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 Vy=2-kip e Vz=2-kip cargas de cisalhamento.
Dados dados:
Coluna:
Seção de coluna: HSS7X4X5/16
Área da coluna: 7.59 no2
Material da coluna: A36
Placa Base:
Dimensões da placa de base: 12 em x 14 no
Espessura da placa de base: 3/4 no
Material da placa de base: A36
Grout:
Grout Thickness: 0.25 no
Concreto:
Dimensões concretas: 12 em x 14 no
Espessura do concreto: 10 no
Material concreto: 3000 psi
Rachado ou sem crack: Rachado
Âncoras:
Diâmetro da âncora: 1/2 no
Comprimento eficaz de incorporação: 8 no
Plate washer thickness: 0.25 no
Plate washer connection: Welded to base plate
Soldas:
Tamanho da solda: 1/4 no
Classificação de metal de enchimento: E70XX
Dados de âncora (a partir de Calculadora Skyciv):
Definições:
Caminho de carga:
The design follows the recommendations of Guia de projeto AISC 1, 3Edição RD, e ACI 318-19. Shear loads applied to the column are transferred to the base plate through the welds, and then to the supporting concrete through the anchor rods. Friction and shear lugs are not considered in this example, as these mechanisms are not supported in the current software.
Por padrão, the applied shear load is distributed equally among all anchors, with each anchor transferring its portion of the load to the concrete support. Como uma alternativa, the software allows a simplified and more conservative assumption, where the entire shear load is assigned only to the anchors nearest the loaded edge. Nesse caso, the shear capacity check is performed on these edge anchors alone, ensuring that potential shear failure is conservatively addressed.
Grupos de âncora:
A Software de design de placa de base SkyCiv inclui um recurso intuitivo que identifica quais âncoras fazem parte de um grupo âncora para avaliar concrete shear breakout e concrete shear pryout falhas.
A grupo âncora is defined as two or more anchors with overlapping projected resistance areas. Nesse caso, the anchors act together, and their combined resistance is checked against the applied load on the group.
A single anchor is defined as an anchor whose projected resistance area does not overlap with any other. Nesse caso, the anchor acts alone, and the applied shear force on that anchor is checked directly against its individual resistance.
This distinction allows the software to capture both group behavior and individual anchor performance when assessing shear-related failure modes.
Cálculos passo a passo:
Verificar #1: Calcule a capacidade de solda
The first step is to calculate the Comprimento total da solda available to resist shear. Since the base plate is welded along the perimeter of the column section, the total weld length is obtained by summing the welds on all sides.
\( EU_{soldar} = 2 \deixou( b_{col} – 2r_{col} – 2t_{col} \direito) + 2 \deixou( d_{col} – 2r_{col} – 2t_{col} \direito) \)
\( EU_{soldar} = 2 \vezes (4\,\texto{no} – 2 \times 0.291\,\text{no} – 2 \times 0.291\,\text{no}) + 2 \vezes (7\,\texto{no} – 2 \times 0.291\,\text{no} – 2 \times 0.291\,\text{no}) = 17.344\,\text{no} \)
Using this weld length, the applied shear forces in the y- and z-directions are divided to determine the average shear force per unit length in each direction:
\( v_{uy} = frac{V_y}{EU_{soldar}} = frac{2\,\texto{kip}}{17.344\,\texto{no}} = 0.11531\,\text{kip/in} \)
\( v_{uz} = frac{V_z}{EU_{soldar}} = frac{2\,\texto{kip}}{17.344\,\texto{no}} = 0.11531\,\text{kip/in} \)
A cisalhamento resultante demand per unit length is then determined using the square root of the sum of the squares (Os métodos de combinação de carga disponíveis incluem) método.
