Steel Box Girder Bridges—Design Guides & Methods
CONRAD P. HEINS
IN MEMORIAM CONRAD P. HEINS September 13, 1937 December 24, 1982
During the past decade, there has been extensive use of steel studied and the appropriate criteria for the design of each box girders for straight and curved highway and transit element of a box (i.e., top flange, bottom flange, web) cat structures.13'14 To meet the need for use of such structural egorized according to working stress method or strength elements, design criteria had to be established. Therefore, method as given in Tables 1 and 2. The working stress the purpose of this paper is to present information relative criteria has recently been incorporated into a design ori to the design criteria in addition to information on pre ented computer program.9 liminary plate sizes, design aids, and computer-aided design In addition to these basic specifications,1'2'3 a new code4 of steel box girder bridges. has been proposed for consideration, but has yet to be adopted. INTRODUCTION Box girders have become a prominent element in the con DESIGN GUIDES struction of major river crossings, highway interchanges, Flange Areas—In the design of any complex structure in and transit systems. These types of structural elements are which the section changes and the forces are not readily particularly attractive because of their high torsional computed, it is useful to have data or empirical equations stiffness, which is required when the bridge is curved. to select plate geometry, which can then be incorporated With the advent of these bridges, appropriate design in a computer program9 to automate the bridge design. specifications1'2'3 design guides5'6'7 computer solutions8'9 Such information has been developed5'6'7 and has resulted are required. Here is a summation of this information: in the following: i) Single-span bridge DESIGN SPECIFICATIONS There are at present a set of standard specifications,1 which pertain to straight box girders for highway bridges. Guide 2 specifications are also being used for curved box structures, A = \?>d\\-j\ but to date have not been incorporated into the standard B code.1 Further research has also been conducted, which has ii) Two-span bridge resulted in a tentative strength or load factor design code 3 1 2 3 for curved bridges. All three of these codes ' ' have been + 2 A B=- (0.00153L - 0.223L + 13) k
A-B = \MA^ Conrad P. Heins was Professor', Institute for Physical Science and A\ = 0AAA+ Technology and Civil Engineering Department, University B of Maryland, College Park, Maryland. This paper is the 1982 T R. Higgins Lectureship Award winner. A-T = \MA%^ ty
121
FOURTH QUARTER / 1983 Table 1. Working Stress Design Requirements
Item Straight Curved
Compression b 4400 Flange = t y/Ty (positive and moment) 2 'H r //\ i i lr/ Fb = 0.55 Fy 1 PBPW 4ir2E 1
where 1 and pw = pw\ or pw2, where; 1 + U) w
Pw\ =" .-(^ 1 - (W 75
l/b 0.95 + - [30 + 8000(0.1 -//fl)2] Pw2 : 1+0.6F
if — (+) use smaller pw\ or pW2 fb
Jw / \ — (-)usepa,i Jb Compression b ^ 6140 6 6140 Flange < = \f~Fy t ^ VTy x (negative Jb tk 0.55 Fy /, moment) Fb = 0.55 Fy 9.2 6140 6 13,300 ^- - ^ 60 or —i=r t y/Fy where X = 1 + % 0.15 Ul TT/13,300-6/^ V^jj fb * 0.S5Fy - 0.224Fy 1 — sin — 6140 6 13,300 2 \ 7160 —= < - ^ _ or 60 13,300 b J - =r < - ^ 60 / y/Fy t f 7r/13,300-6v F/^ sin — l— tV 2 I 13,300-6140X f ^ 57.6 X 106 b where
if 6 13,300
Fb is smaller of the following:
6 Fb = 57.6 -) -10 A
Jv2 ft = 57.6 - X 106- -X 106 mA [bf
122
ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 1. {continued)
Straight Curved
3070 y/K 3070^ *i \/Ty \Z~Fy fb ^ 0.55/*; ^=0.55^y^912^)2 3070 y/K W 6650 y/~K =— < - s 60 or -=r- where y/Fy t yjFy X\ = \(n>\) 6650 y/K-- y/Ty t y fb * 0.55/; - 0.224/*; 1 — sin - 3580 y/K Xx =0.93+1.6 -m*'» 2^K ^4 6650 y/K w 3 1 3 ±— < - * 60 5.34 + 2.84(/,/W ) / ? K> =- £ 5.34 (n+ l)2 fb £ 14.4 X \06K \wl Stiffener requirement with longitudinal Stiffener where 0.01 K^n 4 for n > 1 0 = 0.125AT3forrz = 1
3070^* w 66b0y/K„ _
V^V / \/Fy
y/Fy 6650 y/K X2~
Fb = 0.326/*; + 0.224/*; { sin -=. *-=— y y ! 2 6650V ^AT2 - 3070y/KX^
Where
A
X2 = 1 -2.13 + 0.1 3-Ht 6650^^2 w — < — s 60
/*"/, is smaller value of
6 Fh = 14.4/T - A10
/,2^ ^ = 14.4AT - x 106 -X 106 i4.4(/:,)2l-l
123
FOURTH QUARTER / 1983 Table 1. (continued)
Straight Curved Use same formula, but use K] instead of AT
1 + + 87.3 A'i=- a\2 . (n + \)2 H |1 + 0.1(n + l)|
I, > St3u
A It > 0.10(n + l)33 a/3^3- f J7/)J E a where a: spacing of transverse stiffener
