(b)Stage 2-Conditions at time of placing wet concrete on girder
For the usual case where the girder is not propped during construction the girder alone must carry its own weight of the wet concrete. At this stage, which is some time after prestress transfer, the concrete strength will have reached f’c while the prestressing force will lie between the initial force Pi and the final force, Pf. As a simplification, the prestressing force is conservatively taken as Pf . The concrete stresses at this stage can therefore be calculated as
Ft = - Pi/Ag + Pieg/Stg – (Mdg+Mds)/Stg (6-27)
Fb = - Pi/Ag - Pieg/Stg + (Mdg+Mds)/Stg (6-28)
Where Mds in the moment caused by the dead load of the wet concrete and associated fromwork. These calculated stresses must satisfy the final stress limits for the girder concrete (e.g., see Table 6-2).
(c)Stage 3 – Final conditions
The hardening of the cast-in-place concrete results in a composite section that will resist all future loading as a unit. Because the precast concrete girder was strained when the
cast –in-place concrete was joined to it, there will be a strain discontinuity at the interface of the two concrete, which must be taken into account when predicting the response of the composite girder.
The actual behavior of a composite girder is rather complex, in that with time there will be a redistribution of stresses between the precast concrete and the cast-in-place concrete due to creep and differential shrinkage. Methods for predicting this complex response are discussed in Section 5.17.
For design purposes a simple procedure is typically used to predict the concrete stresses. It is assumed that the stresses on the girder due to prestress(Pf), self-weight of the girder (Dg), and weight of the cast-in-place concrete (Ds) remain unchanged from those calculated in Stage 2. The stresses due to the additional dead load (Dadd) and the live load (L) are assumed to be resisted by the composite section, with the final stresses being found by summing these two sets of stresses (see Fig. 6-23). In computing the stresses in the composite section the cast-in-place concrete, having an elastic modulus of Ecs is transformed to an equivalently stiff area of precast concrete, having an elastic modulus of Ecg.
The stress at the top face of the composite section, fts, is
Fts = (Mda+Ml)/Stc . Ecs/Ecg (6-29)
Where Mda is the moment due to additional dead load applied after the cast-in-place concrete hardens, Ml is the live-load moment, and Stc is the section modulus of the composite transformed section.
The stress at the top face of the precast girder is
Ftg = - Pf/Ag + Pfeg/Stg - (Mdg+Mds)/Stg - (Mda+Ml)/Sic (6-30)
The stress in the bottom face of the precast girder is
Fbg = - Pf/Ag - Pfeg/Sbg + (Mdg+Mds)/Sbg + (Mda+Ml)/Sbc (6-31)
Where Sic and Sbc are the section moduli of the composite transformed section for calculating flexural stresses at the interface of the two concretes and at the bottom face, respectively. These calculated stresses must satisfy the final stress on the bottom fiber, Eq. (6-31), often govens the choice of the prestressing force.
In additions to investigating the stresses at the three stages listed above, it is necessary to satisfy the strength requirements at both stage2 and stage3. In checking the flexural strength of the composite section for the final conditions (stage3) it is conventional to ignore the strain discontinuity at the interface, but of course to account for the actual strength of the cast-in-place concrete in calculating the depth of the compression zone. In checking the shear strength, the full depth of thecomposite member used.
The deflections for composite members can be estimated using the multipliers given in Table 5-10. An example of the design of a composite bridge girder is given in Chapter13
(b)Stage 2-Conditions at time of placing wet concrete on girder
For the usual case where the girder is not propped during construction the girder alone must carry its own weight of the wet concrete. At this stage, which is some time after prestress transfer, the concrete strength will have reached f’c while the prestressing force will lie between the initial force Pi and the final force, Pf. As a simplification, the prestressing force is conservatively taken as Pf . The concrete stresses at this stage can therefore be calculated as
Ft = - Pi/Ag + Pieg/Stg – (Mdg+Mds)/Stg (6-27)
Fb = - Pi/Ag - Pieg/Stg + (Mdg+Mds)/Stg (6-28)
Where Mds in the moment caused by the dead load of the wet concrete and associated fromwork. These calculated stresses must satisfy the final stress limits for the girder concrete (e.g., see Table 6-2).
(c)Stage 3 – Final conditions
The hardening of the cast-in-place concrete results in a composite section that will resist all future loading as a unit. Because the precast concrete girder was strained when the
cast –in-place concrete was joined to it, there will be a strain discontinuity at the interface of the two concrete, which must be taken into account when predicting the response of the composite girder.
The actual behavior of a composite girder is rather complex, in that with time there will be a redistribution of stresses between the precast concrete and the cast-in-place concrete due to creep and differential shrinkage. Methods for predicting this complex response are discussed in Section 5.17.
For design purposes a simple procedure is typically used to predict the concrete stresses. It is assumed that the stresses on the girder due to prestress(Pf), self-weight of the girder (Dg), and weight of the cast-in-place concrete (Ds) remain unchanged from those calculated in Stage 2. The stresses due to the additional dead load (Dadd) and the live load (L) are assumed to be resisted by the composite section, with the final stresses being found by summing these two sets of stresses (see Fig. 6-23). In computing the stresses in the composite section the cast-in-place concrete, having an elastic modulus of Ecs is transformed to an equivalently stiff area of precast concrete, having an elastic modulus of Ecg.
The stress at the top face of the composite section, fts, is
Fts = (Mda+Ml)/Stc . Ecs/Ecg (6-29)
Where Mda is the moment due to additional dead load applied after the cast-in-place concrete hardens, Ml is the live-load moment, and Stc is the section modulus of the composite transformed section.
The stress at the top face of the precast girder is
Ftg = - Pf/Ag + Pfeg/Stg - (Mdg+Mds)/Stg - (Mda+Ml)/Sic (6-30)
The stress in the bottom face of the precast girder is
Fbg = - Pf/Ag - Pfeg/Sbg + (Mdg+Mds)/Sbg + (Mda+Ml)/Sbc (6-31)
Where Sic and Sbc are the section moduli of the composite transformed section for calculating flexural stresses at the interface of the two concretes and at the bottom face, respectively. These calculated stresses must satisfy the final stress on the bottom fiber, Eq. (6-31), often govens the choice of the prestressing force.
In additions to investigating the stresses at the three stages listed above, it is necessary to satisfy the strength requirements at both stage2 and stage3. In checking the flexural strength of the composite section for the final conditions (stage3) it is conventional to ignore the strain discontinuity at the interface, but of course to account for the actual strength of the cast-in-place concrete in calculating the depth of the compression zone. In checking the shear strength, the full depth of thecomposite member used.
The deflections for composite members can be estimated using the multipliers given in Table 5-10. An example of the design of a composite bridge girder is given in Chapter13
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