction CAPACITY = NNot Actual Friction Reaction
OverturningOverturning
Driving Force
Point of Rotation
Resisting Forces
MOT = Driving Force*arm = Demand
MROT = sum(Resisting Moments) = Capacity
FS = MROT / MOT
Design for FS > 2.0
Draw FBDsDraw FBDs
Stem
ToeHeel
Stem DiagramsStem DiagramsFBD
Shear Moment
Dem
an
d
Cap
acity
Dem
an
d
Cap
acity
Make stem thick
enough for
shear
Select Steel to provide flexural capacity
Add T&S Steel
ToeToe
Shear
Moment
Design Shear
Design Moment
Vu can be calculated a distance ‘d’ from face of wall since there is a compressive reaction with the wall.
Mu is computed at the face of the wall.
Flexural Steel extends a
development length into
the heel and should
develop within the
length of the toe.
Add T&S Steel
HeelHeel
Shear
Moment
Design Shear
Design Moment
Vu must be calculated at the face of wall since there is a tensile reaction with the wall.
Mu is computed at the face of the wall.
Flexural Steel extends a
development length into the toe and
should develop
within the length of the
heel.
Add T&S Steel
The Design ProcessThe Design Process Select the overall dimensions (height, embedment, Select the overall dimensions (height, embedment,
footing length and position, and estimated footing & footing length and position, and estimated footing & wall thicknesses) based on stability (sliding and wall thicknesses) based on stability (sliding and overturning) and soil strength (max/min bearing overturning) and soil strength (max/min bearing pressures) using service level loads.pressures) using service level loads.
Check slab (wall and footing) thicknesses using shear Check slab (wall and footing) thicknesses using shear criteria and factored loads. Adjust thicknesses as criteria and factored loads. Adjust thicknesses as necessary, rechecking stability and soil strength of the necessary, rechecking stability and soil strength of the values change.values change.
Select the flexural steel for the three cantilever slab Select the flexural steel for the three cantilever slab elements using factored loads.elements using factored loads.
Select the temperature and shrinkage steel for wall Select the temperature and shrinkage steel for wall and footing.and footing.
Draw the resulting wall cross section (to scale!)Draw the resulting wall cross section (to scale!)