Base Plate Design Example using CSA S16:19 and CSA A23.3:19
Declaração de problemas:
Determine whether the designed column-to-base plate connection is sufficient for a 50-kN tension load.
Dados dados:
Coluna:
Seção de coluna: HS324X9.5
Área da coluna: 9410 milímetros2
Material da coluna: 230G
Placa Base:
Dimensões da placa de base: 500 mm x 500 milímetros
Espessura da placa de base: 20 milímetros
Material da placa de base: 230G
Grout:
Grout thickness: 20 milímetros
Concreto:
Dimensões concretas: 550 mm x 550 milímetros
Espessura do concreto: 200 milímetros
Material concreto: 20.68 MPa
Cracked or Uncracked: Cracked
Anchors:
Anchor diameter: 19.1 milímetros
Effective embedment length: 130.0 milímetros
Hook length: 60milímetros
Anchor offset distance from face of column: 120.84 milímetros
Soldas:
Weld type: CJP
Classificação de metal de enchimento: E43XX
Anchor Data (a partir de SkyCiv Calculator):
Definitions:
Load Path:
When a base plate is subjected to uplift (tração) forças, these forces are transferred to the anchor rods, which in turn induce bending moments in the base plate. The bending action can be visualized as cantilever bending occurring around the flanges or web of the column section, depending on where the anchors are positioned.
No Software de design de placa de base SkyCiv, only anchors located within the anchor tension zone are considered effective in resisting uplift. This zone typically includes areas near the column flanges or web. In the case of a circular column, the anchor tension zone includes the entire area outside the column perimeter. Anchors outside this zone do not contribute to tension resistance and are excluded from the uplift calculations.
To determine the effective area of the base plate that resists bending, uma 45-degree dispersion is assumed from the centerline of each anchor rod toward the column face. This dispersion defines the effective weld length and helps establish the effective bending width da placa.
A suposição simplifica a análise da placa de base, aproximando -se de como a força de elevação se espalha pela placa.
Grupos de âncora:
A Software de design de placa de base SkyCiv includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating fuga de concreto e concrete side-face blowout failures.
A anchor group consists of multiple anchors with similar effective embedment depths and spacing, and are close enough that their projected resistance areas overlap. When anchors are grouped, their capacities are combined to resist the total tension force applied to the group.
Anchors that do not meet the grouping criteria are treated as single anchors. Nesse caso, only the tension force on the individual anchor is checked against its own effective resistance area.
Cálculos passo a passo:
Verificar #1: Calcule a capacidade de solda
Aplicando Cargas Sísmicas, we need to calculate the load per anchor and determine the effective weld length for each anchor. A effective weld length is based on a 45° dispersion line drawn from the center of the anchor to the face of the column. If this 45° line does not intersect the column, a tangent points are used instead. Além disso, if the anchors are closely spaced, the effective weld length is reduced to avoid overlap. Finalmente, the sum of all effective weld lengths must not exceed the actual weldable length available along the column circumference.
Let’s apply this to our example. Based on the given geometry, the 45° line from the anchor does not intersect the column. Como um resultado, the arc length between the tangent points is used instead. This arc length must also account for any adjacent anchors, with any overlapping portions subtracted to avoid double-counting. The calculated arc length is:
\(
eu_{\texto{arc}} = 254.47 \, \texto{milímetros}
\)
This arc length calculation is fully automated in the SkyCiv Base Plate Design Software, but it can also be performed manually using trigonometric methods. You can try the free tool from this link.
Considering the available weldable length along the column’s circumference, the final effective weld length é:
\(
eu_{\texto{ef}} = min left( eu_{\texto{arc}}, \fratura{\pi d_{\texto{col}}}{n_{uma,t}} \direito) = min left( 254.47 \, \texto{milímetros}, \fratura{\pi \times 324 \, \texto{milímetros}}{4} \direito) = 254.47 \, \texto{milímetros}
\)
A continuação, let’s calculate the load per anchor. For a given set of four (4) âncoras, the load per anchor is:
\(
T_{você,\texto{âncora}} = frac{N_x}{n_{uma,t}} = frac{50 \, \texto{kN}}{4} = 12.5 \, \texto{kN}
\)
Using the calculated effective weld length, we can now compute the required force per unit length acting on the weld.
