Base Plate Design Example using CSA S16:19 and CSA A23.3:19
Dichiarazione del problema:
Determine whether the designed column-to-base plate connection is sufficient for a 50-kN tension load.
Dati dati:
Colonna:
Sezione colonna: HS324X9.5
Area colonna: 9410 mm2
Materiale colonna: 230sol
Piastra di base:
Dimensioni della piastra di base: 500 mm x 500 mm
Spessore della piastra di base: 20 mm
Materiale della piastra di base: 230sol
Grout:
Grout thickness: 20 mm
Calcestruzzo:
Dimensioni concrete: 550 mm x 550 mm
Spessore di cemento: 200 mm
Materiale di cemento: 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
saldature:
Weld type: CJP
Classificazione del metallo di riempimento: E43XX
Anchor Data (a partire dal SkyCiv Calculator):
Definitions:
Load Path:
When a base plate is subjected to uplift (trazione) forze, 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.
Nel Software di progettazione della piastra di 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, un carico 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 del piatto.
The assumption simplifies the base plate analysis by approximating how the uplift force spreads through the plate.
Anchor Groups:
La Software di progettazione della piastra di base Skyciv includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating rottura concreta e 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. In questo caso, only the tension force on the individual anchor is checked against its own effective resistance area.
Calcoli passo-passo:
Dai un'occhiata #1: Calcola la capacità di saldatura
Iniziare, we need to calculate the load per anchor and determine the effective weld length for each anchor. La 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, il tangent points are used instead. Inoltre, if the anchors are closely spaced, the effective weld length is reduced to avoid overlap. Infine, 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. Di conseguenza, 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:
\(
l_{\testo{arc}} = 254.47 \, \testo{mm}
\)
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 è:
\(
l_{\testo{eff}} = min sinistra( l_{\testo{arc}}, \frac{\pi d_{\testo{col}}}{n_{un carico,t}} \giusto) = min sinistra( 254.47 \, \testo{mm}, \frac{\pi \times 324 \, \testo{mm}}{4} \giusto) = 254.47 \, \testo{mm}
\)
Successivamente, let’s calculate the load per anchor. For a given set of four (4) ancore, the load per anchor is:
\(
T_{u,\testo{ancorare}} = frac{N_x}{n_{un carico,t}} = frac{50 \, \testo{kN}}{4} = 12.5 \, \testo{kN}
\)
Using the calculated effective weld length, we can now compute the required force per unit length acting on the weld.
\(
v_f = \frac{T_{u,\testo{ancorare}}}{l_{\testo{eff}}} = frac{12.5 \, \testo{kN}}{254.47 \, \testo{mm}} = 0.049122 \, \testo{metri ed è fissato alla base e fissato in alto}
\)
Adesso, we refer to CSA S16:19 Clausola 13.13.3.1 to calculate the factored resistance of the complete joint penetration (CJP) saldare. This requires the base metal resistance, expressed in force per unit length, for both the column and the base plate materials.
\(
v_{r,\testo{bm}} = \phi \left( \min \left( F_{y,\testo{col}} t_{\testo{col}}, F_{y,\testo{p.p}} t_{\testo{p.p}} \giusto) \giusto)
\)
\(
v_{r,\testo{bm}} = 0.9 \volte sinistra( \min \left( 230 \, \testo{MPa} \volte 9.53 \, \testo{mm}, 230 \, \testo{MPa} \volte 20 \, \testo{mm} \giusto) \giusto) = 1.9727 \, \testo{metri ed è fissato alla base e fissato in alto}
\)
Da 0.049122 metri ed è fissato alla base e fissato in alto < 1.9727 metri ed è fissato alla base e fissato in alto, La capacità di saldatura è sufficiente.
Dai un'occhiata #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 a sbalzo assumption. For a circular column, the load eccentricity is determined by considering the sagitta of the welded arc, and can be calculated as follows:
\(
e_{\testo{pipe}} = d_o + r_{\testo{col}} \sinistra( 1 – \cos sinistra( \frac{l_{\testo{eff}}}{2 r_{\testo{col}}} \giusto) \giusto)
\)
\(
e_{\testo{pipe}} = 120.84 \, \testo{mm} + 162 \, \testo{mm} \volte sinistra( 1 – \cos sinistra( \frac{254.47 \, \testo{mm}}{2 \volte 162 \, \testo{mm}} \giusto) \giusto) = 168.29 \, \testo{mm}
\)
The induced moment is computed as:
\(
M_f = T_{u,\testo{ancorare}} e_{\testo{pipe}} = 12.5 \, \testo{kN} \volte 168.29 \, \testo{mm} = 2103.6 \, \testo{kN} \cdot \text{mm}
\)
Successivamente, we will determine the bending width of the base plate. Per questo, we use the chord length corresponding to the effective weld arc.
