C

Area of reinforcement across the flange of a flanged beam Area of tension reinforcement effective at a section

Compressive force in the concrete in the direction of the longitudinal axis

Variation of the longitudinal force acting in a section of flange within the distance av [See 4.3.2.5(3)]

Tensile force in longitudinal reinforcement

Force component in the compression zone, parallel to Vod, of elements with variable depth Shear capacity of the concrete compression zone

Design shear force in the section, uncorrected for effects of variable section depth Force component due to inclined prestressing tendons

Design shear resistance of a section in elements without shear reinforcement Maximum design shear force that can be carried without web failure Reduced value of VRd2, due to axial force

Design shear resistance of a section, in elements with shear reinforcement

Force component in the tensile zone, parallel to Vod, in elements with variable depth

Contribution of shear reinforcement

Distance between points of zero and maximum moment

Nominal web thickness

Design yield strength of shear reinforcement Flange depth

A constant relating to section depth and curtailment Spacing of reinforcing bars across the flange of flanged beams Angle of the shear reinforcement to the longitudinal axis of a member Shear force enhancement coefficient

Angle of the concrete struts with the longitudinal axis of the member Efficiency factor

Reinforcement ratio corresponding to Asl

Average stress in concrete due to axial force

Effective average stress in concrete due to axial force

Basic design shear strength of members without shear reinforcement

Sum of diameter of prestressing ducts at a given level

4.3.2.1 General

P(1) This section applies to beams and slabs designed for flexure in accordance with 4.3.1. It also applies to prestressed elements and columns subjected to significant shear forces designed in accordance with 4.3.1 and 4.3.5.

P(2) In general, a minimum amount of shear reinforcement shall be provided, even where calculation shows that shear reinforcement is unnecessary. This minimum may be omitted in elements such as slabs, (solid, ribbed, hollow), having adequate provision for the transverse distribution of loads, where these are not subjected to significant tensile forces. Minimum shear reinforcement may also be omitted in members of minor importance which do not contribute significantly to the overall strength and stability of the structure.

(3) Rules for minimum shear reinforcement are given in 5.4. An example of a member of minor importance would be a lintel of less than 2 m span.

P(4) In structures of variable depth, the design shear forces shall be modified by a contribution corresponding to the components of the compressive and tensile resultants perpendicular to the member axis.

P(5) In prestressed structures, in the calculation of Vsd account shall be taken of the effect of inclined prestressing tendons.

P(6) When determining the necessary longitudinal reinforcement in areas subjected to shear, account shall be taken of the possible increase of the tensile force beyond the value corresponding to the bending moment. (7) This increase is covered by the "shift" rules given in Section 5.4.2.1.

4.3.2.2 Design method for shear

(1) The method for shear design, set out in the following sections, is based on three values of design shear resistance:

— VRd1 the design shear resistance of the member without shear reinforcement. (See 4.3.2.3).

— VRd2 the maximum design shear force that can be carried without crushing of the notional concrete compressive struts. (See 4.3.2.3, 4.3.2.4.3, 4.3.2.4.4).

— VRd3 the design shear force that can be carried by a member with shear reinforcement.

(2) Any section for which the design shear, VSd, is less than VRd1, requires no design shear reinforcement but except in the cases defined in 4.3.2.1 P(2) and (3), minimum shear reinforcement should be provided in accordance with 5.4.

(3) For sections where VSd exceeds VRd1, shear reinforcement should be provided such that:

VSd r VRd3

The amount of shear reinforcement should not be less than the minimum given in 5.4.2.2.

(4) In the absence of more rigorous analysis, at no section in any element should the design shear force exceed VRd2. (See 4.3.2.3). Where the member is subjected to an applied axial compression, VRd2 should be reduced in accordance with Equation (4.15) below.

where:

VRd2.red is the reduced value of VRd2

Bcp.eff is the effective average stress in the concrete due to axial force. ocpeff is given by

Equation (4.16) below

where:

NSd is the design axial force

As2 is the area of reinforcement in the compression zone at the ultimate limit state fyk is the yield strength of the compression steel.

(fyk/Ys should not exceed 400 N/mm2)

Ac is the total area of the concrete cross-section.

(5) Close to supports where the configuration of concentrated loads and support reaction is such that a proportion of the loads may be carried to the support by direct compression (direct support), an allowance may be made for an enhancement of the shear resistance VRd1 [see (9) below]. Any such enhancement of VRd1 should be ignored when checking VRd2-

(6) The attainment of VRd1 depends significantly on the proper anchorage of the tension reinforcement or prestressing tendons on each side of any possible plane of failure. Rules are provided to ensure this, in Chapter 5.

(7) For cases where Vsd > VRd1, two design methods are given in the following clauses:

The variable truss angle method allows more freedom in the arrangement of reinforcement than the standard method. It will frequently lead to substantial economies in shear reinforcement but may require increases in the longitudinal tension steel.

It should be used when a member is subjected to combined shear and torsion.

(8) If the web contains grouted ducts with a diameter 0 > bw/8 the shear resistance VRd2 should be calculated on the basis of a nominal web thickness given by:

where C 0 is determined for the most unfavourable level.

(9) For members without shear reinforcement, and for members with shear reinforcement where the Standard Method of shear design is used (4.3.2.4.3) and where the conditions set out in (11) below are satisfied, an enhancement of shear resistance, only for concentrated loads situated at a distance x r 2.5 d from the face of the support, is permitted [(5) above]. Solely for this purpose, the value TRd in Equation (4.18) may be multiplied by a factor ", when estimating VRd1, where:

When this enhancement is taken into account, VRd1 and shear reinforcement should be calculated at all critical sections over the length 2.5 d from the face of the support, with " = 1.0 on the span side of the relevant concentrated loads; the maximum shear reinforcement so obtained should be provided over this entire length.

Where the dominant load on a beam is a concentrated load close to a support, the above procedure may lead to minimum reinforcement throughout the beam. In these cases, care is required, and the designer may wish to base the resistance on the unenhanced VRd1.

(10) Because of the increased resistance due to direct transmission of loads close to supports, it will normally be conservative to evaluate VSd at a distance d from the face of a direct support on beams or slabs with continuously distributed loading.

(11) When taking account of the increased shear strength close to the supports in (9) or (10) above, the following conditions should be satisfied.

a) the loading and support reactions are such that they cause diagonal compression in the element (direct support).

b) at an end support, the whole tension reinforcement required within a distance of 2.5 d from the support should be anchored into the support.

c) at an intermediate support the tension reinforcement required at the face of the support should continue for at least 2.5 d + 1b.net into the span.

4.3.2.3 Elements not requiring design shear reinforcement (Vsd r VRd1) (1) The design shear resistance VRd1 is given by:

vRd1 " t ^Rd k (1.2 + AO Pl) + |0.15|(iCp]bwd (4.18)

where rRd = basic design shear strength = (0.25 fctk0.05)/Yc. Yc should be taken as | 1.5 |. Values of rRd are given in Table 4.8.

k = |1| for members where more than 50 % of the bottom reinforcement is curtailed. otherwise, k = | 1.6 - d " 11 (d in metres)

As1 = the area of tension reinforcement extending not less than d + lb.net beyond the section considered (see Figure 4.12). lb.net is defined in 5.2.2.3, and Figure 5.2.

bw = minimum width of the section over the effective depth. Bsp = NSd/Ac

Nsd = longitudinal force in section due to loading or prestressing (compression positive).

Table 4.8 — Values for Tr^ (N/mm2) with Yc = 1.5 for different concrete strengths

fck

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