Índice

• Understanding Rebar Development Length in Pad Footings
• Comprimento de desenvolvimento de compressão
• Comprimento de desenvolvimento de tensão
• Módulo de design da Fundação SkyCiv

This documentation explores the significance of rebar development length in concrete footings and its role in ensuring structural integrity. You can gain insights into design code requirements, factors that influence development length, and practical approaches for incorporating them into your footing designs. Plus, discover how the SkyCiv Foundation Design module simplifies the process of verifying rebar development length for your projects.

Understanding Rebar Development Length in Pad Footings

Proper anchorage and reinforcement are essential for the stability and longevity of concrete structures, especially in pad footings. Development length is the minimum length of rebar embedded in the concrete necessary to achieve the required bond strength between steel and concrete. A development length check ensures that reinforcement is adequately embedded to resist loads without slipping, maintaining structural integrity and enabling safe load transfer to the ground. Verifying development length is a key part of footing design, assuring performance under static and dynamic loads and safeguarding overall structure stability.

Different design standards provide specific guidelines for determining these lengths to ensure that reinforcing bars are securely anchored within the concrete. This article provides an overview of the footing development length requirements as specified by various design standards, incluindo ACI 318-14 (American Concrete Institute), AS 3600 (Normas Australianas), CSA (Associação Canadense de Normas), e EN (Eurocódigo). By examining the distinct approaches and criteria set forth by each standard, engineers can better understand how to apply these guidelines effectively in practice, ensuring robust and compliant structural designs.

Comprimento de desenvolvimento de compressão

The compression development length of a footing is a crucial factor in determining its required thickness to ensure proper anchorage of reinforcing bars. This length is calculated based on the need to embed the bars sufficiently within the concrete to achieve adequate bond strength and prevent slippage under compressive loads. Incorporating the correct development length allows engineers to design footings with optimal thickness for reinforcement, ensuring structural stability and durability and enhancing overall safety.

American Concrete Institute (ACI 318 Seção 25.4.9)

Métrica:

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

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

f_Y = Rebar yield strength (MPa, psi)
f’_c = Concrete strength (MPa, psi)
d_b = Dowel bar diameter (milímetros, no)
ѱ _r = Confinement reinforcement factor (Tabela 25.4.9.3)
ƛ = Concrete type factor (Tabela 25.4.9.3)

Padrão Australiano (AS 3600 Seção 13.1.5)

Basic development length:

\(eu_{seu,cb} = MAX \left[ \fratura{0.22 f_{seu}}{ \sqrt{f_{c}'}} \vezes d_{b}, 0.0435 f_{seu} d_{b}, 200mm \right]\)Onde:

f_seu = Rebar yield strength (MPa)
f_c‘ = Concrete strength
d_b = Starter bar diameter (milímetros)

Canadian Standard Association (CSA Section 12.3)

\(eu_{banco de dados} = MAX \left[ \fratura{0.24 f_{Y}}{ \sqrt{f_{c}'}} \vezes d_{b}, 0.045 f_{Y} d_{b}, 200mm \right]\)Onde:

f_Y = Rebar yield strength (MPa)
f_c‘ = Concrete strength
d_b = Dowel bar diameter (milímetros)

Eurocódigo (EN Section 8.4)

Basic anchorage length (8.4.3)

\(eu_{b,rqd} = frac{\phi}{4} \vezes frac{\sigma_{sd}}{f_{bd}} \)Onde:

f_Y = Rebar yield strength (MPa)
f_bd = Ultimate bond stress (MPa)
σ_sd = Design stress of the bar at the position from where the anchorage is measured from (MPa)
ɸ = Dowel bar diameter (milímetros)

Design anchorage length (8.4.4)

\(eu_{bd} =\alpha_{1} \alfa_{2} \alfa_{3} \alfa_{4} eu_{b,rqd} \)Onde:

uma₁, uma₂, uma₃, uma₄ = 1.0 for Compression (Tabela 8.2)

Minimum anchorage length (8.4.4)

\(eu_{b, min} =MAX \left[ 0.6 eu_{b,rqd}, 10ɸ, 100mm \right]\)Anchorage length in compression

\(eu_{bd,compressão} =MAX\left[ eu_{b, min}, eu_{bd}\direito]\)

Comprimento de desenvolvimento de tensão

The tension development length is key to ensuring that a footing’s dimensions are adequate to anchor reinforcement against tensile forces. This length, calculated to achieve the necessary bond strength between concrete and rebar, directly impacts the footing’s size and design. Properly determining the tension development length allows engineers to design footings capable of securely anchoring the reinforcement, enabling the structure to withstand tensile stresses and maintain stability and performance.

