Basisplatten -Designbeispiel unter Verwendung von AISC 360-22 und ACI 318-19
Problemanweisung:
Determine whether the designed column-to-base plate connection is sufficient for a 20-kip tension load.
Gegebene Daten:
Spalte:
Spaltenabschnitt: W12x53
Säulenbereich: 15.6 im2
Säulenmaterial: A992
Grundplatte:
Grundplattenabmessungen: 18 in x 18 im
Grundplattendicke: 3/4 im
Grundplattenmaterial: A36
Grout:
Grout thickness: 1 im
Beton:
Konkrete Abmessungen: 22 in x 22 im
Betondicke: 15 im
Betonmaterial: 4000 psi
Cracked or Uncracked: Cracked
Anchors:
Anchor diameter: 3/4 im
Effective embedment length: 12 im
Embedded plate width: 3 im
Embedded plate thickness: 1/4 im
Anchor offset distance from face of column web: 2.8275 im
Schweißnähte:
Schweißnahtgröße: 1/4 im
Füllmetallklassifizierung: E70XX
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. 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 the effective weld length per anchor. The effective weld length is determined by the shortest length from the 45° dispersion, constrained by the actual weld length and anchor spacing.
For this calculation, anchors are classified as either end anchors oder intermediate anchors. End anchors are located at the ends of a row or column of anchors, while intermediate anchors are positioned between them. The calculation method differs for each and depends on the column geometry. In diesem Beispiel, there are two anchors along the web, and both are classified as end anchors.
For end anchors, the effective weld length is limited by the available distance from the anchor centerline to the column fillet. The 45° dispersion must not extend beyond this boundary.
\(
l_r = \frac{d_{col} – 2t_f – 2r_{col} – s_y(n_{ein,side} – 1)}{2} = frac{12.1 \, \Text{im} – 2 \mal 0.575 \, \Text{im} – 2 \mal 0.605 \, \Text{im} – 5 \, \Text{im} \mal (2 – 1)}{2} = 2.37 \, \Text{im}
\)
On the inner side, the effective length is limited by half the anchor spacing. The total effective weld length for the end anchor is the sum of the outer and inner lengths.
\(
l_{eff,Ende} = \min(Tun, 0.5s_y) + \Min.(Tun, l_r)
\)
\(
l_{eff,Ende} = \min(2.8275 \, \Text{im}, 0.5 \mal 5 \, \Text{im}) + \Min.(2.8275 \, \Text{im}, 2.37 \, \Text{im}) = 4.87 \, \Text{im}
\)
Für dieses Beispiel, bleibt die final effective weld length for the web anchor is taken as the effective length of the end anchor.
\(
l_{eff} = l_{eff,Ende} = 4.87 \, \Text{im}
\)
Als nächstes, let’s calculate the load per anchor. For a given set of four (4) Anker, the load per anchor is:
\(
T_{u,Anker} = frac{N_x}{n_{ein,t}} = frac{20 \, \Text{kip}}{4} = 5 \, \Text{kip}
\)
Using the calculated effective weld length, we can now determine the required force per unit length on the weld.
\(
r_u = frac{T_{u,Anker}}{l_{eff}} = frac{5 \, \Text{kip}}{4.87 \, \Text{im}} = 1.0267 \, \Text{kip/in}
\)
Jetzt, wir werden verwenden AISC 360-22, Chapter J2.4 to calculate the design strength of the fillet weld.
Since the applied load is purely axial tension, the angle \(\theta\) is taken as 90°, and the directional strength coefficient kds is calculated according to AISC 360-22 Gl. J2-5.
\(
k_{ds} = 1.0 + 0.5(\ohne(\theta))^{1.5} = 1 + 0.5 \mal (\ohne(1.5708))^{1.5} = 1.5
\)
Schließlich, Wir werden uns bewerben AISC 360-22 Gl. J2-4 to determine the design strength of the fillet weld per unit length.
\(
\phi r_n = \phi 0.6 F_{Exx} E_{w,Netz} k_{ds} = 0.75 \mal 0.6 \mal 70 \, \Text{KSI} \mal 0.177 \, \Text{im} \mal 1.5 = 8.3633 \, \Text{kip/in}
\)
Schon seit 1.0267 KPI < 8.3633 KPI, 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 (serving as the load eccentricity), the moment applied to the base plate can be calculated using a Ausleger assumption.