\(
\theta_{\testo{lavoro}} = frac{l_{\testo{eff}}}{0.5 d_{\testo{col}}} = frac{254.47 \, \testo{mm}}{0.5 \volte 324 \, \testo{mm}} = 1.5708
\)
\(
b = d_{\testo{col}} \sinistra( \peccato sinistra( \frac{\theta_{\testo{lavoro}}}{2} \giusto) \giusto) = 324 \, \testo{mm} \volte sinistra( \peccato sinistra( \frac{1.5708}{2} \giusto) \giusto) = 229.1 \, \testo{mm}
\)
Infine, we can calculate the factored flexural resistance of the base plate using CSA S16:19 Clausola 13.5.
\(
M_r = \phi F_{y,\testo{p.p}} Z_{\testo{eff}} = 0.9 \volte 230 \, \testo{MPa} \volte 22910 \, \testo{mm}^3 = 4742.4 \, \testo{kN} \cdot \text{mm}
\)
Dove,
\(
Z_{\testo{eff}} = frac{b (t_{\testo{p.p}})^ 2}{4} = frac{229.1 \, \testo{mm} \volte (20 \, \testo{mm})^ 2}{4} = 22910 \, \testo{mm}^ 3
\)
Da 2103.6 kN-mm < 4742.4 kN-mm, the base plate flexural yielding capacity is sufficiente.
Dai un'occhiata #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 Clausola 25.3.2.1.
Primo, Determiniamo il specified tensile strength of the anchor steel. This is the lowest value permitted by CSA A23.3:19 Clause D.6.1.2.
\(
f_{\testo{uta}} = min sinistra( F_{u,\testo{anc}}, 1.9 F_{y,\testo{anc}}, 860 \giusto) = min sinistra( 400 \, \testo{MPa}, 1.9 \volte 248.2 \, \testo{MPa}, 860.00 \, \testo{MPa} \giusto) = 400 \, \testo{MPa}
\)
Successivamente, Determiniamo il effective cross-sectional area of the anchor rod in tension using CAC Concrete Design Handbook, 3Rd Edition, tavolo 12.3.
\(
UN_{lo so,N} = 215 \, \testo{mm}^ 2
\)
With these values, we apply CSA A23.3:19 Eq. D.2 to compute the factored tensile resistance of the anchor rod.
\(
N_{\testo{sar}} = A_{lo so,N} \phi_s f_{\testo{uta}} R = 215 \, \testo{mm}^2 \times 0.85 \volte 400 \, \testo{MPa} \volte 0.8 = 58.465 \, \testo{kN}
\)
Inoltre, we evaluate the factored tensile resistance according to CSA S16:19 Clausola 25.3.2.1.
\(
T_r = \phi_{ar} 0.85 UN_{ar} F_{u,\testo{anc}} = 0.67 \volte 0.85 \volte 285.02 \, \testo{mm}^2 \times 400 \, \testo{MPa} = 64.912 \, \testo{kN}
\)
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:
\(
N_{fa} = frac{N_x}{n_{un carico,t}} = frac{50 \, \testo{kN}}{4} = 12.5 \, \testo{kN}
\)
Da 12.5 kN < 58.465 kN, the anchor rod tensile capacity is sufficiente.
Dai un'occhiata #4: Calculate concrete breakout capacity in tension
Before calculating the breakout capacity, we must first determine whether the member qualifies as a narrow member. Secondo CSA A23.3:19 Clause D.6.2.3, the member does not meet the criteria for a narrow member. Pertanto, the given effective embedment length will be used in the calculations.
Usando CSA A23.3:19 Eq. D.5, calcoliamo il maximum projected concrete cone area per un'unica ancora, based on the effective embedment length.
\(
UN_{Ricorda} = 9 (h_{ef,Sforzo in alto Rinforzo})^2 = 9 \volte (130 \, \testo{mm})^2 = 152100 \, \testo{mm}^ 2
\)
Allo stesso modo, we use the effective embedment length to calculate the actual projected concrete cone area of the single anchor.
