Comparison of BRASS and AASHTO Standard Specifications in Bridge Engineering

 
Differences Between
BRASS and AASHTO
Standard Spec Engines
 
Virtis Opis BRIDGEWare
Users Group Meeting 2011
Helena, Montana
 
 
Standard Spec refers to ASD and LFD
found in the AASHTO Standard
Specifications
AASHTO Std Engine Version 6.3 and
BRASS-GIRDER Version 6.0.3 are
compared
 
General Features
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
According to Article
3.8.2.2 for the loaded
length L.  Uses the span
length of the point of
interest.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
For moment, L = average span
length of the spans on which the
vehicle is located.
For shear, L = loaded portion of
the span.  For a given node, two
lengths are considered, L1 and
L2. Initially, L1 = span length and
L2 = zero.  If the front or rear axle
is on the span and left of the node
point, L1 = distance from the left
support to the node point.  If the
front or rear axle is on the span
and right of the node point, L2 =
distance from the node point to
the right support.  Then, L = max
of L1 and L2.
 
I
m
p
a
c
t
 
F
a
c
t
o
r
 
C
a
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a
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o
n
 
General Features
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses the corresponding
distribution factors for
shear and moment.  If the
shear factor is not
entered, the moment
factor will be used for
shear effects.
Computed if not entered.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Uses the moment
distribution factor for both
moment and shear
effects.
 
L
i
v
e
 
L
o
a
d
 
D
i
s
t
r
i
b
u
t
i
o
n
 
F
a
c
t
o
r
s
 
General Features
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Applies the transverse
live load at the stringer
locations
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Applies transverse live
load directly to the floor
beam as though the
stringers do not exist
 
T
r
a
n
s
v
e
r
s
e
 
L
i
v
e
 
L
o
a
d
 
A
p
p
l
i
c
a
t
i
o
n
 
t
o
 
F
l
o
o
r
b
e
a
m
s
 
General Features
 
AASHTO and BRASS may result in different critical
vehicle positions.  The relative difference in live load
actions is usually within 5%.
 
A
l
g
o
r
i
t
h
m
 
t
o
 
L
o
c
a
t
e
 
t
h
e
 
C
r
i
t
i
c
a
l
 
V
e
h
i
c
l
e
 
P
o
s
i
t
i
o
n
s
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Loads influence lines by
positioning the vehicle
over the peaks.  Applies
each axle and the CG of
the vehicle to the peak.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Marches the vehicle
across the influence line
based on a wheel
advancement
denominator input by the
user.
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Composite sections are
determined based on the
entered shear connector
ranges.  Where shear
connectors are present,
the beam plus slab
properties are considered
in the FE model.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Uses positive flexure
properties (beam + slab)
in positive moment
regions and negative
flexure properties (beam
+ rebar) in negative
moment regions.  These
regions are entered by
the user in the BRASS
LFD/ASD Engine
Properties window.
 
M
e
m
b
e
r
 
S
t
i
f
f
n
e
s
s
 
U
s
e
d
 
i
n
 
S
t
r
u
c
t
u
r
a
l
 
A
n
a
l
y
s
i
s
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented
 
A
r
t
i
c
l
e
 
1
0
.
4
8
.
3
 
T
r
a
n
s
i
t
i
o
n
s
T
h
e
 
m
a
x
i
m
u
m
 
s
t
r
e
n
g
t
h
 
o
f
 
s
e
c
t
i
o
n
s
 
w
i
t
h
 
g
e
o
m
e
t
r
i
c
 
p
r
o
p
e
r
t
i
e
s
f
a
l
l
i
n
g
 
b
e
t
w
e
e
n
 
t
h
e
 
l
i
m
i
t
s
 
o
f
 
A
r
t
i
c
l
e
s
 
1
0
.
4
8
.
1
 
a
n
d
 
1
0
.
4
8
.
2
 
m
a
y
 
b
e
c
o
m
p
u
t
e
d
 
b
y
 
s
t
r
a
i
g
h
t
-
l
i
n
e
 
i
n
t
e
r
p
o
l
a
t
i
o
n
,
 
e
x
c
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p
t
 
t
h
a
t
 
t
h
e
 
w
e
b
t
h
i
c
k
n
e
s
s
 
m
u
s
t
 
a
l
w
a
y
s
 
s
a
t
i
s
f
y
 
A
r
t
i
c
l
e
 
1
0
.
4
8
.
1
.
1
(
b
)
.
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses 0.95 factor
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Uses 0.80 factor for
composite sections in
negative moment regions.
 
