Project Term Shear Slide
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ACI & AASHTO
ACI and AASHTO have different approaches (and
notation) for the design for shear
ACI uses an empirical, and simple, approach based on a
45 degree angle truss model. Factor = 0.75.
AASHTO follows the latest developments and uses an
approach based on strain compatibility and equilibrium
(modified compression field theory). The critical diagonal
crack does not have to be at 45 degrees.
Factor =
0.90.
In our term project we will use a simplified version of
AASHTO and will set the angle of the diagonal crack at
45 degrees
Term Project Shear Slide
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Effective Girder (Beam) Dimensions
For shear design, effective dimensions are used to
explicitly account for shear flow through a section.
LRFD 5.8.2.9
The effective shear depth, dv, is the distance between
the resultant compressive and tension forces.
However, dv needs not be taken less than the greater of:
90% of the distance from the extreme compression
fiber to the center of action of the reinforcing steel
(jd=0.9d)
72% of the total section height
In your project make dv = min(0.9d+, 0.9d-)
The effective web width, bv, is the minimum web width
anywhere across the section
Term Project Shear Slide
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AASHTO: Shear Design Approach
Variable angle truss mechanism
Vn = Vc + Vs
Vc = 0.083 fc' bw d (normal weight concrete) and Vs = Av fyt
jd
up to a point
s tan ( )
Coefficient and angle are determined u sing strain compatibility and
equilibrium (outside the scope of 151A)
For simplicity we will make = 45o and = 2
= 0.9
C
s
A v fy
jd
T
jd /tan()
Term Project Shear Slide
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Shear Force Limit (Diagonal Compression Failure)
ACI-318 11.4.7.9: Maximum shear resiste d in a section:
Vn = 0.25 fc' bv dv
Term Project Shear Slide
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Design Cases
Vu Vn Factored demand Factored capacity
Any design will fall within the following 5 possible cases:
Vu
1
2
3
4
v. high low
low
moderate
high
5
v. (diagonal compression failure)
Vu >0.25fc bvdv shear cannot be resisted
Increase fc, bv and/or dv
0.25fc bvdv Vu > 0.125fc bvdv - Shear reinforcement as per truss mechanism
Reduced stirrup spacing: s min(0.4dv, 300 mm)
0.125fc bvdv Vu > Vc - Shear reinforcement as per truss mechanism
Stirrup spacing: s min(0.8dv, 600 mm)
Vc Vu > Vc/2 - provide minimum shear reinforcement
Stirrup spacing: s min(d/2, 600 mm)
Vu Vc/2 - shear reinforcement is not needed
Term Project Shear Slide
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Design Cases
Case 1
Vu
very low shear force demand:
Vc
shear reinforcement is not needed
2
Design case typically found in solid
slabs and in column footings:
Term Project Shear Slide
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Design Cases
Case 2
low shear force demand:
Vc Vu >
Vc
provide minimum shear reinforcement
2
A v,min = 0.083
fc'
fyt
bv s
s min ( 0.8dv , 600mm )
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Design Cases
Case 3
moderate shear force demand:
0125 fc' bv dv Vu > Vc shear reinforcement as per truss mechanism.
.
Vu ( Vc + Vs )
Vu
d
Vc but for =45o Vs = Av fyt
s
V
s 1
Av u Vc
dv fyt
Vs
s min ( 0.8dv , 600mm )
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Design Cases
Case 4
high shear force demand:
0.25 fc' bv dv Vu > 0125 fc' bv dv shear reinforcement as per trus s mechanism.
.
Vu ( Vc + Vs )
Vu
d
Vc but for =45o Vs = Av fyt
s
V
s 1
Av u Vc
dv fyt
Vs
s min( 0.4dv , 300mm )
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Girder Flange Under Transverse Shear
(Section 5b)
A significant portion of the shear force is from the
concrete flange dead load. Assume conservatively,
the critical value for Vu is at the face of the girder
Vu
Vu
Most likely Vu will check Case
for shear reinforcement)
1
ok (i.e. no need
Shear Force Envelope (absolute value)
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