Base Plate Design Example using CSA S16:19 and CSA A23.3:19
Problemanweisung:
Determine whether the designed column-to-base plate connection is sufficient for a 50-kN tension load.
Gegebene Daten:
Spalte:
Spaltenabschnitt: HS324X9.5
Säulenbereich: 9410 mm2
Säulenmaterial: 230G
Grundplatte:
Grundplattenabmessungen: 500 mmx 500 mm
Grundplattendicke: 20 mm
Grundplattenmaterial: 230G
Grout:
Grout thickness: 20 mm
Beton:
Konkrete Abmessungen: 550 mmx 550 mm
Betondicke: 200 mm
Betonmaterial: 20.68 MPa
Cracked or Uncracked: Cracked
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
Schweißnähte:
Weld type: CJP
Füllmetallklassifizierung: E43XX
Anchor Data (von SkyCiv Calculator):
Definitions:
Load Path:
When a base plate is subjected to uplift (zugfest) Kräfte, 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.
In dem SkyCiv Basisplatten-Design-Software, 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, ein 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 der Platte.
The assumption simplifies the base plate analysis by approximating how the uplift force spreads through the plate.
Anchor Groups:
Mit der SkyCiv Basisplatten-Design-Software includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating Betonausbruch und concrete side-face blowout failures.
Ein 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. In diesem Fall, only the tension force on the individual anchor is checked against its own effective resistance area.
Schritt-für-Schritt-Berechnungen:
Prüfen #1: Berechnen Sie die Schweißkapazität
Anwenden seismischer Lasten, we need to calculate the load per anchor and determine the effective weld length for each anchor. Mit der 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, bleibt die tangent points are used instead. zusätzlich, if the anchors are closely spaced, the effective weld length is reduced to avoid overlap. Schließlich, 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. Als Ergebnis, 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:
\(
l_{\Text{arc}} = 254.47 \, \Text{mm}
\)
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 ist:
\(
l_{\Text{eff}} = min links( l_{\Text{arc}}, \frac{\pi d_{\Text{col}}}{n_{ein,t}} \richtig) = min links( 254.47 \, \Text{mm}, \frac{\pi \times 324 \, \Text{mm}}{4} \richtig) = 254.47 \, \Text{mm}
\)
Als nächstes, let’s calculate the load per anchor. For a given set of four (4) Anker, the load per anchor is:
\(
T_{u,\Text{Anker}} = frac{N_x}{n_{ein,t}} = frac{50 \, \Text{kN}}{4} = 12.5 \, \Text{kN}
\)
Using the calculated effective weld length, we can now compute the required force per unit length acting on the weld.
\(
v_f = \frac{T_{u,\Text{Anker}}}{l_{\Text{eff}}} = frac{12.5 \, \Text{kN}}{254.47 \, \Text{mm}} = 0.049122 \, \Text{kN / mm}
\)
Jetzt, we refer to CSA S16:19 Klausel 13.13.3.1 to calculate the factored resistance of the complete joint penetration (CJP) schweißen. This requires the base metal resistance, expressed in force per unit length, for both the column and the base plate materials.
\(
v_{r,\Text{bm}} = \phi \left( \min \left( F_{j,\Text{col}} t_{\Text{col}}, F_{j,\Text{bp}} t_{\Text{bp}} \richtig) \richtig)
\)
\(
v_{r,\Text{bm}} = 0.9 \mal links( \min \left( 230 \, \Text{MPa} \mal 9.53 \, \Text{mm}, 230 \, \Text{MPa} \mal 20 \, \Text{mm} \richtig) \richtig) = 1.9727 \, \Text{kN / mm}
\)
Schon seit 0.049122 kN / mm < 1.9727 kN / mm, Die Schweißkapazität ist ausreichend.
Prüfen #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 Ausleger assumption. For a circular column, the load eccentricity is determined by considering the sagitta of the welded arc, and can be calculated as follows:
\(
e_{\Text{pipe}} = d_o + r_{\Text{col}} \links( 1 – \cos links( \frac{l_{\Text{eff}}}{2 r_{\Text{col}}} \richtig) \richtig)
\)
\(
e_{\Text{pipe}} = 120.84 \, \Text{mm} + 162 \, \Text{mm} \mal links( 1 – \cos links( \frac{254.47 \, \Text{mm}}{2 \mal 162 \, \Text{mm}} \richtig) \richtig) = 168.29 \, \Text{mm}
\)
The induced moment is computed as:
\(
M_f = T_{u,\Text{Anker}} e_{\Text{pipe}} = 12.5 \, \Text{kN} \mal 168.29 \, \Text{mm} = 2103.6 \, \Text{kN} \cdot \text{mm}
\)
Als nächstes, we will determine the bending width of the base plate. Dafür, we use the chord length corresponding to the effective weld arc.
