distribution factors box
DESCRIPTION
dist. factorsTRANSCRIPT
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INPUT: Exterior Beam4B20 5B20
1.5 in 1.5 in
4.104 ft 5.104 ft
4 2
not applicable 2.323 ft
0 degrees 0 degrees
5.0 in (if using asphalt type 0)
38.42 ft
Rail Width, RW = 1.0 ft
Roadway Width, W = 24.17 ft
6
2
SECTION PROPERTIES:Interior Exterior
Beam Type 4B20 slab 5B20 slab
43.75 n/a 55.75 n/a
5.5 n/a 5.5 n/a
47.75 n/a 59.75 n/a
5 n/a 5 n/a
5 n/a 5 n/a
47.75 49.25 59.75 58.50
20 5 20 5
Dist from Edge of Beam to Edge of Flange (in) - x 4 n/a 4 n/a
591.8 246.2 717.8 292.5
9.81 22.5 9.88 22.5
28086 513 35233.6 609
Weight (klf) - W 0.616 0.257 0.748 0.305
Notes:
1. For typical cross sections ( f, g (sufficiently connected to act as a unit)). Table 4.6.2.2.1-1
2. If there are mixed beam types in the interior, then this calculation should be completed for each beam type.
3. When the Span Length is greater than 100ft for Beams 4B40 and 5B40, use Beams 4B40+100 and 5B40+100 respectively.
4. Beam spacing is based on the bottom width of the beam plus the joint width.
5. Overhang width is from the center of the beam to the edge of the slab. The default value is based on 1/2 the top width of the beam.
RESULTS: FINAL FINAL LLDF LLDF
0.488 0.671
0.356 0.428
LRFD Live Load Distribution Factors1
Live Load Distribution Factors are calculated according to AASHTO LRFD Bridge Design Specifications, 4th Edition (2007 with no interim revisions) as prescribed by TxDOT policies (LRFD Design Manual July 2008) and practices. The Range of Applicability is ignored.
Interior Beam2
Box Type3
Joint Width, tJoint
Spacing, S4
Number of Beams, Nb
Overhang Width, OH5
Skew, Slab depth, t
s =
CLbrg
to CLbrg
, L =
Total No. of Beams, Nb =
No. of Lanes, NL =
Width of Top Flange (in) - bft
Thickness of Top Flange (in) - tft
Width of Bottom Flange (in) - bfb
Thickness of Bottom Flange (in) - tfb
Design Thickness of Web (in) - tw
Design Beam Width or Effective Slab Width (in) - b6 or EFW6
Beam Height or Slab Height (in) - d or ts
Area (in2) - ADistance to centroid from bottom of beam (in) - y
b
Moment of Inertia (in4) - I
6. The design beam width equals the width of the bottom flange. For box beams topped by a concrete slab, the Effective Flange Width (EFW) is calculated below.
Interior Shear LLDF, gVinterior
Exterior Shear LLDF, gVexterior
Interior Moment LLDF, gMinterior
Exterior Moment LLDF, gMexterior
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CALCULATIONS:
(calculated based on effective flange width)
INTERIOR BEAMS (Int.)Effective Flange Width, EFW (composite section) (AASHTO LRFD Section 4.6.2.6)
49.25 in
13.54 in
Distance from the composite centroid to the slab or box section centroid, d
3.73 in
8.96 in
56,622
EXTERIOR BEAMS (Ext.)
Effective Flange Width, EFW (composite section)
58.50 in
13.53 in
Distance from the composite centroid to the slab or box section centroid, d
3.65 in
8.97 in
Composite Moment of Inertia, Ic
EFWint
= EFWint
=
where tw equals the distance between the outside of the webs
at their tops (AASHTO LRFD Comm. C4.6.2.6.1)
Composite Moment of Inertia, I c
Distance to the composite section centroid, yc
yc = y
c_int =
dbeam
= dbeam_int
=
dslab
= dslab_int
=
Composite Moment of Inertia, Ic
Ic = I
c_int = in4
EFWext
= EFWext
=
where tw equals the distance between the outside of the webs
at their tops (AASHTO LRFD Comm. C4.6.2.6.1)
Composite Moment of Inertia, I c
Distance to the composite section centroid, yc
yc = y
c_ext =
db = d
b_ext =
ds = d
s_ext =
Composite Moment of Inertia, Ic
Abeam ybbeam+A slab ybslab
Abeam+Aslab
yc− yslab
I beam+Abeam (dbeam )2+ I slab+A slab (dslab )
2
Abeam ybbeam+A slab ybslab
Abeam+Aslab
yc− yslab
I beam+Abeam (dbeam )2+ I slab+A slab (dslab )
2
min {L4
12 t s+max[ tw0 .5b ft
]S
}
0 .5EFW int+min {L8
6t s+max [ 0 .5 tw0.25b ft
]OH
}(Calculated based on exterior beam dimesions for the adjacent interior beam.)
