Base Plate Design Example using CSA S16:19 and CSA A23.3:19
Probleemverklaring:
Determine whether the designed column-to-base plate connection is sufficient for a 50-kN tension load.
Gegeven gegevens:
Kolom:
Kolomgedeelte: HS324X9.5
Kolomgebied: 9410 mm2
Kolommateriaal: 230G
Bodemplaat:
Baseplaat afmetingen: 500 mm x 500 mm
Basisplaatdikte: 20 mm
Basisplaatmateriaal: 230G
Grout:
Grout thickness: 20 mm
Beton:
Concrete dimensies: 550 mm x 550 mm
Betonnen dikte: 200 mm
Betonnen materiaal: 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
Lassen:
Weld type: CJP
Vulmetaalclassificatie: E43XX
Anchor Data (van SkyCiv Calculator):
Definitions:
Load Path:
When a base plate is subjected to uplift (treksterkte) krachten, 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 de SkyCiv-software voor het ontwerpen van grondplaten, 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, een 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 van de plaat.
The assumption simplifies the base plate analysis by approximating how the uplift force spreads through the plate.
Anchor Groups:
De SkyCiv-software voor het ontwerpen van grondplaten includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating beton doorbraak en concrete side-face blowout failures.
Een 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 dit geval, only the tension force on the individual anchor is checked against its own effective resistance area.
Stapsgewijze berekeningen:
Controleren #1: Lascapaciteit berekenen
Beginnen, we need to calculate the load per anchor and determine the effective weld length for each anchor. De 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, de tangent points are used instead. Bovendien, if the anchors are closely spaced, the effective weld length is reduced to avoid overlap. Uiteindelijk, 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 gevolg, 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:
\(
l_{\tekst{arc}} = 254.47 \, \tekst{mm}
\)
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 is:
\(
l_{\tekst{eff}} = min links( l_{\tekst{arc}}, \frac{\pi d_{\tekst{col}}}{n_{een,t}} \Rechtsaf) = min links( 254.47 \, \tekst{mm}, \frac{\pi \times 324 \, \tekst{mm}}{4} \Rechtsaf) = 254.47 \, \tekst{mm}
\)
De volgende, let’s calculate the load per anchor. For a given set of four (4) ankers, the load per anchor is:
\(
T_{u,\tekst{anchor}} = frac{N_x}{n_{een,t}} = frac{50 \, \tekst{kN}}{4} = 12.5 \, \tekst{kN}
\)
Using the calculated effective weld length, we can now compute the required force per unit length acting on the weld.
\(
v_f = \frac{T_{u,\tekst{anchor}}}{l_{\tekst{eff}}} = frac{12.5 \, \tekst{kN}}{254.47 \, \tekst{mm}} = 0.049122 \, \tekst{kN / mm}
\)
Nu, we refer to CSA S16:19 Clausule 13.13.3.1 to calculate the factored resistance of the complete joint penetration (CJP) lassen. This requires the base metal resistance, expressed in force per unit length, for both the column and the base plate materials.
\(
v_{r,\tekst{bm}} = \phi \left( \min \left( F_{j,\tekst{col}} t_{\tekst{col}}, F_{j,\tekst{bp}} t_{\tekst{bp}} \Rechtsaf) \Rechtsaf)
\)
\(
v_{r,\tekst{bm}} = 0.9 \keer links( \min \left( 230 \, \tekst{MPa} \keer 9.53 \, \tekst{mm}, 230 \, \tekst{MPa} \keer 20 \, \tekst{mm} \Rechtsaf) \Rechtsaf) = 1.9727 \, \tekst{kN / mm}
\)
Sinds 0.049122 kN / mm < 1.9727 kN / mm, De lascapaciteit is voldoende.
Controleren #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:
\(
e_{\tekst{pipe}} = d_o + R_{\tekst{col}} \links( 1 – \cos links( \frac{l_{\tekst{eff}}}{2 R_{\tekst{col}}} \Rechtsaf) \Rechtsaf)
\)
\(
e_{\tekst{pipe}} = 120.84 \, \tekst{mm} + 162 \, \tekst{mm} \keer links( 1 – \cos links( \frac{254.47 \, \tekst{mm}}{2 \keer 162 \, \tekst{mm}} \Rechtsaf) \Rechtsaf) = 168.29 \, \tekst{mm}
\)
The induced moment is computed as:
\(
M_f = T_{u,\tekst{anchor}} e_{\tekst{pipe}} = 12.5 \, \tekst{kN} \keer 168.29 \, \tekst{mm} = 2103.6 \, \tekst{kN} \cdot \text{mm}
\)
De volgende, we will determine the bending width of the base plate. Voor deze, we use the chord length corresponding to the effective weld arc.