\(
M_u = T_{u,\Text{Anker}} e = 5 \, \Text{kip} \mal 2.8275 \, \Text{im} = 14.137 \, \Text{kip} \cdot \text{im}
\)
Als nächstes, using the calculated effective weld length from the previous check as the bending width, we can calculate the SkyCiv Foundation ist ein Designmodul für die Gestaltung von Spreizfundamenten aus den Überbaulasten of the base plate using AISC 360-22, Gleichung 2-1:
\(
\phi M_n = \phi F_{j,\Text{bp}} Z_{\Text{eff}} = 0.9 \mal 36 \, \Text{KSI} \mal 0.68484 \, \Text{im}^3 = 22.189 \, \Text{kip} \cdot \text{im}
\)
Wo,
\(
Z_{\Text{eff}} = frac{l_{\Text{eff}} (t_{\Text{bp}})^ 2}{4} = frac{4.87 \, \Text{im} \mal (0.75 \, \Text{im})^ 2}{4} = 0.68484 \, \Text{im}^ 3
\)
Schon seit 14.137 Hühnchen < 22.189 Hühnchen, the base plate flexural yielding capacity is ausreichend.
Prüfen #3: Calculate anchor rod tensile capacity
To evaluate the tensile capacity of the anchor rod, wir werden verwenden ACI 318-19 Gleichung 17.6.1.2.
Zuerst, Wir bestimmen die specified tensile strength of the anchor steel. This is the lowest value permitted by ACI 318-19 Klausel 17.6.1.2, with reference to material properties in AISC 360-22 Tabelle J3.2.
\(
f_{\Text{uta}} = min links( 0.75 F_{u,\Text{anc}}, 1.9 F_{j,\Text{anc}}, 125 \richtig) = min links( 0.75 \mal 120 \, \Text{KSI}, 1.9 \mal 92 \, \Text{KSI}, 125.00 \, \Text{KSI} \richtig) = 90 \, \Text{KSI}
\)
Als nächstes, wir berechnen die effective cross-sectional area of the anchor rod. This is based on ACI 318-19 Commentary Clause R17.6.1.2, which accounts for thread geometry. The number of threads per inch is taken from ASME B1.1-2019 Table 1.
\(
EIN_{ich weiß,N.} = frac{\Pi}{4} \links( d_a – \frac{0.9743}{n_t} \richtig)^2 = \frac{\Pi}{4} \mal links( 0.75 \, \Text{im} – \frac{0.9743}{10 \, \Text{im}^{-1}} \richtig)^2 = 0.33446 \, \Text{im}^ 2
\)
With these values, we apply ACI 318-19 Gleichung 17.6.1.2 to compute the design tensile strength of the anchor rod.
\(
\phi N_{zu} = phiA_{ich weiß,N.} f_{\Text{uta}} = 0.75 \mal 0.33446 \, \Text{im}^2 \times 90 \, \Text{KSI} = 22.576 \, \Text{kip}
\)
Recall the previously calculated tension load per anchor:
\(
N_{ua} = frac{N_x}{n_{ein,t}} = frac{20 \, \Text{kip}}{4} = 5 \, \Text{kip}
\)
Schon seit 5 kip < 22.576 kip, 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 ACI 318-19 Klausel 17.6.2.1.2, the member meets the criteria for a narrow member. Deshalb, a modified effective embedment length must be used in the calculations.
It is determined that the modified effective embedment length, h’ef, of the anchor group is:
\(
h’_{\Text{ef}} = 5.667 \, \Text{im}
\)
Verwenden von ACI 318-19 Klausel 17.6.2, wir berechnen die maximum projected concrete cone area für einen einzelnen Anker, based on the modified effective embedment length.
\(
EIN_{N_{co}} = 9 \links( h’_{ef,g1} \richtig)^2 = 9 \mal links( 5.6667 \, \Text{im} \richtig)^2 = 289 \, \Text{im}^ 2
\)
Ähnlich, we use the modified effective embedment length to calculate the actual projected concrete cone area of the anchor group.
