Conclusiones

A connection can be designed to transfer bending moment by means of a force couple of tensile and compressive forces, see Fig. 9-6. Reinforcement bars, bolts or other steel components with tensile capacity are arranged and anchored in such a way that an internal force couple can be developed when the connection is subjected to imposed rotation. On the opposite side of the connection, transfer of the corresponding compressive force through the joint must be ensured. (In such connections various regions, parts and components will be subjected to compression and tension and Chapters 6 and 7 are applicable for the behaviour and design of the individual parts.). Full scale testing by Ferriera et al.

(2003), Fig 9.7 has shown that the negative moment capacity of precast concrete beams made continuous with high tensile rebars placed in topping is at least 85% of the moment of resistance of a fully monolithic connection.

Fig. 9-6: Principle of moment resisting connections in precast frames. Moment continuity exists only for imposed loads after the insitu infill has matured to full strength

lap

projecting bars from beam

projecting loops

self weight (gravity) insitu infill

connecting dowel

imposed loads

moment tension

compression

Fig. 9-7: Full scale testing of support continuity between precast concrete beams with reinforced insitu topping, Ferreira (2002)

The magnitude of the transferred moment depends on the magnitude of the tensile and compressive resultants at the actual rotation and the internal lever arm as

z F z F

M_R = _t⋅ = _c⋅ (9-1)

where Ft = actual tensile force Fc = actual compressive force z = actual internal lever arm

The tensile capacity of the tensile components as well as the strength of the compressed region of the connection can determine the flexural resistance MR of the connection in bending.

Alternatively, a moment capacity can be achieved by force couples of compressive and/or shear forces. A common example of this is the pocket type of column-base connection, as shown in Fig. 9-8, where the bending moment at the column base is resisted by a force couple of horizontal compressive forces in the foundation pocket. Under certain conditions it would also be possible to add the effect of vertical shear forces (force couple) acting along the compressed parts of the vertical joint interfaces.

When a connection in a floor is activated after the erection of the floor, it will give continuity only for that part of the load that is added after erection, and, if the bending moment capacity is limited, only for a part of this additive load, see Fig. 9-9. Cases with partial continuity will require certain consideration in design, since standard methods are not applicable.

A certain moment capacity can be obtained as a secondary effect. Typical examples are connections in floor slabs. The floor elements are designed to be simply supported, but, due to requirements of minimum tensile capacity within floors and between floors and their supports, a certain amount of tie bars is provided. Together with the jointing with grouts and cast insitu concrete, the tie connections will attain a certain bending moment capacity that was not aimed at by purpose.

The moment capacity depends on the position of the tie bars in relation to the sign of the acting moment. This secondary moment capacity can be favourable in case of accidental situations, since it provides ductility and facilitates force redistribution.

However, such a secondary bending moment capacity could also have an unfavourable effect, because of the restraint that it causes. A floor element that is designed to be simply supported could be subjected to a negative moment that it is not prepared for, due to unintended restraint at the supports.

As a result, flexural cracks could appear in positions where they could be dangerous with regard to the load-carrying capacity of the elements, see Section 3.5.2.

Beam 2 Beam 1

Fig. 9-8: Connections for transfer of bending moment at a column foundation pocket

Fig. 9-9: Typical example of floor-wall-floor connection designed to have full or partial capacity for moment in the floor

The mechanical behaviour can vary considerably depending on how the connection is designed.

For this reason it is essential to distinguish the following two extreme cases.

M M

µN µN

µN µN

N N

N N

d h

ls

continuity steel area Asper unit run

cast insitu infill

precast floor

precast wall N

M

h

z Fc

Fc

precast column

submerged part of column surface roughened

insitu concrete or grout

base of column sometimes tapered to aid grout run levelling

shims

insitu concrete foundation usually

300 mm approx 40

1,5 h minimum

In a connection where the joint sections, with regard to their bending moment capacity, are weak in relation to the adjoining elements, the imposed rotation θ will concentrate to such a section, see Fig. 9-10 a. This is typical for connections that are not designed to be moment-resisting, but where single tie bars are placed across the joint. In such connections the ultimate rotation θu will be determined by the elongation capacity or the anchorage of the tie bars. The compressive side of the connection will not be influenced in a critical way.

However, in a connection that has a significant moment capacity, which is of the same order as that of the adjoining elements, a high bending moment will result in flexural deformations that are spread in the whole connection region, including the connection zones of the elements. In the ultimate state plastic deformations can be expected in the whole connection regions, see Fig. 9-10 b. The rotation θ of the connection depends mainly on the curvature distribution within the plastic region and its extension. The ultimate tensile strain in the steel as well as the ultimate compressive strain in the concrete can limit the ultimate rotation θu.

le ?

Fig. 9-10: Extreme cases with regard to the mechanical behaviour, a) connection provided with single tie bars only and where the rotation concentrates at the weak joint section, b) connection with a moment resistance that is about the same as in the elements and where the flexural deformations are spread in the whole connection region

Example 9-1

In the analysis of tests on hollow core floors [Broo et al. (2004)] it was found that the support connection at the end support gave a certain rotational restraint. The floor was fixed to a cast insitu tie beam, which in turn was tied by reinforcement bars to a rigid support beam, see Fig. 9-11. The response of the hollow core floor was modelled by non-linear FE analyses. When assuming that the floor was simply supported, the predicted response was too stiff compared to the observed. Hence, it was assumed that the end restraint needed to be considered in the analysis.

The cast insitu concrete filled the ends of the hollow cores to a certain distance from the end, which means that the connection between the tie beam and the floor was assumed to be rigid.

However, the connection between the cast insitu tie beam and the support beam was much weaker and consequently it was assumed that the tie beam could rotate as a rigid body relative to the support beam, in a similar manner as shown in Fig. 9-10 a. Then the vertical reinforcement bars provide rotational restraint by their pullout resistance. Hence, the relation between moment and rotation at the end depends directly on the relation between tie force and crack opening. This relation was modelled as a non-linear spring according to the principles in Sections 7.2.3.1 and 7.4.1. When the so defined

la

non-linear spring was adopted into the FE analysis, there was a good agreement between the predicted and the observed responses.

Since the rotation was very small, it was sufficient to model the response of the connection before yielding of the bar. The bars were anchored on each side of the joint that opened. Therefore, the bars were treated as continuous tie bar, which was approximate because the anchored length was short. By means of eqs. (7-30) and (7-4) the non-linear spring was modelled as

( )

( )

Fig. 9-11: Connection at the end support of hollow core floors analysed by Broo et al. (2004) a) detail of tested specimen, b) model. The end restraint was modelled assuming a stiff rotation between the transverse tie beam and the support beam with the vertical reinforcement bars acting as non-linear springs