3.1. Torsional Moments vs. Twists
presents the graphs of torque (
the average twists (
) for the tested beams. The torque,
, was obtained multiplying the load applied by the actuator by the horizontal projection of the level arm,
, which remained constant (see Figure 5
). The average twist,
, was obtained by dividing the experimental angle measured in Section A-A to the distance between Sections A-A and J-J,
). In each
curve, identification marks were used to highlight the points corresponding to cracking (
) and to yielding of the transverse (
) and longitudinal (
) reinforcement. The yielding points were calculated from the experimental values of the strains recorded by the strain gauges stuck to the reinforcement bars.
As expected, Figure 8
shows the high influence of prestress in the cracking torque. It is known that prestress delays the formation of cracking. For a moderate concrete stress (induced by prestress) of
(Beam D-1.79) an increase of approximately
on the cracking torque is observed, when compared with the beam without prestress (Beam D-0). This shows the efficiency of uniform longitudinal prestress to delay the cracking in beams under torsion. This high influence of prestress can be explained because in torsion the concrete is under a lower and more uniform level of tensile stresses (in the whole section) when compared with the bending situation. Therefore, even for low levels of prestress, the cracking stage is delayed. It is also observed that, in State I (non-cracked state), the steel bars, including the prestressed wires, generally have little influence on the stiffness of the beams. In fact, the
curves are almost coincident at this state.
In State II (cracked state), the curves are almost parallel to each other. This shows that the contribution of the longitudinal prestress for the stiffness of the beams is small at this state. This is due to the adopted prestressing technique (external longitudinal and centred prestress).
As expected, Figure 8
also shows that the use of prestress increases the resistant torque,
, of the beams. However, there is not a clear tendency with respect to the associated twist at the ultimate torque,
. In fact, since prestress induces a compressive stress state in concrete, it would be expected that the deformation capacity of concrete in the compressed areas of the beam (namely in the struts) would decrease as the level of prestress increases. As a consequence, the twist corresponding to the ultimate torque should decrease as the stress induced by prestress increases. This is not the case for Beam D-3.08, which has the highest level of prestress and reaches a twist
that exceeds the same one of the other beams. However, this observation can be explained due to the type of failure of Beams D-0 and D-1.79, which was fragile and somehow premature (failure by pull off of the concrete corners). This subject will be discussed later. This aspect also justifies the different shape of the descending branches of
curves that is observed and the absence of yielding points before the peak torque is reached for Beam D-0.
curves of Figure 8
also show that, before the peak torque is reached, the prestressed beams only present points corresponding to yielding of the transverse reinforcement. It is observed that the yielding of longitudinal reinforcement only occurs after the peak torque. After cracking, the longitudinal prestress reinforcement starts working as ordinary reinforcement under the torsional loading. Consequently, the beams with balanced longitudinal to transverse reinforcement ratios will lose this balance because of the influence of the prestress wires. Hence, the calculation of the balanced ratio of the longitudinal to transverse reinforcements should account for the area of the prestressed steel (
), which leads to an excess of longitudinal reinforcement of about
. Therefore, the transverse reinforcement should yield before the longitudinal reinforcement, as observed in Figure 8
presents, for each tested beam, the main properties of
curves, namely—the cracking torque and correspondent twist (
), the torsional stiffness in State I (
), the torsional stiffness in State II (
), the torque corresponding to the yielding of the transverse reinforcement and correspondent twist (
), the resistant torque (peak torque) and correspondent twist (
). Since the yielding of the longitudinal reinforcement occurs after the peak torque, the corresponding values are not presented.
The torsional stiffness in State I was calculated dividing
in radians unit). Prior to the calculation of the torsional stiffness in State II, the equation of the line of
curve in the linear elastic stage was previously calculated from linear interpolation. For this calculation, the points of the
curves located in the zone that can be identified as belonging to State II were selected. Only the zone of the curves that is approximately a straight line was considered. After the calculation of the equation,
(see Table 3
), the stiffness
is equal to the slope
of the line (with twists converted to radian units).
The analysis of the values displayed in Table 3
confirms the trends observed in the
curves from Figure 8
and previously discussed.