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Ann-Kathrin Dannwerth, B.Sc.

2026-07-22

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Add-on Concrete Foundation

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Design Properties of Single Foundations

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One-Way Shear

IBC 2021 / ACI 318-19 (LRFD): Design of One-Way Shear

Purpose of Design

The design of one-way shear checks whether the shear force acting on the foundation slab does not exceed the shear resistance of the concrete.
The design check is performed at critical sections at a distance d from the column face, separately for both main directions of the foundation.

Shear Resistance

The shear resistance is determined according to ACI 318-19, Table 22.5.5.1.1(b), for structural components without shear reinforcement as the smaller value from two components:

\begin{matrix} V_{c} = \min (5 \cdot λ \cdot \sqrt{{f^{'}}_{c}} \cdot b_{w} \cdot d, (8 \cdot λ_{s} \cdot λ \cdot {(ρ_{w})}^{1 / 3} \cdot \sqrt{{f^{'}}_{c}} + \min (0.05 \cdot {f^{'}}_{c}, \frac{N_{u}}{6 \cdot A_{g}})) \cdot b_{w} \cdot d) \\ λ_{s} = \min (\sqrt{\frac{2}{1 + 0.1 \cdot d}}; 1) \end{matrix}

λ	Modification factor for lightweight concrete (= 1.0 for normal concrete)
ρ_w	longitudinal reinforcement ratio in the considered section [-]
N_u	Design value of the axial force (positive for compression) [kip]
A_g	Bruttoquerschnittsfläche [in²]
b_w	Width of the considered section [in]
d	effective static height [in]

Shear resistance – Vc and λs

The first component (5·λ·√f'_c·b_w·d) corresponds to the upper limit without considering the reinforcement ratio and axial force. The second component additionally considers the existing longitudinal reinforcement ratio and any axial force component and is usually the governing factor in practice.

In addition, an upper limit for the shear resistance is checked to rule out compressive failure of the concrete, regardless of the reinforcement ratio:

V_{\max} = φ \cdot (V_{c} + 8 \cdot \sqrt{{f^{'}}_{c}} \cdot b_{w} \cdot d)

Upper limit of shear resistance

The design resistance is φ · V_c with φ = 0.75 (strength reduction factor for shear, ACI 21.2).

Shear Stress

The existing shear force results from the soil reactions outside the critical section:

V_{u} = \max (0; V_{C, red +} - V_{A, red +}; V_{C, red -} - V_{A, red -})

V_C	Shear force component from the compressive stress block (soil pressure) outside the critical section
V_A	Shear force component from additional foundation loads (self-weight, earth covering) outside the critical section

Existing Shear Force – Uniaxial Shear

Design Check / Design Ratio

The existing shear force must neither exceed the design resistance nor the upper limit:

\begin{matrix} V_{u} \leq \min (φ \cdot V_{c}; V_{\max}) \\ η = \max (\frac{V_{u}}{φ \cdot V_{c}}; \frac{V_{u}}{V_{\max}}) \end{matrix}

Design condition and utilization factor - Uniaxial shear

Software Configuration

The material properties are adopted from the assigned concrete and reinforcement materials. The effective depth is automatically determined from the foundation geometry, the concrete cover, and the reinforcement layout. The shear force, the longitudinal reinforcement ratio, and the axial force are automatically determined for the governing load combinations.

Parent Chapter

Internal Stability - Reinforced Concrete Design