COMPOSITE SECTION

Effective Flange Width [LRFD Art. 4.6.2.6.1]

Effective flange width is the lesser of

\frac{1}{4} s p a n = \frac{3300}{4} = 8250 m m

12 t_s + greater of (web thickness or 1/2 beam top flange width) is

(12 \times 190 + 0.5 \times 1225) = 2892.5 m m

Average spacing between beams = 3600 mm

Therefore, the effective flange width is = 2892.5 mm

Modular Ratio Between Slab and Beam Materials

Modular ratio between slab and beam materials, n is

n = \frac{E_{c s}}{E_{c}} = \frac{26802.7}{33978.6} = 0.7888

Transformed Section Properties

Transformed flange width = n (Effective flange width)

= (0.7888)(2892.5) = 2281.6 mm

Transformed flange area = n (Effective flange width)(t_s)

= (0.7888)(2892.5)(190) = 433505 mm²

Note: Only the structural thickness of the deck, 190 mm, is considered.

Due to camber of the prestressed precast beam, a minimum haunch thickness of 10 mm, at midspan, is considered in the structural properties of the composite section. Also, the width of haunch must be transformed.

Transformed haunch width= (0.7888)(1225)= 966.28 mm

Transformed area of haunch= (0.7888)(1225)(10)= 9663 mm²

Table 1. TABLE A3-1. (Table 3.2.3-1.1.) Properties of Composite Section
	A	y_b	Ay_b	A(y_bc-y_b)2	I	I+A(y_bc-y_b)²
Girder	523107	722	3.777E+08	1.057E+11	1.908E+11	2.965E+11
Haunch	9663	1605	0.155E+08	0.018E+11	0.805E+05	0.018E+11
Slab	433505	1705	7.391E+08	1.234E+11	1.30E+09	1.247E+11
Slab						4.23E+11

where:

A_c = total area of composite section = 966279 mm²

h_c = overall depth of the composite section = 1800 mm

I_c = moment of inertia of the composite section = 4.230 × 10111 mm⁴

y_bc = distance from the centroid of the composite section to the extreme bottom fiber of the precast beam =1171.5 mm

y_tg = distance from the centroid of the composite section to the extreme top fiber of the precast beam = 428.5 mm

y_tc = distance from the centroid of the composite section to the extreme top fiber of the slab = 628.5 mm

S_bc = composite section modulus for the extreme bottom fiber of the precast beam

= \frac{I_{c}}{y_{b c}} = 3.611 \times 10^{8} {m m}^{3}

S_tg= composite section modulus for the top fiber of the precast beam

= \frac{I_{c}}{y_{t g}} = 9.872 \times 10^{8} {m m}^{3}

S_tc = composite section modulus of extreme top fiber of the slab

\frac{1}{n} \times \frac{I_{c}}{y_{t c}} = 8.532 \times 10^{8} {m m}^{3}