LRFD AASHTO 4-22-39

18
, ¡ Section 4 - Structural Analysis and Evaluation (SI) ; ! SPECIFICATIONS COMMENTARY j \ ¡ i . ~o;n~~i~~~I~:~~~1 ~r~~~ ~ít.h. ~t.I~~~~ ~~.~~ . . . . . 8.0 0 ~ , t; . For all other partiallyfilled gríds . . . . . . . . . . . . . 10.0 i .. i,~ 4.6.2.1.9 Inelastíc Analysis I ~ The ínelastíc finíte element analysís or yíeld líne : analysis may be permitted by the Owner. ~ ~ 4.6.2.2 BEAM-SLAB BRIDGES ~ ~ 4.6.2.2.1 Applícation C4.6.2.2.1 ) ., ~ For beam spacing exceedíng the range of The lever rule ínvolves summíng moments aboutone ; applicabilíty as specified in tables in Artícles 4.6.2.2.2 support to find the reaction at another support by and 4.6.2.2.3, the líve load on each beam shall be the assumíng that the supported component ís hinged at : reaction of the loaded lanes based on the lever rule interior supports. ; unless specifiedotherwíse herein. When usíng the lever rule on a three-gírder bridge, 1 the notíonalmodel should be taken as shown ín Fígure . C1. Momentsshould be taken about the assumed,or i '~ notíonal, hinge in the deck ayer the míddle gírder to find i ~ the reaction on the exteriorgirder. ! ! 1 r\ r Assumed Hinge n I ,. ~ I . ~ :;t:::: ~. I e j , ~ Figure C4.6.2.2.1-1 - NotionalModel for Applying Lever :j Rule to Three-Girder Brídges . 1 ., The provísíons of Article 3.6.1.1.2 specífy that Provisíons ín Artícles 4.6.2.2.2 and 4.6.2.2.3 that do :{ multiple presence factors shall not be used wíth the not appear in earlíer edítíons of the Standard j approximate load assígnment methods other than Specífications come prímaríly from Zokaíe et al. (1991). ;j statical moment or lever arm methods because these Correctíon factors for contínuíty have been deleted for ~ factors are already íncorporated ín the distríbutíon two reasons: ~ factors. ::1 Brídges not meeting the requirements of thís article . Correctíon factors dealing with 5 percent ,;, shall be analyzed as specified ín Artícle 4.6.3. adjustments were thought to imply mísleading levels j : The dístríbution of líve load, specífied in Articles of accuracy ín an approxímate method, and ~ 4.6.2.2.2 and 4.6.2.2.3, may be used for gírders, beams, ~ and stríngers,other than multíplesteel box beams with . Analyses of many continuous beam-slab-type : concrete decks that meet the followíng conditíons and bridges índícate that the dístributíon coefficients for : : any other conditíons ídentified in tables of distríbution negatíve moments exceeds those obtained for ~ , factors as specífied hereín: positive moments by approxímately 10 percent. On '] the other hand, it has been observed that stresses at " . Width of deck ís constant; or near an internal bearíng are reduced due to the ! fanning of the reactíon force. This reductíon is about 1 . Number of beams ís not less than tour, unless the same magnítude as the increase in distríbutíon ~ otherwise specífied; factors, hence the two tend to cancel each other out, i and thus are omítted from these Specífications. :; . Beams are parallel and have approxímately the ;~ same stiffness; In Strength Load Combinatíon 11, applying a el ~ dístribution factor procedure to a loading ínvolvíng a ;j .~ 4 - 22 :1 :1 '1 ,

Transcript of LRFD AASHTO 4-22-39

Page 1: LRFD AASHTO 4-22-39

,¡ Section 4 - Structural Analysis and Evaluation (SI);

! SPECIFICATIONS COMMENTARYj\

¡ i . ~o;n~~i~~~I~:~~~1 ~r~~~ ~ít.h. ~t.I~~~~ ~~. ~~ . . . . . 8.0 0~ ,t; . For all other partially filled gríds . . . . . . . . . . . . . 10.0i ..i,~ 4.6.2.1.9 Inelastíc Analysis

I ~ The ínelastíc finíte element analysís or yíeld líne: analysis may be permitted by the Owner.

~~ 4.6.2.2 BEAM-SLAB BRIDGES

~~ 4.6.2.2.1 Applícation C4.6.2.2.1).,

~ For beam spacing exceedíng the range of The lever rule ínvolves summíng moments about one; applicabilíty as specified in tables in Artícles 4.6.2.2.2 support to find the reaction at another support by.¡ and 4.6.2.2.3, the líve load on each beam shall be the assumíng that the supported component ís hinged at: reaction of the loaded lanes based on the lever rule interior supports.; unless specified otherwíse herein. When usíng the lever rule on a three-gírder bridge,1 the notíonal model should be taken as shown ín Fígure. C1. Moments should be taken about the assumed, ori '~ notíonal, hinge in the deck ayer the míddle gírder to findi ~ the reaction on the exterior girder.!