fs: maximum longitudinal bending stress Af Area of flange including longitudinal stiffener
Same - < 150
7 5.625 X 10 Fv f < < -I Jv (d/ty 3 d 23,000. -< _ < 170 t VTh
d0< l.Sd If do/R < 0.02 use straight girder criteria 0.87(1 - C) Ifdo/R >0.02 ^ c ( [ Vl+WoA02J d 23,000 2 _ < —l _ ,|j (^ < 170 „ 2.2X108[l+(^o)2] t Fb U9 10 + 34 < 1.0 2 Fy{dA) d0< \.Sd
do = stiffener spacing Fv 0.87(1 - C) C + U" 2 VI + (da/d) \ 2 c = 2.2XlQ8|l+(^o) |,iQ Fy(d/t)2
Stiffener Criteria Stiffener Criteria
I > d0t* J 10.92 / = X>5.0 J = 25 —J - 20 > 5.0 do X = 1.0 for—< 0.78 d [do -0.78 X = 1.0 + | Z4;0.78 <—< 1.0 1775 d
d2 Z = 0.95 — Rt b 2600
124
ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 2. Strength Design Requirements
Straight Curved b 3200
t " \/Ty
fb = FbspBPiL where
PB •
1 + i(,+±) (1-001 6 \ 66/ U £[o.3-0.1-^1 = 0.95 + 18 0.1 -- R PBFy/Fbs 2 Fbs = i7(l - 3X ) 1 U\ [Fy_
7T \6j 3200 b 4400 if < - < —=z VTy t y/Fy
fb < Fby where
Fby = FbspBP 1 PB •• - and pw = pw\ or pw2, where; I I 1 +-- Rb 1 Pu/1 =• l-^(l--^
/A \ 756, //6 2 0.95 + 30 + 8000(0.1 -l/R) P™2 : 1 + 0.6(/„//6)
— (+) use smaller p^i or pw2 fb Jw . . — (-) use pwX Jb b 6140 Fy b Rx - ^ —p= then Fcr = ' VTy fv^ 0.75 -L and - ^ —i= 6140 6 13,300 V3 f V^; : <- < • then Fb - Fy • A Fy t VFy #i 6 /? -7= < ~ ^ —=2 z or 60 then ^cr = 0.592 Fy\\+ 0.687 sin - V^ / y/Fy
6 flK thenF6 =26.21 X 10 W- - 13,300-- 26.21 X 10% -j where C — - / 7160 also if b 13,300
A= 6 2 V3 V3 thenFcr = 105 X 10 (;/6)
' = VFy
Fb = FyA
125
FOURTH QUARTER / 1983 Table 2. {continued)
Item Straight Curved
where
3070v^ /?! = '"VM'—ri + A2 + 4 I a 6650VT R2- ViM4-oW
Compression 3070VT — < • /„ < 0.75 —*= and - < —= Flange t VT Vl t VTy (negative thenF =F A moment) b y
With 3070VT w 6650y^ Ri w R2 Stiffener —=z < - < —== or 60 y/Fy VTy t VTy uVTy\ 0.592 Fv 11 + 0.687 sin — /?2-"
then Fb = Fy < A - 0.4 { 1 - sin -I where 2 Ro-Ri t .J JUL. 6650VT - - y/Fy y / R2 Fb=FyA R\,R2 and A are given under compression flange without stiffener section and 2 5.34 + 2.84 (Vw*3)1/3 A, = —^ — < 5.34 (n+1)2 Stiffener Criteria Stiffener Criteria Compression Is ^ 4>t3w /, > (/)t3W Flange 3 4 0.07/s: n forn =2,3,4,5] where: (negative where 4> = 0.125AT3forr2 = 1 J moment) (f) = 0.07 AT3n4 for n > 1 With and Stiffener 0 = 0.125 K*n = 1 b' 2,600 6 2,600 — < I'' VTy t ' VTy where 6': depth of stiffener f: Islat e thickness of stiffener 126 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 2. (continued) Item Straight Curved Web d < 150 Without -< 150 Stiffener Vu < 1.015 X lOW/d or Vu < 0.58 Fydt 3.5£P Vu < or d d 36,500 1 Vu <0.5SFydt With d Transverse -< 150 Stiffener Fp = 0.58 Fydt 2 1 + (d/d )2 11 Wo) C= 18,000 0 -0.3< 1.0 C= {18,000 (*/ Web With d 73,000 36,500 Transverse and - < — y/Ty ,-8„!+M(f Longitudinal t VT y d 73,000 Stiffener d0< \.5d < - < 1 -2.9 and longitudinal stiffener is d/5 for compression flange. t yfFy !•"£ Shear requirements in accordance with transversely d0< 1.5 d stiffened web criteria. m and longitudinal stiffener is J/5 for compression flange shear requirements in accordance with transversely stiffened web criteria. Transverse , 2600 Same as straight except b/t : Stiffener WTy 2 Criteria / = [2.5(d/d0) -2}X< 0.5 b = projected width of stiffener and the gross area 2 X = 1.0 when (d [0ASBdt(\ - C)(V/VU) - \St ]Y where: ido/d - 0.78] A d0 X = \ + {— Z4 when 0.78 <—< 1.0 .6 = 1.0 for stiffener pairs 1775 d " B = 1.8 for single angles 0.95Jp2 B = 2.4 for single plates where Z = /ft C = 18,000 (*/ Fu = as given previously Y = ratio of web plate to stiffener plate yield strengths / > dQtv 2 J = 2.5(d/d0) - 2 > 0.5 Longitudinal V_ 2600 Same criteria as straight Stiffener t' ~ y/Ty Criteria I = dt* 2.4 |^2-0.13 23,000. St = Section modulers of transverse stiffener Ss — Section modulers of longitudinal stiffener 127 iii) Three-span bridge Steel type ^436, Fy = 36 ksi N = 9,3tf = 27,/c = 4ksi A% = {U - 73) Unit weight: steel 490 pcf, concrete 150 pcf 6.4* General parameters ? Exterior section parapit: 300 lbs./ft A n L 2 B=TZ 5k ( i - 52) wearing surface: 15 lbs./ft miscellaneous concrete: 112 lbs./ft n miscellaneous steel: 12% AT = (Li - 100) 2.6£ 2. Procedure Support The determination of the correct plate geometry AB = —(0.964L2-1.65Ll the various bridges, involved the following pre kn dure: X10' -3 _ 70) Fix span length L Select web depth d = 12L/25 A~r = 0.95Ar - 0.0U(Ar)2 \ Select bottom flange width W = 80 in. - 5.4/6 Interior section Select web thickness Select top flange width b < 23t Ai = Wke->-*«> Determine dead-load moments N F d Determine