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Noncomp 438,966 38.81 43.69
CompDL 633,467 50.44 32.06
2 - 18 x 3
CompDL Bars 454,805 39.76 42.74
2 - 78 x 0.5625
83 x 1.5
CompLL 836,080 62.50 20.00
5-5 LS WT 8 x 28.5
36 A = 338 in2
CompLL Bars 484,714 41.55 40.95
Legend:
B = vertical distance from the neutral axis to the outermost edge of the bottom flange
T = vertical distance from the neutral axis to the outermost edge of the top flange
Noncomp = steel section only
Comp DL = steel section plus concrete deck transformed using modular ratio of 3n
Comp DL Bars = steel section plus longitudinal reinforcement area divided by 3
Comp LL = steel section plus concrete deck transformed using modular ratio of n
Comp LL Bars = steel section plus longitudinal reinforcement
LS = single longitudinal bottom flange stiffener
A = total steel area of box section
Composite section properties, including the concrete deck, are computed using the structural deck area including the
overhang and half of the deck width between girders. The area of the deck haunch is not included. For composite
section properties including only the longitudinal reinforcement, a haunch depth is considered when determine the
position of the deck reinforcement relative to the steel girder. The longitudinal reinforcing steel area equal to 20.0 in2 per
box is assumed placed at the neutral axis of the effective structural deck area.
The modular ratio, n, for live load is 7.56 and 3n is used for superimposed dead load. The effective area of reinforcing
steel used for superimposed dead load is adjusted for creep by a factor of 3. Thus, the reinforcing area used for the
superimposed dead load is 6.67 in2 (20.0 in2/3).
The area and moment of inertia of the box section include the longitudinal component of the top flange bracing area, the
longitudinal flange stiffener (where present) and the 1-inch bottom flange lips. A single top-flange bracing member of
8.0 in2 placed at an angle of 30 degrees from tangent to the girder is assumed. The vertical web depth is shown in the
above table. However, the total area of the inclined webs is used in computing all section properties.
C-7
(This page is intentionally left blank.)
C-8
APPENDIX D
Sample Calculations
D-1
(This page is intentionally left blank.)
D-2
Girder Stress Check Section 1-1 G2 Node 10
Girder Section Proportioning
The web and the flanges must be proportioned according to the provisions of Article 6.11.2.
Web proportions per Article 6.11.2.1:
For a web without longitudinal stiffeners, the web is proportioned such that:
D
d" 150
Eq (6.11.2.1.2-1)
tw
Determine the web depth along the incline. The web rise over run is 4:1.
4.123
ëø öø
D = in.
78 = 80.4
ìø
4.0
íø øø
80.4
= 142.9
0.5625
Flange proportions (Article 6.11.2.2):
Top flanges of tub sections subjected to compression and tension are proportioned such that:
Top flanges: 16 in. x 1.0 in.
bf
Eq (6.11.2.2-1)
d" 12.0
2tf
16
= 8
2(1)
D
Eq (6.11.2.2-2)
bf e"
6
80.4
in.
= 13.4
6
Eq (6.11.2.2-3)
tf e" 1.1tw
in.
1.1(0.5625) = 0.62
Therefore, all section proportions for this location are satisfied. Section proportion checks for the other
design locations will not be shown. All subsequent sections satisfy these limits.
D-3
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Web
In accordance with Article 6.11.1, the web bend-buckling provisions of Article 6.10.1.9 for the non-
composite section must be checked for steel weight and for the Cast #1 of the concrete deck. The web
bend-buckling check is not needed for the final condition. The unfactored moments are from Table C1 .
Load Moment
Steel 1,144 k-ft
Cast #1 2,979 k-ft
Total Moment 4,123 k-ft
Constructibility Load Factor = 1.25 according to the provisions of Article 3.4.2. Neglect the effects of
wind on the structure and the presence of construction equipment for this example.
Compute the bending stress at the top of the web due to the above moment using the section properties
for the noncomposite section from Table C5.
D = 80.4 in.
Dc = N.A. to top of top flange - top flange thickness
= - 1.0 = 41.8
in. (vertical distance)
42.80
4.123
ëø öø
= in. (inclined distance)
41.8 = 43.09
ìø
4.0
íø øø
4123(41.8)(12)
fcw = ftop web = - (1.25) = -13.96
ksi (C)
185187
Article C6.10.1.9.1 states that the compression flange stress may be used instead of the compression in
the web since the difference is negligible. This approach will be used in all subsequent web checks in this
example.
The nominal bend-buckling resistance in girder webs for constructibility is determined according to the
provisions of Article 6.10.1.9.
Compute the nominal bend-buckling stress for the transversely stiffened web without longitudinal
stiffeners.
0.9Ek
Fcrw = but cannot exceed RhFyc or Fyw/0.7 Eq (6.10.1.9.1-1)
2
D
ëø öø
ìø
tw
íø øø
9 9
where: k = =
= 31.3
2 2
Dc 43.09
ëø öø ëø öø
ìø
ìø
80.4
íø øø
D
íø øø
D-4
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Web (continued)
0.9(29000)(31.3)
ksi
= 39.99
2
80.4
ëø öø
ìø
0.5625
íø øø
|-13.96| ksi
Æf
D-5
Girder Stress Check Section 1-1 G2 Node 10
Constructibility - Top Flange in Compression
The flanges must be checked in flexure for steel weight and for Cast #1 of the concrete deck on the
noncomposite section according to the provisions of Article 6.11.3.2. The factored steel stresses during
the sequential placement of the concrete are not to exceed the nominal stresses. The effect of the
overhang brackets on the flanges must also be considered since G2 is an outside girder. The provisions
of Articles 6.10.3.2.1 through 6.10.3.2.3 are applied to the design of the top flange of tub box girders.
Overhang Bracket Load
Since G2 is an outside girder, half of the overhang weight is assumed placed on the girder and the other
half is placed on the overhang brackets, as shown in Figure D-1. [ Pobierz całość w formacie PDF ]
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