\( r_u = \sqrt{(v_{uy})^ 2 + (v_{uz})^ 2} \)
\( r_u = \sqrt{(0.11531\,\texto{kip/in})^ 2 + (0.11531\,\texto{kip/in})^ 2} = 0.16308\,\text{kip/in} \)
A continuação, the weld capacity is calculated using AISC 360-22 Eq. J2-4, with the directional strength coefficient taken as kds=1.0 for an HSS section. The weld capacity for a 1/4 in weld is determined as:
\( \phi r_n = \phi 0.6 F_{Exx} E_w k_{ds} = 0.75 \vezes 0.6 \times 70\,\text{ksi} \times 0.177\,\text{no} \vezes 1 = 5.5755\,\text{kip/in} \)
It is also necessary to check the base metals, both the column and the base plate, usando AISC 360-22 Eq. J4-4 to obtain the shear rupture strength. Isso dá:
\( \phi r_{nbm, col} = phi 0.6 F_{u\_col} t_{col} = 0.75 \vezes 0.6 \times 58\,\text{ksi} \times 0.291\,\text{no} = 7.5951\,\text{kip/in} \)
\( \phi r_{nbm, pb} = phi 0.6 F_{u\_bp} t_{pb} = 0.75 \vezes 0.6 \times 58\,\text{ksi} \times 0.75\,\text{no} = 19.575\,\text{kip/in} \)
\( \phi r_{nbm} = \min\left( \phi r_{nbm, pb},\, \phi r_{nbm, col} \direito) = min(19.575\,\texto{kip/in},\, 7.5951\,\texto{kip/in}) = 7.5951\,\text{kip/in} \)
Since the actual weld stress is less than both the weld metal and base metal capacities, 0.16308 KPI < 5.5755 kpi and 0.16308 KPI < 7.5951 KPI, the design weld capacity is suficiente.
Verificar #2: Calculate concrete breakout capacity due to Vy shear
Perpendicular Edge Capacity:
From the layout, Âncoras 1 e 4 are closest to the edge and have the shortest ca1 distance. Using these ca1 values to project the failure cones, the software identified these anchors as âncoras únicas, since their projected cones do not overlap. The support was also determined to be not a narrow member, so the ca1 distance is used directly without modification.
Let’s recall that the shear force is assumed to be distributed among all the anchors. The calculation for the Vy shear load applied to each single anchor is:
\( V_{fa\perp} = frac{V_y}{n_a} = frac{2\,\texto{kip}}{6} = 0.33333\,\text{kip} \)
Let’s consider Anchor 1. The maximum projected area of a single anchor is calculated using ACI 318-19 Eq. 17.7.2.1.3.
\( UMA_{Vco} = 4.5 (c_{a1,s1})A partir da elevação do solo gerada a partir das elevações do Google 4.5 \vezes (2\,\texto{no})^2 = 18\,\text{no}^ 2 \)
The actual projected area is then determined from the width and height of the projected failure cone.
\( B_{Vc} = min(c_{deixou,s1},\, 1.5c_{a1,s1}) + \min(c_{direito,s1},\, 1.5c_{a1,s1}) \)
\( B_{Vc} = min(10\,\texto{no},\, 1.5 \times 2\,\text{no}) + \min(2\,\texto{no},\, 1.5 \times 2\,\text{no}) = 5\,\text{no} \)
\( a força de deslizamento é a soma da força horizontal resultante da pressão ativa do solo no lado ativo do solo e a força horizontal resultante da presença da sobrecarga{Vc} = min(1.5c_{a1,s1},\, t_{conc}) = min(1.5 \times 2\,\text{no},\, 10\,\texto{no}) = 3\,\text{no} \)
\( UMA_{Vc} = B_{Vc} a força de deslizamento é a soma da força horizontal resultante da pressão ativa do solo no lado ativo do solo e a força horizontal resultante da presença da sobrecarga{Vc} = 5\,\text{no} \times 3\,\text{no} = 15\,\text{no}^ 2 \)
The next step is to use Equations 17.7.2.2.1a and 17.7.2.2.1b to calculate the basic breakout strength of a single anchor. The governing capacity is taken as the lesser value.
\( V_{b1} = 7 \deixou( \fratura{\min(l_e,\, 8d_a)}{d_a} \direito)^{0.2} \sqrt{\fratura{d_a}{\texto{no}}} \lambda_a sqrt{\fratura{f’_c}{\texto{psi}}} \deixou( \fratura{c_{a1,s1}}{\texto{no}} \direito)^{1.5} \,\texto{Detalhes e parâmetros do modelo} \)
\( V_{b1} = 7 \times left( \fratura{\min(8\,\texto{no},\, 8 \times 0.5\,\text{no})}{0.5\,\texto{no}} \direito)^{0.2} \times sqrt{\fratura{0.5\,\texto{no}}{1\,\texto{no}}} \vezes 1 \times sqrt{\fratura{3\,\texto{ksi}}{0.001\,\texto{ksi}}} \times left( \fratura{2\,\texto{no}}{1\,\texto{no}} \direito)^{1.5} \times 0.001\,\text{kip} \)
\( V_{b1} = 1.1623\,\text{kip} \)
\( V_{b2} = 9 \lambda_a sqrt{\fratura{f’_c}{\texto{psi}}} \deixou( \fratura{c_{a1,s1}}{\texto{no}} \direito)^{1.5} \,\texto{Detalhes e parâmetros do modelo} \)
\( V_{b2} = 9 \vezes 1 \times sqrt{\fratura{3\,\texto{ksi}}{0.001\,\texto{ksi}}} \times left( \fratura{2\,\texto{no}}{1\,\texto{no}} \direito)^{1.5} \times 0.001\,\text{kip} = 1.3943\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(1.1623\,\texto{kip},\, 1.3943\,\texto{kip}) = 1.1623\,\text{kip} \)
A continuação, a breakout capacity parameters are determined. A breakout edge effect factor is calculated according to ACI 318-19 Cláusula 17.7.2.4, quanto pelo thickness factor is calculated according to Cláusula 17.7.2.6.1.
