Structural Concrete - Hassoun

22.9 Deflections (AASHTO 5.7.3.6) 921
A haunch = nb top_flange t haunch =(0.707)(3.5ft)(1in.) =29.7 in. 2
(Area of transformed haunch)
A gc = A deck = A haunch + A g = 577 + 29.7 + 713 = 1319.7 in. 2
(Area of transformed composite section)
Centroids of the composite section are calculated as below:
[A g (y tg + t haunch + t s )] +
y tc =
=
[A haunch
(
t s + 1 2 t haunch
A gc
[
(577) (30.88 + 1 + 8)+(29.7)
= 23.49 in.
1319.7
y bc = D s − y tc = 72 − 23.49 = 48.51 in.
(
8 + 1 2
y ic = y tc − t haunch − t s = 23.49 − 1 − 8 = 14.49 in.
) ( )]
+ 577 8 2
)] ( )
1
+ A t deck 2 s
I deck = 1 (b 12 eff_int t3 s )= 1 (8.5 × 12)(8)3
12
Moment of inertia of deck
= 4.352 × 10 3 in. 4
I haunch = 1
12 (OHt3 haunch )= 1 (3.915 × 12)(1)3
12
Moment of inertia of haunch
= 3.915 in. 4 )
I gc = I deck + A deck
(y tc − 1 t 2 s + I haunch
Moment of inertia of composite section
) 2
+ A haunch
(y tc − t s − 1 t 2 haunch
( ) 2
= 4352 +(577) 23.49 − 8 2 + 3.9
(
) 2
+ 29.7 23.49 − 8 − 1 2
+ 39.263 +(577)(48.51 − 30.88) 2
= 844465 in. 4
S tc = I gc
y tc
= 844,456
23.49 = 35,956 in.3 Section modulus to top of deck
S bc = I gc
y bc
= 844,456
48.51 = 17,407 in.3 Section modulus to bottom of girder
S ic = I gc
y ic
= 844,456
14.99 = 58,294 in.3 Section modulus to bottom of deck
LOADS ANALYSIS
Dead Loads
1. Interior Girders
DC1: Dead load of structural components
γ c = 150 pcf