\(
\theta_{\tekst{rad}} = frac{l_{\tekst{eff}}}{0.5 d_{\tekst{col}}} = frac{254.47 \, \tekst{mm}}{0.5 \keer 324 \, \tekst{mm}} = 1.5708
\)
\(
b = d_{\tekst{col}} \links( \zonde links( \frac{\theta_{\tekst{rad}}}{2} \Rechtsaf) \Rechtsaf) = 324 \, \tekst{mm} \keer links( \zonde links( \frac{1.5708}{2} \Rechtsaf) \Rechtsaf) = 229.1 \, \tekst{mm}
\)
Uiteindelijk, we kunnen de berekenen factored flexural resistance of the base plate using CSA S16:19 Clausule 13.5.
\(
M_r = \phi F_{j,\tekst{bp}} Z_{\tekst{eff}} = 0.9 \keer 230 \, \tekst{MPa} \keer 22910 \, \tekst{mm}^3 = 4742.4 \, \tekst{kN} \cdot \text{mm}
\)
Waarbij,
\(
Z_{\tekst{eff}} = frac{b (t_{\tekst{bp}})^ 2}{4} = frac{229.1 \, \tekst{mm} \keer (20 \, \tekst{mm})^ 2}{4} = 22910 \, \tekst{mm}^3
\)
Sinds 2103.6 kN-mm < 4742.4 kN-mm, the base plate flexural yielding capacity is voldoende.
Controleren #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 Clausule 25.3.2.1.
Eerste, We bepalen de specified tensile strength of the anchor steel. This is the lowest value permitted by CSA A23.3:19 Clause D.6.1.2.
\(
f_{\tekst{uta}} = min links( F_{u,\tekst{anc}}, 1.9 F_{j,\tekst{anc}}, 860 \Rechtsaf) = min links( 400 \, \tekst{MPa}, 1.9 \keer 248.2 \, \tekst{MPa}, 860.00 \, \tekst{MPa} \Rechtsaf) = 400 \, \tekst{MPa}
\)
De volgende, We bepalen de effective cross-sectional area of the anchor rod in tension using CAC Concrete Design Handbook, 3RD -editie, Tafel 12.3.
\(
EEN_{ik weet,N} = 215 \, \tekst{mm}^ 2
\)
With these values, we apply CSA A23.3:19 Eq. D.2 to compute the factored tensile resistance of the anchor rod.
\(
N_{\tekst{sar}} = A_{ik weet,N} \phi_s f_{\tekst{uta}} R = 215 \, \tekst{mm}^2 \times 0.85 \keer 400 \, \tekst{MPa} \keer 0.8 = 58.465 \, \tekst{kN}
\)
Bovendien, we evaluate the factored tensile resistance according to CSA S16:19 Clausule 25.3.2.1.
\(
T_r = \phi_{ar} 0.85 EEN_{ar} F_{u,\tekst{anc}} = 0.67 \keer 0.85 \keer 285.02 \, \tekst{mm}^2 \times 400 \, \tekst{MPa} = 64.912 \, \tekst{kN}
\)
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:
\(
N_{fa} = frac{N_x}{n_{een,t}} = frac{50 \, \tekst{kN}}{4} = 12.5 \, \tekst{kN}
\)
Sinds 12.5 kN < 58.465 kN, the anchor rod tensile capacity is voldoende.
Controleren #4: Calculate concrete breakout capacity in tension
Before calculating the breakout capacity, we must first determine whether the member qualifies as a narrow member. Volgens CSA A23.3:19 Clause D.6.2.3, the member does not meet the criteria for a narrow member. Daarom, the given effective embedment length will be used in the calculations.
Gebruik makend van CSA A23.3:19 Eq. D.5, we berekenen de maximum projected concrete cone area voor één enkel anker, based on the effective embedment length.
\(
EEN_{Onthouden} = 9 (h_{ef,s1})➔⡔ Koop generieke tadalafil 9 \keer (130 \, \tekst{mm})➔⡔ Koop generieke tadalafil 152100 \, \tekst{mm}^ 2
\)
Evenzo, we use the effective embedment length to calculate the actual projected concrete cone area of the single anchor.