yc− ybeam
yc− ybeam
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68,945Ic = I
c_ext = in4I beam+Abeam (dbeam )
2+ I slab+A slab (dslab )
2
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St Venant's Torsional Constant, J (AASHTO LRFD Eq. C4.6.2.2.1-3 (for thin-walled shapes))
Simplified Beam
Depicting s and t of Elements
INTERIOR BEAMS (Int.) EXTERIOR BEAMS (Ext.)
599.44 806.44
17.160 20.702
83,761 125,655
Where, Ao is the area enclosed by the centerlines of the elements that make up the thin-walled structure, s is
the element lengths, and t is the element thicknesses (see diagrams below for a graphical representation of these variables).
For the calculation of J, the shear key is ignored, and the Box Beam cross section is simplifed to an open box with dimensions equaling d (height) and b
fb - 2x (width).
Depicting Ao
Ao_int
= in2 Ao_ext
= in2
Jint
= in4 Jext
= in4
J=4 A
o2
∑st
Ao= (b fb−2x− tw )(d−t fb+t ft−t s
2 )∑
st=
bfb−2x−twt ft+t s
+b fb−2x− tw
t fb+2( d−
t fb+t ft−t s2
tw)
∑st= ∑
st=
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-0.6 ft
Minimum Distribution Factor
m = 1.0
1.0 x 2 lanes ÷ 6 beams = 0.333
Correction for Skew
INTERIOR BEAMS (Int.)
Shear LLDF Correction for Skew (Table 4.6.2.2.3c-1)
Range of Applicability (ROA) Checks 0° ≤ 0° ≤ 60° OK
Check L: 20' ≤ 38.4' ≤ 120' OK 5 ≤ 6 ≤ 20 OK
Check b: 35'' ≤ 47.8'' ≤ 60'' OKCheck d: 17'' ≤ 20'' ≤ 60'' OK
Corr. = = 1.000
Moment LLDF Correction for Skew (Table 4.6.2.2.2e-1)
EXTERIOR BEAMS (Ext.)
Shear LLDF Correction for Skew (Table 4.6.2.2.3c-1)
Range of Applicability (ROA) Checks 0° ≤ 0° ≤ 60° OK
Check L: 20' ≤ 38.4' ≤ 120' OK 5 ≤ 6 ≤ 20 OK
Check b: 35'' ≤ 59.8'' ≤ 60'' OKCheck d: 17'' ≤ 20'' ≤ 60'' OK
Corr. = = 1.000
Moment LLDF Correction for Skew (Table 4.6.2.2.2e-1)
Distance between the Outside Web and the Face of the Curb, de
de = OH - RW-1/2 * b
fb + x + 1/2*t
w =
gmin
= m · NL ÷ N
b =
Check :
Check Nb:
Based on TxDOT's LRFD Bridge Design Manual, "Do not apply the skew correction factor for moment as suggested in Article 4.6.2.2.2e."
Check :
Check Nb:
Based on TxDOT's LRFD Bridge Design Manual, "Do not apply the skew correction factor for moment as suggested in Article 4.6.2.2.2e."
1.0+12 .0 L90d
√ tan θ
1.0+12 .0 L90d
√ tan θ
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Lever Rule - INTERIOR BEAMS (Int.)
4.1 ft
INTERIOR LEVER RULE for Interior Beams
For S < 4:One Lane = = 0.500
> For 4 ≤ S < 6:One Lane = = 0.500
Two Lanes = = 0.513
For 6 ≤ S < 10:One Lane = = 0.269
Two Lanes = = 0.282
INTERIOR
One Lane Loaded = 0.500
Two Lanes Loaded = 0.513
Load Distribution Factors
INTERIOR BEAMS (Int.)
Moment LL Distribution Per Lane (Table 4.6.2.2.2a-1):
Range of Applicability (ROA) Checks
Check b: 35'' ≤ 47.8'' ≤ 60'' OK
Check L: 20' ≤ 38.4' ≤ 120' OK
5 ≤ 6 ≤ 20 OK
Use the Equations from Table 4.6.2.2.2a-1 because all criteria is OK.
