AISCを使用したベースプレートのデザイン例 360-22 およびACI 318-19
問題ステートメント:
Determine whether the designed column-to-base plate connection is sufficient for a Vy=2-kip そして Vz=2-kip せん断荷重.
指定されたデータ:
カラム:
列セクション: HSS7X4X5/16
列エリア: 7.59 に2
列素材: A36
ベースプレート:
ベースプレートの寸法: 12 xで 14 に
ベースプレートの厚さ: 3/4 に
ベースプレート材料: A36
グラウト:
Grout Thickness: 0.25 に
コンクリート:
具体的な寸法: 12 xで 14 に
コンクリートの厚さ: 10 に
コンクリート材料: 3000 psi
ひび割れまたは破損していません: 割れた
アンカー:
アンカーの直径: 1/2 に
効果的な埋め込み長: 8 に
Plate washer thickness: 0.25 に
Plate washer connection: Welded to base plate
溶接:
溶接サイズ: 1/4 に
フィラー金属分類: E70XX
アンカーデータ (から SkyCIV計算機):
定義:
ロードパス:
The design follows the recommendations of AISC 設計ガイド 1, 3RDエディション, およびACI 318-19. Shear loads applied to the column are transferred to the base plate through the welds, and then to the supporting concrete through the anchor rods. Friction and shear lugs are not considered in this example, as these mechanisms are not supported in the current software.
デフォルトでは, the applied shear load is distributed equally among all anchors, with each anchor transferring its portion of the load to the concrete support. 代替として, the software allows a simplified and more conservative assumption, where the entire shear load is assigned only to the anchors nearest the loaded edge. この場合, the shear capacity check is performed on these edge anchors alone, ensuring that potential shear failure is conservatively addressed.
アンカーグループ:
の SkyCYVベースプレート設計ソフトウェア どのアンカーが評価するためのアンカーグループの一部であるかを識別する直感的な機能が含まれています concrete shear breakout そして concrete shear pryout 障害.
アン アンカーグループ is defined as two or more anchors with overlapping projected resistance areas. この場合, the anchors act together, and their combined resistance is checked against the applied load on the group.
あ single anchor is defined as an anchor whose projected resistance area does not overlap with any other. この場合, the anchor acts alone, and the applied shear force on that anchor is checked directly against its individual resistance.
This distinction allows the software to capture both group behavior and individual anchor performance when assessing shear-related failure modes.
段階的な計算:
小切手 #1: 溶接容量を計算します
The first step is to calculate the 総溶接長 available to resist shear. Since the base plate is welded along the perimeter of the column section, the total weld length is obtained by summing the welds on all sides.
\( L_{溶接} = 2 \左( =最も近いサポートの面までのせん断が考慮されているセクションの距離{col} – 2r_{col} – 2t_{col} \正しい) + 2 \左( d_{col} – 2r_{col} – 2t_{col} \正しい) \)
\( L_{溶接} = 2 \回 (4\,\テキスト{に} – 2 \times 0.291\,\text{に} – 2 \times 0.291\,\text{に}) + 2 \回 (7\,\テキスト{に} – 2 \times 0.291\,\text{に} – 2 \times 0.291\,\text{に}) = 17.344\,\text{に} \)
Using this weld length, the applied shear forces in the y- and z-directions are divided to determine the average shear force per unit length in each direction:
\( v_{あなた} = frac{V_y}{L_{溶接}} = frac{2\,\テキスト{キップ}}{17.344\,\テキスト{に}} = 0.11531\,\text{kip/in} \)
\( v_{uz} = frac{V_z}{L_{溶接}} = frac{2\,\テキスト{キップ}}{17.344\,\テキスト{に}} = 0.11531\,\text{kip/in} \)
の 合力せん断 demand per unit length is then determined using the square root of the sum of the squares (SRSS) 方法.