location of cross sectional chanj where: k = B y using data given in Tables 3 and 4 and Fig. 1 wR X 600 Revise sections and computed dead-load, live-1 forces and stress. F = yield point of material at specified y Revise per specifications. section (ksi) Set bottom flange width W = 100 in., repeat. L, L\ L2 = span length (ft) 9 3. Results WR = roadway width (ft) The procedure outlined above was followed for NB = number of boxes design of 81 bridges. The results of these designs d = girder depth (inches) single, two span and three span bridges are tabuh n = L^/L\, L\ = exterior span, L2 = in in Tables 5, 6, and 7. terior span A%, A j = total top flange area (in.2) in positive Bracing Requirements—The required cross diaphn or negative moment region bracing area,10 as shown in Figs. 2 and 3, can be de A~B, AB = total bottom flange area (in.2) in pos mined from the following; itive or negative moment region Sb t* ,. 9N 750 - (in.2) Box Girder Geometry—To select the final cross-sectional *6 ^ d2(d+b) dimensions of a box girder bridge, along its length, many designs are required. To facilitate such designs, a study6 where was conducted to optimize the cross sections of single, two- s = Diaphragm spacing (in.) and three-span straight box girder bridges. The specific b = Width of box (in.), at bottom flange geometry associated with these bridges are: d = Depth of box (in.) * = n/ J 1 = weighted section thickness (in 1. Parametric details 2(d -r b) Span length A = Total cross sectional plate area (in.2) ai single-span: L = 50 ft, 100 ft, 150 ft diaphragm location two-span: LI = 50 ft, 100 ft, 150 ft Ab = Required area of cross diaphragm bra( L2 = N.L\yN= 1.0,1.2,1.4,1.6 (in.2) three-span: LI = 50 ft, 100 ft, 150 ft The bracing spacing requirement is given by the L2 = JV.L1,AT= 1.0,1.2,1.4,1.6 lowing: where L2 equals end span for two span or L2 equals / R \V2 center span for three span symmetrical bridge. s X2L 30 in Web depth: d/L < V25 - h^r—^r\ - ° - Top flange: b/t < 23. (positive moment region) \200L - 7500/ ~ Bottom flange width: 80 in., 100 in., 120 in. where Bottom flange stiffener: ST 7.5 X 25. (negative mo L = Span length (ft) ment region) R = Radius of girder (ft) Concrete slab 8.5 in. Top lateral bracing is utilized in stiffening the box du shipment and erection. Such bracing can also provide 128 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 3 No. cross Web Top Flange Bottom Flange Bottom Stiffener Span sect. Depth Thickness Width Thickness Width Thickness A Ix no. At/Ab ** 1 24.0 0.375 7.0 0.375 80.0 0.375 0.175 50/-80,/ 2 24.0 0.375 11.75 0.5875 80.0 0.375 0.460 3 24.0 0.375 7.0 0.375 80.0 0.375 0.175 1 24.0 0.375 8.25 0.375 100.0 0.340 0.165 50-100 2 24.0 0.375 13.75 0.625 100.0 0.340 0.510 3 24.0 0.375 8.25 0.375 100.0 0.340 0.165 1 24.0 0.375 8.75 0.4375 120.0 0.310 0.170 50-120 2 24.0 0.375 13.75 0.750 120.0 0.310 0.555 3 24.0 0.375 8.75 0.4375 120.0 0.310 0.170 1 48.0 0.500 10.50 0.5625 80.0 0.500 0.393 100-80 2 48.0 0.500 18.75 1.000 80.0 0.750 0.625 3 48.0 0.500 10.50 0.5625 80.0 0.500 0.393 1 48.0 0.500 11.75 0.750 100.0 0.375 0.470 100-100 2 48.0 0.500 17.75 1.250 100.0 0.6875 0.648 1 3 1 48.0 0.500 11.75 0.750 100.0 0.375 0.470 1 48.0 0.500 15.50 0.750 120.0 0.375 0.517 2 100-120 1 48.0 0.500 20.75 1.250 120.0 0.625 0.692 3 48.0 0.500 15.50 0.750 120.0 0.375 0.517 eral stiffness to create a pseudo closed box and thus mini mize the warping stresses. The required area for such bracing, as shown in Fig. 4, is given by; 2 Abi ^ 0.036 (in. ) Table 4. Location of Section Changes for Negative Moment where Negative Region Moment AM = Required area of lateral bracing (in.2) Natural Frequency—The designer is often required to No. of Length Cros. evaluate the vertical natural frequency/, especially if the (ft) sect. Xi x2 x3 x4 structure is subjected to train loadings. Such evaluation, for 11 curved structures, has been determined and has resulted L<49 3 0.109L 0.239L in the following equations: 2 49 < L < 82 4 0.081L 0.172L 0.282L IT El GK L ' 1/2 /= EL + w T M (cps) 2k2L2 fc R2 82 129 FOURTH QUARTER / 1983 i Dead Load Moment Diagram Fig. 1. Example of location of section changes where: As approximations for the torsional properties, the fol 2 lowing expressions may be used; EIX = bending stiffness (kip-in. ) 4 EIW = warping stiffness (kip-in. ) „ _ 2t'{b'd'Y GKT - torsional stiffness (kip-in.2) 1 (d+b) R = radius (in.) 2 /3 2 t'b' d (\ -b'/d') M = mass (w/g) (kip-sec2/in.) Lw ~ >\2 L = exterior span length (in.) 24 (1 + b'/d'} k = Bn2 + Cn + D (for simple spans, k = 1) and B, Cy D are constants defined as: where b' — average width of box B C D d' = average depth of box tf = average plate thickness Two span 0.242 -0.80 1.55 Three span 0.367 -1.24 1.87 Ultimate Strength—The ultimate strength determination of a curved box girder requires consideration of the inter and n = L-mttT-ior/Lexterior 1.0 < n < 1.7. action between the bending moment and torque. A com- 130 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 5. Single-Span Section Dimensions No. Span cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth 1 Thickness Width Thickness Width Thickness A 1 Ix no. AT/AB 1 24.0 0.375 7.0 0.375 80.0 0.375 0.175 50 2 24.0 0.375 11.75 0.5875 80.0 0.375 0.460 3 24.0 0.375 7.0 0.375 80.0 0.375 0.175 1 24.0 0.375 1 8.25 0.375 100.0 0.340 0.165 50 2 24.0 0.375 13.75 0.625 100.0 0.340 0.510 3 24.0 0.375 8.25 0.375 100.0 0.340 0.165 1 24.0 0.375 8.75 0.4375 120.0 0.310 0.170 1 50 2 24.0 0.375 13.75 0.750 120.0 0.310 0.555 3 24.0 0.375 8.75 0.4375 120.0 0.310 . 0.170 1 48.0 0.500 10.50 0.5625 80.0 0.500 0.393 1 100 2 48.0 0.500 18.75 1.000 80.0 0.750 0.625 3 48.0 0.500 10.50 0.5625 80.0 0.500 0.393 1 48.0 0.500 11.75 0.750 100.0 0.375 0.470 J 100 2 48.0 0.500 17.75 1.250 100.0 0.6875 0.648 3 48.0 0.500 11.75 0.750 100.0 0.375 0.470 1 48.0 0.500 15.50 0.750 120.0 0.375 0.517 100 2 48.0 0.500 20.75 1.250 120.0 0.625 0.692 3 48.0 0.500 15.50 0.750 120.0 0.375 0.517 1 72.0 0.750 7.00 0.375 80.0 0.375 0.175 2 150 1 72.0 0.750 26.25 1.250 80.0 1.1875 0.69 3 1 72.0 0.750 7.00 0.375 80.0 0.375 0.175 1 72.0 0.750 7.00 0.375 100.0 0.375 0.14 150 2 72.0 0.750 28.75 1.3125 100.0 1.0625 0.71 3 72.0 0.750 7.00 0.375 100.0 0.375 0.14 1 72.0 0.750 7.00 0.375 120.0 0.375 0.117 2 150 1 72.0 0.750 30.50 1.4375 120.0 1.000 0.731 3 72.0 0.750 7.00 0.375 120.0 0.375 0.117 131 FOURTH QUARTER / 1983 Table 6. Two-Span Section Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth Thickness Width 1 Thickness Width Thickness A Ix no. 1 AT/AB ** 1 24.0 0.375 7.50 0.375 80.0 0.375 0.187 50-50 2 24.0 0.375 20.25 1.000 80.0 0.500 7.35 40.6 2 1.013 3 24.0 0.375 7.50 0.375 80.0 0.375 0.187 1 24.0 0.375 8.375 0.4375 100.0 0.375 0.195 50-50 2 24.0 0.375 21.25 1.125 100.0 0.5625 7.35 40.6 2 0.850 3 24.0 0.375 8.375 0.4375 100.0 0.375 0.195 1 24.0 0.375 9.375 0.4375 120.0 0.375 0.182 50-50 2 24.0 0.375 25.50 1.125 120.0 0.5625 7.35 40.6 3 0.850 3 24.0 0.375 9.375 0.4375 120.0 0.375 0.182 1 24.0 0.375 6.500 0.375 80.0 0.375 0.163 50-60 2 24.0 0.375 24.00 1.250 80.0 0.6875 7.35 40.6 2 1.090 3 24.0 0.375 9.750 0.625 80.0 0.375 0.406 1 24.0 0.375 7.250 0.375 100.0 0.375 0.145 50-60 2 24.0 0.375 29.00 1.250 100.0 0.6875 7.35 40.6 2 1.054 3 24.0 0.375 11.00 0.625 100.0 0.375 0.366 1 24.0 0.375 7.750 0.375 120.0 0.375 0.129 50-60 2 24.0 0.375 31.00 1.4375 120.0 0.6875 7.35 40.6 2 1.080 3 24.0 0.375 12.75 0.625 120.0 0.375 0.354 1 24.0 0.4375 6.00 0.375 80.0 0.375 0.15 50-70 2 24.0 0.4375 31.00 1.4375 80.0 0.9375 7.35 40.6 3 1.188 3 24.0 0.4375 14.25 0.6875 80.0 0.500 0.49 1 24.0 0.4375 6.00 0.375 100.0 0.375 0.12 50-70 2 24.0 0.4375 36.50 1.375 100.0 0.9375 7.35 40.6 3 1.07 3 1 24.0 0.4375 16.00 0.8125 100.0 0.500 0.52 1 24.0 0.4375 6.00 0.375 120.0 0.375 0.10 2 50-70 1 24.0 0.4375 41.00 1.625 120.0 1.000 7.35 40.6 3 1.11 3 24.0 0.4375 18.00 0.875 120.0 0.4375 0.60 1 24.0 0.500 6.00 0.375 80.0 0.375 0.15 50-80 2 24.0 0.500 31.00 1.500 80.0 1.000 7.35 40.6 3 1.162 3 24.0 0.500 15.75 0.875 80.0 0.625 0.55 132 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 6. Two-Span Section Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth Thickness Width Thickness Width 1 Thickness A Ix no. AT/AB 1 24.0 0.500 6.00 0.375 100.0 0.375 0.12 50-80 2 24.0 0.500 35.50 1.625 100.0 1.000 7.35 40.6 3 1.153 3 24.0 0.500 18.75 0.875 100.0 0.5625 0.583 1 24.0 0.500 6.00 0.375 120.0 0.375 0.100 50-80 2 24.0 0.500 42.00 1.8125 120.0 1.125 7.35 40.6 4 1.127 3 24.0 0.500 19.75 1.000 120.0 0.5625 0.585 | 1 48.0 0.5625 8.00 0.4375 80.0 0.375 0.233 100-100 2 48.0 0.5625 30.50 1.3750 80.0 0.9375 7.35 40.6 2 1.118 3 48.0 0.5625 8.00 0.4375 80.0 0.375 0.233 1 48.0 0.5625 9.50 0.4375 100.0 0.375 0.222 100-100 2 48.0 0.5625 35.50 1.4375 100.0 0.875 7.35 40.6 2 1.166 3 48.0 0.5625 i 9.50 0.4375 100.0 0.375 0.222 1 48.0 0.5625 10.25 0.500 120.0 0.375 0.227 100-100 2 48.0 0.5625 37.25 1.625 120.0 0.9375 7.35 40.6 2 1.076 3 48.0 0.5625 10.25 1.625 120.0 0.375 0.227 1 48.0 0.5625 6.25 0.375 80.0 0.375 0.156 100-120 2 48.0 0.5625 40.5 1.5625 80.0 1.500 