With shear connectors welded to the top flange of a beam or girder, a concrete slab may be cmade to work with that member in carrying bending stresses. In effect, a portion of the slab, called the effective width, functions much like a steel cover plate. In fact, the effective slab area may be transformed into an equivalent steel area for computation of composite-girder stresses and deflection. This is done by dividing the effective concrete area by the modular ratio n, the ratio of modulus of elasticity of steel, 29,000 ksi, to modulus of elasticity of the concrete. The equivalent area is assumed to act at the center of gravity of the effective slab.
The equivalent steel section is called the transformed section.
Allowable-Stress Design. Composite girders, in general, should meet the requirements of plate girders (Art. 11.15). Bending stresses in the steel girder alone and in the transformed section may be computed by the moment-of-inertia method, as indicated in Art. 11.15, or by load-factor design, and should not exceed the allowable for the material. The stress range at the shear connector must not exceed the allowable for a Category C detail.
The allowable concrete stress may be taken as 0.4Æ’c, where Æ’c unit ultimate compressive strength of concrete, psi, as determined by tests of 28-day-old cylinders. The allowable tensile stress of steel reinforcement for concrete should be taken as 20 ksi for A615 Grade 40 steel bars and 24 ksi for A615 Grade 60 steel bars. The modular ratio n may be assumed as follows:
To account for creep of the concrete under dead load, design of the composite section should include the larger of the dead-load stresses when the transformed section is determined with n or 3n.
The neutral axis of the composite section preferably should lie below the top flange of the steel section. Concrete on the tension side should be ignored in stress computations.
Effective Slab Width. The assumed effective width of slab should be equal to or less than one-quarter the span, distance center to center of girders, and 12 times the least slab thickness (Fig. 11.10). For exterior girders, the effective width on the exterior side should not exceed the actual overhang. When an exterior girder has a slab on one side only, the assumed effective width should be equal to or less than one-twelfth the span, half the distance to the next girder, and 6 times the least slab thickness (Fig. 11.10).
Span-Depth Ratios. For composite highway girders, depth of steel girder alone should preferably be at least 1â„30 of the span. Depth from top of concrete slab to bottom of bottom flange should preferably be at least 1â„25 of the span. For continuous girders, spans for this purpose should be taken as the distance between dead-load inflection points.
Girder Web and Stiffeners. The steel web should be proportioned so that the average shear stress over the gross section does not exceed the allowable. The effects of the steel flanges and concrete slab should be ignored. In addition, depth-thickness ratio should meet the requirements of Art. 11.12. Also, stiffeners should be provided, where needed, in accordance with those requirements. For web splices, see Arts. 5.26, 5.27, and 5.30.
Bending Stresses. If, during erection, the steel girder is supported at intermediate points until the concrete slab has attained 75% of its required 28-day strength, the composite section may be assumed to carry the full dead load and all subsequent loads. When such shoring is not used, the steel girder alone must carry the steel and concrete dead loads. The composite section will support all loads subsequently applied. Thus, maximum bending stress in the steel of an unshored girder equals the sum of the dead-load stress in the girder alone plus stresses produced by loads on the composite section. Maximum bending stress in the concrete equals the stresses produced by those loads on the composite section at its top surface.
The positive-moment portion of continuous composite-girder spans should be designed in the same way as for simple spans. The negative-moment region need not be designed for composite action, in which case shear connectors need not be installed there. But additional connectors should be placed in the region of the dead-load inflection point as indicated later.
If composite action is desired in the negative-moment portion, shear connectors should be
installed. Then, longitudinal steel reinforcement in the concrete should be provided to carry the full tensile force. The concrete should be assumed to carry no tension.
Shear Connectors. To ensure composite action, shear connectors must be capable of resisting both horizontal and vertical movements between concrete and steel. They should permit thorough compaction of the concrete so that their entire surfaces are in contact with the concrete. Usually, headed steel studs or channels, welded to the top flange of the girder, are used.
Channels should be attached transverse to the girder axis, with fillet welds at least along heel and toe. Minimum weld size permitted for this purpose is 3â„16 in.
Studs should be 3â„4- or 7â„8-in nominal diameter. Overall length after welding should be at least 4 times the diameter. Steel should be A108, Grades 1015, 1018, or 1020, either fully or semikilled. The studs should be end-welded to the flange with automatically timed equipment.
If a 360 weld is not obtained, the interrupted area may be repaired with a 3â„16-in fillet weld made by low-hydrogen electrodes in the shielded metal-arc process. Usually, two or more studs are installed at specific sections of a composite girder, at least four stud diameters c to c.
Clear depth of concrete cover over the tops of shear connectors should be at least 2 in.
In addition, connectors should penetrate at least 2 in above the bottom of the slab. Clear distance between a flange edge and a shear-connector edge should not be less than 1 in in highway bridges, 11â„2 in in railroad bridges.
Pitch of Shear Connectors. In general, shear connectors should not be spaced more than 24 in c to c along the span. Over interior supports of continuous beams, however, wider spacing may be used to avoid installation of connectors at points of high tensile stress.
Pitch may be determined by fatigue shear stresses due to change in horizontal shear or by ultimate-strength requirements for resisting total horizontal shear, whichever requires the smaller spacing. (Also, see the following method for stress design.)
Fatigue. As live loads move across a bridge, the vertical shear at any point in a girder changes. For some position of the loading, vertical shear at the point due to live load plus impact reaches a maximum. For another position, shear there due to live load plus impact becomes a minimum, which may be opposite in sign to the maximum. The algebraic difference between maximum and minimum shear, kips, is the range of shear Vr.
The range of horizontal shear, kips per lin in, at the junction of a slab and girder at the point may be computed from
where w transverse length of channel, in
d =stud diameter, in
h = overall stud height, in
B = 4 for 100,000 cycles of maximum stress
3 for 500,000 cycles
2.4 for 2,000,000 cycles
2.1 for more than 2,000,000 cycles
alpha= 13 for 100,000 cycles of maximum stress
10.6 for 500,000 cycles
7.85 for 2,000,000 cycles
5.50 for more than 2,000,000 cycles
The required pitch pr , in, of shear connectors for fatigue is obtained from
where Zr is the allowable range of horizontal shear of all connectors at a cross section.
Over interior supports of continuous beams, the pitch may be modified to avoid installation of connectors at points of high tensile stress. But the total number of connectors should not be decreased.
Ultimate Strength. The total number of connectors provided for fatigue, in accordance with Eq. (11.44), should be checked for adequacy at ultimate strength under dead load plus live load and impact. The connectors must be capable of resisting the horizontal forces H, kips, in positive-moment regions and in negative- moment regions. Thus, at points of maximum moment, H may be taken as the smaller of the values given by Eqs. (11.45) and (11.46).
where Qu ultimate strength of shear connector, lb, and reduction factor, 0.85. In Eq. (11.48), the smaller of H1 or H2 should be used for H for determining the number of connectors required between a point of maximum positive moment and an end support in simple beams, and between a point of maximum positive moment and a dead-load inflection point in continuous beams. H3 should be used for H for determining the total number of shear connectors required between a point of maximum negative moment and a dead-load inflection point in continuous beams. H3 = 0 if slab reinforcement is not used in the computation of section properties for negative moment.
Additional Connectors at Inflection Points. In continuous beams, the positive-moment region under live loads may extend beyond the dead-load inflection points, and additional shear connectors are required in the vicinity of those points when longitudinal reinforcing steel in the concrete slab is not used in computing section properties. The number needed is given by
This number should be placed on either side of or centered about the inflection point for which it is computed, within a distance of one-third the effective slab width.