\( \Psi_{ed,V} = \min\left(1.0,\, 0.7 + 0.3 \deixou( \fratura{c_{a2,s1}}{1.5c_{a1,s1}} \direito) \direito) = \min\left(1,\, 0.7 + 0.3 \times left( \fratura{2\,\texto{no}}{1.5 \times 2\,\text{no}} \direito) \direito) = 0.9 \)
\( \Psi_{h,V} = \max\left( \sqrt{ \fratura{1.5c_{a1,s1}}{t_{conc}} },\, 1.0 \direito) = \max\left( \sqrt{ \fratura{1.5 \times 2\,\text{no}}{10\,\texto{no}} },\, 1 \direito) = 1 \)
Finalmente, ACI 318-19 Cláusula 17.7.2.1(uma) is used to determine the concrete breakout capacity of a single anchor in shear. The calculated capacity for Vy shear in the perpendicular direction is 0.69 kips.
\( \phi V_{cb\perp} = phi esquerda( \fratura{UMA_{Vc}}{UMA_{Vco}} \direito) \Psi_{ed,V} \Psi_{c,V} \Psi_{h,V} V_b \)
\( \phi V_{cb\perp} = 0.65 \times left( \fratura{15\,\texto{no}^ 2}{18\,\texto{no}^ 2} \direito) \vezes 0.86 \vezes 1 \vezes 1 \times 1.1623\,\text{kip} = 0.56661\,\text{kip} \)
The calculated capacity for Vy shear no perpendicular direction is 0.56 kips.
Parallel Edge Capacity:
Failure along the edge parallel to the load is also possible in this scenario, so the concrete breakout capacity for the parallel edge must be determined. The anchors or anchor group considered are those aligned with the parallel edge. Consequentemente, a ca1 edge distance is measured from the anchor to the edge along the Z-direction. Based on the figure below, the failure cone projections overlap; Portanto, the anchors are treated as a group.
Caso 1:
Caso 2:
We refer to ACI 318-19 Figura. R17.7.2.1b for the different cases used when evaluating anchor groups. In this base plate design, welded plate washers are specifically used. Portanto, só Caso 2 is checked.
The required load for the anchor group in Case 2 is taken as the total shear load.
\( V_{fa\parallel,case2} = V_y = 2\,\text{kip} \)
In calculating the capacity for the Case 2 failure, the anchors considered are the rear anchors. Como um resultado, the ca1 edge distance is measured from the rear anchor group to the failure edge.
With this ca1 distance and edge orientation, it must be verified whether the support qualifies as a narrow member. Following ACI 318-19 Cláusula 17.7.2.1.2, the SkyCiv Base Plate software identified the support as narrow. Portanto, a modified ca1 distance é usado, which is calculated to be 6.667 no.
The same steps as in the perpendicular case are followed: calculating the projected failure areas, a basic single-anchor breakout strength, quanto pelo breakout parameters. The calculated values for each step are shown below.
\( UMA_{Vco} = 4.5 (c_{‘a1,g2})A partir da elevação do solo gerada a partir das elevações do Google 4.5 \vezes (6.6667\,\texto{no})^2 = 200\,\text{no}^ 2 \)
\( UMA_{Vc} = B_{Vc} a força de deslizamento é a soma da força horizontal resultante da pressão ativa do solo no lado ativo do solo e a força horizontal resultante da presença da sobrecarga{Vc} = 14\,\text{no} \times 10\,\text{no} = 140\,\text{no}^ 2 \)
\( V_{b1} = 7.0733\,\text{kip} \)
\( V_{b2} = 8.4853\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(7.0733\,\texto{kip},\, 8.4853\,\texto{kip}) = 7.0733\,\text{kip} \)
\( \Psi_{ed,V} = 1.0 \)
\( \Psi_{h,V} = 1.0 \)
The equation for the parallel edge capacity differs from the perpendicular edge capacity. ACI 318-19 Cláusula 17.7.2.1(c) é aplicado, where the breakout equation is multiplied by 2.