7.35 40.6 2 1.054 3 48.0 0.5625 15.50 0.750 80.0 0.625 0.465 1 48.0 0.5625 6.50 0.375 100.0 0.375 0.13 100-120 2 48.0 0.5625 42.50 1.875 100.0 1.500 7.35 40.6 2 1.063 3 48.0 0.5625 16.00 0.8125 100.0 0.500 0.52 1 48.0 0.5625 7.00 0.375 120.0 0.375 0.116 100-120 2 48.0 0.5625 48.0 2.0625 120.0 1.5625 7.35 40.6 2 1.056 3 48.0 0.5625 18.25 0.875 120.0 0.500 0.532 1 48.0 0.625 6.75 0.375 80.0 0.375 0.168 100-140 2 48.0 0.625 39.25 1.875 80.0 1.750 7.35 40.6 2 1.051 3 48.0 0.625 24.00 1.125 80.0 1.0625 0.635 1 1 48.0 0.625 6.75 0.375 100.0 0.375 0.135 100-140 1 2 48.0 0.625 51.00 2.000 100.0 1.9375 7.35 40.6 2 1.053 3 1 48.0 0.625 26.50 1.250 100.0 0.9375 0.706 133 FOURTH QUARTER / 1983 Table 6. Two-Span Section Dimensions No. SPANS cross Web J Top Flange Bottom Flange | Bottom Stiffener (ft) sect. 1 Depth Thickness 1 Width Thickness Width Thickness 1 A Ix no. AT/AB 1 48.0 0.625 1 6.75 0.375 120.0 0.375 0.113 100-140 2 48.0 0.625 J 57.00 2.437 120.0 2.1875 7.35 40.6 2 1.058 3 48.0 0.625 28.50 1.375 120.0 0.875 0.75 1 48.0 0.6875 6.75 0.375 80.0 0.375 0.168 100-160 2 48.0 0.6875 40.5 1.9375 80.0 1.8125 7.35 40.6 2 1.083 3 48.0 0.6875 27.00 1.375 80.0 1.3125 0.707 1 48.0 0.6875 6.75 0.375 100.0 0.375 0.135 100-160 2 48.0 0.6875 48.00 2.0625 100.0 1.875 7.35 40.6 2 1.056 3 48.0 0.6875 28.50 1.500 100.0 1.1875 0.72 1 48.0 0.6875 6.75 0.375 120.0 0.375 0.1125 100-160 2 48.0 0.6875 51.0 2.4375 120.0 2.000 7.35 40.6 2 1.036 3 48.0 0.6875 32.25 1.5625 120.0 1.0625 0.79 1 72.0 0.75 7.25 0.4375 80.0 0.4375 0.181 150-150 2 72.0 0.75 39.0 1.6875 80.0 1.4375 7.35 40.6 2 1.144 3 72.0 0.75 7.25 0.4375 80.0 0.4375 0.181 1 72.0 0.75 9.00 0.500 100.0 0.375 0.240 150-150 2 72.0 0.75 41.00 1.875 100.0 1.4375 7.35 40.6 2 1.069 3 72.0 0.75 9.00 0.500 100.0 0.375 0.240 1 72.0 0.75 9.50 0.625 120.0 0.375 0.264 150-150 2 72.0 0.75 46.0 2.000 120.0 1.4375 7.35 40.6 2 1.066 3 72.0 0.75 9.50 0.625 120.0 0.375 0.264 1 86.0 0.8125 6.00 0.375 80.0 0.375 0.150 150-180 2 86.0 0.8125 40.00 1.75 80.0 1.625 7.35 40.6 2 1.076 3 86.0 0.8125 13.0 0.625 80.0 0.5625 0.361 1 86.0 0.8125 6.00 0.375 100.0 0.375 0.12 150-180 2 86.0 0.8125 45.0 1.9375 100.0 1.5625 7.35 40.6 2 1.116 3 86.0 0.8125 14.0 0.75 100.0 0.500 0.42 1 86.0 0.8125 6.0 0.375 120.0 0.375 0.100 150-180 2 86.0 0.8125 49.0 2.125 120.0 1.625 7.35 40.6 2 1.068 3 86.0 0.8125 16.0 0.8125 120.0 0.4375 0.495 134 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 6. Two-Span Section Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth Thickness Width Thickness Width Thickness A Ix no. AT/AB 1 100.0 0.9375 6.00 0.375 80.0 0.375 0.150 150-210 2 100.0 0.9375 40.25 2.000 80.0 1.875 7.35 40.6 2 1.073 3 100.0 0.9375 19.00 0.875 80.0 0.75 0.554 1 100.0 0.9375 6.00 0.375 100.0 0.375 0.12 150-210 2 100.0 0.9375 49.00 2.0625 100.0 1.9375 7.35 40.6 2 1.043 3 100.0 0.9375 20.5 0.9375 100.0 0.6875 0.560 1 100.0 0.9375 6.00 0.375 . 120.0 0.375 0.100 150-210 2 100.0 0.9375 54.00 2.3125 120.0 2.0625 7.35 40.6 2 1.009 3 100.0 0.9375 22.00 1.0625 120.0 0.625 0.623 1 115.0 1.0625 6.00 0.375 80.0 0.375 0.15 150-240 2 115.0 1.0625 45.00 1.9375 80.0 2.0625 7.35 40.6 2 1.046 3 115.0 1.0625 26.00 1.1250 80.0 1.0625 0.688 1 115.0 1.0625 6.00 0.375 100.0 0.375 0.12 150-240 2 115.0 1.0625 50.00 2.4375 100.0 2.3125 7.35 40.6 2 1.054 j 3 115.0 1.0625 28.0 1.25 100.0 0.9375 0.7466 1 115.0 1.0625 6.00 0.375 120.0 0.375 0.100 150-240 2 115.0 1.0625 58.00 2.75 120.0 2.625 7.35 40.6 2 1.012 3 115.0 1.0625 30.0 1.375 120.0 0.9375 0.733 | **L1-L2. prehensive laboratory study,12 in which composite and specifications1 and as given in Table 2, has also permitted noncomposite negative and positive sections were tested, development of a series of design charts17 which permit has resulted in the following interaction equation: rapid evaluation of these moments. Computerized Design—The general response of single or continuous curved box girder bridges can be predicted by the solution of a series of coupled differential equations, where: when written in difference form as given in Fig. 5. These equations have been subsequently incorporated Mp = plastic bending strength 9 M = design bending moment into a computer program, which automates the design/ analysis of prismatic or nonprismatic straight or curved box Tp = plastic torsional strength 1 2 T = design torsional moment girders as governed by the AASHTO criteria. ' The box girder may be either composite or noncomposite Subsequent examination of typical box girders and their construction and can have integral transverse