! 1 r\ r Assumed Hinge nI ,. ~ I . ~ :;t:::: ~. I ej ,~ Figure C4.6.2.2.1-1 - Notional Model for Applying Lever:j Rule to Three-Girder Brídges.1

., The provísíons of Article 3.6.1.1.2 specífy that Provisíons ín Artícles 4.6.2.2.2 and 4.6.2.2.3 that do:{ multiple presence factors shall not be used wíth the not appear in earlíer edítíons of the Standardj approximate load assígnment methods other than Specífications come prímaríly from Zokaíe et al. (1991).;j statical moment or lever arm methods because these Correctíon factors for contínuíty have been deleted for~ factors are already íncorporated ín the distríbutíon two reasons:~ factors.::1 Brídges not meeting the requirements of thís article . Correctíon factors dealing with 5 percent

,;, shall be analyzed as specified ín Artícle 4.6.3. adjustments were thought to imply mísleading levelsj : The dístríbution of líve load, specífied in Articles of accuracy ín an approxímate method, and

~ 4.6.2.2.2 and 4.6.2.2.3, may be used for gírders, beams,~ and stríngers, other than multíple steel box beams with . Analyses of many continuous beam-slab-type: concrete decks that meet the followíng conditíons and bridges índícate that the dístributíon coefficients for

: : any other conditíons ídentified in tables of distríbution negatíve moments exceeds those obtained for~ , factors as specífied hereín: positive moments by approxímately 10 percent. On'] the other hand, it has been observed that stresses at" . Width of deck ís constant; or near an internal bearíng are reduced due to the! fanning of the reactíon force. This reductíon is about1 . Number of beams ís not less than tour, unless the same magnítude as the increase in distríbutíon~ otherwise specífied; factors, hence the two tend to cancel each other out,i and thus are omítted from these Specífications.:; . Beams are parallel and have approxímately the;~ same stiffness; In Strength Load Combinatíon 11, applying a el~ dístribution factor procedure to a loading ínvolvíng a

;j.~ 4 - 22:1:1'1

,

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~ Section 4 - Structural Analysis and Evaluation (SI)j!

I

: SPECIFICATIONS COMMENTARY! ¡.I : ~ . Unless otherwise specified, the roadway part of the heavy permit load can be overly conservative unlessI¡ '~,,!., overhang, de, does not exceed 910 mm; lane-by-lane distribution ~act~rs ~re availabl~. ~se of aI .. refined method of analysls wlll clrcumvent thls sltuation.

. Curvature in plan is less than the limit specified inArticle 4.6.1.2; and

1 : . Cross-section is consistent with one of the cross-, ; sections shown in Table 1..¡I: Where moderate deviations from a constant deck Most of the equatíons for distribution factors were\ width or parallel beams exist, the equations in the tables derived for constant deck width and parallel beams.~ of distribution factors may be used in conjunction with a Past designs with moderate exceptions to these two1 suitable value for beam spacing. assumptions have performed well when the "S/D"~i distribution factors were used. While the distribution~ factors specified herein are more representative of actual~ bridge behavior, common sense indicates that some} exceptions are still possible, especially if the parameter~ "S" is chosen with prudent judgment.: Additional requirements for multiple steel box girders In lieu of more refined information, the Sto Venant~ with concrete decks shall be as specified in Article torsional inertia, J, may be determined as:~ 4.6.2.2.2b.

Where bridges meet the conditions specified herein, . For thin-walled open beam:i ¡ permanent loads of and on the deck may be distributed 1I ~ uniformly among the beams and/or stringers. J - - Lbt3 (C4.6.2.2.1-1)

~ Live load distribution factors, specified herein, may 3

'; be used for permit and rating vehicles whose overalli ¡:;ff~ width is comp~rable to ~he width of the design t~uck. . . For stocky open secti~ns, e,~" prestressed I-beams,¡ ~ The followlng notatlon shall apply to tables In Artlcles T -beams, etc., and salid sectlons:.: 4.6.2.2.2 and 4.6.2.2.3:,, A4i A = area of stringer, beam or girder (mm2) J - ¡o:o¡ (C4.6.2.2.1-2).~ b = width of beam (mm) P

1 C = stiffness para meter . .g d = depth of beam or strlnger (mm) . For closed thln-walled shapes::~ de = distance from exterior web of exterior beam and 2

) the interior edge of curb or traffic barrier (mm) J - ~.j D = width of distribution per lane (mm) s (C4.6.2.2.1-3);~ e = correction factor Lt~ 9 = distribution factor~ Ip = polar moment of inertia (mm4) where:; J = Sto Venant's torsional inertia (mm4)I K = constant for different types of construction b = width of plate element (mm), Kg = longitudinal stiffness parameter (mm4)

:; L = span of beam (mm) t = thickness of plate-like element (mm), ~ Nb = number of beams, stringers or girders

~ : Nc = number of cells in a concrete box girder A = area of cross-section (mm2)! :i NL = number of design lanes as specified in Article..~ 3.6.1: 1.1 Ip = polar moment of inertia (mm4):;) S = spaclng of beams or webs (mm)~. ~ = depth of steel grid or corrugated steel plank Aa = area enclosed by centerlines of elements (mm2)

;1 (mm). ~ = depth of structural overlay (mm) s = length of a side element (mm)

.'~ t. = depth of concrete slab (mm)::~ GJt~ W = edge-to-edge width of bridge (mm) Equation C2 has been shown to substantially.:J ~ underestimate the torsional stiffness of some concrete:.1

::j':1 4 - 23

,j", i

.!

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-J; Section 4 - Structural Analysis and Evaluation (SI)

; SPECIFICATIONS COMMENTARY

I : We = half the web spacing, plus the total overhang I-beam.s a~d a more ac~urate, but more complex, .; (mm) approxlmatlon can be found In Eby et al. (1973). ,~; e = skew angle (DEG) The transverse posttensioning shown for some~ ~ = Poisson's ratio cross-sections herein is intended to make the units act

together. A minimum 1.7 MPa prestress isUnless otherwise stated, the stiffness parameters for recommended.area, moments of interia and torsional stiffness used For beams with variable moment of inertia, Kg may

, herein and in Articles 4.6.2.2.2 and 4.6.2.2.3 shall be be based on average properties.; taken as those of the cross-section to which traffic will be For bridge types "f," "g," "h," "i," and "j," longitudinal) applied, i.e., usually the composite section. joints between precast units of the cross-section are~ shown in Figure 1. This type of construction acts as ai The longitudinal stiffness parameter, Kg, shall be monolithic unit if sufficiently interconnected. In Article¡ taken as: 5.14.4.3.3f, a fully interconnected joint is identified as a( flexura! shear joint. This type of interconnection is.; 2 enhanced by either transverse posttensioning of ani: Kg = n(1 + Aeg ) (4.6.2.2.1-1) intensity specified above or by a reinforced structural

