Ejemplo de diseño de placa base usando AISC 360-22 y ACI 318-19
Declaración del problema:
Determine whether the designed column-to-base plate connection is sufficient for a Vy=2-kip y Vz=2-kip cargas de corte.
Datos dados:
Columna:
Sección de columna: HSS7X4X5/16
Área de columna: 7.59 in2
Material de columna: A36
Plato base:
Dimensiones de placa base: 12 en x 14 in
Espesor de la placa base: 3/4 in
Material de placa base: A36
Lechada:
Grout Thickness: 0.25 in
Hormigón:
Dimensiones concretas: 12 en x 14 in
Espesor de concreto: 10 in
Material de hormigón: 3000 psi
Agrietado o sin crack: Agrietado
Ancla:
Diámetro de anclaje: 1/2 in
Longitud de incrustación efectiva: 8 in
Plate washer thickness: 0.25 in
Plate washer connection: Welded to base plate
Soldaduras:
Tamaño de soldadura: 1/4 in
Clasificación de metal de relleno: E70XX
Aniquilar datos (de Calculadora de SkyCiv):
Definiciones:
Ruta de carga:
The design follows the recommendations of Guía de diseño AISC 1, 3edición RD, y 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 defecto, the applied shear load is distributed equally among all anchors, with each anchor transferring its portion of the load to the concrete support. Como 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. En este caso, the shear capacity check is performed on these edge anchors alone, ensuring that potential shear failure is conservatively addressed.
Grupos de anclaje:
El Software de diseño de placa base SkyCiv Incluye una característica intuitiva que identifica qué anclajes son parte de un grupo de anclaje para evaluar concrete shear breakout y concrete shear pryout fallas.
Un grupo de ancla is defined as two or more anchors with overlapping projected resistance areas. En este 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. En este 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 paso a paso:
Cheque #1: Calcular la capacidad de soldadura
The first step is to calculate the Longitud total de soldadura 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.
\( L_{soldar} = 2 \izquierda( B_{columna} – 2r_{columna} – 2A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{columna} \verdad) + 2 \izquierda( D_{columna} – 2r_{columna} – 2A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{columna} \verdad) \)
\( L_{soldar} = 2 \veces (4\,\texto{in} – 2 \times 0.291\,\text{in} – 2 \times 0.291\,\text{in}) + 2 \veces (7\,\texto{in} – 2 \times 0.291\,\text{in} – 2 \times 0.291\,\text{in}) = 17.344\,\text{in} \)
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:
\( A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{uy} = frac{V_y}{L_{soldar}} = frac{2\,\texto{kip}}{17.344\,\texto{in}} = 0.11531\,\text{kip/in} \)
\( A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{uz} = frac{V_z}{L_{soldar}} = frac{2\,\texto{kip}}{17.344\,\texto{in}} = 0.11531\,\text{kip/in} \)
El resultant shear demand per unit length is then determined using the square root of the sum of the squares (SRSS) método.
\( r_u = \sqrt{(A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{uy})^ 2 + (A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{uz})^ 2} \)
\( r_u = \sqrt{(0.11531\,\texto{kip/in})^ 2 + (0.11531\,\texto{kip/in})^ 2} = 0.16308\,\text{kip/in} \)
próximo, 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:
\( \Phi r_n = phi 0.6 F_{Exx} E_w k_{ds} = 0.75 \veces 0.6 \times 70\,\text{KSI} \times 0.177\,\text{in} \veces 1 = 5.5755\,\text{kip/in} \)
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. This gives:
\( \Phi R_{nbm, columna} = phi 0.6 F_{u\_col} A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{columna} = 0.75 \veces 0.6 \times 58\,\text{KSI} \times 0.291\,\text{in} = 7.5951\,\text{kip/in} \)
\( \Phi R_{nbm, pb} = phi 0.6 F_{u\_bp} A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{pb} = 0.75 \veces 0.6 \times 58\,\text{KSI} \times 0.75\,\text{in} = 19.575\,\text{kip/in} \)
\( \Phi R_{nbm} = \min\left( \Phi R_{nbm, pb},\, \Phi R_{nbm, columna} \verdad) = min(19.575\,\texto{kip/in},\, 7.5951\,\texto{kip/in}) = 7.5951\,\text{kip/in} \)
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.
Cheque #2: Calculate concrete breakout capacity due to Vy shear
Perpendicular Edge Capacity:
From the layout, Ancla 1 y 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 anclajes individuales, 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 Ancla 1. The maximum projected area of a single anchor is calculated using ACI 318-19 Eq. 17.7.2.1.3.
