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Section properties from Table C5 are computed using the effective bottom flange thickness are used to
calculate the vertical bending stresses in the flange at the splice for strength whenever the bottom flange
is subjected to tension. The gross area is used for the top flange in this case. For flanges and splice
plates subjected to compression, net section fracture is not a concern and the effective area is taken
equal to the gross area.
Calculate the factored vertical bending stress in the top and bottom flange mid-thicknesses at the
strength limit state for both the positive and negative live load bending conditions. The longitudinal
component of the top flange bracing area is again included in the effective section properties. The
contribution of deck reinforcement is not included in the section properties at this section. The smaller
section is to be used to design the splice, therefore, the longitudinal flange stiffener is not included. The
provisions of Article 4.5.2.2 are followed to determine which composite section (cracked or uncracked) to
use.
Using the effective section properties (from separate calculations), calculate the average factored bending
stress in the top and bottom flange at the Strength limit state for both the positive and the negative live
load bending conditions.
Negative live load bending case
1.25(2403)(41.29) [ 1.25(326) + 1.5(428) ](43.02) 1.75(-3087)(43.02)
îø ùø
ksi (T)
Ftop flg = - + + 12 = 4.19
ïø úø
179050 179740 179740
ðø ûø
1.25(2403)(37.52) [ 1.25(326) + 1.5(428) ](35.79) 1.75(-3087)(35.79)
îø ùø12 = -2.85 ksi (C)
Fbot flg =
+ +
ïø úø
179050 179740 179740
ðø ûø
Positive live load bending case
1.25(2403)(41.29) [ 1.25(326) + 1.5(428) ](23.18) 1.75(5264)(9.91)
îø ùø
ksi (C)
Ftop flg = - + + 12 = -11.58
ïø úø
179050 338310 456064
ðø ûø
1.25(2403)(37.52) [ 1.25(326) + 1.5(428) ](55.63) 1.75(5264)(68.90)
îø ùø12 = 26.32 ksi (T)
Fbot flg =
+ +
ïø úø
179050 338310 456064
ðø ûø
D-62
Bolted Splice Design Section 2-2 G2 Node 20.3
Strength - Top and Bottom Flange (continued)
An acceptable alternative to the preceding calculation is to calculate the average factored vertical bending
stress in both flanges for both live load bending conditions using the appropriate gross section properties.
Then, for the flange in tension, multiply the calculated average stress times the gross area, A , of the
g
flange, and then divide the resulting force by the effective area, A , of the flange to determine an adjusted
e
average tension-flange stress. Then, for the critical live load bending condition, use the adjusted average
stress in the tension flange and the calculated average stress in the compression flange to determine
which flange is the controllong flange, as defined below.
Separate calculations (similar to subsequent calculations) show that the positive live load bending case is
critical. For this loading case, the bottom flange is the controlling flange since it has the largest ratio of
the flexural stress to the corresponding critical flange stress. Article 6.13.6.1.4c defines the design
stress, Fcf, for the controlling flange as follows:
fcf
ëø öø
+ ±Æf Fyf
ìø
Rh
íø øø
Fcf = Eq (6.13.6.1.4c-1)
e" 0.75±Æf Fyf
2
fcf is the maximum flexural stress due to the factored loads at the mid-thickness of the controlling flange
at the point of splice. The hybrid factor Rh is taken as 1.0 when Fcf does not exceed the specified
minimum yield resistance of the web. ± is taken as 1.0, except that a lower value equal to (Fn/Fyf) may
be used for flanges where Fn is less than Fyf.
26.32
îø ùø
+ 1.0(1.0)(50)
ïø úø
1.0
ðø ûø
Fcf = ksi
= 38.16
2
0.75±Æf ksi; therefore, use 38.16 ksi
Fyf =
0.75(1.0)(1.0)(50) = 37.5
The minimum design force for the controlling (bottom) flange, P , is taken equal to Fcf times the smaller
cf
effective flange area, Ae, on either side of the splice. The area of the smaller flange is used to ensure that
the design force does not exceed the strength of the smaller flange. In this case, the effective flange
areas are the same on both sides of the splice.
Pcf = kips (T)
38.16(43.13) = 1646
The minimum design stress for the noncontrolling (top) flange for this case is specified in Article
6.13.6.1.4c as:
fncf
Fncf = Eq (6.13.6.1.4c-3)
Rcf e" 0.75±Æf Fy
Rh
where ± is again taken as 1.0. For a continuously braced top flange in tension, ± should also be taken
equal to 1.0.
D-63
Bolted Splice Design Section 2-2 G2 Node 20.3
Strength - Top and Bottom Flange (continued)
Fcf 38.16
Rcf = =
= 1.45
fcf 26.32
fncf is the factored vertical bending stress in the noncontrolling flange at the splice concurrent with f .
cf
fncf
-11.58
= ksi
Rcf 1.45 = 16.79
Rh 1.0
0.75±Æf ksi (controls)
Fyf =
0.75(1.0)(1.0)(50) = 37.5
The minimum design force for the noncontrolling flange, P , is computed as:
ncf
Pncf = FncfAe = kips (C)
(37.5)(16.0)(1.0) = 600
where the effective flange area, Ae, is taken equal to the smaller gross flange area, Ag, on either side of
the splice since the flange is subjected to compression. In this case, the gross flange areas are the
same on both sides of the splice.
Top Flange
St. Venant torsional shears are not considered in the top flanges of tub girders. Lateral flange bending in
the top flange is also not considered after the deck has hardened and the section is closed. Therefore:
Fncf Ae 600
No. bolts required = = bolts, use 12 bolts
= 10.8
Rr 55.4
600
k/bolt
= 50
12
Since a fill plate is not required for the top flange splice, no reduction in the bolt design shear resistance
is required per the requirements of Article 6.13.6.1.5.
Bottom Flange
Compute the factored St. Venant torsional shear in the bottom flange at the strength limit state. Warping
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