Exemple de conception de plaque de base utilisant AISC 360-22 et ACI 318-19
Déclaration de problème:
Determine whether the designed column-to-base plate connection is sufficient for a Vy=2-kip et Vz=2-kip charges de cisaillement.
Données données:
Colonne:
Section colonne: HSS7X4X5/16
Zone de colonne: 7.59 in2
Matériau de colonne: A36
Plaque de base:
Dimensions de la plaque de base: 12 en x 14 in
Épaisseur de plaque de base: 3/4 in
Matériau de plaque de base: A36
Jointoyer:
Grout Thickness: 0.25 in
Béton:
Dimensions du béton: 12 en x 14 in
Épaisseur de béton: 10 in
Matériau en béton: 3000 psi
Craquelé ou sans crates: Fissuré
Ancres:
Diamètre d'ancrage: 1/2 in
Durée d'admission efficace: 8 in
Plate washer thickness: 0.25 in
Plate washer connection: Welded to base plate
Soudures:
Taille de soudure: 1/4 in
Classification du métal de remplissage: E70XX
Ancrer les données (de Calculateur de skyciv):
Définitions:
Chemin de chargement:
The design follows the recommendations of Guide de conception AISC 1, 3édition rd, et 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.
Par défaut, the applied shear load is distributed equally among all anchors, with each anchor transferring its portion of the load to the concrete support. Comme alternative, the software allows a simplified and more conservative assumption, where the entire shear load is assigned only to the anchors nearest the loaded edge. Dans le cas présent, the shear capacity check is performed on these edge anchors alone, ensuring that potential shear failure is conservatively addressed.
Groupes d'ancrage:
Ce logiciel Logiciel de conception de plaque de base SkyCiv Comprend une caractéristique intuitive qui identifie les ancres qui font partie d'un groupe d'ancrage pour évaluer concrete shear breakout et concrete shear pryout échecs.
Un groupe d'ancrage is defined as two or more anchors with overlapping projected resistance areas. Dans le cas présent, 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. Dans le cas présent, 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.
Calculs étape par étape:
Vérifier #1: Calculer la capacité de soudure
The first step is to calculate the Longueur totale de soudure 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.
\( L_{souder} = 2 \la gauche( b_{col} – 2r_{col} – 2t_{col} \droite) + 2 \la gauche( ré_{col} – 2r_{col} – 2t_{col} \droite) \)
\( L_{souder} = 2 \fois (4\,\texte{in} – 2 \times 0.291\,\text{in} – 2 \times 0.291\,\text{in}) + 2 \fois (7\,\texte{in} – 2 \times 0.291\,\text{in} – 2 \times 0.291\,\text{in}) = 17.344\,\text{in} \)
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 dans chaque direction:
\( v_{ouais} = frac{V_y}{L_{souder}} = frac{2\,\texte{kip}}{17.344\,\texte{in}} = 0.11531\,\text{kip / in} \)
\( v_{uz} = frac{V_z}{L_{souder}} = frac{2\,\texte{kip}}{17.344\,\texte{in}} = 0.11531\,\text{kip / in} \)
Ce logiciel resultant shear demand per unit length is then determined using the square root of the sum of the squares (SRSS) méthode.
\( r_u = \sqrt{(v_{ouais})^ 2 + (v_{uz})^ 2} \)
\( r_u = \sqrt{(0.11531\,\texte{kip / in})^ 2 + (0.11531\,\texte{kip / in})^ 2} = 0.16308\,\text{kip / in} \)
Prochain, 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:
\( \Phi r_n = phi 0.6 F_{Exx} E_w k_{ds} = 0.75 \fois 0.6 \times 70\,\text{KSI} \times 0.177\,\text{in} \fois 1 = 5.5755\,\text{kip / in} \)
It is also necessary to check the base metals, both the column and the base plate, utilisant AISC 360-22 Eq. J4-4 to obtain the shear rupture strength. This gives:
\( \phi r_{nbm, col} = phi 0.6 F_{u\_col} t_{col} = 0.75 \fois 0.6 \times 58\,\text{KSI} \times 0.291\,\text{in} = 7.5951\,\text{kip / in} \)
\( \phi r_{nbm, pb} = phi 0.6 F_{u\_bp} t_{pb} = 0.75 \fois 0.6 \times 58\,\text{KSI} \times 0.75\,\text{in} = 19.575\,\text{kip / in} \)
\( \phi r_{nbm} = \min\left( \phi r_{nbm, pb},\, \phi r_{nbm, col} \droite) = min(19.575\,\texte{kip / in},\, 7.5951\,\texte{kip / in}) = 7.5951\,\text{kip / in} \)
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 suffisant.
