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approximately 3 feet along the girder.
The unbraced length of the top flange is approximately 16.3 feet in Span 1. Assume that the average
deck thickness in the overhang is 10 inches. The weight of the deck finishing machine is not considered.
Compute the vertical load on the overhang brackets.
1 10
Deck: lbs/ft
× 4 × × 150 = 250
2 12
Deck forms + Screed rail = 224 lbs/ft
Uniform load on brackets = 474 lbs/ft
Compute the lateral force on the flanges due to overhang brackets. See Figure D-1.
78
- 1ëø öø
± = = 49.1 degrees
tan
ìø
67.5
íø øø
474
Fl = k/ft
= 0.411
2À
îø49.1ëø öøùø(1000)
tan
ïø ìø úø
360
ðø íø øøûø
Since the example girder is a tub box girder, the provisions of Article 6.10.3.2 are used. Compute the
lateral flange moment on the outermost tub flange due to the overhang forces. The lateral flange moment
at the brace points due to the overhang forces is negative in the top flange of G2 on the outside of the
curve because the stress due to the lateral moment is compressive on the convex side of the flange at
the brace points. The opposite would be true on the convex side of the G1 top flange on the inside of the
curve at the brace points, as illustrated in later calculations. The flange is treated as a continuous beam
supported at brace points; therefore, the unfactored lateral moment is calculated as follows:
îø0.411 (16.3)2ùø
ïø úø
Ml = Fl Lb2 / 12 = - = -9.1
k-ft Eq (C6.10.3.4-2)
12
ðø ûø
D-6
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Top Flange in Compression (continued)
In addition to the moment due to the overhang brackets, the inclined webs of the box cause a lateral
force on the top flanges. This force is relatively small in this case and will be ignored. A third source of
lateral bending is due to curvature, which can be conservatively estimated by the approximate V-load
Equation (C4.6.1.2.4b-1) given in the LRFD Specifications, as illustrated below.
From Table C1, the moment due to the steel weight plus Cast #1 is 4,123 k-ft. The load factor for
constructibility is 1.25 according to the provisions of Article 3.4.2. Using the section properties from
Table C5, the bending stress, fbu, in the top flange without consideration of longitudinal warping is
computed as:
îø4123(12)(42.80)ùø(1.25) = -14.29 ksi (C)
ftop flg = fbu = -
ïø úø
185187
ðø ûø
The top flange size is constant between brace points in this region. In positive moment regions, the
largest value of fbu may not necessarily be at either brace point. Generally though, fbu will not be
significantly larger than the value at adjacent brace points, which is the case in this example. Therefore,
the computed value of fbu at Section 1-1 will be conservatively used in the strength check. The
approximate Eq (C4.6.1.2.4b-1) is used below to compute the lateral flange bending moment due to
curvature. Eq (C4.6.1.2.4b-1) assumes the presence of a cross frame at the point under investigation
and, as mentioned previously, M is constant over the distance between brace points. Although the use
of Eq (C4.6.1.2.4b-1) is not theoretically pure for tub girders or at locations in-between brace points, it
may conservatively be used. Note that the vertical web depth has been conservatively used in the
following calculation. For a single flange, consider only half of the girder moment due to steel and Cast
#1. M = 4,123/2 = 2062 k-ft.
2
2
îø ùø
Ml 2062 (16.3)
ïø úø k-ft Eq (C4.6.1.2.4b-1)
Mlat = = - = -11.77
NRD 10(716.25)(6.5)
ðø ûø
The lateral flange moment at the brace points due to curvature is negative when the top flanges are
subjected to compression because the stress due to the lateral moment is compressive on the convex
side of the flange at the brace points. The opposite is true whenever the top flanges are subjected to
tension.
Mtot_lat = k-ft (factored)
[-11.77 + (-9.1)](1.25) = -26.09
fl is defined as the flange lateral bending stress determined using the provisions of Article 6.10.1.6 This
value may be determined directly from first-order elastic analysis in discretely braced compression
flanges if the following is satisfied.
D-7
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Top Flange in Compression (continued)
Cb Rb
Eq (6.10.1.6-2)
Lb d" 1.2Lp
fbu
Fyc
where:
29000
1.0(3.77)
E 50
Lp = = ft. Eq (6.10.8.2.3-4)
1.0rt = 7.57
Fyc 12
where:
bfc
rt = Eq (6.10.8.2.3-9)
Dc tw
ëø öø
1
12 +
ìø1 3 bfc tfc
íø øø
16
= in.
= 3.77
îø1 1 43.08(0.5625) ùø
12 +
ïø úø
3 16(1)
ðø ûø
Since the stresses remain reasonably constant over the section, Cb is taken as 1.0.
Article 6.10.1.10.2 indicates that the web load-shedding factor, R , is taken as 1.0 for
b
constructibility.
Check the relation given in Eq (6.10.1.6-2):
1.0(1.0)
Lb = 16.3 ft.
1.2(7.57) = 16.99
- 14.29
50
Therefore, the flange lateral bending stress, fl, may be determined from first-order elastic analysis.
2
1.0 (16)
Stop_flange = in3
= 42.7
6
Mtot_lat
-26.09(12)
fl = = ksi (factored)
= -7.3
Stop_flange 42.7
D-8
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Top Flange in Compression (continued)
Another significant source of lateral flange bending not considered in this calculation is the forces that
develop in single-diagonal top flange bracing members (arranged in the pattern shown in Figure 2 of the
introduction section) as a result of vertical bending of the box girder. This effect is recognized in lateral
flange moments taken directly from a finite element analysis, but a closed-form solution is more elusive.
As mentioned previously, this effect can probably be minimized most effectively by utilizing parallel
single-diagonal bracing members in each bay.
For critical stages of construction, the resistance of the compression flange in noncomposite boxes with
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