\( r_u = \sqrt{(v_{あなた})^ 2 + (v_{uz})^ 2} \)
\( r_u = \sqrt{(0.11531\,\テキスト{kip/in})^ 2 + (0.11531\,\テキスト{kip/in})^ 2} = 0.16308\,\text{kip/in} \)
次, the weld capacity is calculated using AISC 360-22 Eq. J2-4, with the directional strength coefficient taken as kds=1.0 for an HSS section. The weld capacity for a 1/4 in weld is determined as:
\( \phi r_n = phi 0.6 F_{exx} E_w k_{DS} = 0.75 \回 0.6 \times 70\,\text{KSI} \times 0.177\,\text{に} \回 1 = 5.5755\,\text{kip/in} \)
It is also necessary to check the base metals, both the column and the base plate, を使用して AISC 360-22 Eq. J4-4 to obtain the shear rupture strength. This gives:
\( \Phi R_{nbm, col} = phi 0.6 F_{u\_col} t_{col} = 0.75 \回 0.6 \times 58\,\text{KSI} \times 0.291\,\text{に} = 7.5951\,\text{kip/in} \)
\( \Phi R_{nbm, 血圧} = phi 0.6 F_{u\_bp} t_{血圧} = 0.75 \回 0.6 \times 58\,\text{KSI} \times 0.75\,\text{に} = 19.575\,\text{kip/in} \)
\( \Phi R_{nbm} = \min\left( \Phi R_{nbm, 血圧},\, \Phi R_{nbm, col} \正しい) = min(19.575\,\テキスト{kip/in},\, 7.5951\,\テキスト{kip/in}) = 7.5951\,\text{kip/in} \)
Since the actual weld stress is less than both the weld metal and base metal capacities, 0.16308 KPI < 5.5755 kpi and 0.16308 KPI < 7.5951 KPI, the design weld capacity is 十分な.
小切手 #2: Calculate concrete breakout capacity due to Vy shear
Perpendicular Edge Capacity:
From the layout, アンカー 1 そして 4 are closest to the edge and have the shortest ca1 distance. Using these ca1 values to project the failure cones, the software identified these anchors as シングルアンカー, since their projected cones do not overlap. The support was also determined to be not a narrow member, so the ca1 distance is used directly without modification.
Let’s recall that the shear force is assumed to be distributed among all the anchors. The calculation for the Vy shear load applied to each single anchor is:
\( V_{fa\perp} = frac{V_y}{n_a} = frac{2\,\テキスト{キップ}}{6} = 0.33333\,\text{キップ} \)
Let’s consider アンカー 1. The maximum projected area of a single anchor is calculated using ACI 318-19 Eq. 17.7.2.1.3.
\( A_{Vco} = 4.5 (c_{a1,s1})^2 = 4.5 \回 (2\,\テキスト{に})^2 = 18\,\text{に}^ 2 \)
The actual projected area is then determined from the width and height of the projected failure cone.
\( b_{VC} = min(c_{左,s1},\, 1.5c_{a1,s1}) + \分(c_{正しい,s1},\, 1.5c_{a1,s1}) \)
\( b_{VC} = min(10\,\テキスト{に},\, 1.5 \times 2\,\text{に}) + \分(2\,\テキスト{に},\, 1.5 \times 2\,\text{に}) = 5\,\text{に} \)
\( それを計算するために{VC} = min(1.5c_{a1,s1},\, t_{コンク}) = min(1.5 \times 2\,\text{に},\, 10\,\テキスト{に}) = 3\,\text{に} \)
\( A_{VC} = b_{VC} それを計算するために{VC} = 5\,\text{に} \times 3\,\text{に} = 15\,\text{に}^ 2 \)
The next step is to use Equations 17.7.2.2.1a and 17.7.2.2.1b to calculate the basic breakout strength of a single anchor. The governing capacity is taken as the lesser value.
\( V_{b1} = 7 \左( \フラク{\分(l_e,\, 8D_A)}{D_A} \正しい)^{0.2} \平方根{\フラク{D_A}{\テキスト{に}}} \lambda_a sqrt{\フラク{f’_c}{\テキスト{psi}}} \左( \フラク{c_{a1,s1}}{\テキスト{に}} \正しい)^{1.5} \,\テキスト{lbf} \)
\( V_{b1} = 7 \倍左( \フラク{\分(8\,\テキスト{に},\, 8 \times 0.5\,\text{に})}{0.5\,\テキスト{に}} \正しい)^{0.2} \回 sqrt{\フラク{0.5\,\テキスト{に}}{1\,\テキスト{に}}} \回 1 \回 sqrt{\フラク{3\,\テキスト{KSI}}{0.001\,\テキスト{KSI}}} \倍左( \フラク{2\,\テキスト{に}}{1\,\テキスト{に}} \正しい)^{1.5} \times 0.001\,\text{キップ} \)
\( V_{b1} = 1.1623\,\text{キップ} \)
\( V_{b2} = 9 \lambda_a sqrt{\フラク{f’_c}{\テキスト{psi}}} \左( \フラク{c_{a1,s1}}{\テキスト{に}} \正しい)^{1.5} \,\テキスト{lbf} \)
\( V_{b2} = 9 \回 1 \回 sqrt{\フラク{3\,\テキスト{KSI}}{0.001\,\テキスト{KSI}}} \倍左( \フラク{2\,\テキスト{に}}{1\,\テキスト{に}} \正しい)^{1.5} \times 0.001\,\text{キップ} = 1.3943\,\text{キップ} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(1.1623\,\テキスト{キップ},\, 1.3943\,\テキスト{キップ}) = 1.1623\,\text{キップ} \)
次, の breakout capacity parameters are determined. の breakout edge effect factor is calculated according to ACI 318-19 句 17.7.2.4, そしてその thickness factor is calculated according to 句 17.7.2.6.1.
