Distribution Factors Box

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TXDOT County: ANY Highway: Any Design: BRG Date: 2/8/15 2007 LRFD Specs

BRIDGE C-S-J: XXX-XX-XXXX ID #: XXXX Ck Dsn: Date: Rev. 8/08 - (No Interim)DIVISION Descrip: Box-beam Superstructure File: #VALUE! Sheet:

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

=


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 =


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)


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


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


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:


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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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


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


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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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


USE EQUATION0.610

Modify for Skew:skew correc. = 1.000

0.500

0.610


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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Modify for Skew:


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

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