One Lane Loaded
Lever Rulemg = 1.2 * 0.500 = 0.600
Equation
= 0.306 where, k = k = 1.747
USE EQUATION
0.306
Two or More Lanes Loaded
Lever Rulemg = 1.0 * 0.513 = 0.513
Equation
= 0.356
USE EQUATION
0.356
>>0.356
SInt
=
Check Nb:
g =
gVint1
=
g =
gMint2+
=
If W ≥ 20 ft, gMinterior
is the maximum of gMint1
, gMint2+
, and gmin
.gM
interior =
k ( b305 )
0 . 6
( b12 .0 L )
0.2
( IJ )
0 .06
1632
1632
1632 (1+
S−4S )
1632 (1+
S−6S )
1632 (1+
S−6S
+S−4S )
k ( b33 .3 L )
0.5
( IJ )
0 .25
2.5 (Nb )−0 .2
≥1 .5
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0.356gMinterior
=If W < 20 ft, gM
interior is the maximum of gM
int1 and g
min.
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Load Distribution Factors
INTERIOR BEAMS (Int.)
Shear LL Distribution Per Lane (Table 4.6.2.2.3a-1):
Range of Applicability (ROA) Checks
Check b: 35'' ≤ 47.8'' ≤ 60'' OK
Check L: 20' ≤ 38.4' ≤ 120' OK
5 ≤ 6 ≤ 20 OK
Check J: 25,000 ≤ 83,761 ≤ 610,000 OK
Check I: 40,000 ≤ 56,622 ≤ 610,000 OK
Use the Equations from Table 4.6.2.2.3a-1 because all criteria is OK.
One Lane Loaded
Lever Rulemg = 1.2 * 0.500 = 0.600
Equation
= 0.488
USE EQUATION
0.488
Modify for Skew:
skew correc. = 1.000
0.488
Two or More Lanes Loaded Equation
Lever Rulemg = 1.0 * 0.513 = 0.513
Equation
= 0.487 where,
USE EQUATION
0.487
Modify for Skew:
skew correc. = 1.000
0.487
>>0.488
Check Nb:
g =
gVint1
=
gVint1
=
g =
gVint2+
=
gVint2+
=
If W ≥ 20 ft, gVinterior
is the maximum of gVint1
, gVint2+
, and gmin
.gV
interior =
If W < 20 ft, gVinterior
is the maximum of gVint1
and gmin
.
( b48 )≥1.0
( b130 L )
0 .15
( IJ )
0.05
( b156 )
0 .4
( b12.0 L )
0.1
( IJ )
0 .05
( b48 )
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Load Distribution Factor Calculations for Exterior Beams
Lever Rule - EXTERIOR BEAMS (Ext.)
5.1 ft OH = 2.3 ft RW = 1.0 ft 4.4 ft
INTERIOR LEVER RULE for Exterior Beams EXTERIOR LEVER RULE for Exterior Beams
For S < 4: > For X < 6:One Lane = = 0.500 One Lane = = 0.434
> For 4 ≤ S < 6: For 6 ≤ X < 12:One Lane = = 0.500 One Lane = = 0.280
Two Lanes = = 0.608
For 6 ≤ S < 10: For 12 ≤ X < 18:One Lane = = 0.412 One Lane = = 0.280
Two Lanes = = 0.520 Two Lanes = = -0.462
INTERIOR EXTERIOR
One Lane Loaded = 0.500 One Lane Loaded = 0.434
Two Lanes Loaded = 0.608 Two Lanes Loaded = 0.434
Note: The exterior Live Load Distribution Factor calculations require the interior Live Load Distribution Factors to be calculated. Since the exterior beam can be of a different width than the interior beam, the Live Load Distribution Factors need to be calculated for an interior beam that has the same width as the exterior beam. The Live Load Distribution Factors for this 'equivilant interior beam' will be used in the calculation of the Live Load Distribution Factors for the exterior beam.
SExt
= X = SExt
+OH-RW-2ft =
1632
1632
1632 (1+
S−4S )
1632 (1+
S−6S )
1632 (1+
S−6S
+S−4S )
1632 ( X
S )
1632 ( X
S+
X−6S )
1632 ( X
S+
X−6S )
S
X
S
X
S
X 126
32
16
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EXTERIOR BEAMS (Ext.)
Moment LL Distribution Per Lane (Table 4.6.2.2.2):
Range of Applicability (ROA) Checks -0.6' ≤ 2' OK
Check b: 35'' ≤ 59.8'' ≤ 60'' OK
Check L: 20' ≤ 38.4' ≤ 120' OK
5 ≤ 6 ≤ 20 OK
Use the Equations from Table 4.6.2.2.3b-1 because all criteria is OK.