\( \psi_{ed,V } = \min\left(1.0,\, 0.7 + 0.3 \左( \フラク{c_{a2,s1}}{1.5c_{a1,s1}} \正しい) \正しい) = \min\left(1,\, 0.7 + 0.3 \倍左( \フラク{2\,\テキスト{に}}{1.5 \times 2\,\text{に}} \正しい) \正しい) = 0.9 \)
\( \psi_{h,V } = \max\left( \平方根{ \フラク{1.5c_{a1,s1}}{t_{コンク}} },\, 1.0 \正しい) = \max\left( \平方根{ \フラク{1.5 \times 2\,\text{に}}{10\,\テキスト{に}} },\, 1 \正しい) = 1 \)
最後に, ACI 318-19 句 17.7.2.1(a) is used to determine the concrete breakout capacity of a single anchor in shear. The calculated capacity for Vy shear in the perpendicular direction is 0.69 キップ.
\( \ファイV_{cb\perp} = phi 左( \フラク{A_{VC}}{A_{Vco}} \正しい) \psi_{ed,V } \psi_{c,V } \psi_{h,V } V_b \)
\( \ファイV_{cb\perp} = 0.65 \倍左( \フラク{15\,\テキスト{に}^ 2}{18\,\テキスト{に}^ 2} \正しい) \回 0.86 \回 1 \回 1 \times 1.1623\,\text{キップ} = 0.56661\,\text{キップ} \)
The calculated capacity for Vy shear の中に perpendicular direction is 0.56 キップ.
Parallel Edge Capacity:
Failure along the edge parallel to the load is also possible in this scenario, so the concrete breakout capacity for the parallel edge must be determined. The anchors or anchor group considered are those aligned with the parallel edge. したがって, の ca1 edge distance is measured from the anchor to the edge along the Z-direction. Based on the figure below, the failure cone projections overlap; したがって, the anchors are treated as a group.
場合 1:
場合 2:
We refer to ACI 318-19 図. R17.7.2.1b for the different cases used when evaluating anchor groups. In this base plate design, welded plate washers are specifically used. したがって, のみ 場合 2 is checked.
The required load for the anchor group in Case 2 is taken as the total shear load.
\( V_{fa\parallel,case2} = V_y = 2\,\text{キップ} \)
In calculating the capacity for the Case 2 失敗, the anchors considered are the rear anchors. 結果として, the ca1 edge distance is measured from the rear anchor group to the failure edge.
With this ca1 distance and edge orientation, it must be verified whether the support qualifies as a narrow member. Following ACI 318-19 句 17.7.2.1.2, the SkyCiv Base Plate software identified the support as narrow. したがって, の modified ca1 distance 使用されている, which is calculated to be 6.667 に.
The same steps as in the perpendicular case are followed: を計算する projected failure areas, の basic single-anchor breakout strength, そしてその breakout parameters. The calculated values for each step are shown below.
\( A_{Vco} = 4.5 (c_{‘a1,g2})^2 = 4.5 \回 (6.6667\,\テキスト{に})^2 = 200\,\text{に}^ 2 \)
\( A_{VC} = b_{VC} それを計算するために{VC} = 14\,\text{に} \times 10\,\text{に} = 140\,\text{に}^ 2 \)
\( V_{b1} = 7.0733\,\text{キップ} \)
\( V_{b2} = 8.4853\,\text{キップ} \)
\( V_b = \min(V_{b1},\, V_{b2}) = min(7.0733\,\テキスト{キップ},\, 8.4853\,\テキスト{キップ}) = 7.0733\,\text{キップ} \)
\( \psi_{ed,V } = 1.0 \)
\( \psi_{h,V } = 1.0 \)
The equation for the parallel edge capacity differs from the perpendicular edge capacity. ACI 318-19 句 17.7.2.1(c) 適用されます, where the breakout equation is 掛ける 2.