A
r
t
i
c
l
e
 
1
0
.
5
7
.
2
 
C
o
m
p
o
s
i
t
e
 
S
e
c
t
i
o
n
s
A
t
 
c
o
m
p
o
s
i
t
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s
e
c
t
i
o
n
s
,
 
t
h
e
 
m
a
x
i
m
u
m
 
o
v
e
r
l
o
a
d
 
f
l
a
n
g
e
 
s
t
r
e
s
s
 
s
h
a
l
l
n
o
t
 
e
x
c
e
e
d
 
0
.
9
5
F
y
.
 
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented
 
A
r
t
i
c
l
e
 
1
0
.
5
7
 
O
V
E
R
L
O
A
D
 
W
e
b
 
b
e
n
d
-
b
u
c
k
l
i
n
g
 
s
h
a
l
l
 
b
e
 
c
h
e
c
k
e
d
 
f
o
r
 
t
h
e
 
o
v
e
r
l
o
a
d
 
a
c
c
o
r
d
i
n
g
t
o
 
E
q
u
a
t
i
o
n
 
(
1
0
-
1
7
3
)
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented.  Plastic
moment capacity is
computed if the section
meets the Spec
requirements to be
considered compact.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented.  Uses its
Member Alternative engine
properties to indicate the adjacent
support POI are compact.  If these
POI are compact, plastic analysis
is allowed if the section meets the
spec requirements.  If not, plastic
analysis is not allowed.  This
engine setting is done on a span
basis, so one span could be
analyzed plastic while another one
wouldn’t be.
 
A
l
l
o
w
 
 
P
l
a
s
t
i
c
 
A
n
a
l
y
s
i
s
 
C
o
n
t
r
o
l
 
O
p
t
i
o
n
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses plate depth entered
by user
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Computes web depth as
back-back angle depth
minus the flange
thicknesses
 
B
u
i
l
t
-
u
p
 
S
e
c
t
i
o
n
 
W
e
b
 
D
e
p
t
h
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Not implemented
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Implemented
 
R
a
t
e
 
B
e
a
r
i
n
g
 
S
t
i
f
f
e
n
e
r
s
 
C
o
n
t
r
o
l
 
O
p
t
i
o
n
 
Steel Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Considers holes in
tension flanges when
computing the allowable
stress as per MBE Tables
6B.6.2.1.1 and
6B.6.2.1.2.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Does not consider holes
in the beam.
 
A
S
D
 
 
C
o
n
s
i
d
e
r
 
h
o
l
e
s
 
i
n
 
t
e
n
s
i
o
n
 
f
l
a
n
g
e
s
w
h
e
n
 
c
o
m
p
u
t
i
n
g
 
a
l
l
o
w
a
b
l
e
 
t
e
n
s
i
o
n
 
s
t
r
e
s
s
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented
 
P
r
e
s
t
r
e
s
s
i
n
g
 
S
t
e
e
l
 
T
e
n
s
i
o
n
 
R
a
t
i
n
g
 
F
a
c
t
o
r
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
No limit on Mcr/Mmax
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Controlled by engine
data:
No limit on Mcr/Mmax
Limit Mcr/Mmax to 1.0
 
A
r
t
i
c
l
e
 
9
.
2
0
.
2
.
2
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Varies linearly from zero
to a force corresponding
to stress fse at the
transfer length and to a
force corresponding to
stress f
*
su at the
development length and
beyond
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Constant
 
P
r
e
s
t
r
e
s
s
i
n
g
 
F
o
r
c
e
 
A
l
o
n
g
 
t
h
e
 
L
e
n
g
t
h
 
o
f
 
B
e
a
m
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented. Sections
located within h/2 from
face of support are
evaluated for shear acting
at the h/2 location.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented
 
A
r
t
i
c
l
e
 
9
.
2
0
.
1
.
4
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented. Controlled
by a control option on the
Member Alternative
window.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Not implemented
 