diaphragms moment capacities, as controlled by the current AASHTO spaced along the box and contain top lateral bracing. The 135 FOURTH QUARTER / 1983 Table 7. Three-Span Box Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth Thickness Width Thickness Width Thickness A Ix no. ATMB ** 1 24.0 0.375 8.25 0.4375 80.0 0.375 0.241 2 50-50-50 1 24.0 0.375 19.00 0.8125 80.0 0.4375 .7.35 40.6 4 0.882 3 1 24.0 0.375 6.00 0.375 80.0 0.375 0.15 1 24.0 0.375 9.75 0.4375 100.0 0.375 0.227 50-50-50 2 24.0 0.375 20.25 0.875 100.0 0.4375 7.35 40.6 3 0.81 3 24.0 0.375 6.00 0.375 100.0 0.375 0.12 1 24.0 0.375 10.25 0.500 120.0 0.375 0.227 1 50-50-50 2 24.0 0.375 22.25 0.9375 120.0 0.500 7.35 40.6 3 0.695 3 24.0 0.375 6.00 0.375 120.0 0.375 0.100 1 24.0 0.375 7.00 0.375 80.0 0.375 0.175 | 50-60-50 2 24.0 0.375 22.25 1.000 80.0 0.375 7.35 40.6 3 1.483 1 3 24.0 0.375 6.75 0.375 80.0 0.375 0.1687 1 1 24.0 0.375 7.75 0.375 100.0 0.375 0.155 1 50-60-50 2 24.0 0.375 24.00 1.0625 100.0 0.4375 7.35 40.6 3 1.165 | 3 24.0 0.375 7.25 0.375 100.0 0.375 0.145 | 1 24.0 0.375 7.75 0.375 120.0 0.375 0.129 1 50-60-50 2 24.0 0.375 24.50 1.0625 120.0 0.500 7.35 40.6 3 0.8677 3 24.0 0.375 7.00 0.375 120.0 0.375 0.1167 1 24.0 0.375 7.00 0.375 80.0 0.375 0.175 | 50-70-50 2 24.0 0.375 24.0 1.125 80.0 0.5625 7.35 40.6 2 1.200 1 3 24.0 0.375 8.50 0.375 80.0 0.375 0.212 | 1 24.0 0.375 8.00 0.375 100.0 0.375 0.16 50-70-50 2 24.0 0.375 26.25 1.1875 100.0 0.5625 7.35 40.6 2 1.108 1 3 24.0 0.375 9.00 0.4375 100.0 0.375 0.21 1 24.0 0.375 8.50 0.4375 120.0 0.375 0.165 1 50-70-50 2 24.0 0.375 28.5 1.3125 120.0 0.6875 7.35 40.6 2 0.906 3 24.0 0.375 10.00 0.500 120.0 0.375 0.222 1 1 24.0 0.4375 6.00 0.375 80.0 0.375 0.15 J 50-80-50 2 24.0 0.4375 28.00 1.3125 80.0 0.8125 7.35 40.6 2 1.13 1 3 24.0 0.4375 9.50 0.4375 80.0 0.375 0.277 1 136 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 7. Three-Span Box Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener (ft) sect. Depth Thickness Width Thickness Width Thickness A Ix no. AT/AB 1 24.0 0.4375 6.00 0.375 100.0 0.375 0.12 50-80-50 2 24.0 0.4375 31.00 1.375 100.0 0.750 7.35 40.6 2 1.136 3 24.0 0.4375 11.50 0.500 100.0 0.375 0.306 1 24.0 0.4375 6.00 0.375 120.0 0.375 0.100 50-80-50 2 24.0 0.4375 33.00 1.500 120.0 0.750 7.35 40.6 2 1.10 3 24.0 0.4375 11.50 0.5625 120.0 0.375 0.287 1 48.0 0.5625 12.75 0.5625 80.0 0.4375 0.410 100-100-100 2 48.0 0.5625 25.50 1.125 80.0 0.5625 7.35 40.6 2 1.275 3 48.0 0.5625 6.00 0.375 80.0 0.375 0.15 1 48.0 0.5625 14.00 0.625 100.0 0.4375 0.40 100-100-100 2 48.0 0.5625 28.50 1.1875 100.0 0.5625 7.35 40.6 2 1.203 3 48.0 0.5625 6.00 0.375 100.0 0.375 0.12 1 48.0 0.5625 15.50 0.6875 120.0 0.375 0.4376 100-100-100 2 48.0 0.5625 31.00 1.3125 120.0 0.6875 7.35 40.6 2 0.986 3 48.0 0.5625 6.00 0.375 120.0 0.375 0.100 1 48.0 0.5625 8.00 0.4375 80.0 0.375 0.238 100-120-100 2 48.0 0.5625 30.00 1.4375 80.0 0.9375 7.35 40.6 2 1.15 3 48.0 0.5625 7.00 0.375 80.0 0.375 0.175 1 48.0 0.5625 9.50 0.4375 100.0 0.375 0.222 100-120-100 2 48.0 0.5625 33.50 1.500 100.0 0.875 7.35 40.6 2 1.148 3 48.0 0.5625 7.50 0.375 100.0 0.375 0.15 1 48.0 0.5625 10.25 0.500 120.0 0.375 0.228 100-120-100 2 48.0 0.5625 37.00 1.625 120.0 0.875 7.35 40.6 2 1.145 3 48.0 0.5625 8.50 0.375 120.0 0.375 0.142 1 48.0 0.5625 7.50 0.4375 80.0 0.375 0.219 100-140-100 2 48.0 0.5625 34.0 1.6250 80.0 1.250 7.35 40.6 2 1.105 3 48.0 0.5625 11.00 0.5625 80.0 0.4375 0.353 1 48.0 0.5625 8.75 0.4375 100.0 0.375 0.204 100-140-100 2 48.0 0.5625 40.00 1.6875 100.0 1.250 7.35 40.6 2 1.08 3 48.0 0.5625 12.50 0.625 100.0 0.4375 0.357 137 FOURTH QUARTER / 1983 Table 7. Three-Span Box Dimensions No. SPANS cross 1 Web 1 Top Flange Bottom Flange Bottom Stiffener (ft) sect, j Depth Thickness 1 Width Thickness Width Thickness A Ix no. AT/AB 1 48.0 0.5625 9.50 0.4375 120.0 0.375 0.185 100-140-100 2 48.0 0.5625 44.50 1.875 120.0 1.3125 7.35 40.6 2 1.059 3 48.0 0.5625 15.00 0.6875 120.0 0.375 0.458 1 48.0 0.625 6.00 0.375 80.0 0.375 0.15 100-160-100 2 48.0 0.625 39.00 1.750 80.0 1.5625 7.35 40.6 2 1.092 3 48.0 0.625 18.00 0.8125 80.0 0.750 0.332 1 48.0 0.625 6.00 0.375 100.0 0.375 0.12 100-160-100 2 48.0 0.625 43.00 1.875 100.0 1.500 7.35 40.6 2 1.075 3 1 48.0 0.625 18.00 0.875 100.0 0.625 0.504 1 48.0 0.625 6.00 0.375 120.0 0.375 0.100 100160-100 2 48.0 0.625 46.00 2.0625 120.0 1.500 7.35 40.6 2 1.054 3 48.0 0.625 20.00 0.875 120.0 0.5625 0.519 1 72.0 0.750 17.25 0.750 80.0 0.6875 0.47 150-150-150 2 72.0 0.750 31.50 1.375 80.0 0.9375 7.35 40.6 2 1.154 3 72.0 0.750 6.00 0.375 80.0 0.375 