\( \ファイV_{cbg\parallel} = 2 \Phi 左( \フラク{A_{VC}}{A_{Vco}} \正しい) \psi_{ed,V } \psi_{c,V } \psi_{h,V } V_b \)
\( \ファイV_{cbg\parallel} = 2 \回 0.65 \倍左( \フラク{140\,\テキスト{に}^ 2}{200\テキスト{に}^ 2} \正しい) \回 1 \回 1 \回 1 \times 7.0733\,\text{キップ} = 6.4367\,\text{キップ} \)
The calculated capacity for Vy shear の中に 平行 direction is 6.43 キップ.
We now assess the perpendicular and parallel failures separately.
- For the perpendicular edge failure, 以来 0.33 キップ < 0.56 キップ, the design concrete shear breakout capacity is 十分な.
- For the parallel edge failure, 以来 2 キップ < 6.43 キップ, the design concrete shear breakout capacity is 十分な.
小切手 #3: Calculate concrete breakout capacity due to Vz shear
The base plate is also subjected to Vz shear, so the failure edges perpendicular and parallel to the Vz shear must be checked. Using the same approach, the perpendicular and parallel capacities are calculated as 2.45 キップ そして 1.26 キップ, それぞれ.
Perpendicular Edge:
Parallel Edge:
These capacities are then compared to the required strengths.
- For the perpendicular edge failure, 以来 2 キップ < 2.45 キップ, the concrete shear breakout capacity is 十分な.
- For the parallel edge failure, 以来 0.33 キップ < 1.26 キップ, the concrete shear breakout capacity is 十分な.
小切手 #4: Calculate concrete pryout capacity
の concrete cone for pryout failure is the same cone used in the tensile breakout check. To calculate the shear pryout capacity, the nominal tensile breakout strength of the single anchors or anchor group must first be determined. The detailed calculations for the tensile breakout check are already covered in the SkyCiv Design Examples for Tension Load.
It is important to note that the anchor group determination for shear pryout is different from that for shear breakout. したがって, the anchors in the design must still be checked to determine whether they 行為 限られた亀裂幅と同様に グループ or as シングルアンカー against the shear pryout failure. The classification of the support as a narrow section must also be verified and should follow the same conditions used for tension breakout.
From the SkyCiv calculations, の nominal tensile breakout strength アンカーグループの 12.772 キップ. With a pryout factor of kcp=2, the design pryout capacity is:
\( \ファイV_{日用品} = \phi k_{cp} N_{cbg} = 0.65 \回 2 \回 12.772 \,\テキスト{キップ} = 16.604\,\text{キップ} \)
The required strength is the resultant of the applied shear loads. Since all anchors belong to a single group, the total resultant shear is assigned to the group.
\( V_{する} = sqrt{(V_y)^ 2 + (V_z)^ 2} = sqrt{(2\,\テキスト{キップ})^ 2 + (2\,\テキスト{キップ})^ 2} = 2.8284\,\text{キップ} \)
\( V_{する} = left( \フラク{V_{する}}{n_a} \正しい) n_{a,G1} = left( \フラク{2.8284\,\テキスト{キップ}}{6} \正しい) \回 6 = 2.8284\,\text{キップ} \)
Since the total shear load is less than anchor group capacity, 2.82 キップ < 18.976 キップ, the design pryout capacity is 十分な.
小切手 #5: Calculate anchor rod shear capacity
Recall that in this design example, shear is distributed to all anchors. The total shear load per anchor is therefore the resultant of its share of the Vy load and its share of the Vz load.