M
B
E
 
6
B
.
5
.
3
.
3
 
P
r
e
s
t
r
e
s
s
e
d
 
C
o
n
c
r
e
t
e
U
s
e
 
f
l
e
x
u
r
a
l
 
s
t
r
e
n
g
t
h
 
r
e
d
u
c
t
i
o
n
 
f
a
c
t
o
r
 
k
 
w
h
e
n
 
Φ
M
n
 
i
s
 
l
e
s
s
 
t
h
a
n
1
.
2
M
c
r
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses simple span bearing span
lengths for DL1 analysis and
centerline of support span lengths
for DL2 and LL analyses.
Analysis points considered for
DL1 analysis correspond to tenth
points of the continuous span
lengths used for DL2 and LL
analyses.  Analysis points for
which the results are reported
correspond to tenth points of the
continuous span lengths.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Uses the same support positions,
simple span bearing span lengths
or centerline of support span
lengths, for all stages.  Non-
composite stage is considered as
simple spans and composite stage
as continuous spans.
 
S
u
p
p
o
r
t
 
P
o
s
i
t
i
o
n
s
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Tenth points and user-
defined points of interest.
Section change points
selection will cause
ratings to be computed at
the h/2 distance from
support, drape points,
etc.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Tenth points and user-
defined points of interest
only
 
A
n
a
l
y
s
i
s
 
P
o
i
n
t
s
 
o
f
 
I
n
t
e
r
e
s
t
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses the values entered
on the Stress Limits Sets
window.  If the values are
not entered, computes
the allowables as per the
Std Specifications.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Does not use the values
entered on the Stress
Limits Sets window.
Computes the allowables
as per the Std
Specifications.
 
L
o
a
d
 
F
a
c
t
o
r
C
o
n
c
r
e
t
e
 
S
t
r
e
s
s
 
L
i
m
i
t
s
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Uses the LFD Final allowable
tension in the Stress Limit Sets
window.  If this value is not
entered, uses the INVY ASD
Factors P/S Concrete Tens. in
the Member Alternative
window. If INV ASD factor is
not entered, the allowable is
computed as per the Std Spec.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Uses the INVY ASD Factors
P/S Concrete Tens. in the
Member Alternative window. If
INV ASD factor is not entered,
the allowable is computed as
per the Std Spec.
 
F
i
n
a
l
 
A
l
l
o
w
a
b
l
e
T
e
n
s
i
l
e
 
S
t
r
e
s
s
 
Prestressed Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Considers regions of the deck to
be composite if the effective slab
thickness and width are entered
on the Deck Profile window and
one of the following are entered
on the PS Shear Reinforcement
Ranges window:
Vertical reinforcement extends into
deck
"Composite" horizontal reinforcement
range entered
Horizontal shear reinforcement range
entered
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Considers the total length of deck
to be composite if the effective
slab thickness and width are
entered on the Deck Profile
window.
 
C
o
m
p
o
s
i
t
e
 
S
l
a
b
 
D
e
s
i
g
n
a
t
i
o
n
 
Reinforced Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Advanced AASHTO Eq. 8-48
 
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Simplified AASHTO Eq. 8-49
 
L
F
D
 
S
h
e
a
r
 
C
a
p
a
c
i
t
y
 
Reinforced Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Advanced AASHTO Eq. 8-4
 
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Simplified AASHTO equation in
Article 8.15.5.2.1
 
A
S
D
 
S
h
e
a
r
 
C
a
p
a
c
i
t
y
 
Reinforced Concrete Girders
 
A
A
S
H
T
O
 
S
t
d
 
E
n
g
i
n
e
 
Implemented. Sections
located within d from face
of support are evaluated
for shear acting at the d
location.
 
B
R
A
S
S
-
G
I
R
D
E
R
 
Only the support
locations are evaluated
for shear acting at the d
location.
 
A
r
t
i
c
l
e
 
8
.
1
6
.
6
.
1
.
2
 
 
 
Thank you
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Explore the key differences between the BRASS-GIRDER and AASHTO Standard Specification engines in bridge design calculations. Topics covered include load factor calculations, live load distribution factors, transverse live load application, critical vehicle positions, and member stiffness considerations for steel girders. Get insights into how these engines handle various aspects of structural analysis in bridge design.

