Exemple de conception de plaque de base à l'aide de CSA S16:19 et CSA A23.3:19
Déclaration de problème:
Determine whether the designed column-to-base plate connection is sufficient for a 50-kN tension load.
Données données:
Colonne:
Section colonne: HS324X9.5
Zone de colonne: 9410 mm2
Matériau de colonne: 230g
Plaque de base:
Dimensions de la plaque de base: 500 millimètre x 500 mm
Épaisseur de plaque de base: 20 mm
Matériau de plaque de base: 230g
Jointoyer:
Épaisseur de coulis: 20 mm
Béton:
Dimensions du béton: 550 millimètre x 550 mm
Épaisseur de béton: 200 mm
Matériau en béton: 20.68 MPa
Cracked or Uncracked: Fissuré
Anchors:
Anchor diameter: 19.1 mm
Effective embedment length: 130.0 mm
Hook length: 60mm
Anchor offset distance from face of column: 120.84 mm
Soudures:
Weld type: CJP
Classification du métal de remplissage: E43xx
Anchor Data (de SkyCiv Calculator):
Definitions:
Load Path:
When a base plate is subjected to uplift (traction) les forces, 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.
Dans le Logiciel de conception de plaque 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, a 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 de la plaque.
The assumption simplifies the base plate analysis by approximating how the uplift force spreads through the plate.
Anchor Groups:
Ce logiciel Logiciel de conception de plaque de base SkyCiv includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating évasion de béton et concrete side-face blowout failures.
Un 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. Dans le cas présent, only the tension force on the individual anchor is checked against its own effective resistance area.
Calculs étape par étape:
Vérifier #1: Calculer la capacité de soudure
Pour commencer, we need to calculate the load per anchor and determine the effective weld length for each anchor. Ce logiciel 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, l' tangent points are used instead. Aussi, if the anchors are closely spaced, the effective weld length is reduced to avoid overlap. Ensuite, 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. Donc, 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:
\(
l_{\texte{arc}} = 254.47 \, \texte{mm}
\)
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 est:
\(
l_{\texte{eff}} = min gauche( l_{\texte{arc}}, \frac{\pi d_{\texte{col}}}{n_{a,t}} \droite) = min gauche( 254.47 \, \texte{mm}, \frac{\pi \times 324 \, \texte{mm}}{4} \droite) = 254.47 \, \texte{mm}
\)
Prochain, let’s calculate the load per anchor. For a given set of four (4) ancres, the load per anchor is:
\(
T_{u,\texte{ancre}} = frac{N_x}{n_{a,t}} = frac{50 \, \texte{kN}}{4} = 12.5 \, \texte{kN}
\)
Using the calculated effective weld length, we can now compute the required force per unit length acting on the weld.
\(
v_f = \frac{T_{u,\texte{ancre}}}{l_{\texte{eff}}} = frac{12.5 \, \texte{kN}}{254.47 \, \texte{mm}} = 0.049122 \, \texte{kN / mm}
\)
Maintenant, we refer to CSA S16:19 Clause 13.13.3.1 to calculate the factored resistance of the complete joint penetration (CJP) souder. This requires the base metal resistance, expressed in force per unit length, for both the column and the base plate materials.
\(
v_{r,\texte{bm}} = \phi \left( \min gauche( F_{Y,\texte{col}} t_{\texte{col}}, F_{Y,\texte{pb}} t_{\texte{pb}} \droite) \droite)
\)
\(
v_{r,\texte{bm}} = 0.9 \fois gauche( \min gauche( 230 \, \texte{MPa} \fois 9.53 \, \texte{mm}, 230 \, \texte{MPa} \fois 20 \, \texte{mm} \droite) \droite) = 1.9727 \, \texte{kN / mm}
\)
Puisque 0.049122 kN / mm < 1.9727 kN / mm, La capacité de soudure est suffisant.
Vérifier #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 cantilever assumption. For a circular column, the load eccentricity is determined by considering the sagitta of the welded arc, and can be calculated as follows:
\(
e_{\texte{pipe}} = d_o + r_{\texte{col}} \la gauche( 1 – \car gauche( \frac{l_{\texte{eff}}}{2 r_{\texte{col}}} \droite) \droite)
\)
\(
e_{\texte{pipe}} = 120.84 \, \texte{mm} + 162 \, \texte{mm} \fois gauche( 1 – \car gauche( \frac{254.47 \, \texte{mm}}{2 \fois 162 \, \texte{mm}} \droite) \droite) = 168.29 \, \texte{mm}
\)
The induced moment is computed as:
\(
M_f = T_{u,\texte{ancre}} e_{\texte{pipe}} = 12.5 \, \texte{kN} \fois 168.29 \, \texte{mm} = 2103.6 \, \texte{kN} \CDOT Texte{mm}
\)
Prochain, we will determine the bending width of the base plate. Pour ça, we use the chord length corresponding to the effective weld arc.