\( v_{する,そして} = frac{V_y}{n_a} = frac{2\,\テキスト{キップ}}{6} = 0.33333\,\text{キップ} \)
\( v_{する,と} = frac{V_z}{n_a} = frac{2\,\テキスト{キップ}}{6} = 0.33333\,\text{キップ} \)
\( V_{する} = sqrt{(v_{する,そして})^ 2 + (v_{する,と})^ 2} \)
\( V_{する} = sqrt{(0.33333\,\テキスト{キップ})^ 2 + (0.33333\,\テキスト{キップ})^ 2} = 0.4714\,\text{キップ} \)
This gives the shear stress on the anchor rod なので:
\( f_v = \frac{V_{する}}{A_{ロッド}} = frac{0.4714\,\テキスト{キップ}}{0.19635\,\テキスト{に}^ 2} = 2.4008\,\text{KSI} \)
Because a plate washer is present, AN eccentric shear load is induced in the anchor rod. The eccentricity is taken as half of the distance measured from the top of the concrete support to the center of the plate washer, accounting for the thickness of the base plate. 参照してください AISC 設計ガイド 1, 3rd Edition Section 4.3.3.
\( e = 0.5 \左( \フラク{t_{pw}}{2} + t_{血圧} \正しい) = 0.5 \倍左( \フラク{0.25\,\テキスト{に}}{2} + 0.75\,\テキスト{に} \正しい) = 0.4375\,\text{に} \)
The moment from the eccentric shear is then expressed as an axial stress in the anchor rod. Using the section modulus, the axial stress due to this moment is calculated as:
\( Z_{ロッド} = frac{\パイ}{32} (D_A)^3 = \frac{\パイ}{32} \回 (0.5\,\テキスト{に})^3 = 0.012272\,\text{に}他のいくつかの例は \)
\( f_t = \frac{V_{する} e}{Z_{ロッド}} = frac{0.4714\,\テキスト{キップ} \times 0.4375\,\text{に}}{0.012272\,\テキスト{に}他のいくつかの例は} = 16.806\,\text{KSI} \)
ACI Anchor Rod Shear Capacity:
Following ACI 318-19 句 17.7.1, the design strength is then determined. あ 0.8 削減率 is applied due to the presence of grout pads. The design capacity is therefore:
\( \ファイV_{に,ここに} = 0.8 \ファイ 0.6 A_{知っている,v} f_{uta} = 0.8 \回 0.65 \回 0.6 \times 0.1419\text{に}^2 \times 90\text{KSI} = 3.9845\text{キップ} \)
代替として, の SkyCiv Base Plate software allows the 0.8 simplification to be disabled, and use the actual grout pad thickness in the calculations. この場合, the total eccentricity includes the grout pad, and the combined shear and axial strength is determined in accordance with AISC provisions.
AISC Anchor Rod Shear Capacity:
最初, の nominal shear and tensile stresses are determined for an A325 rod.
\( F_{NV} = 0.45 F_{あなた,anc} = 0.45 \回 120\ \テキスト{KSI} = 54\ \テキスト{KSI} \)
\( F_{nt} = 0.75 F_{あなた,anc} = 0.75 \回 120\ \テキスト{KSI} = 90\ \テキスト{KSI} \)
The AISC method uses AISC 360-22 Eq. J3-3a, which may be expressed to include the effects of axial stress. This is carried out as follows.
\( F’_{NV} = min left( 1.3 F_{NV} – \左( \フラク{F_{NV}}{\phi f_{nt}} \正しい) f_t,\; F_{NV} \正しい) \)
\( F’_{NV} = min left( 1.3 \回 54\ \テキスト{KSI} – \左( \フラク{54\ \テキスト{KSI}}{0.75 \回 90\ \テキスト{KSI}} \正しい) \回 16.806\ \テキスト{KSI},\; 54\ \テキスト{KSI} \正しい) = 54\ \テキスト{KSI} \)
The design shear capacity from the AISC method is then calculated as:
\( \ファイR_{ん,\mathrm{aisc}} = \phi F’_{NV} A_{ロッド} = 0.75 \回 54\ \テキスト{KSI} \回 0.19635\ \テキスト{に}^2 = 7.9522\)
To ensure both methods are covered, the governing capacity is taken as the lesser of the two, それは 3.98 キップ.
\( \phi V_n = \min \left( \ファイV_{に,ここに},\; \ファイR_{ん,\mathrm{aisc}} \正しい) = min (3.9845\ \テキスト{キップ},\; 7.9522\ \テキスト{キップ}) = 3.9845\ \テキスト{キップ} \)
Since the shear load per anchor rod is less than the governing anchor rod capacity in shear, 0.47 キップ < 3.98 キップ, the design anchor rod shear capacity is 十分な.
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