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Ann-Kathrin Dannwerth, B.Sc.

2026-07-22

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Design Properties of Single Foundations

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Documentation

Bending

IBC 2021 / ACI 318-19 (LRFD): Bending Design

Design Purpose

The bending design checks whether the existing longitudinal reinforcement can absorb the bending moments resulting from the design loads.
The design is performed separately for:

Top and bottom reinforcement
Both foundation directions (x and y)

Determination of Design Moment

The design moment for each reinforcement layer is obtained by superposing the moment from the compressive stress block (soil pressure) and the moment from additional foundation loads (self-weight, earth covering), related to the design section at the column edge:

M_{f, (Achse), (top), u} = \frac{\min (M_{C, + x, (top)} + M_{A, + x, (top)}; M_{C, - x, (top)} + M_{A, - x, (top)}; 0)}{Φ}

M_C	Moment from the compression stress block (soil pressure) in the positive/negative axis direction
M_A	Moment from additional foundation loads in the positive/negative axis direction
Φ	Reduction factor (see below)

Design Moment – Top Reinforcement

M_{f, (Achse), (bottom), u} = \frac{\max (M_{C, + x, (bottom)} + M_{A, + x, (bottom)}; M_{C, - x, (bottom)} + M_{A, - x, (bottom)}; 0)}{Φ}

M_C	Moment from the compressive stress block (soil pressure) in the positive/negative axis direction
M_A	Moment from additional foundation loads in the positive/negative axis direction
Φ	Reduction factor (see below)

Design Moment – Bottom Reinforcement

Additionally, for columns located on the interior, the moment resulting from the asymmetric shear stress distribution during punching shear (moment transfer through the basic control perimeter) is taken into account:

M_{2 w, u} = \frac{\sqrt{{(γ_{f, 1} \cdot M_{sc, 1})}^{2} + {(γ_{f, 2} \cdot M_{sc, 2})}^{2}}}{Φ}

Moment from Moment Transfer in Punching

The governing design moment is the greater of the two components:

M_{(Achse), (Seite), u} = \max (M_{f, (Achse), (Seite), u}; M_{2 w, u})

Governing Design Moment

Reduction Factor Φ

The reduction factor depends on the strain state of the cross-section (ACI 21.2, Table 21.2.1):

ε_{t, y} = \frac{f_{y}}{E_{s}}

Yield Strain of Reinforcement

ε_t,t = 0.003 – concrete strain upon reaching the failure compression (ACI 318-19, 22.2.2.1), as a constant addition to the yield strain for determining the limit strain of tension-loaded cross-sections

Φ = Φ_tens = 0.90 if the cross-section is under tensile stress: ε_t > ε_t,y + ε_t,t
Φ = Φtens = 0.90, if the cross-section is under tensile stress: εt > εt,y + εt,t

RFEM automatically checks this strain state for each reinforcement layer—unlike simplified calculations. This can lead to different, more conservative results for the upper reinforcement (subjected to compression).

Required Reinforcement

The statically required reinforcement area is determined from the design moment, taking into account the component from the minimum reinforcement:

A_{s, stat} = \max (A_{s, stat, t}; A_{s, stat, p})

A_s,stat,t	Required reinforcement for flexural tension (design moment)
A_s,stat,p	Required reinforcement from soil pressure / minimum reinforcement (ACI 8.6.1.1)

Statically Required Reinforcement

Design / Design Ratio

A_{s, prov} \geq A_{s, stat}

A_s,prov

Provided (inserted) reinforcement area [in²]

Design Condition – Bending Design

η = \frac{A_{s, stat}}{A_{s, prov}}

Design Ratio – Bending Design

Software Configuration

The provided reinforcement is taken from the defined foundation parameters.
The material properties are taken from the assigned concrete and reinforcement materials.
The design moment and the strain state (and thus Φ) are automatically determined for each reinforcement layer and each design section from the governing load combinations.

Parent Chapter

Internal Stability – Reinforced Concrete Design