~ overlay, which is al so specified in Article 5.14.4.3.3f, or: . h' h' both. The ~s~ of transverse mild steel rods secured by! In w IC . nuts or similar unstressed dowels should not be

i considered sufficient to achieve full transverse flexural,~ Es continuity unless demonstrated by testing or experience.

n = E (4.6.2.2.1-2) Generally, posttensioning is thought to be more effectiveD than a structural overlay if the intensity specified above

! isachieved.i where' In some cases, the lower limit of deck slab thickness,

I ~ . 1., shown in the range of applicability, column in tables in

I : E = modulus of elasticity of beam material (MPa) Articles 4.6.2.2.2 and 4.6.2.2.3 is less. tha~ 180 mm. The a! B research used to develop the equatlon In those tables .

1 E = modulus of elasticity of deck material (MPa) reflects . th~ range of slab thickness shown. Articleí D 9.7.1.1 Indlcates that concrete decks less than 180 mm

';¡ I = moment of inertia of beam (mm4) in thickness should not be used u~less appro,:,ed b~ the... Owner. Lesser values shown In tables In ArtlclesI

~ eg = distance between the centers of gravity of the 4.6:2.2.2 and 4.6.2.2.3 are not intended to override~ basicbeamanddeck(mm) Artlcle9.7.1.1. .i Table 1 describes how the term L (Iength) may be¡ The parameters A and I in Equation 1 shall be taken as determined. for .use i.n the live load distribution factor:) those of the noncomposite beam. equatlons glven In Artlcles 4.6.2.2.2 and 4.6.2.2.3.

¡:;! The bridge types indicated in tables in Articles:; 4.6.2.2.2 and 4.6.2.2.3, with reference to Figure 1, mayj:'.{ be taken as representative of the type of bridge to which

each approximate equation applies.

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~ .1«¡

4j

...¡ 4 - 24:¡"

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!Section 4 - Structural Analysis and Evaluation (SI)

,;"

1: SPECIFICATIONS COMMENTARY:1

l', ~, Table C4.6.2.2.1-1 - L for Use in Live Load Distribution Factor Equations

~~:'

¡ I FORCE EFFECT I L (mm) I

.. Positive Moment The length of the span for which

~ . moment is being calculated,1 Negative Moment - Near interior The average length of the twoJ supports of continuous spans from point adjacent spans¡ of contraflexure to point of contraflexure

i under a uniform load on all spans

i Negative Moment - Other than near The length of the span for which

.i interior supports of continuous spans moment is beinq calculated

~ Shear The length of the span for which1 shear is beinq calculated

;.1~ Exterior Reaction The lenqth of the exterior span

1 Interior Reaction of Continuous Span The average length of the two

j

¡ adiacent spans

'.

~i :j

~: Except as permitted by Article 2.5.2.7.1, regardless In the rare occasion when the continuous span

lc~ of the method of analysis used, i.e., approximate or arrangement is such that an interior span does not have

¡ refined, exterior girders of multibeam bridges shall not any positive uniform load moment, i.e., no uniform load

í ~ have less resistance than an interior beam. points of contraflexure, the regían of negative moment

,~ ~f near the interior supports would be increased to the

~ centerline of the span, and the L used in determining the

.j live load distribution factors would be the average of the

~ two adjacent spans.

,~

1,.,

:1~

:1

:1:¡"~~ -

,,

"

'jc

'"

~

\

:

.!, ..:1"4

:~

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:.}

.

i

:.Á

,'.

~ Ii~!\

1 't{~;'~.

.")

~~ 4 - 25

.:,e,

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~ Section 4 - Structural Analysis and Evaluation (SI)J¡ SPECIFICATIONS COMMENTARY~

1 Table 4.6.2.2.1-1 - Common Deck Superstructures Covered in Articles 4.6.2.2.2 and 4.6.2.2.3 ~J ,,~)

) SUPPORTING, COMPONENTS TYPE OF DECK TYPICAL CROSS-SECTION,: Steel Beam Cast-in-place concrete slab,

~ 1 1. - , 1 1 ~ ,~ precast concrete slab, steel

~ grid, glued/spiked panels,i ~ stressed wood

~

~ (a),~

.} Closed Steel or Precast Cast-in-place concrete slab ~O ffi U ~ 1 Concrete Boxes I

~"') D1 I

j

.

!~ (b)i -, 'jI ~~

; .~ Open Steel or Precast Cast-in-place concrete slab,

~ U ~ U ~' ] Concrete Boxes precast concrete deck slab

~:; ,

,;t"