\( UNA_{vco} = 4.5 (C_{a1,s1})^2 = 4.5 \veces (2\,\texto{in})^2 = 18\,\text{in}^ 2 \)
The actual projected area is then determined from the width and height of the projected failure cone.
\( SI_{U} = min(C_{izquierda,s1},\, 1.5C_{a1,s1}) + \min(C_{verdad,s1},\, 1.5C_{a1,s1}) \)
\( SI_{U} = min(10\,\texto{in},\, 1.5 \times 2\,\text{in}) + \min(2\,\texto{in},\, 1.5 \times 2\,\text{in}) = 5\,\text{in} \)
\( se requiere realizar una sumatoria de momentos con respecto al punto mencionado de todas las cargas verticales{U} = min(1.5C_{a1,s1},\, A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{sobre}) = min(1.5 \times 2\,\text{in},\, 10\,\texto{in}) = 3\,\text{in} \)
\( UNA_{U} = B_{U} se requiere realizar una sumatoria de momentos con respecto al punto mencionado de todas las cargas verticales{U} = 5\,\text{in} \times 3\,\text{in} = 15\,\text{in}^ 2 \)
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.
\( V_{b1} = 7 \izquierda( \frac{\min(l_e,\, 8D_A)}{D_A} \verdad)^{0.2} \sqrt{\frac{D_A}{\texto{in}}} \lambda_a sqrt{\frac{f’_c}{\texto{psi}}} \izquierda( \frac{C_{a1,s1}}{\texto{in}} \verdad)^{1.5} \,\texto{lbf} \)
\( V_{b1} = 7 \veces left( \frac{\min(8\,\texto{in},\, 8 \times 0.5\,\text{in})}{0.5\,\texto{in}} \verdad)^{0.2} \veces sqrt{\frac{0.5\,\texto{in}}{1\,\texto{in}}} \veces 1 \veces sqrt{\frac{3\,\texto{KSI}}{0.001\,\texto{KSI}}} \veces left( \frac{2\,\texto{in}}{1\,\texto{in}} \verdad)^{1.5} \times 0.001\,\text{kip} \)
\( V_{b1} = 1.1623\,\text{kip} \)
\( V_{b2} = 9 \lambda_a sqrt{\frac{f’_c}{\texto{psi}}} \izquierda( \frac{C_{a1,s1}}{\texto{in}} \verdad)^{1.5} \,\texto{lbf} \)
\( V_{b2} = 9 \veces 1 \veces sqrt{\frac{3\,\texto{KSI}}{0.001\,\texto{KSI}}} \veces left( \frac{2\,\texto{in}}{1\,\texto{in}} \verdad)^{1.5} \times 0.001\,\text{kip} = 1.3943\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(1.1623\,\texto{kip},\, 1.3943\,\texto{kip}) = 1.1623\,\text{kip} \)
próximo, la breakout capacity parameters are determined. El breakout edge effect factor is calculated according to ACI 318-19 Cláusula 17.7.2.4, y el thickness factor is calculated according to Cláusula 17.7.2.6.1.
\( \Psi_{ed,V } = \min\left(1.0,\, 0.7 + 0.3 \izquierda( \frac{C_{a2,s1}}{1.5C_{a1,s1}} \verdad) \verdad) = \min\left(1,\, 0.7 + 0.3 \veces left( \frac{2\,\texto{in}}{1.5 \times 2\,\text{in}} \verdad) \verdad) = 0.9 \)
\( \Psi_{h,V } = \max\left( \sqrt{ \frac{1.5C_{a1,s1}}{A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{sobre}} },\, 1.0 \verdad) = \max\left( \sqrt{ \frac{1.5 \times 2\,\text{in}}{10\,\texto{in}} },\, 1 \verdad) = 1 \)
Finalmente, ACI 318-19 Cláusula 17.7.2.1(a) 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 .
\( \no V_{cb\perp} = phi izquierda( \frac{UNA_{U}}{UNA_{vco}} \verdad) \Psi_{ed,V } \Psi_{c,V } \Psi_{h,V } V_b \)
\( \no V_{cb\perp} = 0.65 \veces left( \frac{15\,\texto{in}^ 2}{18\,\texto{in}^ 2} \verdad) \veces 0.86 \veces 1 \veces 1 \times 1.1623\,\text{kip} = 0.56661\,\text{kip} \)
The calculated capacity for Vy shear en el perpendicular direction is 0.56 kips .