\(
v_f = \frac{T_{você,\texto{âncora}}}{eu_{\texto{ef}}} = frac{12.5 \, \texto{kN}}{254.47 \, \texto{milímetros}} = 0.049122 \, \texto{kN / mm}
\)
Agora, we refer to CSA S16:19 Cláusula 13.13.3.1 to calculate the factored resistance of the complete joint penetration (CJP) soldar. This requires the base metal resistance, expressed in force per unit length, for both the column and the base plate materials.
\(
v_{r,\texto{bm}} = \phi \left( \Min esquerda( F_{Y,\texto{col}} t_{\texto{col}}, F_{Y,\texto{pb}} t_{\texto{pb}} \direito) \direito)
\)
\(
v_{r,\texto{bm}} = 0.9 \times left( \Min esquerda( 230 \, \texto{MPa} \vezes 9.53 \, \texto{milímetros}, 230 \, \texto{MPa} \vezes 20 \, \texto{milímetros} \direito) \direito) = 1.9727 \, \texto{kN / mm}
\)
Desde a 0.049122 kN / mm < 1.9727 kN / mm, A capacidade de solda é suficiente.
Verificar #2: Calculate base plate flexural yielding capacity due to tension load
Using the load per anchor and the offset distance from the center of the anchor to the face of the column, the moment applied to the base plate can be calculated using a em balanço assumption. For a circular column, the load eccentricity is determined by considering the sagitta of the welded arc, and can be calculated as follows:
\(
e_{\texto{pipe}} = d_o + r_{\texto{col}} \deixou( 1 – \cos esquerda( \fratura{eu_{\texto{ef}}}{2 r_{\texto{col}}} \direito) \direito)
\)
\(
e_{\texto{pipe}} = 120.84 \, \texto{milímetros} + 162 \, \texto{milímetros} \times left( 1 – \cos esquerda( \fratura{254.47 \, \texto{milímetros}}{2 \vezes 162 \, \texto{milímetros}} \direito) \direito) = 168.29 \, \texto{milímetros}
\)
The induced moment is computed as:
\(
M_f = T_{você,\texto{âncora}} e_{\texto{pipe}} = 12.5 \, \texto{kN} \vezes 168.29 \, \texto{milímetros} = 2103.6 \, \texto{kN} \cdot \text{milímetros}
\)
A continuação, we will determine the bending width of the base plate. Por esta, we use the chord length corresponding to the effective weld arc.
\(
\theta_{\texto{trabalhar}} = frac{eu_{\texto{ef}}}{0.5 d_{\texto{col}}} = frac{254.47 \, \texto{milímetros}}{0.5 \vezes 324 \, \texto{milímetros}} = 1.5708
\)
\(
b = d_{\texto{col}} \deixou( \pecado esquerda( \fratura{\theta_{\texto{trabalhar}}}{2} \direito) \direito) = 324 \, \texto{milímetros} \times left( \pecado esquerda( \fratura{1.5708}{2} \direito) \direito) = 229.1 \, \texto{milímetros}
\)
Finalmente, we can calculate the factored flexural resistance of the base plate using CSA S16:19 Cláusula 13.5.
\(
M_r = \phi F_{Y,\texto{pb}} Z_{\texto{ef}} = 0.9 \vezes 230 \, \texto{MPa} \vezes 22910 \, \texto{milímetros}^3 = 4742.4 \, \texto{kN} \cdot \text{milímetros}
\)
Onde,
\(
Z_{\texto{ef}} = frac{b (t_{\texto{pb}})^ 2}{4} = frac{229.1 \, \texto{milímetros} \vezes (20 \, \texto{milímetros})^ 2}{4} = 22910 \, \texto{milímetros}^ 3
\)
Desde a 2103.6 kN-mm < 4742.4 kN-mm, the base plate flexural yielding capacity is suficiente.
Verificar #3: Calculate anchor rod tensile capacity
To evaluate the tensile capacity of the anchor rod, we refer to CSA A23.3:19 Clause D.6.1.2 and CSA S16:19 Cláusula 25.3.2.1.
Primeiro, Nós determinamos o specified tensile strength of the anchor steel. This is the lowest value permitted by CSA A23.3:19 Clause D.6.1.2.