  • Bridge Engineering
  • BRASS
  • AASHTO
  • Specifications
  • Structural Analysis

Uploaded on Aug 28, 2024 | 1 Views


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  1. Differences Between BRASS and AASHTO Standard Spec Engines Virtis Opis BRIDGEWare Users Group Meeting 2011 Helena, Montana 1

  2. Standard Spec refers to ASD and LFD found in the AASHTO Standard Specifications AASHTO Std Engine Version 6.3 and BRASS-GIRDER Version 6.0.3 are compared 2

  3. General Features Impact Factor Calculation BRASS-GIRDER For moment, L = average span length of the spans on which the vehicle is located. For shear, L = loaded portion of the span. For a given node, two lengths are considered, L1 and L2. Initially, L1 = span length and L2 = zero. If the front or rear axle is on the span and left of the node point, L1 = distance from the left support to the node point. If the front or rear axle is on the span and right of the node point, L2 = distance from the node point to the right support. Then, L = max of L1 and L2. AASHTO Std Engine According to Article 3.8.2.2 for the loaded length L. Uses the span length of the point of interest. 3

  4. General Features Live Load Distribution Factors AASHTO Std Engine Uses the corresponding distribution factors for shear and moment. If the shear factor is not entered, the moment factor will be used for shear effects. Computed if not entered. BRASS-GIRDER Uses the moment distribution factor for both moment and shear effects. 4

  5. General Features Transverse Live Load Application to Floorbeams AASHTO Std Engine Applies the transverse live load at the stringer locations BRASS-GIRDER Applies transverse live load directly to the floor beam as though the stringers do not exist 5

  6. General Features Algorithm to Locate the Critical Vehicle Positions AASHTO and BRASS may result in different critical vehicle positions. The relative difference in live load actions is usually within 5%. AASHTO Std Engine Loads influence lines by positioning the vehicle over the peaks. Applies each axle and the CG of the vehicle to the peak. BRASS-GIRDER Marches the vehicle across the influence line based on a wheel advancement denominator input by the user. 6

  7. Steel Girders Member Stiffness Used in Structural Analysis AASHTO Std Engine Composite sections are determined based on the entered shear connector ranges. Where shear connectors are present, the beam plus slab properties are considered in the FE model. BRASS-GIRDER Uses positive flexure properties (beam + slab) in positive moment regions and negative flexure properties (beam + rebar) in negative moment regions. These regions are entered by the user in the BRASS LFD/ASD Engine Properties window. 7

  8. Steel Girders Article 10.48.3 Transitions The maximum strength of sections with geometric properties falling between the limits of Articles 10.48.1 and 10.48.2 may be computed by straight-line interpolation, except that the web thickness must always satisfy Article 10.48.1.1(b). AASHTO Std Engine Implemented BRASS-GIRDER Not implemented 8

  9. Steel Girders Article 10.57.2 Composite Sections At composite sections, the maximum overload flange stress shall not exceed 0.95Fy. AASHTO Std Engine Uses 0.95 factor BRASS-GIRDER Uses 0.80 factor for composite sections in negative moment regions. 9

  10. Steel Girders Article 10.57 OVERLOAD Web bend-buckling shall be checked for the overload according to Equation (10-173) AASHTO Std Engine Implemented BRASS-GIRDER Not implemented 10

  11. Steel Girders Allow Plastic Analysis Control Option AASHTO Std Engine Implemented. Plastic moment capacity is computed if the section meets the Spec requirements to be considered compact. BRASS-GIRDER Not implemented. Uses its Member Alternative engine properties to indicate the adjacent support POI are compact. If these POI are compact, plastic analysis is allowed if the section meets the spec requirements. If not, plastic analysis is not allowed. This engine setting is done on a span basis, so one span could be analyzed plastic while another one wouldn t be. 11

  12. Steel Girders Built-up Section Web Depth AASHTO Std Engine Uses plate depth entered by user BRASS-GIRDER Computes web depth as back-back angle depth minus the flange thicknesses 12

  13. Steel Girders Rate Bearing Stiffeners Control Option AASHTO Std Engine Not implemented BRASS-GIRDER Implemented 13

  14. Steel Girders ASD Consider holes in tension flanges when computing allowable tension stress AASHTO Std Engine Considers holes in tension flanges when computing the allowable stress as per MBE Tables 6B.6.2.1.1 and 6B.6.2.1.2. BRASS-GIRDER Does not consider holes in the beam. 14

