Exemplo de design da placa de base usando AISC 360-22 e ACI 318-19
Declaração de problemas:
Determine whether the designed column-to-base plate connection is sufficient for a 20-kip tension load.
Dados dados:
Coluna:
Seção de coluna: W12x53
Área da coluna: 15.6 no2
Material da coluna: A992
Placa Base:
Dimensões da placa de base: 18 em x 18 no
Espessura da placa de base: 3/4 no
Material da placa de base: A36
Grout:
Grout thickness: 1 no
Concreto:
Dimensões concretas: 22 em x 22 no
Espessura do concreto: 15 no
Material concreto: 4000 psi
Cracked or Uncracked: Cracked
Anchors:
Anchor diameter: 3/4 no
Effective embedment length: 12 no
Embedded plate width: 3 no
Embedded plate thickness: 1/4 no
Anchor offset distance from face of column web: 2.8275 no
Soldas:
Tamanho da solda: 1/4 no
Classificação de metal de enchimento: E70XX
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. 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 the effective weld length per anchor. The effective weld length is determined by the shortest length from the 45° dispersion, constrained by the actual weld length and anchor spacing.
For this calculation, anchors are classified as either end anchors ou intermediate anchors. End anchors are located at the ends of a row or column of anchors, while intermediate anchors are positioned between them. The calculation method differs for each and depends on the column geometry. Neste exemplo, there are two anchors along the web, and both are classified as end anchors.
For end anchors, the effective weld length is limited by the available distance from the anchor centerline to the column fillet. The 45° dispersion must not extend beyond this boundary.
\(
l_r = \frac{d_{col} – 2t_f – 2r_{col} – s_y(n_{uma,lado} – 1)}{2} = frac{12.1 \, \texto{no} – 2 \vezes 0.575 \, \texto{no} – 2 \vezes 0.605 \, \texto{no} – 5 \, \texto{no} \vezes (2 – 1)}{2} = 2.37 \, \texto{no}
\)
On the inner side, the effective length is limited by half the anchor spacing. The total effective weld length for the end anchor is the sum of the outer and inner lengths.
\(
eu_{ef,fim} = \min(fazer, 0.5s_y) + \min(fazer, l_r)
\)
\(
eu_{ef,fim} = \min(2.8275 \, \texto{no}, 0.5 \vezes 5 \, \texto{no}) + \min(2.8275 \, \texto{no}, 2.37 \, \texto{no}) = 4.87 \, \texto{no}
\)
Para este exemplo, a final effective weld length for the web anchor is taken as the effective length of the end anchor.
\(
eu_{ef} = l_{ef,fim} = 4.87 \, \texto{no}
\)
A continuação, let’s calculate the load per anchor. For a given set of four (4) âncoras, the load per anchor is:
\(
T_{você,âncora} = frac{N_x}{n_{uma,t}} = frac{20 \, \texto{kip}}{4} = 5 \, \texto{kip}
\)
Using the calculated effective weld length, we can now determine the required force per unit length on the weld.
\(
r_u = frac{T_{você,âncora}}{eu_{ef}} = frac{5 \, \texto{kip}}{4.87 \, \texto{no}} = 1.0267 \, \texto{kip/in}
\)
Agora, nós vamos usar AISC 360-22, Chapter J2.4 to calculate the design strength of the fillet weld.
Since the applied load is purely axial tension, the angle \(\theta\) is taken as 90°, and the directional strength coefficient kds is calculated according to AISC 360-22 Eq. J2-5.
\(
inclui cálculos detalhados passo a passo{ds} = 1.0 + 0.5(\sem(\theta))^{1.5} = 1 + 0.5 \vezes (\sem(1.5708))^{1.5} = 1.5
\)
Finalmente, nós vamos aplicar AISC 360-22 Eq. J2-4 to determine the design strength of the fillet weld per unit length.
\(
\phi r_n = \phi 0.6 F_{Exx} E_{C,rede} inclui cálculos detalhados passo a passo{ds} = 0.75 \vezes 0.6 \vezes 70 \, \texto{ksi} \vezes 0.177 \, \texto{no} \vezes 1.5 = 8.3633 \, \texto{kip/in}
\)
Desde a 1.0267 KPI < 8.3633 KPI, 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 (serving as the load eccentricity), the moment applied to the base plate can be calculated using a em balanço assumption.