; (C).; 8\1 Cas~-in-Place Concrete Monolithic concrete

~{::::JC:J[:::::Jl:d]~ Multlcell Box

":) [~~~~~=J[~~~~~~~~ J[~~~~~~~~ ]:;1 (d)~

.'1

;~ Cast-in-Place Concrete Monolithic concrete

~~~r=l~r~lJ====::l1 ,.;¡ Tee Beam !'~

¡"! c;

l.:

': ( ).~: e;;

':f

;¡ Precast Salid, Voided or Cast-in-place concrete overlay t jEJdI2]~J2J ~ I I '1 Cellular Concrete Boxes

¡ with Shear Keys D D.! I O O O

:1 (f).¡

'1

."

"

,1 e:i

i:i

ti!,\

'/1,1:;: 4 - 26

;

. , ,. ,

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Section 4 - Structural Analysis and Evaluation (SI)

1: SPECIFICATIONS COMMENTARY!

¡~: SUPPORTING: - COMPONENTS TYPE OF DECK TYPICAL CROSS-SECTION

, Precast Salid, Voided, or Integral concrete b lDIDlod I Cellular Concrete Box[ with Shear Keys and with D D D D D ~1, j or without Transverse ~ost

I! Post- Tensioning (g) tension; ¡! !: j

I ¡ Precast Concrete Cast-in-place concrete overlay~~~'~T~T~~W~~ ¡ Channel Sections with

¡ Shear Keys,i

~ (h)!,! Precast Concrete Double Integral concrete ~=¡J1f:'lFIY=lnJ~ ~ Tee Section with Shear --1 Keys and with or without !i Transverse . post: Posttensioning (1) tension~

~! 6;~i~ prec.ast C?ncrete Tee Integral concrete ~='r==11="'f ;~ %.~ Sectlo.n wlth ~hear Keys '7" and wlth or wlthout L post;1 Transver~e . (j) tension1 Posttenslonlngj

:j Precast Concrete I or Cast-in-place concrete, precast~K K 1r 1r ~ ,~ Bulb- Tee Sections concrete

:~:1~~

:~ (k).~,

..1

'; Wood Beams Cast-in-place c?ncrete or n n~ plank, glued/splked panels or I '" / I: ;~ stressed wood I~I . I~I I~I I~I I~I

i .. ! l;J l;J ~ ~ l;J

;~ tI);.~.~;1~

.í 4.6.2.2.2 Distribution Factor Method for Moment and

} Shear¡'o

:; fJ~" 4.6.2.2.2a Interior Beams with Wood Oecks,,1 ~W,~ The live load flexural moment and shear for interiorI ,

:1 beams with transverse wood decks may be determlned','o..¡

I:!

;',

.~ 4 - 27,1

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]1 Section 4 - Structural Analysis and Evaluation (SI)

; 5PECIFICATION5 COMMENTARY

J: by applying the lane fraction specified in Table 1 and AEquatlon 1. ,~Y

When investigation of shear parallel to the grain inwood components is required, the distributed live loadshear shall be determined by the following expression:

; VLL=O.50[(O.60VLU)+VW] (4.6.2.2.2a-1)I~¡: where:,¡

~ VLL = distributed live load vertical shear (N),

l', II j VLu = maximum vertical shear at 3d or U4 due to

! undistributed wheelloads (N).,;~ VLD = maximum vertical shear at 3d or U4 due to, wheel loads distributed laterally as specified~ herein (N)

For undistributed wheel loads, one line of wheels is1: assumed to be carried by one bending member.l'

; Table 4.6.2.2.2a-1 - Distribution of Live Load Per Lane for Moment and 5hear in Interior Beams, ." wlth Wood Decks

~ Type of Deck Applicable One Design Two or More Range of e.~ Cross-Section Lane Design Lanes Applicabilityj from Table Loaded Loaded,j 4.6.2.2.1-1

i~ Plank a, I 5/2000 5/2300 5 ~ 1500

',o;.~ 5tressed a, I 5/2800 5/2700 S ~ 1800

j Laminated~.,I i 5pike Laminated a, I 5/2500 5/2600 S ~ 1800

1';; Glued Laminated a, I 5/3000 5/3000 S ~ 1800

Panels on GluedLaminated5trinQers

Glue Laminated a, I 5/2670 5/2700 S ~ 1800Panels on 5teel

.; 5trinQers:\,.

~ 4.6.2.2.2b Interior Beams with Concrete Decks C4.6.2.2.2bj

1 The live load flexural moment for interior beams withi concrete decks may be determined by applying the lane~ frction specified in Table 1.

1 For preliminary design, the terms KJ(Lis 3) and I/J ~-1 may be taken as 1.0. W; For the concrete beams, other than box beams, used

,1 in multibeam decks with shear keys:l'I\i

1

: 4-28

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lr- Section 4 - Structural Analysis and Evaluation (SI)j.i¡: SPECIFICATIONS COMMENTARY

j~ ~ . Deep, rigid end diaphragms shall be provided to~t!I ensure proper load distribution, and

. If the stem spacing of stemmed beams is less than,.J~ 1200 mm or more than 3000 mm, a refined analysis:' complying with Article 4.6.3 shall be used.

: ~or multiple steel box girders with a con~rete de~k,: the Ilve load flexural moment may be determlned uslngI the distribution factor specified in Table 1.I When the spacing of the box girders varies along the The results of analytical and model studies of simple~ length of the bridge, the value of NL shall be determined, span multiple box section bridges, reported in JohnstonI as specified in Article 3.6.1.1.1, using the width, W, taken and Mattock (1967), showed that folded plate theoryI at midspan. could be used to analyze the behavior of bridges of this

