The development length of reinforcement is a critical parameter in structural concrete design, ensuring that reinforcing bars can adequately transfer stresses between the concrete and steel. Seção 25.4 de ACI 318 provides the requirements and methodologies for calculating development length to achieve proper anchorage of reinforcement. This ensures structural integrity, segurança, and serviceability under various loading conditions. The development length is influenced by bar size, resistência do concreto, bond conditions, cobrir, espaçamento, and whether the bar is in tension or compression. The provision covers basic development lengths for straight bars, adjustments for epoxy coatings, confinement effects, and conditions where bars are hooked or bundled.

The latest SkyCiv Foundation Design update supports standard hooked reinforcements, enabling precise development length checks. Users can now customize footing bar ends as straight bars, 90° hooks, or 180° hooks, ensuring flexibility for various design needs. This guide outlines the step-by-step process for determining the required development length for pad footings following ACI 318 Seção 25.4, considering relevant modification factors to comply with code requirements.

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Dowel Bar Development Length Check

Dowel bars in pad footings ensure a strong connection between the footing and columns, effectively transferring loads and maintaining structural integrity. Factors such as bar diameter, grau de aço, and concrete strength determine the required embedment. Ensure the embedment meets or exceeds the calculated length for safe load transfer and anchorage. Normalmente, column pedestals are subjected to compression loads, and the required development length is calculated using the provisions under Sectio 25.4.9 (Development of deformed bars in compression).

 

Seção 25.4.9.2: Compression development length (eu_CC)

Métrica:

\(eu_{CC} = MAX \left[ \fratura{0.24 f_{Y} \psi_{r}}{\lambda \sqrt{f’_{c}}} \vezes d_{b}, 0.042 f_{Y} \psi_{r} d_{b}, 200mm \right]\) Eq.1Imperial:

\(eu_{CC} = MAX \left[ \fratura{f_{Y} \psi_{r}}{50 \lambda sqrt{f’_{c}}} \vezes d_{b}, 0.0003 f_{Y} \psi_{r} d_{b}, 8inch \right]\) Eq. 2Onde:

f_Y = Rebar yield strength (MPa, psi)
f’_c = Concrete strength (MPa, psi)
d_b = Dowel bar diameter (milímetros, no)

Tabela 25.4.9.3: Modification factors for deformed bars or wires in compression

 

The SkyCiv Foundation Design module checks each load combination to determine if the column is subjected to tensile forces. Se for assim, the required development length is calculated following Section 25.4.2 (Development of bars or wires in tension). A brief explanation of this calculation is provided later in the guide.

Required footing thickness (h_req’d)

The thickness of the footing should be greater than or equal to the calculated required embedment of the dowel bars. The minimum footing thickness is checked by using Equations 3 e 4.

Minimum Footing Thickness

\(h_{req’d} = cover + d_{b,x} + d_{b,z} + d_{b, dowel} + r + eu_{d} \) (Eq. 3)

\(h_{req’d} \leq t\) (Eq. 4)

Onde:

t = Footing Thickness (milímetros, no)
cover = Bottom concrete cover (milímetros, no)
d_b,x, d_b,z = Footing bar size in the x and z directions (milímetros, no)
d_b,dowel = Dowel bar size (milímetros, no)
eu_d = Development length required in compression or tension (milímetros, no)
r = Minimum bend radius (milímetros, no)

 

Development Length Check For Footing Reinforcements

The SkyCiv Foundation Design module allows users to specify bar end configurations as straight or hooked bars (90° or 180°).

 

Calculating the required development length for footing reinforcements directly influences the footing’s dimensions, ensuring they are adequate to anchor the reinforcement against tensile forces. Seção 25.4.2 provides a guide on determining the required development length of the footing reinforcements.

Straight bars (Seção 25.4.2.3)

Métrica:

\(eu_{d} = MAX \left[ \deixou( \fratura{f_{Y}}{1.1 \lambda sqrt{f’_{c}}} \vezes frac{\psi_{!} \psi_{2} \psi_3}{\deixou(c_{b} + A seguir estão as diferentes maneiras de determinar os coeficientes de pressão de terra para calcular a resistência ao atrito unitária de estacas em areia{tr} \direito) / d_{b}} \direito)\vezes d_{b}, 300mm \right]\) (Eq. 5)Imperial:

\(eu_{d} = MAX \left[ \deixou( \fratura{3 f_{Y}}{40\lambda sqrt{f’_{c}}} \vezes frac{\psi_{!} \psi_{2} \psi_3}{\deixou(c_{b} + A seguir estão as diferentes maneiras de determinar os coeficientes de pressão de terra para calcular a resistência ao atrito unitária de estacas em areia{tr} \direito) / d_{b}} \direito) \vezes d_{b}, 12in\right]\) (Eq. 6)

Onde:

Tabela 25.4.2.4: Modification factors for the development of deformed bars and wires in tension

c_b = Minimum bar clear distance (milímetros, no)
K_tr = Transverse reinforcement index (milímetros, no)
(c_b + K_tr) / d_b ≤ 2.5

Standard hooked bars (Seção 25.4.3.1)

Métrica:

\(eu_{d} = MAX \left[ \deixou( \fratura{0.24 f_{Y} \psi_{e} \psi_{c} \psi_{r}}{\lambda sqrt{f’_{c}}} \direito)\vezes d_{b}, 8d_{b}, 150 mm \right]\) (Eq. 7)Imperial:

\(eu_{d} = MAX \left[ \deixou( \fratura{f_{Y} \psi_{e} \psi_{c} \psi_{r}}{50 \lambda sqrt{f’_{c}}} \direito)\vezes d_{b}, 8d_{b}, 6 à direita]\) (Eq. 8)

Onde:

Tabela 25.4.3.2: Modification factors for the development of hooked bars in tension

 

Minimum Extension Length (7.7.3.3)

Reinforcement shall extend beyond the point at which it is no longer required to resist flexure for a distance at least the greater of d and 12d_b.

\(eu_{ext,min} = MAX \left[d, 12d_{b}\direito]\) (Eq. 9)

Onde:

d = Effective depth (milímetros, no)
d_b = Bar size (milímetros, no)

 

Anchorage Length Provided

\(eu_{provided} \geq MAX \left( eu_{d,req’d}, eu_{ext, min} \direito)\) (Eq. 10)

 

Verificação de Detalhamento: Verification of Footing Thickness (t):

The SkyCiv Foundation Design module checks whether the footing thickness is adequate based on bar configuration and concrete cover. If it is insufficient or the bars protrude, it issues a warning instead of a design failure. The module evaluates the footing thickness at each end of the longitudinal and transverse reinforcements in both the top and bottom layers.

\(\deixou(\texto{h + cobrir}\direito) \leq t\) (Eq. 11)

 

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