American Concrete Institute (ACI 318 Seção 25.4)

Straight bars (Seção 25.4.2.3)

Métrica:

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

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

Onde:

ѱ_t = Casting position factor (Tabela 25.4.2.4)
ѱ_e = Bar coating factor (Tabela 25.4.2.4)
ѱ_s = Bar size factor (Tabela 25.4.2.4)
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:

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

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

Onde:

ѱ_e = Bar coating factor (Tabela 25.4.3.2)
ѱ_c = Bar concrete cover factor (Tabela 25.4.3.2)
ѱ_r = Confining reinforcement factor (Tabela 25.4.3.2)

Padrão Australiano (AS 3600 Seção 13.1.2.2)

Basic development length:

\(eu_{seu,tb} = MAX \left[ \fratura{0.5 inclui cálculos detalhados passo a passo{1} inclui cálculos detalhados passo a passo{3} f_{Y} d_{b}}{inclui cálculos detalhados passo a passo{2} \sqrt{f’_{c}}}, 0.058 f_{Y} inclui cálculos detalhados passo a passo{1} d_{b} \direito]\)Onde:

k₁ = 1.3 for rebar with more than 300 mm concrete cast below the bar (1.0 de outra forma)
k₂ = (132 – d_b)/100
k₃ = 1-[0.15(c_d – d_b)/d_b]
c_d = Minimum bar clear distance (milímetros)

Straight bar:

\(eu_{seu,t} = l_{seu,tb}\)

Standard hook or cog:

\(eu_{seu,t} =0.5 \times l_{seu,tb}\)

Canadian Standard Association (CSA Section 12)

Straight bars (Seção 12.2.3)

\(eu_{d} = MAX \left[ 0.45 inclui cálculos detalhados passo a passo{1} inclui cálculos detalhados passo a passo{2} inclui cálculos detalhados passo a passo{3} inclui cálculos detalhados passo a passo{4} \fratura{f_{Y}}{\sqrt{f’_{c}}} d_{b}, 300 mm \right]\)Onde:

k₁ = Bar location factor (12.2.4)
k₂ = Coating factor (12.2.4)
k₃ = Concrete density factor (12.2.4)
k₄ = Bar size factor (12.2.4)

Standard hooked bars (Seção 12.5)

\(eu_{d} = MAX \left[ \fratura{100 d_{b}}{\sqrt{f’_{c}}}\times left(0.7 \fratura{f_{Y}}{40}\direito), 8 d_{b}, 150 mm \right]\)

Eurocódigo (EN Section 8.4)

Basic anchorage length (8.4.3)

\(eu_{b,rqd} = frac{\phi}{4} \vezes frac{\sigma_{sd}}{f_{bd}} \)Design anchorage length (8.4.4)

\(eu_{bd} =\alpha_{1} \alfa_{2} \alfa_{3} \alfa_{4} eu_{b,rqd} \)Onde:

uma₁, uma₂, uma₃, uma₄ = values shown in Table 8.2 for bars in tension

Minimum anchorage length (8.4.4)

\(eu_{b, min} =MAX \left[ 0.3 eu_{b,rqd}, 10ɸ, 100mm \right]\)Anchorage length in compression

\(eu_{bd,tensão} =MAX\left[ eu_{b, min}, eu_{bd}\direito]\)

For a detailed guide on how the SkyCiv Design module verifies development length, refer to the following links:

• American Concrete Institute (ACI 318)
• Padrão Australiano (AS 3600)
• Canadian Standard Association (CSA A23.3)
• Eurocódigo (EN 1992)

Módulo de design da Fundação SkyCiv

The latest update to the SkyCiv Foundation Design module enhances its functionality by introducing the ability to incorporate standard hooked reinforcements, enabling more precise and detailed development length checks. This new feature provides users with greater flexibility by allowing them to customize the reinforcement detailing at each end of the footing bars. Users can now specify reinforcement ends as straight bars, 90-degree hooks (cogs), or 180-degree hooks, catering to various design requirements and standards.

The module also features updated graphics that visually aid in inspecting reinforcement detailing checks. Column dowel or starter bars are now also visible in the 3D graphics. With the newly added solver settings under the Miscellaneous tab, users can toggle to ignore specific design checks, such as development length checks and other advanced solving options.

 

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