type. The folded plate theory was used to obtain the'. maximum load per girder produced by various criticali combinations of loading on 31 bridges having various1 spans, numbers of box girders, and numbers of traffic¡, lanes.

~ Multiple presence factors, specified in Table:1 3.6.1.1.2-1, are not applied because the multiple factors~ in past editions of the Standard Specifications were" considered in the development of the equation in Table.', 1 for multiple steel box girders.~ The lateral load distribution obtained for simple¡ spans is al so considered applicable to continuc:.Js~ structures.¡ ~~ T~e bridges. con.sidered in. the development. of the~ ~ equatlons had Interior end dlaphragms only, I.e, no~ interior diaphragms within the spans, and no exterior1 diaphragms anywhere between boxes. If interior or'1 exterior diaphragms are provided within the span, the.1 transverse load distribution characteristics of the bridge"" will be improved to some degree. This improvement can-1 be evaluated, if desired, using the analysis methods1 identified in Article 4.4..,;

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I~. Section 4 - Structural Analysis and Evaluation (SI)

Table 4.6.2.2.2b-1 - Distribution of Live Loads Per Lane for Moment in Interior Beams

Type of Beams Applicable Distribution Factors Range of O; Cross-Section Applicability,i from Tablef 4.6.2.2.1-1;\'':" Wood Deck on Wood a I 8ee Table 4.6.2.2.2a-1,j or 8teel BeamsJ

i; Concrete Deck on I One Design Lane Loaded: 8/3700 8 ~ 1800i J Wood Beams Two or More Desiqn Lanes Loaded: 8/3000I ~':-

~ Concrete Deck, Filled a, e, k and One Design Lane Loaded: 11 00 ~ S oS 4900t Grid, or Partially Filled also i, j ( ] 0'1 110 ~ ~ ~ 300

¡:i Grid on 8teel or if sufficiently 0.06 + ( ~ ) 0.4 ( ~) 0.3 ~ 6000 ~ L ~ 73000

i¡ Concrete Beams; connected ~o 4300 L Lt3 Nb ~ 4~ Concrete T -Beams, act as a unlt s

J T - and Double T - Two or More Design Lanes Loaded:'; 8ections

~ ( 8 ) 0.6 ( 8 ) °,2 ( Kg ] 0'1 0.075+ - - -

2900 L Lt3s

, use lesser of the values obtained from the Nb = 3,. equation above with Nb = 3 or the lever rule

¡.~ Multicell Concrete d One Design Lane Loaded: 2100 ~ S ~ 4000 ~"; Box Beam ) ( ) 0.35( ) 0.45 18 000 ~ L ~ 73 000 .~ ( 1.75 + ~ ~ ~ Nc ~ 3,. 1100 L N~ c,

¡ .,: Two or More Design Lanes Loaded: If N > 8 use N = 8. c c~

i ( ~ ) 03 ( ~ ) ( ..:!. ) 0.25

.. N 430 L~ c

.~

i,~ Concrete Deck on b, c One Design Lane Loaded: 1800 ~ S ~ 3500,~~ Concrete 8pread Box 035( ) 0.25 6000 ~ L ~ 43 000

I~..;: Beams( ~ ) . ~ 450 ~ d ~ 1700

-' 910 L 2 Nb ~ 3

Two or More Design Lanes Loaded:

( ~ ) 06 ( ~ ) 0125

1900 L2~ ,IJ

.'.: Use Lever Rule S > 3500"

:~I ,

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J"

"..

.;\.1

j~: 4 - 30

i,'1 ': ..

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li Section 4 - Structural Analysis and Evaluation (SI)

.,:¡ Type of Beams Applicable Distribution Factors Range of

~ Cross-Section Applicability¡ ~~, from Table

~ 4.6.2.2.1-1!Ii,¡ ; Concrete Beams f One Design Lane Loaded: 900 .s b ~ 1500

l. used in Multibeam( b ) 0.5 ( 1) 0.25 6000 ~ L ~ 37 000

ii Oecks k - - 5 .s Nb ~ 20i ¡ 2.8L J1~ where: k = 2.5(Nb)-0.2 ~ 1.5,~ 9~ if sufficiently Two or More Oesign Lanes Loaded:~ connected t.o ( b ) 0.6 ( b ) 0.2 ( 1) 0.06 act as a unlt k - - -

) 7600 L J~~..!J h Regardless of Number of Loaded Lanes: S/O!!;

i ~ where:1:'i

~ C = K (W/L)

\ 0= 300 [11.5 - NL + 1.4NL (1 - 0.2C)2]

~"11 O=300[11.5-NJ. . .: ~~ g, 1, J ~j ,~ if connected K = i~t only enough to J

~ prevent. .. ., relative vertical for prellmlnary deslgn, the followlng values of~ displacement K may be used:

!} at the interface~ Beam T~pe .!.s:

.~ Nonvoided rectangular beams 0.7

.~ Rectangular beams with

;~ circular voids: 0.8

,., Box section beams 1.0

,(íi Channel beams 2.2

!i~ T -beam 2.0

I~ Oouble T -beam 2.0:

'~; Steel Grids on Steel a One Oesign Lane Loaded: S .s 1800 mm':i Beams S/2300 If 19 < 100 mm

1 ' 8/3050 If 19~ 100 mm

,j ~ Two or More Design Lanes Loaded:

11 S/2400 If 19 < 100 mm S ~ 3200 mm

: ::1 8/3050 Ift~ 100 mm: :.~

:i Concrete Deck on b, c Regardless of Number of Loaded Lanes: N

':~ Multiple 8teel Box N 0.5 .s ~ .s 1.5

~ Girders 0.05 + 0.85~ + ~ Nb; Nb NL.~

,:; ~

':¡.,¡

;1~.1: 4 - 31.~

I :;

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~~ Section 4 - Structural Analysis and Evaluation (SI),~ SPECIFICATIONS COMMENTARY.

4.6.2.2.2c Interior Beams with Corrugated Steel Decks

¡ The live load flexural moment for interior beams with "