\(
UN_{Nc} = L_{Nc} B_{Nc} = 270 \, \testo{mm} \volte 270 \, \testo{mm} = 72900 \, \testo{mm}^ 2
\)
Dove,
\(
L_{Nc} = sinistra( \min \left( c_{\testo{sinistra},Sforzo in alto Rinforzo}, 1.5 h_{ef,Sforzo in alto Rinforzo} \giusto) \giusto) + \sinistra( \min \left( c_{\testo{giusto},Sforzo in alto Rinforzo}, 1.5 h_{ef,Sforzo in alto Rinforzo} \giusto) \giusto)
\)
\(
L_{Nc} = sinistra( \min \left( 475 \, \testo{mm}, 1.5 \volte 130 \, \testo{mm} \giusto) \giusto) + \sinistra( \min \left( 75 \, \testo{mm}, 1.5 \volte 130 \, \testo{mm} \giusto) \giusto)
\)
\(
L_{Nc} = 270 \, \testo{mm}
\)
\(
B_{Nc} = sinistra( \min \left( c_{\testo{superiore},Sforzo in alto Rinforzo}, 1.5 h_{ef,Sforzo in alto Rinforzo} \giusto) \giusto) + \sinistra( \min \left( c_{\testo{parte inferiore},Sforzo in alto Rinforzo}, 1.5 h_{ef,Sforzo in alto Rinforzo} \giusto) \giusto)
\)
\(
B_{Nc} = sinistra( \min \left( 75 \, \testo{mm}, 1.5 \volte 130 \, \testo{mm} \giusto) \giusto) + \sinistra( \min \left( 475 \, \testo{mm}, 1.5 \volte 130 \, \testo{mm} \giusto) \giusto)
\)
\(
B_{Nc} = 270 \, \testo{mm}
\)
Successivamente, we evaluate the factored basic concrete breakout resistance of a single anchor using CSA A23.3:19 Eq. D.6
\(
N_{br} = k_c \phi \lambda_a \sqrt{\frac{f'_c}{\testo{MPa}}} \sinistra( \frac{h_{ef,Sforzo in alto Rinforzo}}{\testo{mm}} \giusto)^{1.5} R N
\)
\(
N_{br} = 10 \volte 0.65 \volte 1 \volte sqrt{\frac{20.68 \, \testo{MPa}}{1 \, \testo{MPa}}} \volte sinistra( \frac{130 \, \testo{mm}}{1 \, \testo{mm}} \giusto)^{1.5} \volte 1 \volte 0.001 \, \testo{kN} = 43.813 \, \testo{kN}
\)
Dove,
- \(Eurocodice di design con piastra di base in acciaio{c} = 10\) per ancore gettate
- \(\lambda = 1.0 \) for normal-weight concrete
Adesso, we assess the effects of geometry by calculating the edge effect factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{un carico,\testo{min}} = min sinistra( c_{\testo{sinistra},Sforzo in alto Rinforzo}, c_{\testo{giusto},Sforzo in alto Rinforzo}, c_{\testo{superiore},Sforzo in alto Rinforzo}, c_{\testo{parte inferiore},Sforzo in alto Rinforzo} \giusto) = min sinistra( 475 \, \testo{mm}, 75 \, \testo{mm}, 75 \, \testo{mm}, 475 \, \testo{mm} \giusto) = 75 \, \testo{mm}
\)
Secondo CSA A23.3:19 Eq. D.10 and D.11, the breakout edge effect factor è:
\(
\Psi_{ed,N} = min sinistra( 1.0, 0.7 + 0.3 \sinistra( \frac{c_{un carico,\testo{min}}}{1.5 h_{ef,Sforzo in alto Rinforzo}} \giusto) \giusto) = min sinistra( 1, 0.7 + 0.3 \volte sinistra( \frac{75 \, \testo{mm}}{1.5 \volte 130 \, \testo{mm}} \giusto) \giusto) = 0.81538
\)
Inoltre, both the cracking factor che per il splitting factor are taken as:
\(
\Psi_{c,N} = 1
\)
\(
\Psi_{cp,N} = 1
\)
Poi, 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:
\(
N_{cbr} = sinistra( \frac{UN_{Nc}}{UN_{Ricorda}} \giusto) \Psi_{ed,N} \Psi_{c,N} \Psi_{cp,N} N_{br} = sinistra( \frac{72900 \, \testo{mm}^ 2}{152100 \, \testo{mm}^ 2} \giusto) \volte 0.81538 \volte 1 \volte 1 \volte 43.813 \, \testo{kN} = 17.122 \, \testo{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{un carico,S}} = frac{50 \, \testo{kN}}{4} = 12.5 \, \testo{kN}
\)
Da 12.5 kN < 17.122 kN the concrete breakout capacity is sufficiente.
This concrete breakout calculation is based on Anchor ID #1. The same capacity will apply to the other anchors due to the symmetric design.
Dai un'occhiata #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.
\(
N_{pr} = \Psi_{c,p} 0.9 \phi (f'_c) e_h d_a R = 1 \volte 0.9 \volte 0.65 \volte (20.68 \, \testo{MPa}) \volte 60 \, \testo{mm} \volte 19.05 \, \testo{mm} \volte 1 = 13.828 \, \testo{kN}
\)
Recall the previously calculated tension load per anchor:
\(
N_{fa} = frac{N_x}{n_{un carico,t}} = frac{50 \, \testo{kN}}{4} = 12.5 \, \testo{kN}
\)
Da 12.5 kN < 13.828 kN, the anchor pullout capacity is sufficiente.
Dai un'occhiata #6: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for hooked anchors.
Dai un'occhiata #7: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for hooked anchors.
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