\(
M_u = T_{você,\texto{âncora}} e = 5 \, \texto{kip} \vezes 2.8275 \, \texto{no} = 14.137 \, \texto{kip} \cdot \text{no}
\)
A continuação, using the calculated effective weld length from the previous check as the bending width, we can calculate the SkyCiv Foundation é um módulo de projeto para o projeto de sapatas articuladas a partir das cargas da superestrutura of the base plate using AISC 360-22, Equação 2-1:
\(
\phi M_n = \phi F_{Y,\texto{pb}} Z_{\texto{ef}} = 0.9 \vezes 36 \, \texto{ksi} \vezes 0.68484 \, \texto{no}^3 = 22.189 \, \texto{kip} \cdot \text{no}
\)
Onde,
\(
Z_{\texto{ef}} = frac{eu_{\texto{ef}} (t_{\texto{pb}})^ 2}{4} = frac{4.87 \, \texto{no} \vezes (0.75 \, \texto{no})^ 2}{4} = 0.68484 \, \texto{no}^ 3
\)
Desde a 14.137 frango em < 22.189 frango em, the base plate flexural yielding capacity is suficiente.
Verificar #3: Calculate anchor rod tensile capacity
To evaluate the tensile capacity of the anchor rod, nós vamos usar ACI 318-19 Equação 17.6.1.2.
Primeiro, Nós determinamos o specified tensile strength of the anchor steel. This is the lowest value permitted by ACI 318-19 Cláusula 17.6.1.2, with reference to material properties in AISC 360-22 Tabela J3.2.
\(
f_{\texto{uta}} = min left( 0.75 F_{você,\texto{anc}}, 1.9 F_{Y,\texto{anc}}, 125 \direito) = min left( 0.75 \vezes 120 \, \texto{ksi}, 1.9 \vezes 92 \, \texto{ksi}, 125.00 \, \texto{ksi} \direito) = 90 \, \texto{ksi}
\)
A continuação, nós calculamos o effective cross-sectional area of the anchor rod. This is based on ACI 318-19 Commentary Clause R17.6.1.2, which accounts for thread geometry. The number of threads per inch is taken from ASME B1.1-2019 Table 1.
\(
UMA_{eu sei,N} = frac{\pi}{4} \deixou( d_a – \fratura{0.9743}{n_t} \direito)^2 = \frac{\pi}{4} \times left( 0.75 \, \texto{no} – \fratura{0.9743}{10 \, \texto{no}^{-1}} \direito)A partir da elevação do solo gerada a partir das elevações do Google 0.33446 \, \texto{no}^ 2
\)
With these values, nós aplicamos ACI 318-19 Equação 17.6.1.2 to compute the design tensile strength of the anchor rod.
\(
\phi N_{para} = phi A_{eu sei,N} f_{\texto{uta}} = 0.75 \vezes 0.33446 \, \texto{no}^2 \times 90 \, \texto{ksi} = 22.576 \, \texto{kip}
\)
Recall the previously calculated tension load per anchor:
\(
N_{ua} = frac{N_x}{n_{uma,t}} = frac{20 \, \texto{kip}}{4} = 5 \, \texto{kip}
\)
Desde a 5 kip < 22.576 kip, 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 ACI 318-19 Cláusula 17.6.2.1.2, the member meets the criteria for a narrow member. Portanto, a modified effective embedment length must be used in the calculations.
It is determined that the modified effective embedment length, h’ef, of the anchor group is:
\(
h’_{\texto{ef}} = 5.667 \, \texto{no}
\)
Usando ACI 318-19 Cláusula 17.6.2, nós calculamos o maximum projected concrete cone area para uma única âncora, based on the modified effective embedment length.
\(
UMA_{N_{co}} = 9 \deixou( h’_{ef,g1} \direito)A partir da elevação do solo gerada a partir das elevações do Google 9 \times left( 5.6667 \, \texto{no} \direito)A partir da elevação do solo gerada a partir das elevações do Google 289 \, \texto{no}^ 2
\)
similarmente, we use the modified effective embedment length to calculate the actual projected concrete cone area of the anchor group.
