90 Beam-and-slab decks

concrete slab. The grillage model has one longitudinal beam to each two prototype beams. While sufficient transverse members are provided for detailed analysis, their precise positions are chosen so that they intersect support beams at the same points as longitudinal beams. The skew of the grillage, but not the span, differs slightly from that of the prototype to make the mesh regular. (Such expediency greatly reduces the risk of human errors in calculations and thus is likely to improve the accuracy of analysis.)

The longitudinal members are calculated for sections in Fig. 4.7(c) assuming full concrete areas effective, but with in situ slab transformedby modular ratio m = 0.85 of Young's moduli for in situ and prestressedconcrete.

fxl = 0.24 fx2 = 0.174

The torsion constants are calculated separately for the 'beam' and 'slab' parts of each member and added to give

Cxl = 2 X 0.004 + 20 X 02

2 X 085 + 0.006 = 0.016 6

Cx2 = 2 X 0.004 + 20 X 02

3X 0.85 = 0.010

6

The percentage area of reinforcement spanning transversely in such a slab is usually quite high and the inertia calculated on the transformed cracked section does not differ very much from the inertia calculated on the uncracked section ignoring reinforcement. Consequently, since initially the area of reinforcement is not known, the inertia is calculated on the uncracked section with m = 0.85. Transverse grillage membersthen have

fy = 40 X 023 X 0.85 = 0.0023 12

Cy =

40 X 023

X 0.85 = 0.0045.6

The torsion constant of the cracked concrete is likely to be in error by an unknown amount, but here has little effect.

The percentage area of reinforcement in the support diaphragm is low, and so the inertia is calculated on the transformed cracked section, with the effect of slab as flange ignored. The torsion constant of such a beam is also very low, as it is not prestressed and it is made up of discontinuous sections of in situ concrete and precast beam web.Without relevant experimental evidence, it is suggested that

C is

calculated for the area of uncracked concrete used in calculating /. A complete worked example for a composite prestressed concrete

beam bridge is included in references (3] and (4]; and further advice on the design of such decks is included in references [ 5] and [ 6].

Fig. 4.8 (a) Crosssection of composite steeUconcrete deck and of grillage and (b) section represented by longitudinal grillage member.

Grillage examples 91

I I

..l.

4.5.2 Spaced steel 1-beams with reinforced concrete slab Figure 4.8 shows part of a composite deck constructed of reinforced concrete slab on steel beams. Longitudinal grillage members are placed coincident with the centre lines of steel beams, and each represents the part of the deck section shown in (b). Using modular ratio m= 7 forsteel (short-term loading) we obtain

fx = 0.21

ex = 0.000 031 X 7 + 22 X 02

3= 0.0032.

6

The slab is similar to that in Fig. 4.7 so that transverse grillage member properties are calculated in the same way.

Complete worked examples for composite steel beam bridges are included in references [7] and [8], and further advice on the design of such decks is included in references [9] and [10].

4.5.3 Spaced box beam with slab deck Figure 4.9 shows the cross-section of a beam-and-slab deck constructed of spaced prestressed precast concrete box beams supporting a reinforced concrete slab. Longitudinal grillage members are placed coincident with centre lines of beams, with additional 'nominal' members running along centre lines of slab strips.

The section properties of the nominal members are calculated for width of slab to midway to neighbouring beams, hence

fx = 1.4 X 0253

= 0.0018 ex = 1.4 X 0253 = 0 .0036.

12 6

The properties of the beam members are calculated for the sections with flanges including the area in nominal members (unless shear lag has

!al

22

(b)