0.15 1 72.0 0.750 18.75 0.8125 100.0 0.5625 0.542 150-150-150 2 72.0 0.750 34.50 1.500 100.0 0.875 7.35 40.6 2 1.183 3 72.0 0.750 6.00 0.375 100.0 0.375 0.12 1 72.0 0.750 20.00 0.9375 120.0 0.5625 0.555 150-150 150 2 72.0 0.750 37.50 1.625 120.0 0.875 7.35 40.6 2 1.161 3 72.0 0.750 6.00 0.375 120.0 0.375 0.100 1 72.0 0.750 10.00 0.4375 80.0 0.4375 0.25 150 180-150 2 72.0 0.750 37.50 1.750 80.0 1.500 7.35 40.6 2 1.093 3 72.0 0.750 7.00 0.375 80.0 0.375 0.15 1 72.0 0.750 11.00 0.5625 100.0 0.375 0.33 150 180 150 2 72.0 0.750 43.00 1.8125 100.0 1.4375 7.35 40.6 2 1.084 3 72.0 0.750 7.75 0.375 100.0 0.375 0.155 1 72.0 0.750 14.00 0.625 120.0 0.375 0.388 150 180 150 2 72.0 0.750 46.00 2.00 120.0 1.4375 7.35 40.6 2 1.066 3 72.0 0.750 8.50 0.375 120.0 0.375 0.142 138 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION Table 7. Three-Span Box Dimensions No. SPANS cross Web Top Flange Bottom Flange Bottom Stiffener ! (ft) sect. Depth Thickness Width Thickness Width Thickness A Ix no. AT/AB 1 72.0 0.750 8.50 0.375 80.0 0.4375 0.182 150-210-150 2 72.0 0.750 45.00 2.000 80.0 2.125 7.35 40.6 . 2 1.059 3 72.0 0.750 17.00 0.750 80.0 0.6875 0.464 1 72.0 0.750 9.50 0.4375 100.0 0.375 0.222 150-210-150 2 72.0 0.750 51.50 2.1875 100.0 2.125 7.35 40.6 2 1.06 3 72.0 0.750 18.00 0.8750 100.0 0.625 0.504 1 72.0 0.750 9.00 0.4375 120.0 0.375 0.175 150-210-150 2 72.0 0.750 58.00 2.500 120.0 2.250 7.35 40.6 2 1.086 3 72.0 0.750 21.50 0.9375 120.0 0.5625 0.597 1 72.0 0.8125 7.00 0.375 80.0 0.375 0.175 150-240-150 2 72.0 0.8125 52.00 2.250 80.0 2.750 7.35 40.6 2 1.063 3 72.0 0.8125 23.50 1.125 80.0 1.0625 0.622 1 72.0 0.8125 7.00 . 0.375 100.0 0.375 0.140 150-240-150 2 72.0 0.8125 57.50 2.500 100.0 2.6875 7.35 40.6 2 1.069 3 72.0 0.8125 24.50 1.125 100.0 0.875 0.63 1 72.0 0.8125 7.00 0.375 120.0 0.375 0.117 150-240-150 2 72.0 0.8125 62.00 2.750 120.0 2.625 7.35 40.6 2 1.082 3 72.0 0.8125 26.0 1.125 120.0 0.750 0.65 **L\-L2-L3. basic configuration of a typical box and the type of cross specified length of pours. Composite/noncomposite actions diaphragms is shown in Figs. 2, 3 and 4. may be assured after the concrete hardens. The computer output contains influence line ordinates, The entire output sequence is as follows: stresses on top and bottom flanges at locations along the span due to dead load, superimposed dead load, and live Basic Data load plus impact. The stress resultants include the effects Job description of bending, warping and distortion, utilizing the auto Girder geometry matically computed section properties. Structural details Stress envelopes are given for fatigue design. Specifica Concrete properties tions (AASHTO) are used to establish allowable stresses, Loading properties web and flange stiffening requirements and shear connector Section details: span length, plate sizes, section spacing, as given in Tables 1 and 2. properties, stiffener and bracing de Resulting girder deflections and rotations, due to se tails, dead loads quential concrete placements, can also be determined for Pouring sequence geometry 139 FOURTH QUARTER / 1983 Clear roadway width -N- Wsw Wc tc tsw so CROSS DIAPHRAGM (Ab) Inside overhang Fig. 2. Structural details Stresses Torsion envelope Dead-load normal stress Bimoment envelope Superimposed dead-load normal stress Normal stress envelope Live-load normal stress (positive and negative mo Stress range envelope ment) d/ty b/t requirements, web stress Theoretical web stiffener requirement Forces Total stresses Moment envelope Shear connector spacing requirements Deflection envelope Fatigue criteria Shear envelope Pouring sequence deflections Vertical reaction envelope Natural frequency Torsion reaction envelope Pouring sequence rotations Right Flange Fig. 3. Cross section Left Web Right Web Transverse Bottom Stiff Flange Stiff. 140 Ef^pERINeaQlJBNi?!/; AMERICAN INSTITUTE OF STEEL CONSTRUCTION Diaphragm spacing Field-Test Comparison to Theoretical Results—The | 1 1 1 I i static and dynamic response of a full scale bridge structure, when subjected to a known truck loading, was examined during the Fall 1973.16 The bridge consisted of twin steel ^T^ boxes (4.5 ft X 8.8 ft) in composite action with a 9V2-in. concrete slab. That part of the bridge under test was a X / three-span continuous with span lengths 100 ft, 130 ft, and 120 ft and centerline radius of 1,317 ft. The bridge was designed as a two-lane structure. The deformations and strains throughout the structure were measured during the application of the test vehicle. The