\(
UMA_{N_c} = min left( n_{uma,g1} UMA_{N_{co}}, EU_{N_c} B_{N_c} \direito) = min left( 4 \vezes 289 \, \texto{no}^ 2, 22 \, \texto{no} \vezes 22 \, \texto{no} \direito) = 484 \, \texto{no}^ 2
\)
Onde,
\(
EU_{N_c} = min left( c_{\texto{deixou},g1}, 1.5 h’_{\texto{ef},g1} \direito)
+ \deixou( \Min esquerda( s_{\texto{soma},z,g1}, 3 h’_{\texto{ef},g1} \deixou( n_{z,g1} – 1 \direito) \direito) \direito)
+ \Min esquerda( c_{\texto{direito},g1}, 1.5 h’_{\texto{ef},g1} \direito)
\)
\(
EU_{N_c} = min left( 8 \, \texto{no}, 1.5 \vezes 5.6667 \, \texto{no} \direito)
+ \deixou( \Min esquerda( 6 \, \texto{no}, 3 \vezes 5.6667 \, \texto{no} \times left( 2 – 1 \direito) \direito) \direito)
+ \Min esquerda( 8 \, \texto{no}, 1.5 \vezes 5.6667 \, \texto{no} \direito)
\)
\(
EU_{N_c} = 22 \, \texto{no}
\)
\(
B_{N_c} = min left( c_{\texto{figura superior},g1}, 1.5 h’_{\texto{ef},g1} \direito)
+ \deixou( \Min esquerda( s_{\texto{soma},Y,g1}, 3 h’_{\texto{ef},g1} \deixou( n_{Y,g1} – 1 \direito) \direito) \direito)
+ \Min esquerda( c_{\texto{figura inferior},g1}, 1.5 h’_{\texto{ef},g1} \direito)
\)
\(
B_{N_c} = min left( 8.5 \, \texto{no}, 1.5 \vezes 5.6667 \, \texto{no} \direito)
+ \deixou( \Min esquerda( 5 \, \texto{no}, 3 \vezes 5.6667 \, \texto{no} \times left( 2 – 1 \direito) \direito) \direito)
+ \Min esquerda( 8.5 \, \texto{no}, 1.5 \vezes 5.6667 \, \texto{no} \direito)
\)
\(
B_{N_c} = 22 \, \texto{no}
\)
A continuação, we evaluate the basic concrete breakout strength of a single anchor using ACI 318-19 Cláusula 17.6.2.2.1
\(
N_b = k_c lambda_a sqrt{\fratura{f’_c}{\texto{psi}}} \deixou( \fratura{h’_{\texto{ef},g1}}{\texto{no}} \direito)^{1.5} \, \texto{Detalhes e parâmetros do modelo}
\)
\(
N_b = 24 \vezes 1 \times sqrt{\fratura{4 \, \texto{ksi}}{0.001 \, \texto{ksi}}} \times left( \fratura{5.6667 \, \texto{no}}{1 \, \texto{no}} \direito)^{1.5} \vezes 0.001 \, \texto{kip} = 20.475 \, \texto{kip}
\)
Onde,
- \(inclui cálculos detalhados passo a passo{c} = 24\) para âncoras fundidas
- \(\lambda = 1.0 \) for normal-weight concrete
Agora, we assess the effects of geometry by calculating the edge effect factor e o eccentricity factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{uma,\texto{min}} = min left( c_{\texto{deixou},g1}, c_{\texto{direito},g1}, c_{\texto{figura superior},g1}, c_{\texto{figura inferior},g1} \direito)
= min left( 8 \, \texto{no}, 8 \, \texto{no}, 8.5 \, \texto{no}, 8.5 \, \texto{no} \direito) = 8 \, \texto{no}
\)
De acordo com ACI 318-19 Cláusula 17.6.2.4.1, the breakout edge effect factor é:
\(
\Psi_{ed,N} = min left( 1.0, 0.7 + 0.3 \deixou( \fratura{c_{uma,\texto{min}}}{1.5 h’_{\texto{ef},g1}} \direito) \direito)
= min left( 1, 0.7 + 0.3 \times left( \fratura{8 \, \texto{no}}{1.5 \vezes 5.6667 \, \texto{no}} \direito) \direito) = 0.98235
\)
Since the tension load is applied at the centroid of the anchor group, the eccentricity is zero. Por isso, a eccentricity factor, also from Clause 17.6.2.4.1, é:
\(
\Psi_{ec,N} = min left( 1.0, \fratura{1}{1 + \fratura{2 e n}{3 h’_{\texto{ef},g1}}} \direito)
= min left( 1, \fratura{1}{1 + \fratura{2 \vezes 0}{3 \vezes 5.6667 \, \texto{no}}} \direito) = 1
\)
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 concrete breakout strength of the anchor group:
\(
\phi N_{cbg} = \phi \left( \fratura{UMA_{N_c}}{UMA_{N_{co}}} \direito) \Psi_{ec,N} \Psi_{ed,N} \Psi_{c,N} \Psi_{cp,N} N_b
\)
\(
\phi N_{cbg} = 0.7 \times left( \fratura{484 \, \texto{no}^ 2}{289 \, \texto{no}^ 2} \direito) \vezes 1 \vezes 0.98235 \vezes 1 \vezes 1 \vezes 20.475 \, \texto{kip} = 23.58 \, \texto{kip}
\)
A total applied tension load on the anchor group is the product of the individual anchor load and the number of anchors:
\(
N_{ua} = left( \fratura{N_x}{n_{uma,t}} \direito) n_{uma,g1} = left( \fratura{20 \, \texto{kip}}{4} \direito) \vezes 4 = 20 \, \texto{kip}
\)
Desde a 20 kips < 23.58 kips, the concrete breakout capacity is suficiente.