corru~ated steel plank deck may be determined byapplYlng the lane fraction, g, specified in Table 1.

I : Table 4.6.2.2.2c-1 - Distribution of Live Load Per Lane

~ for Moment in Interior Beams with Corrugated Steel Plank

1 Decks,

i~ One Design Two or More Design Range of

; Lane Loaded Lanes Loaded Applicability

~

I 8/2800 I 8/2700 I 8t,',,1~~0 1/2800 S/2700 S ~ 1700~ 19~ 50

i~~ 4.6.2.2.2d Exterior Beams C4. 6.2. 2. 2d

:,.~ The live load flexural moment for exterior beamsi ; may be determined by applying the lane fraction, g,i : specified in Table 1.i ~ The distance, de. shall be taken as positive if the

., exterior web is inboard of the interior face of the traffic; railing and negative if it is outboard of the curb or traffic This additional investigation is required because the

barrier. distr!bution factor for girders in a multigirder cross-" In beam-slab bridge cross-sections with diaphragms sectlon: Type~ "a," "e," and "k" in Table 4.6.2.2.1-1. was1 or cross-frames, the distribution factor for the exterior determlned wlthout consideration of diaphragm or cross-

.;1 beam shall not be taken to be less than that which would trames. The recommended procedure is an interim

~¡ be obtained by assuming that the cross-section deflects provision until research provides a better solution.~ and rotates as a rigid cross-section. The provisions of The procedure outlined in this section is the same as.! Article 3.6.1.1.2 shall apply. the conventional approximation for loads on piles.

'!~ NL

~ NL XextL e\ R- +:¡ - -N N (C4.6.2.2.2d-1 ). b b

! 1 LX2

1:: where:

R = reaction on exterior beam in terms of lanes

NL = number of loaded lanes under consideration

" ; e = eccentricity of a design truck or a design, lane load from the center of gravity of the; pattern of girders (mm)

J,; X = horizontal distance from the center of gravityi of the pattern of girders to each girder (mm)

i Xext = horizontal distanc~ from the center of gravity~ of the pattern of glrders to the exterior girder

:¡ (mm) ei .;¡i Nb = number of beams or girders

1¡ :',1'1 4.32

l.)

Page 12: LRFD AASHTO 4-22-39

I. Section 4 - Structural Analysis and Evaluation (SI)!¡ Table 4.6.2.2.2d-1 - Distribution of Live Loads Per Lane for Moment in Exterior Longitudinal Beams1j

,! ~ Type of Superstructure Applicable Cross- One Design Two or More Range ofI ; Section from Table Lane Loaded Design Lanes Applicabilityj : 4.6.2.2.1-1 Loaded

Wood Deck on Wood or a, I Lever Rule Lever Rule N/ASteel Beams

j

~ Concrete Deck on Wood I Lever Rule Lever Rule N/A1 Beams,.1

i Concrete Deck, Filled a, e, k and Lever Rule 9 = e ginterior -300 oS de oS 1700

, Grid, or Partially Filled al so ir j di Grid on Steel or if sufficiently e := 0.77 + -.!.--¡ Concrete Beams; connected to act as 2800,1 Concrete T -Beams, T a unit~ and Double T Sections!'J use lesser of the Nb = 3~ values obtained~ from the equation\; above with Nb = 3'1 or the lever rule,

) Multicell Concrete Box d W W We oS Si Beams, Box Sections g := --!... g := --!...:j 4300 4300"j

j @ Concrete Deck on b, c Lever Rule 9 = e ginterior O oS de oS 1400~~ Concrete Spread Box d 1800 < S oS 3500,~ Beams e := 0.97 + -!.-

..j 8700

i1 Use Lever Rule S > 3500!~:J Concrete Box Beams f, 9 Lever Rule 9 = e ginterior -300 oS de $ 600:~ Used in Multibeam d;1 Decks e := 1.04 + -.!.--:j 7600

'~;~ Concrete Beams Other h Lever Rule Lever Rule N/A'fI .-; than Box Beams Used . .., : in Multibeam Decks 1, J If connected only

"

~'i enough to prevent..; relative vertical

.~ displacement at the, ;1 interface

1, .,

.":i Steel Grid Deck on Steel a Lever Rule Lever Rule N/A::i Beams

I Concrete Deck on b, c As specified in Table b-1'; Multiple Steel Box:{ Girders'J ~,,~~ .~ .~!. ,.. ,)..

~ .-

,~

{~;.. 4 - 33,

",i I

I ::¡

¡ !.

Page 13: LRFD AASHTO 4-22-39

",

Section 4 - Structural Analysis and Evaluation (SI)

SPECIFICATIONS COMMENTARY

,l¡' 4.6.2.2.2e Skewed Bridges C4.6.2.2.2e e: . When the line supports are skewed and the Accepted reduction factors are not currently

i difference between skew angles of two adjacent lines of available for cases not covered in Table 1.supports does not exceed 10°, the bending moment inthe beams may be reduced in accordance with Table 1.

: Table 4.6.2.2.2e-1 - Reduction of Load Distribution Factors for Moment in Longitudinal Beams on

~ Skewed Supports..

I1 Type of Superstructure Applicable Any Number of Design Range of1 Cross-Section Lanes Loaded Applicability¡ from Table:¡ 4.6.2.2.1-1

~¡ Concrete Deck, Filled Grid, a, e, k and 1 - (t 8)15 30° $ 8 $ 60°.1 or Partially Filled Grid on al so i, j c1 an 1100 $ S $ 4900