Vérifier #2: Calculate concrete breakout capacity due to Vy shear
Perpendicular Edge Capacity:
From the layout, Ancres 1 et 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 ancres simples, 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:
\( V_{fa\perp} = frac{V_y}{n_a} = frac{2\,\texte{kip}}{6} = 0.33333\,\text{kip} \)
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.
\( UNE_{Vco} = 4.5 (c_{a1,s1})À partir de l'élévation du sol générée à partir des élévations Google 4.5 \fois (2\,\texte{in})^2 = 18\,\text{in}^ 2 \)
The actual projected area is then determined from the width and height of the projected failure cone.
\( B_{U} = min(c_{la gauche,s1},\, 1.5c_{a1,s1}) + \min(c_{droite,s1},\, 1.5c_{a1,s1}) \)
\( B_{U} = min(10\,\texte{in},\, 1.5 \times 2\,\text{in}) + \min(2\,\texte{in},\, 1.5 \times 2\,\text{in}) = 5\,\text{in} \)
\( H_{U} = min(1.5c_{a1,s1},\, t_{concurrence}) = min(1.5 \times 2\,\text{in},\, 10\,\texte{in}) = 3\,\text{in} \)
\( UNE_{U} = B_{U} H_{U} = 5\,\text{in} \times 3\,\text{in} = 15\,\text{in}^ 2 \)
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.
\( V_{b1} = 7 \la gauche( \frac{\min(l_e,\, 8d_a)}{d_a} \droite)^{0.2} \sqrt{\frac{d_a}{\texte{in}}} \lambda_a sqrt{\frac{f'_c}{\texte{psi}}} \la gauche( \frac{c_{a1,s1}}{\texte{in}} \droite)^{1.5} \,\texte{lbf} \)
\( V_{b1} = 7 \fois gauche( \frac{\min(8\,\texte{in},\, 8 \times 0.5\,\text{in})}{0.5\,\texte{in}} \droite)^{0.2} \fois sqrt{\frac{0.5\,\texte{in}}{1\,\texte{in}}} \fois 1 \fois sqrt{\frac{3\,\texte{KSI}}{0.001\,\texte{KSI}}} \fois gauche( \frac{2\,\texte{in}}{1\,\texte{in}} \droite)^{1.5} \times 0.001\,\text{kip} \)
\( V_{b1} = 1.1623\,\text{kip} \)
\( V_{b2} = 9 \lambda_a sqrt{\frac{f'_c}{\texte{psi}}} \la gauche( \frac{c_{a1,s1}}{\texte{in}} \droite)^{1.5} \,\texte{lbf} \)
\( V_{b2} = 9 \fois 1 \fois sqrt{\frac{3\,\texte{KSI}}{0.001\,\texte{KSI}}} \fois gauche( \frac{2\,\texte{in}}{1\,\texte{in}} \droite)^{1.5} \times 0.001\,\text{kip} = 1.3943\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(1.1623\,\texte{kip},\, 1.3943\,\texte{kip}) = 1.1623\,\text{kip} \)
Prochain, l' breakout capacity parameters are determined. Ce logiciel breakout edge effect factor is calculated according to ACI 318-19 Clause 17.7.2.4, et la thickness factor is calculated according to Clause 17.7.2.6.1.
\( \Psi_{ed,V} = \min\left(1.0,\, 0.7 + 0.3 \la gauche( \frac{c_{a2,s1}}{1.5c_{a1,s1}} \droite) \droite) = \min\left(1,\, 0.7 + 0.3 \fois gauche( \frac{2\,\texte{in}}{1.5 \times 2\,\text{in}} \droite) \droite) = 0.9 \)
\( \Psi_{h,V} = \max\left( \sqrt{ \frac{1.5c_{a1,s1}}{t_{concurrence}} },\, 1.0 \droite) = \max\left( \sqrt{ \frac{1.5 \times 2\,\text{in}}{10\,\texte{in}} },\, 1 \droite) = 1 \)
Ensuite, ACI 318-19 Clause 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.
\( \phi V_{cb\perp} = phi Left( \frac{UNE_{U}}{UNE_{Vco}} \droite) \Psi_{ed,V} \Psi_{c,V} \Psi_{h,V} V_b \)
\( \phi V_{cb\perp} = 0.65 \fois gauche( \frac{15\,\texte{in}^ 2}{18\,\texte{in}^ 2} \droite) \fois 0.86 \fois 1 \fois 1 \times 1.1623\,\text{kip} = 0.56661\,\text{kip} \)
The calculated capacity for Vy shear dans le perpendicular direction is 0.56 kips.
