4. Shear Strength

Shear strength of the slab in the vicinity of columns/supports includes an evaluation of one-way shear (beam action) and two-way shear (punching) in accordance with ACI 318 Chapter 22.

4.1. One-Way (Beam Action) Shear Strength

ACI 318-14 (22.5)

One-way shear is critical at a distance d from the face of the column as shown in Figure 3. Figure 24 and Figure 26 show the factored shear forces (V_u) at the critical sections around each column and each drop panel, respectively. In members without shear reinforcement, the design shear capacity of the section equals to the design shear capacity of the concrete:

4.1.1. At Distance d from the Supporting Column

for middle span with #6 reinforcement.

Where λ = 1 for normal weight concrete

(see the Figure 23)

Figure 23 – Frame Strip Cross Section (at Distance d from the Face of the Supporting Column)

The one-way shear capacity for the ribbed slab portions shown in Figure 23 is permitted to be increased by 10%.

ACI 318-14 (9.8.1.5)

Because ϕV_c ≥ V_u at all the critical sections, the slab has adequate one-way shear strength.

Figure 24 - One-way Shear at Critical Sections (at Distance d from the Face of the Supporting Column)

4.1.2. At the Face of the Drop Panel

for middle span with #6 reinforcement.

Where λ = 1 for normal weight concrete

(see the Figure 25)

Figure 25 – Frame Strip Cross Section (at Distance d from the Face of the Drop Panel)

The one-way shear capacity for the ribbed slab portions shown in Figure 25 is permitted to be increased by 10%.

ACI 318-14 (9.8.1.5)

Because ϕV_c ≥ V_u at all the critical sections, the slab has adequate one-way shear strength.

Figure 26 - One-Way Shear at Critical Sections (at the Face of the Drop Panel)

4.2. Two-Way (Punching) Shear Strength

4.2.1. Around the Columns Faces

Two-way shear is critical on a rectangular section located at d/2 away from the face of the column as shown in Figure 20.

a) Exterior column:

The factored shear force (V_u) in the critical section is computed as the reaction at the centroid of the critical section minus the self-weight and any superimposed surface dead and live load acting within the critical section (d/2 away from column face).

The factored unbalanced moment used for shear transfer, M_unb, is computed as the sum of the joint moments to the left and right. Moment of the vertical reaction with respect to the centroid of the critical section is also taken into account.

For the exterior column in Figure 18 the location of the centroidal axis z-z is:

Where:

b) Interior column:

For the interior column in Figure 18, the location of the centroidal axis z-z is:

Where:

c) Corner column:

In this example, interior equivalent frame strip was selected where it only have exterior and interior supports (no corner supports are included in this strip). However, the two-way shear strength of corner supports usually governs. Thus, the two-way shear strength for the corner column in this example will be checked for educational purposes. Same procedure is used to find the reaction and factored unbalanced moment used for shear transfer at the centroid of the critical section for the corner support for the exterior equivalent frame strip.

For the corner column in Figure 18, the location of the centroidal axis z-z is:

Where:

4.2.2. Around Drop Panels

Two-way shear is critical on a rectangular section located at d/2 away from the face of the drop panel.

The factored shear force (V_u) in the critical section is computed as the reaction at the centroid of the critical section minus the self-weight and any superimposed surface dead and live load acting within the critical section (d/2 away from column face).

Note: For simplicity, it is conservative to deduct only the self-weight of the slab and joists in the critical section from the shear reaction in punching shear calculations. This approach is also adopted in the spSlab program for the punching shear check around the drop panels.

a) Exterior drop panel:

d value is used in the calculation of v_u is given by (see the Figure 27).

Figure 27 – Equivalent Thickness based on Shear Area Calculation

In waffle slab design where the drop panels create a large critical shear perimeter, the factor (b_o/d) has limited contribution and is traditionally neglected for simplicity and conservatism. This approach is adopted in this calculation and in the spSlab program (spSlab software manual, Eq. 2-46).

b) Interior drop panel:

c) Corner drop panel: