Structural Concrete - Hassoun

17.7 Shear Strength of Slabs 625
Figure 17.8
Areas supported by beams in two-way slab floor system.
17.7.1 Two-Way Slabs Supported on Beams
In two-way slabs supported on beams, the critical sections are at a distance d from the face of
the supporting beams, and the shear capacity of each section is φV c = φ(2λ √ f ′ cbd). When the
supporting beams are stiff and are capable of transmitting floor loads to the columns, they are
assumed to carry loads acting on floor areas bounded by 45 ∘ lines drawn from the corners, as
shown in Fig. 17.8. The loads on the trapezoidal areas will be carried by the long beams AB and
CD, whereas the loads on the triangular areas will be carried by the short beams AC and BD. The
shear per unit width of slab is highest between E and F in both directions, and V u = q u (l 2 /2), where
q u is the uniform factored load per unit area.
If no shear reinforcement is provided, the shearing force at a distance d from the face of the
beam, V ud , must be equal to
V ud ≤ φV c ≤ φ(2λ √ f ′ cbd)
where
V ud = q u
(
l2
2 − d )
17.7.2 Two-Way Slabs without Beams
In flat plates and flat slabs, beams are not provided, and the slabs are directly supported by columns.
In such slabs, two types of shear stresses must be investigated; the first is one-way shear, or beam
shear. The critical sections are taken at a distance d from the face of the column, and the slab is
considered as a wide beam spanning between supports, as in the case of one-way beams. The shear
capacity of the concrete section is φV c = φ(2λ √ f ′ cbd). The second type of shear to be studied is
two-way, or punching, shear, as was previously discussed in the design of footings. Shear failure