One Lane Loaded
Equivalent Interior Beam (Table 4.6.2.2.2b-1):Lever Rule
mg = 1.2 * 0.500 = 0.600
Equation= 0.325 where, k = k = 1.747
USE EQUATION0.325
Exterior Beam (Table 4.6.2.2.2d-1):Lever Rule
mg = 1.2 * 0.434 = 0.521
Equation0.359 where, e = e = 1.105
USE EQUATION0.359
Two or More Lanes Loaded
Equivalent Interior Beam (Table 4.6.2.2.2b-1):Lever Rule
mg = 1.0 * 0.608 = 0.608
Equation= 0.421
USE EQUATION0.421
Exterior Beam (Table 4.6.2.2.2d-1):Lever Rule
mg = 1.0 * 0.434 = 0.434
Equation0.428 where, e = e = 1.016
USE EQUATION0.428
>>
0.428
Check de:
Check Nb:
gint
=
gMint1(ext)
=
g = e * gint
=
gMext1
=
gint
=
gMint2+(ext)
=
g = e * gint
=
gMext2+
=
If W ≥ 20 ft, gMexterior
is the maximum of gMext1
, gMext2+
, gMint1(ext)
,
gMint2+(ext)
, and gmin
.gM
exterior =
If W < 20 ft, gMexterior
is the maximum of gMext1
, gMint1(ext)
, and gmin
.
k ( b33 .3 L )
0.5
( IJ )
0 . 25
k ( b305 )
0 .6
( b12 .0 L )
0.2
( IJ )
0 .06
1.04+de
25≥1.0
1.125+de
30≥1 .0
2.5 (Nb )−0 .2
≥1 .5
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EXTERIOR BEAMS (Ext.)
Shear LL Distribution Per Lane (Table 4.6.2.2.3):
Range of Applicability (ROA) Checks -0.6' ≤ 2' OK
Check b: 35'' ≤ 59.8'' ≤ 60'' OK
Check L: 20' ≤ 38.4' ≤ 120' OK
5 ≤ 6 ≤ 20 OK
Check J: 25,000 ≤ 125,655 ≤ 610,000 OK
Check I: 40,000 ≤ 68,945 ≤ 610,000 OK
Use the Equations from Table 4.6.2.2.3b-1 because all criteria is OK.
One Lane Loaded
Equivalent Interior Beam (Table 4.6.2.2.3a-1):Lever Rule
mg = 1.2 * 0.500 = 0.600
Equation= 0.500
USE EQUATION0.500
Exterior Beam (Table 4.6.2.2.3b-1):Lever Rule
mg = 1.2 * 0.434 = 0.521
Equation0.610 where, e = e = 1.220
USE EQUATION0.610
Modify for Skew:skew correc. = 1.000
0.500
0.610
Two or More Lanes Loaded
Equivalent Interior Beam (Table 4.6.2.2.3a-1):Lever Rule
mg = 1.0 * 0.608 = 0.608
Equation= 0.671 where,
USE EQUATION0.671
Exterior Beam (Table 4.6.2.2.3b-1):Lever Rule
mg = 1.0 * 0.434 = 0.434
Equationg = where, & e = e = 1.244
g = 0.671
USE EQUATION
Check de:
Check Nb:
gint
=
gVint1(ext)
=
g = e * gint
=
gVext1
=
gVint1(ext)
=
gVext1
=
gint
=
gVint2+(ext)
=
48b
≤1 .0
( b130 L )
0 .15
( IJ )
0.05
( b48 )≥1.0
1.25+de
20≥1 .0
e∗g int(48b ) 1+( de+b
12−2
40 )0 .5
≥1.0
( b156 )
0 .4
( b12.0 L )
0.1
( IJ )
0 .05
( b48 )
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0.671gVext2+
=
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EXTERIOR BEAMS (Ext.)
Modify for Skew:
skew correc. = 1.000
0.671
0.671
>>
0.671
Shear LL Distribution Per Lane (Table 4.6.2.2.3): (Continued)
Two or More Lanes Loaded (Continued)
gVint2+(ext)
=
gVext2+
=
If W ≥ 20 ft, gVexterior
is the maximum of gVext1
, gVext2+
, gVint1(ext)
,
gVint2+(ext)
, and gmin
.gV
exterior =
If W < 20 ft, gVexterior
is the maximum of gVext1
, gVint1(ext)
, and gmin
.
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Beam Sectional PropertiesAll of these beams have 3/4" chamfers on the bottom two corners of the beam.
