INVESTIGATION ON CRACKS CREATION AND PROPAGATION IN CONCRETE SLAB OF COMPOSITE BEAMS INVESTIGATION ON CRACKS CREATION AND PROPAGATION IN CONCRETE SLAB OF COMPOSITE BEAMS

Analytical and experimental research illustrated initiation of cracks in concrete deck immediately after its casting and placing on the upper flange of steel beams, especially prior to application of additional permanent load on composite element. Not only value of concrete shrinkage strain may influence creation and propagation of cracks in concrete. However ratio of deck reinforcement, cross-sectional area of reinforcement steel and strength of concrete can modify the process. Moreover, the


Introduction
Steel-concrete composite bridges are nowadays considered to be an appropriate structural system for the bridge engineering (Fig. 1). The innovative systems using concrete deck can act both as a roadway resisting local traffic loads and as an integral part of the bridge girders or trusses. In such a design, the concrete slab may act also as an integral part of the compression flanges of the stringers, and cross-beams. The contribution presents problems with rheological effects estimation and concrete cracking consideration, which can be found in the design of especially continuous type composite girders of the steel and concrete. Detail requirements for advanced design of concrete members of these composite steel and concrete structures as outputs of our investigation are given in graphic form.

Failure of the concrete slab by cracking
Composite slab of steel and concrete structural members as shown in Fig. 2 can be affected by tensile cracking induced by shrinkage. The strength degradation may be significant, if there were not enough reinforcing bars crossing the planes of cracking. Shrinkage of the concrete element depends on the environment and the constituents of the concrete. Corresponding strains can reach values accessing of 500 microstrains. Furthermore, shrinkage is time-dependent, and therefore the forces that are created will cause creep. Longitudinal strains can be induced in composite beam due to thermal gradients. The changes in strains are the similar as for shrinkage. The tensile cracking can also be initiated by effects of concrete hydration. considered only subsidiary. The main attention is generally paid to the ultimate strength analyses. Design, analysis and detailing of the bridge concrete deck are actually just in general given in Eurocode 4 [1]. Primary, the slabs are required to be designed to transmit in-plane forces as well as bending moments and shears. Where composite action becomes effective as concrete hardens, effects of heat of hydration of cement and corresponding thermal shrinkage should be taken into account during the construction stage in areas where tension is expected. Specific measures should be provided to limit the effects of heat of hydration of cement. For simplification a constant temperature difference between the concrete section and the steel beam as concrete cooler can be assumed for the determination of the cracked regions. Unless a more accurate method is used, minimum reinforcement area for the slabs of composite beams is essential for limitation of crack width.
Factor specifying capacity of composite steel and concrete beams to prevent slab cracking due thermal effects can be expressed by the ratio of cross-sectional area of the structural steel beam A a to cross-sectional area of concrete slab A c , i.e. β ϭ A a /A c . In fact this factor can be only approximate, because the beam shape or proportion of the flanges is not taken into account.
Based on results of the investigation [2,3,4], it can be supposed that thermal stresses created by effects of hydration of cement can be neglected for the values of ratio β Յ 0.5. Moreover, this effect occurs only during concrete casting and its curing, when magnitude of concrete modulus is rather smaller. Contraction of the concrete through shrinkage is of prime importance for tensile cracking in the case of a composite beam design. These short timevarying deformations of concrete affect greatly serviceability limit state. In hogging region, cracks due to concrete shrinkage during the hydration process have also a significant effect on the ultimate flexural capacity of composite beams. The magnitude and rate of development of the shrinkage strain depend on such characteristics as the relative humidity, temperature, mix proportions as well as shape and size of members. With time increasing, the rate of shrinkage decreases and the shrinkage strains approach its limit value ε sh at the period obviously 28 days.

Stresses and strains in concrete slab produced by shrinkage
In the absence of shear connection, the concrete shrinkage in the sagging region would produce the contraction of the slab and slip at the steel-concrete interface. In reality, the shear connectors resist this lack of slip. Contraction of the concrete through shrinkage will induce deflections and flexural stresses in the steel that are in the same direction as those induced by gravity loads. In order to prevent slip and hence the lack of fit, an axial force P sh , shown in Fig. 2, has to be applied at the steel-concrete interface. This force acts at eccentricities from the shear connection plane to the centroids of both structural parts.
As the force in the shear connection induced by shrinkage acts on the concrete rectangular slab at the vertical distance h c /2 from the plane of application of force P sh to the slab centroid concerned, the strains at the top and bottom fibre of concrete slab in Fig. 3 are given from elementary mechanics by . ( where E c is modulus of elasticity for concrete, b c width and h c thickness of the concrete slab. The axial force in the concrete element N c (t) as well as the axial force in the steel element N a (t), which are generally timedependent, should be equal to the axial force P sh with N c (t) and N a (t) as axial forces variable in time t acting in concrete slab and steel beam at the level of the shear connection interface.
The force corresponding to shrinkage strain of concrete ε s (t) applied at the interface plane (Fig. 2) is given by: where ε s (t) is value of shrinkage strain, ε as (t) conventional strains produced by steel beam at the level of concrete slab neutral axis, ε cs (t) strains in concrete caused by steel beam prevention to the concrete shrinkage, E c (t) modulus of elasticity for concrete, A c cross-sectional area of concrete, z distance between the centroid of concrete slab and the centroid of the beam steel section, E a modulus of elasticity of structural steel, A a cross-sectional area of the structural steel section, I a second moment of area of the structural steel section and conventional factor of flexural stiffness of the steel beam section can be expressed by .
For the strains, the following relationships can be derived: and .
with δ c coefficient of longitudinal stiffness of concrete slab given by δ c ϭ 1/(E c A c ). (6)

Stresses and strains in concrete slab due to direct load actions
The flexure obviously causes compression in concrete element. For the standard forms of composite beams as shown in Fig. 2, the reduction in the flexural rigidity that can occur through accidental cracking is very small. Possible tensile cracking in bottom fibres of slab can exist if the neutral axis is found to lie in the concrete element. Composite beams with full shear connection are assumed to have full shear interaction so that slip and hence slip strain are ignored. The linear strain profile without any step change is shown in Fig. 2 for this configuration. The steel modulus E a and the short-term concrete modulus E c can be considered to be elastic, and for the case of obvious analysis transformed area principles may be adopted. The composite section can be changed into a concrete section by increasing the components of steel elements by the modular ratio of the constituent materials n ϭ E a /E c . The composite beam is supposed to be subjected to positive bending so that the top fibre of the concrete is in compression. The size and position of all elements are obviously known so that the position of the neutral axis lies at the centroid of the transformed section. Once the neutral axis has been located, the stresses and deformations at top and bottom fibre of the concrete slab may be calculated easily. and . ( With the second moment of area of the effective composite section transformed into the concrete section I zc ϭ nI a ϩ I c ϩ ϩ nA a a 2 a ϩ A c a 2 c , modular ratio of the constituent materials defined as n ϭ E a /E c , z c distance between the centroid of the composite section to the extreme fibre of the composite slab in compression, hc thickness of the concrete slab, a c distance between the centroid of concrete slab to the neutral axis of composite beam, a a distance between the centroid of steel beam to the neutral axis of composite section, I c second moment of area of the un-cracked concrete slab, flexural rigidity of the composite beam with full interaction This work has been to some extent supported by the Slovak Grant Agency within the scope of Grant No. 1/0311/09.