\(
\theta_{\Text{Arbeit}} = frac{l_{\Text{eff}}}{0.5 d_{\Text{col}}} = frac{254.47 \, \Text{mm}}{0.5 \mal 324 \, \Text{mm}} = 1.5708
\)
\(
b = d_{\Text{col}} \links( \Sünde links( \frac{\theta_{\Text{Arbeit}}}{2} \richtig) \richtig) = 324 \, \Text{mm} \mal links( \Sünde links( \frac{1.5708}{2} \richtig) \richtig) = 229.1 \, \Text{mm}
\)
Schließlich, we can calculate the factored flexural resistance of the base plate using CSA S16:19 Klausel 13.5.
\(
M_r = \phi F_{j,\Text{bp}} Z_{\Text{eff}} = 0.9 \mal 230 \, \Text{MPa} \mal 22910 \, \Text{mm}^3 = 4742.4 \, \Text{kN} \cdot \text{mm}
\)
Wo,
\(
Z_{\Text{eff}} = frac{b (t_{\Text{bp}})^ 2}{4} = frac{229.1 \, \Text{mm} \mal (20 \, \Text{mm})^ 2}{4} = 22910 \, \Text{mm}^ 3
\)
Schon seit 2103.6 kN-mm < 4742.4 kN-mm, the base plate flexural yielding capacity is ausreichend.
Prüfen #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 Klausel 25.3.2.1.
Zuerst, Wir bestimmen die specified tensile strength of the anchor steel. This is the lowest value permitted by CSA A23.3:19 Clause D.6.1.2.
\(
f_{\Text{uta}} = min links( F_{u,\Text{anc}}, 1.9 F_{j,\Text{anc}}, 860 \richtig) = min links( 400 \, \Text{MPa}, 1.9 \mal 248.2 \, \Text{MPa}, 860.00 \, \Text{MPa} \richtig) = 400 \, \Text{MPa}
\)
Als nächstes, Wir bestimmen die effective cross-sectional area of the anchor rod in tension using CAC Concrete Design Handbook, 3RD Edition, Tabelle 12.3.
\(
EIN_{ich weiß,N.} = 215 \, \Text{mm}^ 2
\)
With these values, we apply CSA A23.3:19 Gl. D.2 to compute the factored tensile resistance of the anchor rod.
\(
N_{\Text{sar}} = A_{ich weiß,N.} \phi_s f_{\Text{uta}} R = 215 \, \Text{mm}^2 \times 0.85 \mal 400 \, \Text{MPa} \mal 0.8 = 58.465 \, \Text{kN}
\)
zusätzlich, we evaluate the factored tensile resistance according to CSA S16:19 Klausel 25.3.2.1.
\(
T_r = \phi_{ar} 0.85 EIN_{ar} F_{u,\Text{anc}} = 0.67 \mal 0.85 \mal 285.02 \, \Text{mm}^2 \times 400 \, \Text{MPa} = 64.912 \, \Text{kN}
\)
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:
\(
N_{fa} = frac{N_x}{n_{ein,t}} = frac{50 \, \Text{kN}}{4} = 12.5 \, \Text{kN}
\)
Schon seit 12.5 kN < 58.465 kN, the anchor rod tensile capacity is ausreichend.
Prüfen #4: Calculate concrete breakout capacity in tension
Before calculating the breakout capacity, we must first determine whether the member qualifies as a narrow member. Gemäß CSA A23.3:19 Clause D.6.2.3, the member does not meet the criteria for a narrow member. Deshalb, the given effective embedment length will be used in the calculations.
Verwenden von CSA A23.3:19 Gl. D.5, wir berechnen die maximum projected concrete cone area für einen einzelnen Anker, based on the effective embedment length.
\(
EIN_{Merken} = 9 (h_{ef,s1})^2 = 9 \mal (130 \, \Text{mm})^2 = 152100 \, \Text{mm}^ 2
\)
Ähnlich, we use the effective embedment length to calculate the actual projected concrete cone area of the single anchor.