; Steel or Concrete Beams; if sufficiently 6000 $ L $ 73 000~ Concrete T -B~ams, T or connected t.o act c = O.2S[ ~

] 025 (~)0.5 Nb ~ 4

1 Double T Sectlons as a unlt 1 Lt3 L.

, ¡ If 8 < 30° then c1 = 0.0:,.. If 8> 60° use 8 = 60°

Concrete Deck on b, c, f, 9 1.05 - 0.25 tan 8 $ 1.0 0$ 8 $ 60°" Concrete Spread Box¡ Beams, Concrete Box If 8> 60° use 8 = 60° e~ Beams, and Double T1 Sections used in~ Multibeam Decks~i"\ .i 4.6.2.2.2f Flexural Moments and Shear In Transverse;~ Floorbeams..:.~;;~ If the deck is supported directly by transverse:~ floorbeams, the floorbeams may be designed for loads~~ determined in accordance with Table 1.

I ~ The fractions provided in Table 1 shall be used inf:: conjunction with the 145 kN design axle load alone. For

. spacings of floorbeams outside the given ranges of

i ~ appli~ability, all of the design live loads shall beI ~ consldered, and the lever rule may be used.

;11 ::

]~'1.1{~

.~:-~ I~:1 W

)

¡j}j 4 34". -ti\!

Page 14: LRFD AASHTO 4-22-39

11 Section 4 - Structural Analysis and Evaluation (SI)

SPECIFICATIONS COMMENTARY

l' ~ Table 4.6.2.2.2f-1 - Distribution of Live Load perl' 't:'w Lane for Transverse Beams for Moment and Shear

Type of Fraction of Wheel Range ofOeck Load to Each Applicability

. Floorbeam

j Plank ~ N/A

; 1200ii1 Laminated S S =' 1500~ Wood Deck -;:1500'.;1 Concrete ~ S =' 1800

-1 1800j;

.~

:: Steel Grid S 19 =' 100I ; - S =' 1500; 1400,,

','"¡

:] Steel Grid S 19 ~ 100! - S =' 1800, ~s. 1800, ~A..VI ~>

éi! Steel Bridge S 19 ~ 50~ Corrugated -i Plank 1700\

'1:'~ 4.6.2.2.3 Distribution Factor Method for Shear,-

1 4.6.2.2. 3a Interior Beams;}

:.:~ The live load shear for interior beams may be,~ determined by applying the Jane fractions specified in

¡,:; Table 1. For interior beam types not listed in Table 1,I :~ lateral distribution of the wheel or axle adjacent to the:: end of span shall be that produced by use of the lever

1 ;

;: rule.I;j 1.0. For preliminary design, the term I/J may be taken as

'~1 For concrete box beams used in multibeam decks,! ~ if the values of I or J do not comply with the limitations in~~ Table 1, the distribution factor for shear may be taken as

~

J) that for momento:,

:~,.J

,'"

i{ ~ ... :; .~ ;10',

'( 1;19,I;

l.

.;1~ 4-35

~~t'1

Page 15: LRFD AASHTO 4-22-39

TI.

~ Section 4 - Structural Analysis and Evaluation (SI)

! Table 4.6.2.2.3a-1 - Oistribution of Live Load per Lane for Shear in Interior Beams

; ,

1; Type of Applicable Cross- One Design Two or More Design Range of Applicability 1:.I ~ Superstructure Section from Lane Loaded Lanes Loaded

. Table 4.6.2.2.1-1

..

1 ; Wood Oeck on See Table 4.6.2.2.2a-1, ¡ Wood or Steel

!! Beams

)1 Concrete Oeck on I Lever Rule Lever Rule N/A

! Wood Beams~

~ C.oncret~ Deck, a, ~, k ando also i, j o 36 + ~ S - ( S ) 2.0 11 00 ~ S ~ 4900

.\ Fllle? Grld: or. If sufficlently . 7600 0.2 + ~ w-7OO 6000 ~ L ~ 73 000

~ Partlally Fllled Grld connected to act 11 O ~ ~ ~ 300

~ on Steel or Concrete as a unit 4x1 09 ~ Kg ~ 3x1012

í Beams; Concrete T - Nb ~ 4

; Beams, T - and,i Double T -Sections

~i Lever Rule Lever Rule N" = 3

Multicell Concrete d (~)o.S (~ )o., (~ )0.8 ( !!. )o., 1800 ~ S ~ 4000 ) Box Beam, Box 2900 L 2200 L 6000 ~ L ~ 73 000

i ;: Sections 890 ~ d ~ 2800. N~ ~ 3

".. Concrete Deck on b, c ( S

)o.S(d)O.' ( S )o.S(d)0.1 1800 ~ S ~ 3500 ¡ Concrete Spread 3050 L 2250 L 6000 ~ L ~ 43 000 A

.~ Box Beams 450 ~ d ~ 1700 -

.1 N.. ~ 3

;1

i~ Lever Rule Lever Rule S > 3500

".~j

'~ Concrete Box f, 9 ( b)0.'5 ( 1)°.05 ( b )0.4 ( b ) O.' ( 1)°.05 900 ~ b ~ 1500 .~ Bear:ns Used in 0.70 L J 4000 L J 6000 ~ L ~ 37000

~ Multlbeam Decks 5 ~ Nb ~ 20

~ 1.0x101O~J~2.5x1011

;.] 1.7x101O~I~2.5x1011

~,~; Concrete Beams h Lever Rule Lever Rule N/A

1 '; Other Than Box

: Bear:ns Used in i, j

Multlbeam Decks if connected only

; enough to prevent

i : relative verticali i displ~cement at, ¡ the Interface

.!

, Steel Grid Deck on a Lever Rule Lever Rule N/A

í~ Steel Beams.) Concrete Deck on b, c As specified in Table 4.6.2.2.2b-1

~ Multiple Steel Box

\¡ Beams~.." e..1 'Í

.

. ~

4 - 36

. .

Page 16: LRFD AASHTO 4-22-39

'jI. Section 4 - Structural Analysis and Evaluation (SI)i! SPECIFICATIONS COMMENTARY!¡i ~ 4.6.2.2.3b Exterior Beams

".;!" ~1~