\(
EIN_{N_c} = min links( n_{ein,g1} EIN_{N_{co}}, L_{N_c} B_{N_c} \richtig) = min links( 4 \mal 289 \, \Text{im}^ 2, 22 \, \Text{im} \mal 22 \, \Text{im} \richtig) = 484 \, \Text{im}^ 2
\)
Wo,
\(
L_{N_c} = min links( c_{\Text{links},g1}, 1.5 h’_{\Text{ef},g1} \richtig)
+ \links( \min \left( s_{\Text{Summe},mit,g1}, 3 h’_{\Text{ef},g1} \links( n_{mit,g1} – 1 \richtig) \richtig) \richtig)
+ \min \left( c_{\Text{richtig},g1}, 1.5 h’_{\Text{ef},g1} \richtig)
\)
\(
L_{N_c} = min links( 8 \, \Text{im}, 1.5 \mal 5.6667 \, \Text{im} \richtig)
+ \links( \min \left( 6 \, \Text{im}, 3 \mal 5.6667 \, \Text{im} \mal links( 2 – 1 \richtig) \richtig) \richtig)
+ \min \left( 8 \, \Text{im}, 1.5 \mal 5.6667 \, \Text{im} \richtig)
\)
\(
L_{N_c} = 22 \, \Text{im}
\)
\(
B_{N_c} = min links( c_{\Text{oben},g1}, 1.5 h’_{\Text{ef},g1} \richtig)
+ \links( \min \left( s_{\Text{Summe},j,g1}, 3 h’_{\Text{ef},g1} \links( n_{j,g1} – 1 \richtig) \richtig) \richtig)
+ \min \left( c_{\Text{Unterseite},g1}, 1.5 h’_{\Text{ef},g1} \richtig)
\)
\(
B_{N_c} = min links( 8.5 \, \Text{im}, 1.5 \mal 5.6667 \, \Text{im} \richtig)
+ \links( \min \left( 5 \, \Text{im}, 3 \mal 5.6667 \, \Text{im} \mal links( 2 – 1 \richtig) \richtig) \richtig)
+ \min \left( 8.5 \, \Text{im}, 1.5 \mal 5.6667 \, \Text{im} \richtig)
\)
\(
B_{N_c} = 22 \, \Text{im}
\)
Als nächstes, we evaluate the basic concrete breakout strength of a single anchor using ACI 318-19 Klausel 17.6.2.2.1
\(
N_b = k_c lambda_a sqrt{\frac{f’_c}{\Text{psi}}} \links( \frac{h’_{\Text{ef},g1}}{\Text{im}} \richtig)^{1.5} \, \Text{lbf}
\)
\(
N_b = 24 \mal 1 \mal sqrt{\frac{4 \, \Text{KSI}}{0.001 \, \Text{KSI}}} \mal links( \frac{5.6667 \, \Text{im}}{1 \, \Text{im}} \richtig)^{1.5} \mal 0.001 \, \Text{kip} = 20.475 \, \Text{kip}
\)
Wo,
- \(k_{c} = 24\) für einbetonierte Anker
- \(\lambda = 1.0 \) for normal-weight concrete
Jetzt, we assess the effects of geometry by calculating the edge effect factor und das eccentricity factor.
The shortest edge distance of the anchor group is determined as:
\(
c_{ein,\Text{Min.}} = min links( c_{\Text{links},g1}, c_{\Text{richtig},g1}, c_{\Text{oben},g1}, c_{\Text{Unterseite},g1} \richtig)
= min links( 8 \, \Text{im}, 8 \, \Text{im}, 8.5 \, \Text{im}, 8.5 \, \Text{im} \richtig) = 8 \, \Text{im}
\)
Gemäß ACI 318-19 Klausel 17.6.2.4.1, the breakout edge effect factor ist:
\(
\Psi_{ed,N.} = min links( 1.0, 0.7 + 0.3 \links( \frac{c_{ein,\Text{Min.}}}{1.5 h’_{\Text{ef},g1}} \richtig) \richtig)
= min links( 1, 0.7 + 0.3 \mal links( \frac{8 \, \Text{im}}{1.5 \mal 5.6667 \, \Text{im}} \richtig) \richtig) = 0.98235
\)
Since the tension load is applied at the centroid of the anchor group, the eccentricity is zero. So, bleibt die eccentricity factor, also from Clause 17.6.2.4.1, ist:
\(
\Psi_{ec,N.} = min links( 1.0, \frac{1}{1 + \frac{2 und’_N}{3 h’_{\Text{ef},g1}}} \richtig)
= min links( 1, \frac{1}{1 + \frac{2 \mal 0}{3 \mal 5.6667 \, \Text{im}}} \richtig) = 1
\)
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 concrete breakout strength of the anchor group:
\(
\phi N_{cbg} = \phi \left( \frac{EIN_{N_c}}{EIN_{N_{co}}} \richtig) \Psi_{ec,N.} \Psi_{ed,N.} \Psi_{c,N.} \Psi_{cp,N.} N_b
\)
\(
\phi N_{cbg} = 0.7 \mal links( \frac{484 \, \Text{im}^ 2}{289 \, \Text{im}^ 2} \richtig) \mal 1 \mal 0.98235 \mal 1 \mal 1 \mal 20.475 \, \Text{kip} = 23.58 \, \Text{kip}
\)
Mit der total applied tension load on the anchor group is the product of the individual anchor load and the number of anchors:
\(
N_{ua} = left( \frac{N_x}{n_{ein,t}} \richtig) n_{ein,g1} = left( \frac{20 \, \Text{kip}}{4} \richtig) \mal 4 = 20 \, \Text{kip}
\)
Schon seit 20 Kips < 23.58 Kips, the concrete breakout capacity is ausreichend.