1 2 3 4 5 6 7 8
Beam B (in) C (in) D (in) E (in) F (in) G (in) H (in)
4B20 43.75 2 5 4 4 5 05B20 55.75 2 5 4 4 5 04B28 43.75 3 4 11 5 5 05B28 55.75 3 4 11 5 5 04B34 43.75 3 4 11 5 5 65B34 55.75 3 4 11 5 5 64B40 43.75 3 4 11 5 5 125B40 55.75 3 4 11 5 5 12
4B40+100 43.75 3 4 11 5 5 125B40+100 55.75 3 4 11 5 5 12
UserDefined 43.75 2 5 2 4 5 0
AASHTO LRFD, p4-25, closed thin-walled shapes
Beam x (in) d (in)
4B20 43.75 5.5 47.75 5 5 4 205B20 55.75 5.5 59.75 5 5 4 204B28 43.75 5.5 47.75 5 5 5 285B28 55.75 5.5 59.75 5 5 5 284B34 43.75 5.5 47.75 5 5 5 345B34 55.75 5.5 59.75 5 5 5 344B40 43.75 5.5 47.75 5 5 5 405B40 55.75 5.5 59.75 5 5 5 40
4B40+100 43.75 5.5 47.75 5 5 5 405B40+100 55.75 5.5 59.75 5 5 5 40
UserDefined 43.75 5.5 47.75 5 5 4 181 2 3 4 5 6 7 8
1
Torsion Constant2
bft (in) t
ft (in) b
fb (in) t
fb (in) t
w (in)
TYPICAL SECTION
Multiple Presence Factors
m1 1.22 13 0.854 0.65
NL
9 10 11 12 13 14 15 17
I (in) J(in)
20 47.75 10.19 9.81 591.81 28086 616 40.0020 59.75 10.12 9.88 717.81 35234 748 40.0028 47.75 14.38 13.62 678.81 68745 707 86.0028 59.75 14.26 13.74 804.81 85370 838 86.0034 47.75 17.92 16.08 798.81 115655 832 86.0034 59.75 17.72 16.28 924.81 142161 963 86.0040 47.75 21.31 18.69 918.81 176607 957 86.0040 59.75 21.07 18.93 1044.81 215300 1088 86.0040 47.75 21.63 18.37 943.81 180159 983 86.0040 59.75 21.36 18.64 1069.81 219007 1114 86.00
18 47.75 9.17 8.83 571.81 21032 596 32.00
yt (in) y
b (in) A (in2) I (in4)
Weight (plf)
Shear Key Area (in2)
Values are for half of one shear key,
2 Shear keys are neglected for the calculations of Icomp
and J.
1 Enter Values in Green Shaded Cells.
TYPICAL SECTION
18 19 20 22 23 24 25
Void 1 Void 2
12.39 535.20 15.00 29.75 9.50 282.63 9.75 2125.5812.39 535.20 15.00 41.75 9.50 396.63 9.75 2982.9516.26 2547.36 23.00 27.75 17.50 485.63 13.75 12393.5516.26 2547.36 23.00 39.75 17.50 695.63 13.75 17752.9322.26 2547.36 23.00 27.75 23.50 652.13 16.75 30011.3422.26 2547.36 23.00 39.75 23.50 934.13 16.75 42989.2128.26 2547.36 23.00 27.75 29.50 818.63 19.75 59367.3728.26 2547.36 23.00 39.75 29.50 1172.63 19.75 85039.7428.26 2547.36 23.00 27.75 29.50 793.63 20.16 54918.5028.26 2547.36 23.00 39.75 29.50 1147.63 20.04 80632.46
11.49 329.00 13.00 29.75 7.50 223.13 8.75 1045.90
Shear Key y
b (in)
Shear Key I (in4)
Shear Key H (in)
Void Area (in2)
Void yb
(in)Void I (in4)
Values are for half of one shear key, neglecting the joint.
There are 5" chamfers on the bottom two corners of the void in this beam.There are 5" chamfers on the bottom two corners of the void in this beam.
Revision History:
8/18/2006 Spreadsheet Created
11/1/2007 Updated for AASHTO LRFD 4th Edition 2007 & Bridge Design Manual April 2007.
6/16/2008
g must be ≥ m·NL/Nb
Macro added to reinitialize default values Corrected Shear Key I Added User Defined Beam
8/20/2008 Made consistant with AASHTO LRFD (when Shear is outside ROA, Lever Rule is used)
11/12/2008 Fixed bug in Ext Shear LLDF CalculationsAdded Options to give the user choices on what to do outside the ROA.
Neglect Shear Keys in Ic and J calculations
When W < 20ft, g = g1 Lane Loaded
Show gint
for exterior beams
gext
must be ≥ gint