resulting static load data were then examined and the results compared to the data obtained by the previously described analytical tech Section A 0.4 (exterior span) Section B l.OLi (first interior support) X X Section C O.5L2 (midspan of interior span) te Examination of the data given in Table 8 indicates rea sonable correlation between theory and experiment and the importance of the top lateral bracing during the dead-load response. Ab The resulting girder deflections at Section A and Section Nf C are given in Table 9. The data shown in this table show comparisons between theory and tests, indicating reason able correlation especially for live load effects. The dis crepancy in the dead-load results is due to the sequential Afr = Bracing member area. placement of the concrete and time dependent composite actions. Fig. 4. Bracing types (top lateral) 2 2 2 lEIvv ^/EIwV h (EIx + CKt) _ T6 EIw + 2h (EIw + CKt)1 h (EIx + CKt) EIW R <*) R : 2 -mzh 4 2 2 h EIx "| 2 -EI 4EI + h CK 6EIW + 2h CKt + 4EIW + h GKt -EIw W W t -[• R2 J n-2 n-1 n+1 n+2 2 EIw h CKt 6Kt + EI ) + -(^+EIX) R2 X R2 \R2 / R2 2 -qyh 2 2 2 EIW' V+ h (EI>c + CKt) r6/EIw\2h (EIx + CKn! t/EIwV h (EIx + 6Kt) EIw R ,t R R Fig. 5. Curved girder finite difference equation 141 FOURTH QUARTER / 1983 Table 8. Prototype Bridge Test-Stresses REFERENCES Theory (ksi) 1. Standard Specifications for Highway Bridges 1'2th Edition, Cross Test With Without AASHTO, Washington, D.C, 1977. Sections Loading (ksi) bracing bracing 2. Guide Specifications for Horizontally Curved Highway Bridges AASHTO, Washington, DC, 1980. DL 7.70 6.25 9.02 3. Galambos, T. V. Tentative Load Factor Design Criteria 1 A LL + I 2.32 2.65 2.65 for Curved Steel Bridges Rept.No. 50, Washington Univ., Total 10.02 8.90 11.67 St. Louis, Mo., May 1978. 4. Wolchuck, R., and R. Mayrbaurl Proposed Design DL -5.14 -4.96 -6.66 Specifications for Steel Box Girder Bridges FHWA Rept. B LL + I - .76 -1.05 -1.05 TS-80-205Jan. 1980. Total -5.90 -6.01 -7.71 5. Hems, C. P. Box Girder Bridge Design AISC Engi neering Journal, Vol. 15, No. 4, Dec. 1978. DL 6.12 3,26 4.27 6. Heins, C. P., and L. J. Hua Proportioning Box Girder C LL + I 1.83 2.07 2.07 Bridges ASCE St. Dw. journal, Vol 106, No. ST11, Nov. Total 7.95 5.33 6.34 1980. 7. Heins, C. P., and D. H Hall Designers Guide to Steel Box Girder Bridges Bethlehem Steel Corp., Bethlehem, Pa., 1981. 8. Heins, C. P., and J. C. Olenick Curved Box Beam Bridges Table 9. Prototype Bridge Test-Vertical Deflections Analysis Computers and Structures Journal, Vol. 6, pp. 65-73, Pergamon Press, London, 1976. Theory 9. Heins, C P., and F. H. Sheu Computer Analysis of Steel Cross Test With Without Box Girder Bridges Civil Engineering Dept. Report, Univ. Section Loading (in.) bracing bracing of Maryland, June 1981. 10. Heins, C. P., and J. C. Olenick Diaphragms for Curved DL 1.19 0.88 0.93 Box Beam Bridges ASCE St. Dw. Journal, Vol. 101, No. A LL + I 0.20 0.23 0.23 ST10, October 1975. Total 1.39 1.11 1.16 11. Heins, C. P., and A. Sahin Natural Frequency of Curved Box Girder Bridges ASCE St. Dw. Journal, Vol. 105, No. DL 0.50 0.51 0.47 ST12, Dec. 1979. C LL + I 0.26 0.27 0.27 12. Heins, C. P., and R. Humphrey Bending and Torsion Total 0.76 0.78 0.74 Interaction of Box Girders ASCE St. Div. Journal, Vol. 105, No. ST5, May 1979. 13. Heins, C P., et al. Curved Steel Box Girder Bridges: A Survey ASCE St. Dw. Journal, Vol. 104, No. ST11, Nov. 1978. 14. Heins, C P.,et al. Curved Steel Box Girder Bridges: State In general, results indicate the curved girder finite dif of Art ASCE St. Dw. Journal, Vol. 104, No. ST11, Nov. ference theory provides an excellent technique for box 1978. girder design. 15. Heins, C P., and W. H. Lee Curved Box Girder Field Test ASCE St. Dw. Journal, Vol. 107, No. ST2, Feb. CONCLUSIONS 1981. 16. Yoo, C H., J. Buchanan, C P. Heins, and W. L. Arm This paper presents the results of various research which strong Loading Response of a Continuous Box Girder has permitted a better understanding of steel box girder Bridge Proceedings ASCE Specialty Conference on Metal bridges and the development of design criteria. Through Bridges, St. Louis, Mo., Nov. 1974. use of these design data, more efficient and rapid design of 17. Heins, C P., and J. Y. Shyu Moment Capacity of Box such structures can be achieved, and a better service to the Girders Institute for Physical Science and Technology public provided. Report, University of Maryland, June 1981. 142 ENGINEERING JOURNAL / AMERICAN INSTITUTE OF STEEL CONSTRUCTION