\(
f_{\texto{uta}} = min left( F_{você,\texto{anc}}, 1.9 F_{Y,\texto{anc}}, 860 \direito) = min left( 400 \, \texto{MPa}, 1.9 \vezes 248.2 \, \texto{MPa}, 860.00 \, \texto{MPa} \direito) = 400 \, \texto{MPa}
\)
A continuação, Nós determinamos o effective cross-sectional area of the anchor rod in tension using CAC Concrete Design Handbook, 3Edição RD, Tabela 12.3.
\(
UMA_{eu sei,N} = 215 \, \texto{milímetros}^ 2
\)
With these values, nós aplicamos CSA A23.3:19 Eq. D.2 to compute the factored tensile resistance of the anchor rod.
\(
N_{\texto{sar}} = A_{eu sei,N} \phi_s f_{\texto{uta}} R = 215 \, \texto{milímetros}^2 \times 0.85 \vezes 400 \, \texto{MPa} \vezes 0.8 = 58.465 \, \texto{kN}
\)
Além disso, we evaluate the factored tensile resistance according to CSA S16:19 Cláusula 25.3.2.1.
\(
T_r = \phi_{ar} 0.85 UMA_{ar} F_{você,\texto{anc}} = 0.67 \vezes 0.85 \vezes 285.02 \, \texto{milímetros}^2 \times 400 \, \texto{MPa} = 64.912 \, \texto{kN}
\)
After comparing the two, we identify that the factored resistance calculated using CSA A23.3:19 governs in this case.
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{uma,t}} = frac{50 \, \texto{kN}}{4} = 12.5 \, \texto{kN}
\)
Desde a 12.5 kN < 58.465 kN, the anchor rod tensile capacity is suficiente.
Verificar #4: Calculate concrete breakout capacity in tension
Before calculating the breakout capacity, we must first determine whether the member qualifies as a narrow member. De acordo com CSA A23.3:19 Clause D.6.2.3, the member does not meet the criteria for a narrow member. Portanto, the given effective embedment length will be used in the calculations.
Usando CSA A23.3:19 Eq. D.5, nós calculamos o maximum projected concrete cone area para uma única âncora, based on the effective embedment length.
\(
UMA_{Lembrar} = 9 (h_{ef,s1})A partir da elevação do solo gerada a partir das elevações do Google 9 \vezes (130 \, \texto{milímetros})A partir da elevação do solo gerada a partir das elevações do Google 152100 \, \texto{milímetros}^ 2
\)
similarmente, we use the effective embedment length to calculate the actual projected concrete cone area of the single anchor.
\(
UMA_{Nc} = L_{Nc} B_{Nc} = 270 \, \texto{milímetros} \vezes 270 \, \texto{milímetros} = 72900 \, \texto{milímetros}^ 2
\)
Onde,
\(
EU_{Nc} = left( \Min esquerda( c_{\texto{deixou},s1}, 1.5 h_{ef,s1} \direito) \direito) + \deixou( \Min esquerda( c_{\texto{direito},s1}, 1.5 h_{ef,s1} \direito) \direito)
\)
\(
EU_{Nc} = left( \Min esquerda( 475 \, \texto{milímetros}, 1.5 \vezes 130 \, \texto{milímetros} \direito) \direito) + \deixou( \Min esquerda( 75 \, \texto{milímetros}, 1.5 \vezes 130 \, \texto{milímetros} \direito) \direito)
\)
\(
EU_{Nc} = 270 \, \texto{milímetros}
\)
\(
B_{Nc} = left( \Min esquerda( c_{\texto{figura superior},s1}, 1.5 h_{ef,s1} \direito) \direito) + \deixou( \Min esquerda( c_{\texto{figura inferior},s1}, 1.5 h_{ef,s1} \direito) \direito)
\)
\(
B_{Nc} = left( \Min esquerda( 75 \, \texto{milímetros}, 1.5 \vezes 130 \, \texto{milímetros} \direito) \direito) + \deixou( \Min esquerda( 475 \, \texto{milímetros}, 1.5 \vezes 130 \, \texto{milímetros} \direito) \direito)
\)
\(
B_{Nc} = 270 \, \texto{milímetros}
\)
A continuação, we evaluate the factored basic concrete breakout resistance of a single anchor using CSA A23.3:19 Eq. D.6
\(
N_{br} = k_c \phi \lambda_a \sqrt{\fratura{f’_c}{\texto{MPa}}} \deixou( \fratura{h_{ef,s1}}{\texto{milímetros}} \direito)^{1.5} R N
\)
\(