Prüfen #5: Calculate anchor pullout capacity
The pullout capacity of an anchor is governed by the resistance at its embedded end. Anwenden seismischer Lasten, we calculate the bearing area of the embedded plate, which is the net area after subtracting the area occupied by the anchor rod.
For a rectangular embedded plate, bleibt die bearing area is calculated as:
\(
EIN_{brg} = left( \links( = Abstand des Abschnitts, in dem die Scherung berücksichtigt wird, zur Fläche des nächsten Auflagers{embed\_plate} \richtig)^2 \right) – EIN_{Stange} = left( \links( 3 \, \Text{im} \richtig)^2 \right) – 0.44179 \, \Text{im}^2 = 8.5582 \, \Text{im}^ 2
\)
Wo,
\(
EIN_{Stange} = frac{\Pi}{4} \links( d_a \right)^2 = \frac{\Pi}{4} \mal links( 0.75 \, \Text{im} \richtig)^2 = 0.44179 \, \Text{im}^ 2
\)
Als nächstes, Wir bestimmen die basic anchor pullout strength mit ACI 318-19 Equation 17.6.3.2.2a.
\(
N_b = 8 EIN_{brg} \links( f’_c \right) = 8 \mal 8.5582 \, \Text{im}^2 \times \left( 4 \, \Text{KSI} \richtig) = 273.86 \, \Text{kip}
\)
We then apply the appropriate resistance factor and pullout cracking factor:
- Zum cracked Beton, \(\Psi_{cp} = 1.0\)
- Zum uncracked Beton, \(\Psi_{cp} = 1.4\)
Using these, Wir berechnen die design anchor pullout strength in tension pro ACI 318-19 Gleichung 17.6.3.1.
\(
\phi N_{pn} = \phi \Psi_{c,p} N_b = 0.7 \mal 1 \mal 273.86 \, \Text{kip} = 191.7 \, \Text{kip}
\)
Recall the previously calculated tension load per anchor:
\(
N_{ua} = frac{N_x}{n_{ein,t}} = frac{20 \, \Text{kip}}{4} = 5 \, \Text{kip}
\)
Schon seit 5 Kips < 191.7 Kips, the anchor pullout capacity is ausreichend.
Prüfen #6: Calculate embed plate flexural capacity
This is a supplementary check performed using the Skyciv Base Plate Design Software to verify that the embedded plate has sufficient flexural capacity and will not yield under the applied pullout loads.
Zuerst, we determine the length of the free (unsupported) end of the embedded plate, measured from the edge of the support to the face of the rod.
\(
b’ = frac{= Abstand des Abschnitts, in dem die Scherung berücksichtigt wird, zur Fläche des nächsten Auflagers{embed\_plate} – d_a}{2} = frac{3 \, \Text{im} – 0.75 \, \Text{im}}{2} = 1.125 \, \Text{im}
\)
Als nächstes, wir berechnen die Biegemoment induced by the uniform bearing pressure. This pressure represents the force transferred from the anchor pullout action onto the embedded plate.
\(
m_f = \frac{\links( \frac{T_a}{EIN_{brg}} \richtig) \links( b’ \richtig)^ 2}{2} = frac{\links( \frac{5 \, \Text{kip}}{8.5582 \, \Text{im}^ 2} \richtig) \mal links( 1.125 \, \Text{im} \richtig)^ 2}{2} = 0.36971 \, \Text{kip}
\)
Schließlich, using the calculated moment and given material properties, we will determine the minimum required plate thickness to resist flexural yielding.
\(
t_{Min.} = Quadrat{\frac{4 m_f}{\phi F_{y\_ep}}} = Quadrat{\frac{4 \mal 0.36971 \, \Text{kip}}{0.9 \mal 36 \, \Text{KSI}}} = 0.21364 \, \Text{im}
\)
Recall actual embedded plate thickness:
\(
t_{actual} = t_{embed\_plate} = 0.25 \, \Text{im}
\)
Schon seit 0.21364 im < 0.25 im, the embedded plate flexural capacity is ausreichend.
Prüfen #7: Calculate side-face blowout capacity in Y-direction
This calculation is not applicable for this example, as the conditions specified in ACI 318-19 Klausel 17.6.4 are not met. Deshalb, side-face blowout failure along the Y-direction will not occur.
Prüfen #8: Calculate side-face blowout capacity in Z-direction
This calculation is not applicable for this example, as the conditions specified in ACI 318-19 Klausel 17.6.4 are not met. Deshalb, side-face blowout failure along the Z-direction will not occur.
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
Klicke hier to download a sample report.
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