Parallel Edge Capacity:
Failure along the edge parallel to the load is also possible in this scenario, entonces el concrete breakout capacity for the parallel edge must be determined. The anchors or anchor group considered are those aligned with the parallel edge. Por consiguiente, la 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; por lo tanto, the anchors are treated as a group.
Caso 1:
Caso 2:
We refer to ACI 318-19 Fig. R17.7.2.1b for the different cases used when evaluating anchor groups. In this base plate design, welded plate washers are specifically used. Por lo tanto, solo 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 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. Por lo tanto, la modified ca1 distance se usa, which is calculated to be 6.667 in.
The same steps as in the perpendicular case are followed: calculando el projected failure areas, la basic single-anchor breakout strength, y el breakout parameters. The calculated values for each step are shown below.
\( UNA_{vco} = 4.5 (C_{‘a1,g2})^2 = 4.5 \veces (6.6667\,\texto{in})^2 = 200\,\text{in}^ 2 \)
\( UNA_{U} = B_{U} se requiere realizar una sumatoria de momentos con respecto al punto mencionado de todas las cargas verticales{U} = 14\,\text{in} \times 10\,\text{in} = 140\,\text{in}^ 2 \)
\( V_{b1} = 7.0733\,\text{kip} \)
\( V_{b2} = 8.4853\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(7.0733\,\texto{kip},\, 8.4853\,\texto{kip}) = 7.0733\,\text{kip} \)
\( \Psi_{ed,V } = 1.0 \)
\( \Psi_{h,V } = 1.0 \)
The equation for the parallel edge capacity differs from the perpendicular edge capacity. ACI 318-19 Cláusula 17.7.2.1(c) se aplica, where the breakout equation is multiplied by 2.
\( \no V_{cbg\parallel} = 2 \Phi Izquierda( \frac{UNA_{U}}{UNA_{vco}} \verdad) \Psi_{ed,V } \Psi_{c,V } \Psi_{h,V } V_b \)
\( \no V_{cbg\parallel} = 2 \veces 0.65 \veces left( \frac{140\,\texto{in}^ 2}{200\texto{in}^ 2} \verdad) \veces 1 \veces 1 \veces 1 \times 7.0733\,\text{kip} = 6.4367\,\text{kip} \)
The calculated capacity for Vy shear en el paralelo direction is 6.43 kips .
We now assess the perpendicular and parallel failures separately.
- For the perpendicular edge failure, ya que 0.33 kip < 0.56 kip, the design concrete shear breakout capacity is suficiente.
- For the parallel edge failure, ya que 2 kip < 6.43 kip, the design concrete shear breakout capacity is suficiente.
Cheque #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 y 1.26 kips , respectivamente.
Perpendicular Edge:
Parallel Edge:
These capacities are then compared to the required strengths.
- For the perpendicular edge failure, ya que 2 kip < 2.45 kip, the concrete shear breakout capacity is suficiente.
- For the parallel edge failure, ya que 0.33 kip < 1.26 kip, the concrete shear breakout capacity is suficiente.
Cheque #4: Calculate concrete pryout capacity
El 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. Por lo tanto, the anchors in the design must still be checked to determine whether they act tener un grupo or as anclajes individuales 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, la nominal tensile breakout strength del grupo de ancla es 12.772 kips . With a pryout factor of kcp=2, the design pryout capacity is:
\( \no V_{cpg} = \phi k_{cp} NORTE_{cbg} = 0.65 \veces 2 \veces 12.772 \,\texto{kip} = 16.604\,\text{kip} \)
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.
\( V_{hacer} = sqrt{(V_y)^ 2 + (V_z)^ 2} = sqrt{(2\,\texto{kip})^ 2 + (2\,\texto{kip})^ 2} = 2.8284\,\text{kip} \)
\( V_{hacer} = left( \frac{V_{hacer}}{n_a} \verdad) norte_{a,G1} = left( \frac{2.8284\,\texto{kip}}{6} \verdad) \veces 6 = 2.8284\,\text{kip} \)
Since the total shear load is less than anchor group capacity, 2.82 kips < 18.976 kips , the design pryout capacity is suficiente.
Cheque #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.
