When the reinforcement is known, 0 and T^d2 may be determined from Equations (4.44) and (4.45) below.
If the resulting value of 0 lies outside the limits given by (4.42) the nearest limit should be taken.
(8) The resultant of the tensile forces Fs1 = As1 • fyld is assumed to act at the centre of gravity of the equivalent hollow section; a portion of the longitudinal steel (or the prestressing tendons) may therefore be placed along the centre line of the member; however, in order to ensure that the outward pressure exerted by the struts is transmitted to the stirrups, it is necessary for at least one longitudinal bar to be located at each corner of the actual section.
(9) For pure torsion, the following detailing requirements apply:
— the minimum percentage of reinforcement in 5.4.2.2
— the limitation of the crack widths in 4.4.2
— the detailing arrangement of reinforcement in 5.4.2.3
4.3.3.2 Combined effects of actions
(1) The same procedure is used to define an equivalent thin walled closed section as for pure torsion. The normal and shear stresses in this section are determined by conventional elastic or plastic methods
(2) When the stresses have been found, the necessary reinforcement at any point of the thin-walled section can be determined by plane stress distribution formulae. The concrete stress can also be determined. If the reinforcement so found is not feasible in practice, it may be changed to another statically equivalent reinforcement lay-out, provided that the effects of this change are taken into account in regions near beam ends and holes (See A2.8).
(3) The concrete stress resulting from combined shear and torsion in the individual walls of the equivalent thin-walled section should not exceed Bc = vfcd where V is given by Equation (4.41) in 4.3.3.1.
(4) For box sections with reinforcement in both faces of each wall, V may be taken as 0.7 - fck/200 @ 0.5 for walls subjected to shear stresses from combined shear and torsion.
4.3.3.2.2 Simplified procedure
Torsion combined with flexure and/or with longitudinal forces
(1) The longitudinal steel required for flexure and torsion should be determined separately in accordance with (4.3.1) and this section respectively and the following rules then applied.
— in the flexural tension zone, the longitudinal torsion steel should be additional to that required to resist flexure and longitudinal forces;
— in the flexural compression zone, if the tensile force due to torsion is less than the concrete compression stress due to flexure, no additional longitudinal torsion steel is necessary.
(2) Where torsion is combined with a large bending moment, this can give rise to a critical principal stress in the compression zone, particularly in box girders. In such cases the principal compressive stress should not exceed !fcd, (see Section 4.2.1.3.3), that stress being derived from the mean longitudinal compression in flexure and the tangential stress due to torsion, taken as TSd = TSd/(2 Ak.t). For Ak and t, see 4.3.3.1. Torsion combined with shear
(3) The design torsional moment and the applied design shear TSd and VSd respectively, should satisfy the following condition:
where TM1 is the design torsional resistance moment according to Equation (4.40)
VRd2 is the design resistance shear relating to a strut inclined at an angle 0 according to Equation (4.26) or (4.28) in 4.3.2.4.4.
(4) The calculations for the design of the stirrups can be made separately for torsion, in accordance with 4.3.3.1, and for shear in accordance with Equation (4.27) or (4.29) in 4.3.2.4.4. The angle 0 of the equivalent concrete struts is the same for both torsion and shear design.
(5) For a solid, approximately rectangular section no shear and torsion reinforcement is necessary, apart from the minimum reinforcement given in section 5.4.2.2(5), Table 5.5, if the following conditions are satisfied:
4.3.3.3 Warping torsion
P(1) Stresses due to restrained warping of a section (warping stresses) may be significant and may need to be taken into account.
(2) Generally, it will be safe to ignore warping stresses in the ultimate limit state.
(3) For closed thin-walled sections and solid sections, warping stresses may normally be neglected.
4.3.4 Punching
VRds d
"crit crit,ex
Prestressing force corresponding to initial value without losses (Pmo in 2.5.4 and 4.2.3) Total resistance to flexural and punching shear
Distance of critical section for punching shear from the centroid of a column See Figure 4.23
ucrit,ln dH
Equivalent effective depth, when checking punching shear within a column head (Figure 4.23)
Respectively the effective depth in x and y directions, at the point of intersection between the design failure surface and the longitudinal reinforcement
Depth of an enlarged column head (Figure 4.22 and Figure 4.23)
A coefficient (Equation 4.56)
Overall dimensions of a rectangular column head
Diameter of a circular column
Dimensions of a rectangular column
Distance from the column face to the edge of column head (Figure 4.22 and Figure 4.23)
Distance from the column face to the edge of the corresponding column head (rectangular columns) Figure 4.22 and Figure 4.23
Spans between columns on the x and y directions respectively (Figure 4.24) msdx, msdy Minimum design bending moments in the x and y directions respectively (Equation 4.59) Perimeter of critical section for punching shear
Design shear resistance per unit length of the critical perimeter, for a slab without shear reinforcement dx dy hH k ll,l2 lc lc1, lc2
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