\( \phi V_{cbg\parallel} = 2 \phi esquerda( \fratura{UMA_{Vc}}{UMA_{Vco}} \direito) \Psi_{ed,V} \Psi_{c,V} \Psi_{h,V} V_b \)
\( \phi V_{cbg\parallel} = 2 \vezes 0.65 \times left( \fratura{140\,\texto{no}^ 2}{200\texto{no}^ 2} \direito) \vezes 1 \vezes 1 \vezes 1 \times 7.0733\,\text{kip} = 6.4367\,\text{kip} \)
The calculated capacity for Vy shear no paralelo direction is 6.43 kips.
We now assess the perpendicular and parallel failures separately.
- For the perpendicular edge failure, optimizada 0.33 kip < 0.56 kip, the design concrete shear breakout capacity is suficiente.
- For the parallel edge failure, optimizada 2 kip < 6.43 kip, the design concrete shear breakout capacity is suficiente.
Verificar #3: Calculate concrete breakout capacity due to Vz shear
The base plate is also subjected to Vz shear, so the failure edges perpendicular and parallel to the Vz shear must be checked. Using the same approach, the perpendicular and parallel capacities are calculated as 2.45 kips e 1.26 kips, respectivamente.
Perpendicular Edge:
Parallel Edge:
These capacities are then compared to the required strengths.
- For the perpendicular edge failure, optimizada 2 kip < 2.45 kip, the concrete shear breakout capacity is suficiente.
- For the parallel edge failure, optimizada 0.33 kip < 1.26 kip, the concrete shear breakout capacity is suficiente.
Verificar #4: Calculate concrete pryout capacity
A concrete cone for pryout failure is the same cone used in the tensile breakout check. To calculate the shear pryout capacity, the nominal tensile breakout strength of the single anchors or anchor group must first be determined. The detailed calculations for the tensile breakout check are already covered in the SkyCiv Design Examples for Tension Load.
It is important to note that the anchor group determination for shear pryout is different from that for shear breakout. Portanto, the anchors in the design must still be checked to determine whether they act seção retangular de madeira padronizada de acordo com group or as âncoras únicas against the shear pryout failure. The classification of the support as a narrow section must also be verified and should follow the same conditions used for tension breakout.
From the SkyCiv calculations, a nominal tensile breakout strength do grupo âncora é 12.772 kips. With a pryout factor of kcp=2, the design pryout capacity is:
\( \phi V_{cpg} = \phi k_{cp} N_{cbg} = 0.65 \vezes 2 \vezes 12.772 \,\texto{kip} = 16.604\,\text{kip} \)
The required strength is the resultant of the applied shear loads. Since all anchors belong to a single group, the total resultant shear is assigned to the group.
\( V_{fazer} = sqrt{(V_y)^ 2 + (V_z)^ 2} = sqrt{(2\,\texto{kip})^ 2 + (2\,\texto{kip})^ 2} = 2.8284\,\text{kip} \)
\( V_{fazer} = left( \fratura{V_{fazer}}{n_a} \direito) n_{uma,G1} = left( \fratura{2.8284\,\texto{kip}}{6} \direito) \vezes 6 = 2.8284\,\text{kip} \)
Since the total shear load is less than anchor group capacity, 2.82 kips < 18.976 kips, the design pryout capacity is suficiente.
Verificar #5: Calculate anchor rod shear capacity
Recall that in this design example, shear is distributed to all anchors. The total shear load per anchor is therefore the resultant of its share of the Vy load and its share of the Vz load.
