REINFORCED CONCRETE DESIGN
M,, for design
6.5 CRITICAL SECTIONS FOR SHEAR DESIGN
In for flexural shear, the to be investigated first calculating the nominal shear stress are ones where the shear force is maximum cross-sectional area is minimal.
The maximum force usually occurs in a flexural member at the face of the support, and progressively reduces with increasing from the support. When concentrated loads are involved, shear remains high in the span the support and the first concentrated load.
When a support reaction introduces compression in the end region of the member, the shear strength of this region is enhanced, and inclined cracks do develop near the of the support (which is usually the location of maximum shew). In such a case, the Code 22.6.2.1) allows section located at a distanced (effective depth) from the face of support to be as the section [Fig. The beam segment between this critical section and the face of the support need he designed only for the shear force the critical section. As the shear force at this critical section will he less than (or equal to) the value at the face of the support, the Code recommendation will usually result, in a
value of than otherwise. This is of particular significance in base slabs of footing where flexural (one-way) shcar is a major design consideration [refer Chapter 141.
FOR SHEAR 237
6.6 Critical sections for shear at support
However, when a heavy concentrated load is introduced within the distance from the face of the support, then the face of the support becomes the critical section [Fig. as inclined cracks can develop within this region if the shear strength is exceeded. In such cases, stirrups should he designed and provided in the region between the concentrated load and the support face.
Also, when the favourable effect of transverse compression from the reaction is absent as in a suspended beam [Fig. or a beam (or bracket) connected to the side of another supporting beam [Fig.
-
the critical section for shear should be taken at the face of the support.In the latter case [Fig. special shear reinforcement detailing is called for
-
to ensure that effective shear transfer takes place between the supported (or bracket in some situation) and the supporting beam. It is recommended [Ref. 6.81 that full depth stirrups should be designed in both the supported member and the supporting member in the vicinity of the interface for 'hanging up' a portion of the shear, equal to - the dimensions and D being as shown in Fig. 6.7. The shear reinforcement (stirrups) so designed must be accommodated in the effective regions indicated in Fig. 6.7 [refer Section 6.8 for design procedure].
CONCRETE
BEAM
(a) section of supporting section of supported beam
effective region supporting member
effective region
for member
Fig. 6.7 Detailing stirrups for interface shear at indirect support
6.6 DESIGN SHEAR STRENGTH WITHOUT SHEAR REINFORCEMENT
6.6.1 D e s i g n S h e a r S t r e n g t h of C o n c r e t e in B e a m s
As explained earlier in Section 6.3.2, the margin of strength diagonal cracking is subject to considerable fluctuation on of various factors, and hence is ignored for design purposes [Ref. 6.4, Accordingly, the (average) design shear strength of concrete in reinforced concrete beams without shear
limited to the value of the nominal shear stress corresponding to the load at which the first inclined crack develops; factor of safety 1.2) is also introduced.
magnitude of the design shear strength depends on various factors Section that related to the of concrete and percentage
steely, The values of in Code (Table based on
following empirical formula
=
-
(6.10)FOR SHEAR 239 Table 6.1 Design Shear Strength of Concrete
240 REINFORCED CONCRETE
Typical values of 2 , are listed in 6.1 for different values
It may bc observed that, for a is value o f p , (corresponding to 1 in Eq. which remains constant, implying that beneficial effects due to action, control of crack propagation and increased depth of uncracked concrete in compression, cannot increase indefinitely with
Further, it may be noted that the use of the values of listed in Table 6.1 (based on 6.10) for a given value of p, are applicable at bar cut-off regions, only if the detailing requirements are adequately satisfied (refer Section 5.9.3). Where bars are proposed to be curtailed at locations where the shear requirements are not otherwise satisfied, it is necessary to provide additional locally near the cut-off points (thereby satisfying 26.2.3.2 of the Code).
As explained in Section 6.5 [Fig. the shear strength of concrete is enhanced in regions close to the support (located away from the face of the support), the support reaction introduces It is seen that a substantial portion of the load is transmitted to the support directly through stmt action, rather than through flexural shear. A recent revision in the Code allows for enhancement of shear strength of concrete in this region, provided the flexural tension reinforcement is extended beyond this region and well anchored. The Code 40.5) permits an increase in at any section located at a distance a, (less than from the face of the support by a factor However, this increase should be used with caution, as it is implied that as the critical approaches the face of the support, the shear strength will increase asymptotically, which is not realistic. The authors suggest that the shear strength in concrete for within a distance d from the face of the support should be limited to 22,
.
6.6.2 Design Shear Strength of Concrete in Slabs
Experimental studies [Ref. have shown that slabs and shallow beams fail at loads corresponding to a nominal stress that is higher than that applicable for beams of proportion. Moreover, the thinner the slab, the greater is the increase in shear strength. In recognition of this, the Code 40.2.1.1) suggests an increased shear strength, equal to for 'solid slabs' not including ribbed slabs), the multiplication factor k having a value in the range 1.0 to 1.3, expressed as follows:
1.3 for D 150 mm
for 150 300 (6.11)
for D 300 where D is the overall depth of the slab in mm
DESIGN FOR SHEAR 241
It should be noted that these provisions for design shear strength are applicable only for considerations of shear (or 'one-way shear'). slabs and column footings, punching shear ('two-way shear') has to b e considered, which involve different considerations of strength [refer Chapter
In general, slabs subjected to distributed loads satisfy the requirement , and hence do not need shear reinforcement. This is mainly attributable to the fact that the thickness of the slab (controlled by limiting deflection criteria) is usually adequate in terms of shear capacity. This is demonstrated i n Example 6.1.
6.6.3 Influence of Force on Shear Strength
In 2.10.2, it was indicated that the actual shear strength of concrete is generally improved in the presence of uniaxial compression and weakened in presence of uniaxial tension.
As explained earlier (in Section 6.6.1) the design shear strength, i s based on a safe estimate of the limiting nominal stress at which the first inclined crack develops. The effect of an axial compressive force is to delay the formation of both flexural and inclined cracks, and also to decrease the angle of inclination a of the inclined cracks to the longitudinal axis [Ref. Likewise, an axial tensile is expected to do exactly the it will decrease the shear strength, accelerate the process of cracking and increase the angle the inclined cracks.
Accordingly, the Code 40.2.2) specifies that the design shear strength in the presence of axial should be taken as , the multiplying factor being defined as:
where is the factored compressive force (in A, is the gross area of the section (in and is the characteristic strength of concrete (in
Although the Code does not explicitly mention the case of axial tension, it is evident that some reduction in design shear strength is called for in such a case. The following simplified expression for
6 ,
based on the ACI Code [Ref. 6.71, may be used:where is the factored axial tension (in N), with a negative sign.
Alternatively, when axial tension is also present, design for shear may be done based on the Compression Field Theory or the Strut-and-Tie Model, described in Chapter 17.
242 REINFORCED CONCRETE DESIGN
6.7 DESIGN SHEAR STRENGTH SHEAR REINFORCEMENT