Parallel Edge Capacity:
Failure along the edge parallel to the load is also possible in this scenario, alors le concrete breakout capacity for the parallel edge must be determined. The anchors or anchor group considered are those aligned with the parallel edge. par conséquent, l' 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; donc, the anchors are treated as a group.
Cas 1:
Cas 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. Par conséquent, seul Cas 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 échec, the anchors considered are the rear anchors. Donc, 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 Clause 17.7.2.1.2, the SkyCiv Base Plate software identified the support as narrow. Par conséquent, l' modified ca1 distance est utilisé, which is calculated to be 6.667 in.
The same steps as in the perpendicular case are followed: calculating the projected failure areas, l' basic single-anchor breakout strength, et la breakout parameters. The calculated values for each step are shown below.
\( UNE_{Vco} = 4.5 (c_{‘a1,g2})À partir de l'élévation du sol générée à partir des élévations Google 4.5 \fois (6.6667\,\texte{in})^2 = 200\,\text{in}^ 2 \)
\( UNE_{U} = B_{U} H_{U} = 14\,\text{in} \times 10\,\text{in} = 140\,\text{in}^ 2 \)
\( V_{b1} = 7.0733\,\text{kip} \)
\( V_{b2} = 8.4853\,\text{kip} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(7.0733\,\texte{kip},\, 8.4853\,\texte{kip}) = 7.0733\,\text{kip} \)
\( \Psi_{ed,V} = 1.0 \)
\( \Psi_{h,V} = 1.0 \)
The equation for the parallel edge capacity differs from the perpendicular edge capacity. ACI 318-19 Clause 17.7.2.1(c) est appliqué, where the breakout equation is multiplied by 2.
\( \phi V_{cbg\parallel} = 2 \phi gauche( \frac{UNE_{U}}{UNE_{Vco}} \droite) \Psi_{ed,V} \Psi_{c,V} \Psi_{h,V} V_b \)
\( \phi V_{cbg\parallel} = 2 \fois 0.65 \fois gauche( \frac{140\,\texte{in}^ 2}{200\texte{in}^ 2} \droite) \fois 1 \fois 1 \fois 1 \times 7.0733\,\text{kip} = 6.4367\,\text{kip} \)
The calculated capacity for Vy shear dans le parallèle direction is 6.43 kips.
We now assess the perpendicular and parallel failures separately.
- For the perpendicular edge failure, puisque 0.33 kip < 0.56 kip, the design concrete shear breakout capacity is suffisant.
- For the parallel edge failure, puisque 2 kip < 6.43 kip, the design concrete shear breakout capacity is suffisant.
Vérifier #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 et 1.26 kips, respectivement.
Perpendicular Edge:
Parallel Edge:
These capacities are then compared to the required strengths.
- For the perpendicular edge failure, puisque 2 kip < 2.45 kip, the concrete shear breakout capacity is suffisant.
- For the parallel edge failure, puisque 0.33 kip < 1.26 kip, the concrete shear breakout capacity is suffisant.
Vérifier #4: Calculate concrete pryout capacity
Ce logiciel 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. Par conséquent, the anchors in the design must still be checked to determine whether they act as a grouper or as ancres simples 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, l' nominal tensile breakout strength du groupe d'ancrage est 12.772 kips. With a pryout factor of kcp=2, the design pryout capacity is:
\( \phi V_{cpg} = \phi k_{cp} N_{cbg} = 0.65 \fois 2 \fois 12.772 \,\texte{kip} = 16.604\,\text{kip} \)
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.
\( V_{faire} = sqrt{(V_y)^ 2 + (V_z)^ 2} = sqrt{(2\,\texte{kip})^ 2 + (2\,\texte{kip})^ 2} = 2.8284\,\text{kip} \)
\( V_{faire} = gauche( \frac{V_{faire}}{n_a} \droite) n_{a,G1} = gauche( \frac{2.8284\,\texte{kip}}{6} \droite) \fois 6 = 2.8284\,\text{kip} \)
Since the total shear load is less than anchor group capacity, 2.82 kips < 18.976 kips, the design pryout capacity is suffisant.
Vérifier #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.