N_{br} = 10 \vezes 0.65 \vezes 1 \times sqrt{\fratura{20.68 \, \texto{MPa}}{1 \, \texto{MPa}}} \times left( \fratura{130 \, \texto{milímetros}}{1 \, \texto{milímetros}} \direito)^{1.5} \vezes 1 \vezes 0.001 \, \texto{kN} = 43.813 \, \texto{kN}
\)
Onde,
- \(inclui cálculos detalhados passo a passo{c} = 10\) para âncoras fundidas
- \(\lambda = 1.0 \) for normal-weight concrete
Agora, we assess the effects of geometry by calculating the edge effect factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{uma,\texto{min}} = min left( c_{\texto{deixou},s1}, c_{\texto{direito},s1}, c_{\texto{figura superior},s1}, c_{\texto{figura inferior},s1} \direito) = min left( 475 \, \texto{milímetros}, 75 \, \texto{milímetros}, 75 \, \texto{milímetros}, 475 \, \texto{milímetros} \direito) = 75 \, \texto{milímetros}
\)
De acordo com CSA A23.3:19 Eq. D.10 and D.11, the breakout edge effect factor é:
\(
\Psi_{ed,N} = min left( 1.0, 0.7 + 0.3 \deixou( \fratura{c_{uma,\texto{min}}}{1.5 h_{ef,s1}} \direito) \direito) = min left( 1, 0.7 + 0.3 \times left( \fratura{75 \, \texto{milímetros}}{1.5 \vezes 130 \, \texto{milímetros}} \direito) \direito) = 0.81538
\)
Além disso, both the cracking factor e o splitting factor are taken as:
\(
\Psi_{c,N} = 1
\)
\(
\Psi_{cp,N} = 1
\)
Então, we combine all these factors and use ACI 318-19 Eq. 17.6.2.1b to evaluate the factored concrete breakout resistance of the single anchor:
\(
N_{cbr} = left( \fratura{UMA_{Nc}}{UMA_{Lembrar}} \direito) \Psi_{ed,N} \Psi_{c,N} \Psi_{cp,N} N_{br} = left( \fratura{72900 \, \texto{milímetros}^ 2}{152100 \, \texto{milímetros}^ 2} \direito) \vezes 0.81538 \vezes 1 \vezes 1 \vezes 43.813 \, \texto{kN} = 17.122 \, \texto{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{uma,s}} = frac{50 \, \texto{kN}}{4} = 12.5 \, \texto{kN}
\)
Desde a 12.5 kN < 17.122 kN the concrete breakout capacity is suficiente.
This concrete breakout calculation is based on Anchor ID #1. The same capacity will apply to the other anchors due to the symmetric design.
Verificar #5: Calculate anchor pullout capacity
The pullout capacity of an anchor is governed by the resistance at its embedded end. For hooked anchors, it is dependent on its hook length.
We compute the factored basic anchor pullout resistance por CSA A23.3:19 Eq. D.17.
\(
N_{pr} = \Psi_{c,p} 0.9 \phi (f’_c) e_h d_a R = 1 \vezes 0.9 \vezes 0.65 \vezes (20.68 \, \texto{MPa}) \vezes 60 \, \texto{milímetros} \vezes 19.05 \, \texto{milímetros} \vezes 1 = 13.828 \, \texto{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{uma,t}} = frac{50 \, \texto{kN}}{4} = 12.5 \, \texto{kN}
\)
Desde a 12.5 kN < 13.828 kN, the anchor pullout capacity is suficiente.
Verificar #6: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for hooked anchors.
Verificar #7: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for hooked anchors.
Resumo do projeto
A Software de design de placa de base skyciv can automatically generate a step-by-step calculation report for this design example. Ele também fornece um resumo dos cheques executados e suas proporções resultantes, facilitando o entendimento da informação. Abaixo está uma tabela de resumo de amostra, que está incluído no relatório.
Relatório de amostra de Skyciv
Sample report will be added soon.
Compre software de placa de base
Purchase the full version of the base plate design module onits own without any other SkyCiv modules. Isso oferece um conjunto completo de resultados para o design da placa de base, incluindo relatórios detalhados e mais funcionalidade.