\(
\theta_{\texte{travailler}} = frac{l_{\texte{eff}}}{0.5 ré_{\texte{col}}} = frac{254.47 \, \texte{mm}}{0.5 \fois 324 \, \texte{mm}} = 1.5708
\)
\(
b = d_{\texte{col}} \la gauche( \péché gauche( \frac{\theta_{\texte{travailler}}}{2} \droite) \droite) = 324 \, \texte{mm} \fois gauche( \péché gauche( \frac{1.5708}{2} \droite) \droite) = 229.1 \, \texte{mm}
\)
Ensuite, Nous pouvons calculer le factored flexural resistance of the base plate using CSA S16:19 Clause 13.5.
\(
M_r = \phi F_{Y,\texte{pb}} Z_{\texte{eff}} = 0.9 \fois 230 \, \texte{MPa} \fois 22910 \, \texte{mm}^3 = 4742.4 \, \texte{kN} \CDOT Texte{mm}
\)
Où,
\(
Z_{\texte{eff}} = frac{b (t_{\texte{pb}})^ 2}{4} = frac{229.1 \, \texte{mm} \fois (20 \, \texte{mm})^ 2}{4} = 22910 \, \texte{mm}^ 3
\)
Puisque 2103.6 kN-mm < 4742.4 kN-mm, the base plate flexural yielding capacity is suffisant.
Vérifier #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 Clause 25.3.2.1.
Première, Nous déterminons le specified tensile strength of the anchor steel. This is the lowest value permitted by CSA A23.3:19 Clause D.6.1.2.
\(
F_{\texte{uta}} = min gauche( F_{u,\texte{anc}}, 1.9 F_{Y,\texte{anc}}, 860 \droite) = min gauche( 400 \, \texte{MPa}, 1.9 \fois 248.2 \, \texte{MPa}, 860.00 \, \texte{MPa} \droite) = 400 \, \texte{MPa}
\)
Prochain, Nous déterminons le effective cross-sectional area of the anchor rod in tension using CAC Concrete Design Handbook, 3édition rd, Le tableau 12.3.
\(
UNE_{je connais,N} = 215 \, \texte{mm}^ 2
\)
With these values, Nous appliquons CSA A23.3:19 Eq. D.2 to compute the factored tensile resistance of the anchor rod.
\(
N_{\texte{sar}} = A_{je connais,N} \phi_s f_{\texte{uta}} R = 215 \, \texte{mm}^2 \times 0.85 \fois 400 \, \texte{MPa} \fois 0.8 = 58.465 \, \texte{kN}
\)
Aussi, we evaluate the factored tensile resistance according to CSA S16:19 Clause 25.3.2.1.
\(
T_r = \phi_{ar} 0.85 UNE_{ar} F_{u,\texte{anc}} = 0.67 \fois 0.85 \fois 285.02 \, \texte{mm}^2 \times 400 \, \texte{MPa} = 64.912 \, \texte{kN}
\)
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:
\(
N_{fa} = frac{N_x}{n_{a,t}} = frac{50 \, \texte{kN}}{4} = 12.5 \, \texte{kN}
\)
Puisque 12.5 kN < 58.465 kN, the anchor rod tensile capacity is suffisant.
Vérifier #4: Calculate concrete breakout capacity in tension
Before calculating the breakout capacity, we must first determine whether the member qualifies as a narrow member. Selon CSA A23.3:19 Clause D.6.2.3, the member does not meet the criteria for a narrow member. Par conséquent, the given effective embedment length will be used in the calculations.
En utilisant CSA A23.3:19 Eq. D.5, on calcule le maximum projected concrete cone area pour une seule ancre, based on the effective embedment length.
\(
UNE_{Rappelles toi} = 9 (h_{ef,s1})À partir de l'élévation du sol générée à partir des élévations Google 9 \fois (130 \, \texte{mm})À partir de l'élévation du sol générée à partir des élévations Google 152100 \, \texte{mm}^ 2
\)
De manière similaire, we use the effective embedment length to calculate the actual projected concrete cone area of the single anchor.