\( v_{fazer,Y} = frac{V_y}{n_a} = frac{2\,\texto{kip}}{6} = 0.33333\,\text{kip} \)
\( v_{fazer,z} = frac{V_z}{n_a} = frac{2\,\texto{kip}}{6} = 0.33333\,\text{kip} \)
\( V_{fazer} = sqrt{(v_{fazer,Y})^ 2 + (v_{fazer,z})^ 2} \)
\( V_{fazer} = sqrt{(0.33333\,\texto{kip})^ 2 + (0.33333\,\texto{kip})^ 2} = 0.4714\,\text{kip} \)
This gives the shear stress on the anchor rod como:
\( f_v = \frac{V_{fazer}}{UMA_{haste}} = frac{0.4714\,\texto{kip}}{0.19635\,\texto{no}^ 2} = 2.4008\,\text{ksi} \)
Because a plate washer is present, a eccentric shear load is induced in the anchor rod. The eccentricity is taken as half of the distance measured from the top of the concrete support to the center of the plate washer, accounting for the thickness of the base plate. Consulte Guia de projeto AISC 1, 3rd Edition Section 4.3.3.
\( e = 0.5 \deixou( \fratura{t_{pw}}{2} + t_{pb} \direito) = 0.5 \times left( \fratura{0.25\,\texto{no}}{2} + 0.75\,\texto{no} \direito) = 0.4375\,\text{no} \)
The moment from the eccentric shear is then expressed as an axial stress in the anchor rod. Using the section modulus, the axial stress due to this moment is calculated as:
\( Z_{haste} = frac{\pi}{32} (d_a)^3 = \frac{\pi}{32} \vezes (0.5\,\texto{no})^3 = 0.012272\,\text{no}^ 3 \)
\( f_t = \frac{V_{fazer} e}{Z_{haste}} = frac{0.4714\,\texto{kip} \times 0.4375\,\text{no}}{0.012272\,\texto{no}^ 3} = 16.806\,\text{ksi} \)
ACI Anchor Rod Shear Capacity:
Following ACI 318-19 Cláusula 17.7.1, the design strength is then determined. A 0.8 fator de redução is applied due to the presence of grout pads. The design capacity is therefore:
\( \phi V_{para,aqui} = 0.8 \phi 0.6 UMA_{eu sei,v} f_{uta} = 0.8 \vezes 0.65 \vezes 0.6 \times 0.1419\text{no}^2 \times 90\text{ksi} = 3.9845\text{kip} \)
Como uma alternativa, a SkyCiv Base Plate software allows the 0.8 simplification to be disabled, and use the actual grout pad thickness in the calculations. Nesse caso, the total eccentricity includes the grout pad, and the combined shear and axial strength is determined in accordance with AISC provisions.
AISC Anchor Rod Shear Capacity:
Primeiro, a nominal shear and tensile stresses are determined for an A325 rod.
\( F_{novo} = 0.45 F_{você,anc} = 0.45 \vezes 120\ \texto{ksi} = 54\ \texto{ksi} \)
\( F_{não} = 0.75 F_{você,anc} = 0.75 \vezes 120\ \texto{ksi} = 90\ \texto{ksi} \)
The AISC method uses AISC 360-22 Eq. J3-3a, which may be expressed to include the effects of axial stress. This is carried out as follows.
\( F’_{novo} = min left( 1.3 F_{novo} – \deixou( \fratura{F_{novo}}{\Phi f_{não}} \direito) f_t,\; F_{novo} \direito) \)
\( F’_{novo} = min left( 1.3 \vezes 54\ \texto{ksi} – \deixou( \fratura{54\ \texto{ksi}}{0.75 \vezes 90\ \texto{ksi}} \direito) \vezes 16.806\ \texto{ksi},\; 54\ \texto{ksi} \direito) = 54\ \texto{ksi} \)
The design shear capacity from the AISC method is then calculated as:
\( \phi R_{n,\mathrm{aisc}} = \phi F’_{novo} UMA_{haste} = 0.75 \vezes 54\ \texto{ksi} \vezes 0.19635\ \texto{no}A partir da elevação do solo gerada a partir das elevações do Google 7.9522\)
To ensure both methods are covered, the governing capacity is taken as the lesser of the two, qual é 3.98 kip.
\( \phi V_n = \min \left( \phi V_{para,aqui},\; \phi R_{n,\mathrm{aisc}} \direito) = min (3.9845\ \texto{kip},\; 7.9522\ \texto{kip}) = 3.9845\ \texto{kip} \)
Since the shear load per anchor rod is less than the governing anchor rod capacity in shear, 0.47 kip < 3.98 kip, the design anchor rod shear capacity is suficiente.
Resumo do projeto
A Software de design de placa de base skyciv pode gerar automaticamente um relatório de cálculo passo a passo para este exemplo de design. 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.