; The live load shear for exterior beams shall be1 determined by applying the lane fractions specified in! Table 1. For cases not addressed in Table 4.6.2.2.3a-11 and Table 1, the live load distribution to exterior beams; shall be determined by using the lever rule.j The parameter de shall be taken as positive if thei exterior web is inboard of the curb or traffic barrier and¡ negative if it is outboard.i The additional provisions for exterior beams in! beam-slab bridges with cross-frames or diaphragms,,¡ specified in Articles 4.6.2.2.2d, shall apply.

i~i)t,¡.¡~> '

1}.;. .~i...

"'

;¡¡i:,o.¡J

.j

~ ~'~'1 .¡ .,..4~

.;J~

.1

f...,1"~~,¡~

:1~'j'..."~

: ~~

~;;

1. ,'1~~

~;"

~!

"

.j"o¡ ~~, ..r":~ :OO::J

~\,,~'3.1'f 4 - 37"",

';:¡ . ...,..,

Page 17: LRFD AASHTO 4-22-39

l~1 ¡ Section 4 - Structural Analysis and Evaluation (SI)

,i SPECIFICATIONS COMMENTARY.¡¡ Table 4.6.22.3b-1 - Distribution of Live Load per Lane for Shear in Exterior Beams G

¡: : Type of Superstructure Applicable One Design Two or More Range of! . Cross-Section Lane Design Lanes Applicability1; from Table Loaded Loaded

4.6.2.2.1-1.

¡! Wood Deck on Wood or a, I Lever Rule Lever Rule N/A1

~ Steel Beams...!¡ Concrete Deck on Wood I Lever Rule Lever Rule N/A1 BeamsJ.'~ Concrete Deck, Filled Grid, a, e, k and Lever Rule 9 = e ginterior -300 ~ de ~ 1700

~ or Partially Filled Grid on al so i, j d~ Steel or Concrete Beams; if sufficiently e = 0.6 + --.!-.~ Concrete T -Beams, T - and connected to 3000: ¡ Double T -Beams act as a unitI~ Lever Rule Nb = 3, I

l.; Multicell Concrete Box d Lever Rule 9 = e ginterior -600 ~ de ~ 1500

c Beams, Box Sections d: e = 0.64 + --.!-':: 3800,.

;1 Concrete Deck on b, c Lever Rule 9 = e ginterior O ~ de ~ 1400 ej Concrete Spread Box dj Beams 8 = 0.8 + --.!-~ 3050

,.j Lever Rule S > 3500.'.\"1, Concrete Box Beams f, 9 Lever Rule 9 = e ginterior -300 ~ de ~ 600

;: Used in Multibeam Decks d1 8=1.02+ e

.,' 15 000

¡ti.J:

I Concrete Beams Other h Lever Rule Lever Rule N/A': Than Box Beams Used in, . .

Multibeam Decks 1, Ji :.' if connectedi ',' only enough to

1 ... prevent " !; relative vertical

(.¡ displacementI ::1 at the interface,;i Steel Grid Deck on Steel a Lever Rule Lever Rule N/A

] Beams

\: Concrete Deck on Multiple b, c As specified in Table 4.6.2.2.2b-1'o:1 Steel Box Beams a'1 ..1,l.:;)

:.~! "~ 4 - 38

I ;! ..", .

Page 18: LRFD AASHTO 4-22-39

,1

Section 4 - Structural Analysis and Evaluation (SI)

SPECIFICATIONS COMMENTARY

@ 4.6.2.2.3c SkewedBridges C4.6.2.2.3c

Shear in the exterior beam at the obtuse corner of Verifiable correction factors are not available forthe bridge shall be adjusted when the line of support is cases not covered in Table 1.skewed. The value of the correction factor shall be The equal treatment of all beams in a multibeamobtained from Table 1. It is applied to the lane fraction bridge is conservative regarding positive reaction andspecified in Table 4.6.2.2.3a-1 for interior beams and in shear. However, it is not necessarily conservative

: Table 4.6.2.2.3b-1 for exterior beams. regarding uplift in the case of large skew and shortIn determining the end shear in multibeam bridges, exterior spans of continuous beams. A supplementary

; the skew correction at the obtuse corner shall be applied investigation of uplift should be considered using the! to all the beams. correction factor from Table 1, ¡.e., the terms other than! 1.0, taken as negative for the exterior beam at the acute¡ carnero¡~ Table 4.6.2.2.3c-1 - Correction Factors for Load Distribution Factors for Support Shear of the Obtuse CornerIt

!¡ Type of Superstructure Applicable Correction Factor Range of ApplicabilityJ Cross-Section~ from Tablet 4.6.2.2.1-1

Concrete Deck, Filled Grid, a, e, k and also 0.3 0° ~ e ~ 60°or Partially Filled Grid on i, j [ Lt: ] 11 00 ~ s ~ 4900Steel or Concrete Beams; if sufficiently 1.0 + 0.20 K tan e 6000 ~ L ~ 73 000

~ Concrete T -Beams, T - and connected to act g Nb ~ 4

; G Double T Section as a unit; ',. \ Multicell Concrete Box d[ L } 0° < e ~ 60°

~ Beams, Box Sections 1.0 + 0.25 + - tan e 1800 < S ~ 40001 70d 6000 ~ L ~ 73 000~~ 900 ~ d ~ 2700j N" ~ 3~i.~ Concrete Deck on Spread b, c 00 < e ~ 600J Concrete Box Beams 1.0 + ~ tan e 1800 ~ S ~ 3500;~ 6S 6000 ~ L ~ 43 000:¡ 450 ~ d ~ 1700: N. ~ 3) ."

i ~¡~1 Concrete Box Beams f, 9 00 < e ~ 600¡ Used in Multibeam Decks 1.0 + ~~ 6000 ~ L ~ 37 000

90d 430 ~ d ~ 1500900 ~ b ~ 1500

5..::.~Q -_o1 "

"1 i 4.6.2.3 EQUIVALENT STRIP WIDTHS FOR SLAB- C4.6.2.3I i TYPE BRIDGES

!O.¡

! This article shall be applied to the types of cross-~ sections shown schematically in Table 1 and culverts.: under less than 600 mm of fill. For the purpose of this

article, cast-in-place voided slab bridges may be1 ~\ considered as slab bridges.

.4 ~,.'j;: 4 - 39-,t,-1:

é~