\(
EEN_{Nc} = L_{Nc} B_{Nc} = 270 \, \tekst{mm} \keer 270 \, \tekst{mm} = 72900 \, \tekst{mm}^ 2
\)
Waarbij,
\(
L_{Nc} = links( \min \left( c_{\tekst{links},s1}, 1.5 h_{ef,s1} \Rechtsaf) \Rechtsaf) + \links( \min \left( c_{\tekst{Rechtsaf},s1}, 1.5 h_{ef,s1} \Rechtsaf) \Rechtsaf)
\)
\(
L_{Nc} = links( \min \left( 475 \, \tekst{mm}, 1.5 \keer 130 \, \tekst{mm} \Rechtsaf) \Rechtsaf) + \links( \min \left( 75 \, \tekst{mm}, 1.5 \keer 130 \, \tekst{mm} \Rechtsaf) \Rechtsaf)
\)
\(
L_{Nc} = 270 \, \tekst{mm}
\)
\(
B_{Nc} = links( \min \left( c_{\tekst{top},s1}, 1.5 h_{ef,s1} \Rechtsaf) \Rechtsaf) + \links( \min \left( c_{\tekst{bodem},s1}, 1.5 h_{ef,s1} \Rechtsaf) \Rechtsaf)
\)
\(
B_{Nc} = links( \min \left( 75 \, \tekst{mm}, 1.5 \keer 130 \, \tekst{mm} \Rechtsaf) \Rechtsaf) + \links( \min \left( 475 \, \tekst{mm}, 1.5 \keer 130 \, \tekst{mm} \Rechtsaf) \Rechtsaf)
\)
\(
B_{Nc} = 270 \, \tekst{mm}
\)
De volgende, we evaluate the factored basic concrete breakout resistance of a single anchor using CSA A23.3:19 Eq. D.6
\(
N_{br} = k_c \phi \lambda_a \sqrt{\frac{f'_c}{\tekst{MPa}}} \links( \frac{h_{ef,s1}}{\tekst{mm}} \Rechtsaf)^{1.5} R N
\)
\(
N_{br} = 10 \keer 0.65 \keer 1 \keer sqrt{\frac{20.68 \, \tekst{MPa}}{1 \, \tekst{MPa}}} \keer links( \frac{130 \, \tekst{mm}}{1 \, \tekst{mm}} \Rechtsaf)^{1.5} \keer 1 \keer 0.001 \, \tekst{kN} = 43.813 \, \tekst{kN}
\)
Waarbij,
- \(zodat ingenieurs precies kunnen nagaan hoe deze berekeningen zijn gemaakt{c} = 10\) voor ingestorte ankers
- \(\lambda = 1.0 \) for normal-weight concrete
Nu, we assess the effects of geometry by calculating the edge effect factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{een,\tekst{min}} = min links( c_{\tekst{links},s1}, c_{\tekst{Rechtsaf},s1}, c_{\tekst{top},s1}, c_{\tekst{bodem},s1} \Rechtsaf) = min links( 475 \, \tekst{mm}, 75 \, \tekst{mm}, 75 \, \tekst{mm}, 475 \, \tekst{mm} \Rechtsaf) = 75 \, \tekst{mm}
\)
Volgens CSA A23.3:19 Eq. D.10 and D.11, the breakout edge effect factor is:
\(
\Psi_{ed,N} = min links( 1.0, 0.7 + 0.3 \links( \frac{c_{een,\tekst{min}}}{1.5 h_{ef,s1}} \Rechtsaf) \Rechtsaf) = min links( 1, 0.7 + 0.3 \keer links( \frac{75 \, \tekst{mm}}{1.5 \keer 130 \, \tekst{mm}} \Rechtsaf) \Rechtsaf) = 0.81538
\)
Daarnaast, both the cracking factor als de splitting factor are taken as:
\(
\Psi_{c,N} = 1
\)
\(
\Psi_{cp,N} = 1
\)
Vervolgens, 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:
\(
N_{cbr} = links( \frac{EEN_{Nc}}{EEN_{Onthouden}} \Rechtsaf) \Psi_{ed,N} \Psi_{c,N} \Psi_{cp,N} N_{br} = links( \frac{72900 \, \tekst{mm}^ 2}{152100 \, \tekst{mm}^ 2} \Rechtsaf) \keer 0.81538 \keer 1 \keer 1 \keer 43.813 \, \tekst{kN} = 17.122 \, \tekst{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{een,s}} = frac{50 \, \tekst{kN}}{4} = 12.5 \, \tekst{kN}
\)
Sinds 12.5 kN < 17.122 kN the concrete breakout capacity is voldoende.
This concrete breakout calculation is based on Anchor ID #1. The same capacity will apply to the other anchors due to the symmetric design.
Controleren #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 per CSA A23.3:19 Eq. D.17.
\(
N_{pr} = \Psi_{c,p} 0.9 \phi (f'_c) e_h d_a R = 1 \keer 0.9 \keer 0.65 \keer (20.68 \, \tekst{MPa}) \keer 60 \, \tekst{mm} \keer 19.05 \, \tekst{mm} \keer 1 = 13.828 \, \tekst{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{een,t}} = frac{50 \, \tekst{kN}}{4} = 12.5 \, \tekst{kN}
\)
Sinds 12.5 kN < 13.828 kN, the anchor pullout capacity is voldoende.
Controleren #6: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for hooked anchors.
Controleren #7: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for hooked anchors.
Ontwerp Samenvatting
De Skyciv Base Plate Design Software can automatically generate a step-by-step calculation report for this design example. Het biedt ook een samenvatting van de uitgevoerde controles en hun resulterende verhoudingen, De informatie in één oogopslag gemakkelijk te begrijpen maken. Hieronder is een sample samenvattende tabel, die is opgenomen in het rapport.
Skyciv Sample Report
Sample report will be added soon.
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