\(
EIN_{Nc} = L_{Nc} B_{Nc} = 270 \, \Text{mm} \mal 270 \, \Text{mm} = 72900 \, \Text{mm}^ 2
\)
Wo,
\(
L_{Nc} = left( \min \left( c_{\Text{links},s1}, 1.5 h_{ef,s1} \richtig) \richtig) + \links( \min \left( c_{\Text{richtig},s1}, 1.5 h_{ef,s1} \richtig) \richtig)
\)
\(
L_{Nc} = left( \min \left( 475 \, \Text{mm}, 1.5 \mal 130 \, \Text{mm} \richtig) \richtig) + \links( \min \left( 75 \, \Text{mm}, 1.5 \mal 130 \, \Text{mm} \richtig) \richtig)
\)
\(
L_{Nc} = 270 \, \Text{mm}
\)
\(
B_{Nc} = left( \min \left( c_{\Text{oben},s1}, 1.5 h_{ef,s1} \richtig) \richtig) + \links( \min \left( c_{\Text{Unterseite},s1}, 1.5 h_{ef,s1} \richtig) \richtig)
\)
\(
B_{Nc} = left( \min \left( 75 \, \Text{mm}, 1.5 \mal 130 \, \Text{mm} \richtig) \richtig) + \links( \min \left( 475 \, \Text{mm}, 1.5 \mal 130 \, \Text{mm} \richtig) \richtig)
\)
\(
B_{Nc} = 270 \, \Text{mm}
\)
Als nächstes, we evaluate the factored basic concrete breakout resistance of a single anchor using CSA A23.3:19 Gl. D.6
\(
N_{br} = k_c \phi \lambda_a \sqrt{\frac{f’_c}{\Text{MPa}}} \links( \frac{h_{ef,s1}}{\Text{mm}} \richtig)^{1.5} R N
\)
\(
N_{br} = 10 \mal 0.65 \mal 1 \mal sqrt{\frac{20.68 \, \Text{MPa}}{1 \, \Text{MPa}}} \mal links( \frac{130 \, \Text{mm}}{1 \, \Text{mm}} \richtig)^{1.5} \mal 1 \mal 0.001 \, \Text{kN} = 43.813 \, \Text{kN}
\)
Wo,
- \(k_{c} = 10\) für einbetonierte Anker
- \(\lambda = 1.0 \) for normal-weight concrete
Jetzt, we assess the effects of geometry by calculating the edge effect factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{ein,\Text{Min.}} = min links( c_{\Text{links},s1}, c_{\Text{richtig},s1}, c_{\Text{oben},s1}, c_{\Text{Unterseite},s1} \richtig) = min links( 475 \, \Text{mm}, 75 \, \Text{mm}, 75 \, \Text{mm}, 475 \, \Text{mm} \richtig) = 75 \, \Text{mm}
\)
Gemäß CSA A23.3:19 Gl. D.10 and D.11, the breakout edge effect factor ist:
\(
\Psi_{ed,N.} = min links( 1.0, 0.7 + 0.3 \links( \frac{c_{ein,\Text{Min.}}}{1.5 h_{ef,s1}} \richtig) \richtig) = min links( 1, 0.7 + 0.3 \mal links( \frac{75 \, \Text{mm}}{1.5 \mal 130 \, \Text{mm}} \richtig) \richtig) = 0.81538
\)
Zusätzlich, both the cracking factor und das splitting factor are taken as:
\(
\Psi_{c,N.} = 1
\)
\(
\Psi_{cp,N.} = 1
\)
Dann, we combine all these factors and use ACI 318-19 Gl. 17.6.2.1b to evaluate the factored concrete breakout resistance of the single anchor:
\(
N_{cbr} = left( \frac{EIN_{Nc}}{EIN_{Merken}} \richtig) \Psi_{ed,N.} \Psi_{c,N.} \Psi_{cp,N.} N_{br} = left( \frac{72900 \, \Text{mm}^ 2}{152100 \, \Text{mm}^ 2} \richtig) \mal 0.81538 \mal 1 \mal 1 \mal 43.813 \, \Text{kN} = 17.122 \, \Text{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{ein,s}} = frac{50 \, \Text{kN}}{4} = 12.5 \, \Text{kN}
\)
Schon seit 12.5 kN < 17.122 kN the concrete breakout capacity is ausreichend.
This concrete breakout calculation is based on Anchor ID #1. The same capacity will apply to the other anchors due to the symmetric design.
Prüfen #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 pro CSA A23.3:19 Gl. D.17.
\(
N_{pr} = \Psi_{c,p} 0.9 \phi (f’_c) e_h d_a R = 1 \mal 0.9 \mal 0.65 \mal (20.68 \, \Text{MPa}) \mal 60 \, \Text{mm} \mal 19.05 \, \Text{mm} \mal 1 = 13.828 \, \Text{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{ein,t}} = frac{50 \, \Text{kN}}{4} = 12.5 \, \Text{kN}
\)
Schon seit 12.5 kN < 13.828 kN, the anchor pullout capacity is ausreichend.
Prüfen #6: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for hooked anchors.
Prüfen #7: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for hooked anchors.
Entwurfszusammenfassung
Mit der Skyciv Base Plate Design Software can automatically generate a step-by-step calculation report for this design example. Es enthält auch eine Zusammenfassung der durchgeführten Schecks und deren resultierenden Verhältnisse, Die Informationen auf einen Blick leicht zu verstehen machen. Im Folgenden finden Sie eine Stichprobenzusammenfassungstabelle, Welches ist im Bericht enthalten.
SKYCIV -Beispielbericht
Sample report will be added soon.
Basisplattensoftware kaufen
Purchase the full version of the base plate design module onits own without any other SkyCiv modules. Auf diese Weise erhalten Sie einen vollständigen Satz von Ergebnissen für die Basisplattendesign, Einbeziehung detaillierter Berichte und mehr Funktionen.