  15. Prestressed Concrete Girders Prestressing Steel Tension Rating Factor AASHTO Std Engine Implemented BRASS-GIRDER Not implemented 15

  16. Prestressed Concrete Girders Article 9.20.2.2 AASHTO Std Engine No limit on Mcr/Mmax BRASS-GIRDER Controlled by engine data: No limit on Mcr/Mmax Limit Mcr/Mmax to 1.0 16

  17. Prestressed Concrete Girders Prestressing Force Along the Length of Beam AASHTO Std Engine Varies linearly from zero to a force corresponding to stress fse at the transfer length and to a force corresponding to stress f*su at the development length and beyond BRASS-GIRDER Constant 17

  18. Prestressed Concrete Girders Article 9.20.1.4 AASHTO Std Engine Implemented. Sections located within h/2 from face of support are evaluated for shear acting at the h/2 location. BRASS-GIRDER Not implemented 18

  19. Prestressed Concrete Girders MBE 6B.5.3.3 Prestressed Concrete Use flexural strength reduction factor k when Mn is less than 1.2Mcr AASHTO Std Engine Implemented. Controlled by a control option on the Member Alternative window. BRASS-GIRDER Not implemented 19

  20. Prestressed Concrete Girders Support Positions AASHTO Std Engine Uses simple span bearing span lengths for DL1 analysis and centerline of support span lengths for DL2 and LL analyses. Analysis points considered for DL1 analysis correspond to tenth points of the continuous span lengths used for DL2 and LL analyses. Analysis points for which the results are reported correspond to tenth points of the continuous span lengths. BRASS-GIRDER Uses the same support positions, simple span bearing span lengths or centerline of support span lengths, for all stages. Non- composite stage is considered as simple spans and composite stage as continuous spans. 20

  21. Prestressed Concrete Girders Analysis Points of Interest AASHTO Std Engine Tenth points and user- defined points of interest. Section change points selection will cause ratings to be computed at the h/2 distance from support, drape points, etc. BRASS-GIRDER Tenth points and user- defined points of interest only 21

  22. Prestressed Concrete Girders Load Factor Concrete Stress Limits AASHTO Std Engine Uses the values entered on the Stress Limits Sets window. If the values are not entered, computes the allowables as per the Std Specifications. BRASS-GIRDER Does not use the values entered on the Stress Limits Sets window. Computes the allowables as per the Std Specifications. 22

  23. Prestressed Concrete Girders Final Allowable Tensile Stress AASHTO Std Engine Uses the LFD Final allowable tension in the Stress Limit Sets window. If this value is not entered, uses the INVY ASD Factors P/S Concrete Tens. in the Member Alternative window. If INV ASD factor is not entered, the allowable is computed as per the Std Spec. BRASS-GIRDER Uses the INVY ASD Factors P/S Concrete Tens. in the Member Alternative window. If INV ASD factor is not entered, the allowable is computed as per the Std Spec. 23

  24. Prestressed Concrete Girders Composite Slab Designation AASHTO Std Engine Considers regions of the deck to be composite if the effective slab thickness and width are entered on the Deck Profile window and one of the following are entered on the PS Shear Reinforcement Ranges window: Vertical reinforcement extends into deck "Composite" horizontal reinforcement range entered Horizontal shear reinforcement range entered BRASS-GIRDER Considers the total length of deck to be composite if the effective slab thickness and width are entered on the Deck Profile window. 24

  25. Reinforced Concrete Girders LFD Shear Capacity AASHTO Std Engine Advanced AASHTO Eq. 8-48 BRASS-GIRDER Simplified AASHTO Eq. 8-49 25

  26. Reinforced Concrete Girders ASD Shear Capacity AASHTO Std Engine Advanced AASHTO Eq. 8-4 BRASS-GIRDER Simplified AASHTO equation in Article 8.15.5.2.1 26

  27. Reinforced Concrete Girders Article 8.16.6.1.2 AASHTO Std Engine Implemented. Sections located within d from face of support are evaluated for shear acting at the d location. BRASS-GIRDER Only the support locations are evaluated for shear acting at the d location. 27

  28. Thank you 28

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