Also, because the basis of the proposed design equation is
diagonal tension, the lightweight concrete factor λ should be
considered to account for the lower tensile-compressive
strength ratio of lightweight concrete compared with
Including size effect and the reduced tensilecompressive
strength properties of lightweight concrete,
Eq. (1a) becomes
Vc = φ5λλs tan θ fc′bwd (2)
The strut-and-tie method is derived from the lower-bound
theorem of plasticity. Distributed reinforcement in
discontinuity regions helps redistribute internal forces, which
is especially important where the assumed strut-and-tie model
is not entirely consistent with the flow of internal stresses. In
addition to allowing force redistribution, distributed
reinforcement controls cracking at service loads and promotes
ductile behavior. Analysis of the joint ACI-DAfStb Database6
for members with a distributed reinforcement ratio of at least
0.25% indicates the current βs value of 0.75 is safe such that
an independent check of shear strength of the section is not
required. However, we recommend verifying diagonal tension
strength using Eq. (2) in regions where struts connect to
hanger reinforcement, such as the nibs of dapped-end
connections, even if distributed reinforcement is provided.
Testing sponsored by PCI12 indicates such regions are
vulnerable to diagonal tension failure due to tensile stress
induced by the hanger reinforcement, despite distributed
Code Changes for ACI 318-19
Based on these findings, several changes to the ACI Code
were approved by ACI Committee 318: ••Struts that extend diagonally through the interior of D-regions
will be defined as interior struts rather than bottle-shaped
struts. Struts that carry compressive force along a boundary
of a D-region will be defined as boundary struts; ••Distributed reinforcement will be required in all
discontinuity regions unless the strut is laterally confined.
The minimum effective reinforcement ratio is 0.25%. The
lateral confinement exception applies to members like pile
caps and continuous beam ledges, where distributed
reinforcement is unnecessary and impractical. If distributed
reinforcement is provided, the strut efficiency factor βs may
be taken as 0.75; ••For members without transverse reinforcement, an
independent check of shear stress in accordance with Eq. (2)
will be required unless βs is taken as 0.4. Equation (2)
accounts for both size effect and the reduced mechanical
properties of lightweight concrete. If Eq. (2) is satisfied, βs
may be taken as 0.75; and ••In accordance with Eq. (2), shear stress exceeding the
current Code limit of 10 c f ′ will be permitted for steeply
inclined struts between load and reaction areas.
40 MAY 2019 | Ci | www.concreteinternational.com
These updated provisions resolve the concerns and
inconsistencies listed in the introduction. Additionally, the
changes should lead to more economical design of deep
footings and thick slabs because the beneficial effect of steep
strut angles counteracts the size effect.
The experimental study described herein was funded by Florida
International University. The authors wish to express their sincere gratitude
for the university’s support. The authors also gratefully acknowledge
technical assistance and guidance from Joint ACI-ASCE Subcommittee
445-A, Shear & Torsion-Strut & Tie, and ACI Subcommittee 318-E,
Section and Member Strength, as well as numerous ACI colleagues,
including Jeff Rautenberg, Santiago Pujol, David Sanders, Dan Kuchma,
Karl-Heinz Reineck, Evan Benz, and the late Mete A. Sözen.
1. ACI Committee 318, “Building Code Requirements for Structural
Concrete (ACI 318-02) and Commentary (ACI 318R-02),” American
Concrete Institute, Farmington Hills, MI, 2002, 443 pp.
2. Schlaich, J.; Schäfer, K.; and Jennewein, M., “Toward a Consistent
Design of Structural Concrete,” PCI Journal, V. 32, No. 3, May-June 1987,
3. ACI Committee 318, “Building Code Requirements for Structural
Concrete (ACI 318-14) and Commentary (ACI 318R-14),” American
Concrete Institute, Farmington Hills, MI, 2014, 519 pp.
4. Laughery, L., and Pujol, S., “Compressive Strength of Unreinforced
Struts,” ACI Structural Journal, V. 112, No. 5, Sept.-Oct. 2015, pp. 617-624.
5. Reineck, K.-H., and Todisco, L., “Database of Shear Tests for
Non-Slender Reinforced Concrete Beams without Stirrups,” ACI
Structural Journal, V. 111, No. 6, Nov.-Dec. 2014, pp. 1363-1372.
6. Reineck, K.-H.; Bentz, E.C.; Fitik, B.; Kuchma, D.A.; and
Bayrak, O., “ACI-DAfStb Database of Shear Tests on Slender
Reinforced Concrete Beams without Stirrups,” ACI Structural Journal,
V. 110, No. 5, Sept.-Oct. 2013, pp. 867-875.
7. Rezaei, N.; Klein, G.; and Garber, D., “Struts Strength and Failure
in Full-Scale Concrete Deep Beams,” ACI Structural Journal, V. 116,
No. 3, May-June 2019, DOI: 10.14359/51713306.
8. Van den Hoogen, M.G.M., “Beam or Truss Mechanism for Shear
in Concrete: Problems Converting a Beam into a Truss,” MSc. thesis,
Department of Structural Engineering, Technical University Delft, Delft,
the Netherlands, 2013, 128 pp.
9. Zsutty, T.C., “Shear Strength Prediction for Separate Categories of
Simple Beams Tests,” ACI Journal Proceedings, V. 68, No. 2, Feb. 1971,
10. Bazant, Z., and Kim, J.-K., “Size Effect in Shear Failure of
Longitudinally Reinforced Beams,” ACI Structural Journal, V. 85, No. 5,
Sept.-Oct. 1984, pp. 456-468.
11. Belarbi, A.; Kuchma, D.A.; and Sanders, D.H., “Proposals for
New One-Way Shear Equations for the 318 Building Code,” Concrete
International, V. 39, No. 9, Sept. 2017, pp. 29-32.
12. Klein, G.; Botros, A.; Andrews, B.; and Holloway, K., “Dapped
Ends of Prestressed Concrete Thin-Stemmed Members: Part 2, Design,”
PCI Journal, V. 62, No. 2, Mar.-Apr. 2017, pp. 83-100.
Received and reviewed under Institute publication policies.