Structural Concrete - Hassoun

5.7 Design of Vertical Stirrups 201
5.6.6 Anchorage of Stirrups
The ACI Code, Section 25.7.1.1, requires that shear reinforcement be carried as close as possible
to the compression and tension extreme fibers, within the Code requirements for concrete cover,
because near maximum load the flexural tension cracks penetrate deep into the beam. Also, for
stirrups to achieve their full yield strength, they must be well anchored. Near maximum load, the
stress in a stirrup reaches its yield stress at the point where a diagonal crack intercepts that stirrup.
The ACI Code requirements for stirrup anchorage, Section 25.7, are as follows:
1. Each bend in the continuous portion of a simple U-stirrup or multiple U-stirrups shall enclose
a longitudinal bar (ACI Code, Section 25.7.1.1). See Fig. 5.8a.
2. The code allows the use of a standard hook of 90 ∘ , 135 ∘ , or 180 ∘ around longitudinal bars
for no. 5 bars or D31 wire stirrups and no. 6, 7, and 8 bars with f yt < 40 ksi. If no. 6, 7, or 8
stirrups with f yt > 40 ksi are used, the Code (Section 25.7.1.3) requires a standard hook plus an
embedment length of 0.014d b f yt ∕(λ √ f c) ′ between midheight of the member and the outside
of the hook. If the bars are bent at 90 ∘ , extensions shall not be less than 12d b . For no. 5 bars
or smaller stirrups, the extension is 6d b (ACI Code, Section 25.3.2). See Fig. 5.8b.
3. If spliced double U-stirrups are used to form closed stirrups, the lap length shall not be less
than 1.3l d (ACI Code, Section 25.7.1.7). See Fig. 5.8c.
4. Welded wire fabric is used for shear reinforcement in the precast industry. Anchorage details
are given in the ACI Code, Section 25.7.1.4, and in its commentary.
5. Closed stirrups are required for beams subjected to torsion or stress reversals (ACI Code,
Section 9.7.6.4).
6. Beams at the perimeter of the structure should contain closed stirrups to maintain the structural
integrity of the member (ACI Code, Section 9.7.7.2).
5.6.7 Stirrups Adjacent to the Support
The ACI Code, Section 7.4.3.2, specifies that shear reinforcement provided between the face of the
support and the critical section at a distance d from it may be designed for the same shear V u at the
critical section. It is common practice to place the first stirrup at a distance S/2 from the face of the
support, where s is the spacing calculated by Eq. 5.16 for V u at the critical section.
5.6.8 Effective Length of Bent Bars
Only the center three-fourths of the inclined portion of any longitudinal bar shall be considered
effective for shear reinforcement. This means that the maximum spacing of bent bars is 0.75
(d − d ′ ). From Fig. 5.9, the effective length of the bent bar is 0.75(d − d ′ )∕(sin 45 ∘ )=
0.75(1.414)(d − d ′ )=1.06 (d − d ′ ). The maximum spacing S is equal to the horizontal projection
of the effective length of the bent bar. Thus S max = 1.06(d − d ′ ) cos 45 ∘ , or S max = 0.707
[1.06(d − d ′ )] = 0.75(d − d ′ ).
5.7 DESIGN OF VERTICAL STIRRUPS
Stirrups are needed when V u ≥ φV c . Minimum stirrups are used when V u is greater than 1 2 φV c but
less than φV. This is achieved by using no. 3 stirrups placed at maximum spacing. When V u is
greater than φV, stirrups must be provided. The spacing of stirrups may be less than the maximum
spacing and can be calculated using Eq. 5.16: S = A v f yt d∕V s .