\( A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{hacer,y} = frac{V_y}{n_a} = frac{2\,\texto{kip}}{6} = 0.33333\,\text{kip} \)
\( A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{hacer,z} = frac{V_z}{n_a} = frac{2\,\texto{kip}}{6} = 0.33333\,\text{kip} \)
\( V_{hacer} = sqrt{(A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{hacer,y})^ 2 + (A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{hacer,z})^ 2} \)
\( V_{hacer} = sqrt{(0.33333\,\texto{kip})^ 2 + (0.33333\,\texto{kip})^ 2} = 0.4714\,\text{kip} \)
This gives the shear stress on the anchor rod como:
\( f_v = \frac{V_{hacer}}{UNA_{vara}} = frac{0.4714\,\texto{kip}}{0.19635\,\texto{in}^ 2} = 2.4008\,\text{KSI} \)
Because a plate washer is present, un 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. Referirse a Guía de diseño AISC 1, 3rd Edition Section 4.3.3.
\( e = 0.5 \izquierda( \frac{A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{pw}}{2} + A continuación se muestra un ejemplo de algunos cálculos de placa base australianos que se usan comúnmente en el diseño de placa base{pb} \verdad) = 0.5 \veces left( \frac{0.25\,\texto{in}}{2} + 0.75\,\texto{in} \verdad) = 0.4375\,\text{in} \)
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:
\( Z_{vara} = frac{\pi}{32} (D_A)^3 = \frac{\pi}{32} \veces (0.5\,\texto{in})^3 = 0.012272\,\text{in}^ 3 \)
\( f_t = \frac{V_{hacer} mi}{Z_{vara}} = frac{0.4714\,\texto{kip} \times 0.4375\,\text{in}}{0.012272\,\texto{in}^ 3} = 16.806\,\text{KSI} \)
ACI Anchor Rod Shear Capacity:
Following ACI 318-19 Cláusula 17.7.1, the design strength is then determined. A 0.8 factor de reducción is applied due to the presence of grout pads. The design capacity is therefore:
\( \no V_{a,aquí} = 0.8 \fi 0.6 UNA_{se,v} F_{uta} = 0.8 \veces 0.65 \veces 0.6 \times 0.1419\text{in}^2 \times 90\text{KSI} = 3.9845\text{kip} \)
Como alternativa, la SkyCiv Base Plate software allows the 0.8 simplification to be disabled, and use the actual grout pad thickness in the calculations. En este 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:
primero, la nominal shear and tensile stresses are determined for an A325 rod.
\( F_{Nevada} = 0.45 F_{tu,Congreso Nacional Africano} = 0.45 \veces 120\ \texto{KSI} = 54\ \texto{KSI} \)
\( F_{Nuevo Testamento} = 0.75 F_{tu,Congreso Nacional Africano} = 0.75 \veces 120\ \texto{KSI} = 90\ \texto{KSI} \)
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.
\( F’_{Nevada} = min left( 1.3 F_{Nevada} – \izquierda( \frac{F_{Nevada}}{\Phi F_{Nuevo Testamento}} \verdad) pie,\; F_{Nevada} \verdad) \)
\( F’_{Nevada} = min left( 1.3 \veces 54\ \texto{KSI} – \izquierda( \frac{54\ \texto{KSI}}{0.75 \veces 90\ \texto{KSI}} \verdad) \veces 16.806\ \texto{KSI},\; 54\ \texto{KSI} \verdad) = 54\ \texto{KSI} \)
The design shear capacity from the AISC method is then calculated as:
\( \fi R_{norte,\mathrm{aisc}} = \phi F’_{Nevada} UNA_{vara} = 0.75 \veces 54\ \texto{KSI} \veces 0.19635\ \texto{in}^2 = 7.9522\)
To ensure both methods are covered, the governing capacity is taken as the lesser of the two, que es 3.98 kip.
\( \phi V_n = \min \left( \no V_{a,aquí},\; \fi R_{norte,\mathrm{aisc}} \verdad) = min (3.9845\ \texto{kip},\; 7.9522\ \texto{kip}) = 3.9845\ \texto{kip} \)
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.
Resumen de diseño
El Software de diseño de placa base de SkyCiv puede generar automáticamente un informe de cálculo paso a paso para este ejemplo de diseño. También proporciona un resumen de los controles realizados y sus proporciones resultantes, Hacer que la información sea fácil de entender de un vistazo. A continuación se muestra una tabla de resumen de muestra, que se incluye en el informe.
Informe de muestra de SkyCiv
haga clic aquí Para descargar un informe de muestra.
Comprar software de placa base
Compre la versión completa del módulo de diseño de la placa base por sí solo sin ningún otro módulo SkyCiv. Esto le da un conjunto completo de resultados para el diseño de placa base, incluyendo informes detallados y más funcionalidad.