Verificar #5: Calculate anchor pullout capacity
The pullout capacity of an anchor is governed by the resistance at its embedded end. Aplicando Cargas Sísmicas, we calculate the bearing area of the embedded plate, which is the net area after subtracting the area occupied by the anchor rod.
For a rectangular embedded plate, a bearing area is calculated as:
\(
UMA_{brg} = left( \deixou( b_{embed\_plate} \direito)^2 certo) – UMA_{haste} = left( \deixou( 3 \, \texto{no} \direito)^2 certo) – 0.44179 \, \texto{no}A partir da elevação do solo gerada a partir das elevações do Google 8.5582 \, \texto{no}^ 2
\)
Onde,
\(
UMA_{haste} = frac{\pi}{4} \deixou( d_a \right)^2 = \frac{\pi}{4} \times left( 0.75 \, \texto{no} \direito)A partir da elevação do solo gerada a partir das elevações do Google 0.44179 \, \texto{no}^ 2
\)
A continuação, Nós determinamos o basic anchor pullout strength usando ACI 318-19 Equation 17.6.3.2.2a.
\(
N_b = 8 UMA_{brg} \deixou( f’_c \right) = 8 \vezes 8.5582 \, \texto{no}^2 \times \left( 4 \, \texto{ksi} \direito) = 273.86 \, \texto{kip}
\)
We then apply the appropriate resistance factor and pullout cracking factor:
- Pra cracked concreto, \(\Psi_{cp} = 1.0\)
- Pra uncracked concreto, \(\Psi_{cp} = 1.4\)
Using these, nós calculamos o design anchor pullout strength in tension por ACI 318-19 Equação 17.6.3.1.
\(
\phi N_{pn} = \phi \Psi_{c,p} N_b = 0.7 \vezes 1 \vezes 273.86 \, \texto{kip} = 191.7 \, \texto{kip}
\)
Recall the previously calculated tension load per anchor:
\(
N_{ua} = frac{N_x}{n_{uma,t}} = frac{20 \, \texto{kip}}{4} = 5 \, \texto{kip}
\)
Desde a 5 kips < 191.7 kips, the anchor pullout capacity is suficiente.
Verificar #6: Calculate embed plate flexural capacity
This is a supplementary check performed using the Software de design de placa de base skyciv to verify that the embedded plate has sufficient flexural capacity and will not yield under the applied pullout loads.
Primeiro, we determine the length of the free (unsupported) end of the embedded plate, measured from the edge of the support to the face of the rod.
\(
b’ = frac{b_{embed\_plate} – d_a}{2} = frac{3 \, \texto{no} – 0.75 \, \texto{no}}{2} = 1.125 \, \texto{no}
\)
A continuação, nós calculamos o momentos de flexão induced by the uniform bearing pressure. This pressure represents the force transferred from the anchor pullout action onto the embedded plate.
\(
m_f = \frac{\deixou( \fratura{T_a}{UMA_{brg}} \direito) \deixou( b’ \direito)^ 2}{2} = frac{\deixou( \fratura{5 \, \texto{kip}}{8.5582 \, \texto{no}^ 2} \direito) \times left( 1.125 \, \texto{no} \direito)^ 2}{2} = 0.36971 \, \texto{kip}
\)
Finalmente, using the calculated moment and given material properties, we will determine the minimum required plate thickness to resist flexural yielding.
\(
t_{min} = sqrt{\fratura{4 m_f}{\phi F_{y\_ep}}} = sqrt{\fratura{4 \vezes 0.36971 \, \texto{kip}}{0.9 \vezes 36 \, \texto{ksi}}} = 0.21364 \, \texto{no}
\)
Recall actual embedded plate thickness:
\(
t_{actual} = t_{embed\_plate} = 0.25 \, \texto{no}
\)
Desde a 0.21364 no < 0.25 no, the embedded plate flexural capacity is suficiente.
Verificar #7: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for this example, as the conditions specified in ACI 318-19 Cláusula 17.6.4 are not met. Portanto, side-face blowout failure along the Y-direction will not occur.
Verificar #8: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for this example, as the conditions specified in ACI 318-19 Cláusula 17.6.4 are not met. Portanto, side-face blowout failure along the Z-direction will not occur.
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
Clique aqui Para baixar um relatório de amostra.
Compre software de placa de base
Compre a versão completa do módulo de design da placa de base por conta própria, sem outros módulos Skyciv. Isso oferece um conjunto completo de resultados para o design da placa de base, incluindo relatórios detalhados e mais funcionalidade.