\( v_{faire,Y} = frac{V_y}{n_a} = frac{2\,\texte{kip}}{6} = 0.33333\,\text{kip} \)
\( v_{faire,z} = frac{V_z}{n_a} = frac{2\,\texte{kip}}{6} = 0.33333\,\text{kip} \)
\( V_{faire} = sqrt{(v_{faire,Y})^ 2 + (v_{faire,z})^ 2} \)
\( V_{faire} = sqrt{(0.33333\,\texte{kip})^ 2 + (0.33333\,\texte{kip})^ 2} = 0.4714\,\text{kip} \)
This gives the shear stress on the anchor rod comme:
\( f_v = \frac{V_{faire}}{UNE_{canne à pêche}} = frac{0.4714\,\texte{kip}}{0.19635\,\texte{in}^ 2} = 2.4008\,\text{KSI} \)
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. Se référer à Guide de conception AISC 1, 3rd Edition Section 4.3.3.
\( e = 0.5 \la gauche( \frac{t_{pw}}{2} + t_{pb} \droite) = 0.5 \fois gauche( \frac{0.25\,\texte{in}}{2} + 0.75\,\texte{in} \droite) = 0.4375\,\text{in} \)
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:
\( Z_{canne à pêche} = frac{\pi}{32} (d_a)^3 = \frac{\pi}{32} \fois (0.5\,\texte{in})^3 = 0.012272\,\text{in}^ 3 \)
\( f_t = \frac{V_{faire} e}{Z_{canne à pêche}} = frac{0.4714\,\texte{kip} \times 0.4375\,\text{in}}{0.012272\,\texte{in}^ 3} = 16.806\,\text{KSI} \)
ACI Anchor Rod Shear Capacity:
Following ACI 318-19 Clause 17.7.1, the design strength is then determined. A 0.8 reduction factor is applied due to the presence of grout pads. The design capacity is therefore:
\( \phi V_{à,ici} = 0.8 \phi 0.6 UNE_{je connais,v} F_{uta} = 0.8 \fois 0.65 \fois 0.6 \times 0.1419\text{in}^2 \times 90\text{KSI} = 3.9845\text{kip} \)
Comme alternative, l' SkyCiv Base Plate software allows the 0.8 simplification to be disabled, and use the actual grout pad thickness in the calculations. Dans le cas présent, 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:
Première, l' nominal shear and tensile stresses are determined for an A325 rod.
\( F_{nv} = 0.45 F_{u,anc} = 0.45 \fois 120\ \texte{KSI} = 54\ \texte{KSI} \)
\( F_{NT} = 0.75 F_{u,anc} = 0.75 \fois 120\ \texte{KSI} = 90\ \texte{KSI} \)
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.
\( F’_{nv} = min gauche( 1.3 F_{nv} – \la gauche( \frac{F_{nv}}{\Phi f_{NT}} \droite) f_t,\; F_{nv} \droite) \)
\( F’_{nv} = min gauche( 1.3 \fois 54\ \texte{KSI} – \la gauche( \frac{54\ \texte{KSI}}{0.75 \fois 90\ \texte{KSI}} \droite) \fois 16.806\ \texte{KSI},\; 54\ \texte{KSI} \droite) = 54\ \texte{KSI} \)
The design shear capacity from the AISC method is then calculated as:
\( \phi R_{n,\mathrm{aisc}} = \phi F’_{nv} UNE_{canne à pêche} = 0.75 \fois 54\ \texte{KSI} \fois 0.19635\ \texte{in}À partir de l'élévation du sol générée à partir des élévations Google 7.9522\)
To ensure both methods are covered, the governing capacity is taken as the lesser of the two, lequel est 3.98 kip.
\( \phi V_n = \min \left( \phi V_{à,ici},\; \phi R_{n,\mathrm{aisc}} \droite) = min (3.9845\ \texte{kip},\; 7.9522\ \texte{kip}) = 3.9845\ \texte{kip} \)
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 suffisant.
Résumé de la conception
Ce logiciel Logiciel de conception de plaques de base Skyciv peut générer automatiquement un rapport de calcul étape par étape pour cet exemple de conception. Il fournit également un résumé des contrôles effectués et de leurs ratios résultants, rendre les informations faciles à comprendre en un coup d'œil. Vous trouverez ci-dessous un échantillon de tableau de résumé, qui est inclus dans le rapport.
Rapport d'échantillon de skyciv
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Logiciel d'achat de plaques de base
Achetez la version complète du module de conception de la plaque de base seul sans aucun autre module Skyviv. Cela vous donne un ensemble complet de résultats pour la conception de la plaque de base, y compris des rapports détaillés et plus de fonctionnalités.