\(
UNE_{NC} = L_{NC} B_{NC} = 270 \, \texte{mm} \fois 270 \, \texte{mm} = 72900 \, \texte{mm}^ 2
\)
Où,
\(
L_{NC} = gauche( \min gauche( c_{\texte{la gauche},s1}, 1.5 h_{ef,s1} \droite) \droite) + \la gauche( \min gauche( c_{\texte{droite},s1}, 1.5 h_{ef,s1} \droite) \droite)
\)
\(
L_{NC} = gauche( \min gauche( 475 \, \texte{mm}, 1.5 \fois 130 \, \texte{mm} \droite) \droite) + \la gauche( \min gauche( 75 \, \texte{mm}, 1.5 \fois 130 \, \texte{mm} \droite) \droite)
\)
\(
L_{NC} = 270 \, \texte{mm}
\)
\(
B_{NC} = gauche( \min gauche( c_{\texte{Haut},s1}, 1.5 h_{ef,s1} \droite) \droite) + \la gauche( \min gauche( c_{\texte{bas},s1}, 1.5 h_{ef,s1} \droite) \droite)
\)
\(
B_{NC} = gauche( \min gauche( 75 \, \texte{mm}, 1.5 \fois 130 \, \texte{mm} \droite) \droite) + \la gauche( \min gauche( 475 \, \texte{mm}, 1.5 \fois 130 \, \texte{mm} \droite) \droite)
\)
\(
B_{NC} = 270 \, \texte{mm}
\)
Prochain, we evaluate the factored basic concrete breakout resistance of a single anchor using CSA A23.3:19 Eq. D.6
\(
N_{br} = k_c \phi \lambda_a \sqrt{\frac{f'_c}{\texte{MPa}}} \la gauche( \frac{h_{ef,s1}}{\texte{mm}} \droite)^{1.5} R N
\)
\(
N_{br} = 10 \fois 0.65 \fois 1 \fois sqrt{\frac{20.68 \, \texte{MPa}}{1 \, \texte{MPa}}} \fois gauche( \frac{130 \, \texte{mm}}{1 \, \texte{mm}} \droite)^{1.5} \fois 1 \fois 0.001 \, \texte{kN} = 43.813 \, \texte{kN}
\)
Où,
- \(afin que les ingénieurs puissent revoir exactement comment ces calculs sont effectués{c} = 10\) pour ancres coulées
- \(\lambda = 1.0 \) for normal-weight concrete
Maintenant, we assess the effects of geometry by calculating the edge effect factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{a,\texte{min}} = min gauche( c_{\texte{la gauche},s1}, c_{\texte{droite},s1}, c_{\texte{Haut},s1}, c_{\texte{bas},s1} \droite) = min gauche( 475 \, \texte{mm}, 75 \, \texte{mm}, 75 \, \texte{mm}, 475 \, \texte{mm} \droite) = 75 \, \texte{mm}
\)
Selon CSA A23.3:19 Eq. D.10 and D.11, the breakout edge effect factor est:
\(
\Psi_{ed,N} = min gauche( 1.0, 0.7 + 0.3 \la gauche( \frac{c_{a,\texte{min}}}{1.5 h_{ef,s1}} \droite) \droite) = min gauche( 1, 0.7 + 0.3 \fois gauche( \frac{75 \, \texte{mm}}{1.5 \fois 130 \, \texte{mm}} \droite) \droite) = 0.81538
\)
Aussi, both the cracking factor et la splitting factor are taken as:
\(
\Psi_{c,N} = 1
\)
\(
\Psi_{cp,N} = 1
\)
ensuite, 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:
\(
N_{cbr} = gauche( \frac{UNE_{NC}}{UNE_{Rappelles toi}} \droite) \Psi_{ed,N} \Psi_{c,N} \Psi_{cp,N} N_{br} = gauche( \frac{72900 \, \texte{mm}^ 2}{152100 \, \texte{mm}^ 2} \droite) \fois 0.81538 \fois 1 \fois 1 \fois 43.813 \, \texte{kN} = 17.122 \, \texte{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{a,s}} = frac{50 \, \texte{kN}}{4} = 12.5 \, \texte{kN}
\)
Puisque 12.5 kN < 17.122 kN the concrete breakout capacity is suffisant.
This concrete breakout calculation is based on Anchor ID #1. The same capacity will apply to the other anchors due to the symmetric design.
Vérifier #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 par CSA A23.3:19 Eq. D.17.
\(
N_{pr} = \Psi_{c,p} 0.9 \phi (f'_c) e_h d_a R = 1 \fois 0.9 \fois 0.65 \fois (20.68 \, \texte{MPa}) \fois 60 \, \texte{mm} \fois 19.05 \, \texte{mm} \fois 1 = 13.828 \, \texte{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{a,t}} = frac{50 \, \texte{kN}}{4} = 12.5 \, \texte{kN}
\)
Puisque 12.5 kN < 13.828 kN, the anchor pullout capacity is suffisant.
Vérifier #6: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for hooked anchors.
Vérifier #7: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for hooked anchors.
Résumé de la conception
Ce logiciel Logiciel de conception de plaques de base Skyciv can automatically generate a step-by-step calculation report for this design example. 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
Sample report will be added soon.
Logiciel d'achat de plaques de base
Purchase the full version of the base plate design module onits own without any other SkyCiv modules. 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.
