基本板设计示例使用AISC 360-22 和ACI 318-19

问题陈述:

Determine whether the designed column-to-base plate connection is sufficient for a Vy=2-kip 和 Vz=2-kip 剪力.

给定数据:

柱:

列部分: HSS7X4X5/16
列区域: 7.59 在²
列材料: A36

底盘:

基板尺寸: 12 在x 14 在
基板厚度: 3/4 在
底板材料: A36

灌浆:

Grout Thickness: 0.25 在

具体:

混凝土尺寸: 12 在x 14 在
混凝土厚度: 10 在
混凝土材料: 3000 压力
破裂或无裂缝: 破裂

锚:

锚直径: 1/2 在
有效嵌入长度: 8 在
Plate washer thickness: 0.25 在
Plate washer connection: Welded to base plate

焊缝:

焊缝尺寸: 1/4 在
填充金属分类: E70XX

锚数据 (从 SkyCiv计算器):

定义:

负载路径:

The design follows the recommendations of AISC 设计指南 1, 3RD版, 和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.

默认, the applied shear load is distributed equally among all anchors, with each anchor transferring its portion of the load to the concrete support. 作为备选, the software allows a simplified and more conservative assumption, where the entire shear load is assigned only to the anchors nearest the loaded edge. 在这种情况下, the shear capacity check is performed on these edge anchors alone, ensuring that potential shear failure is conservatively addressed.

锚群:

的 SkyCiv 底板设计软件 包括一个直观的功能，该功能标识哪些锚定为评估的锚点组的一部分 concrete shear breakout 和 concrete shear pryout 失败.

一个 锚群 is defined as two or more anchors with overlapping projected resistance areas. 在这种情况下, the anchors act together, and their combined resistance is checked against the applied load on the group.

一个 single anchor is defined as an anchor whose projected resistance area does not overlap with any other. 在这种情况下, 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.

分步计算:

检查一下 #1: 计算焊接容量

The first step is to calculate the 总焊接长度 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.

\( L_{焊接} = 2 \剩下( b_{上校} – 2r_{上校} – 2t_{上校} \对) + 2 \剩下( d_{上校} – 2r_{上校} – 2t_{上校} \对) \)

\( L_{焊接} = 2 \次 (4\,\文本{在} – 2 \times 0.291\,\text{在} – 2 \times 0.291\,\text{在}) + 2 \次 (7\,\文本{在} – 2 \times 0.291\,\text{在} – 2 \times 0.291\,\text{在}) = 17.344\,\text{在} \)

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:

\( v_{你} = frac{V_y}{L_{焊接}} = frac{2\,\文本{基普}}{17.344\,\文本{在}} = 0.11531\,\text{kip/in} \)

\( v_{uz} = frac{V_z}{L_{焊接}} = frac{2\,\文本{基普}}{17.344\,\文本{在}} = 0.11531\,\text{kip/in} \)

的 resultant shear demand per unit length is then determined using the square root of the sum of the squares (SRSS) 方法.

\( r_u = \sqrt{(v_{你})^ 2 + (v_{uz})^ 2} \)

\( r_u = \sqrt{(0.11531\,\文本{kip/in})^ 2 + (0.11531\,\文本{kip/in})^ 2} = 0.16308\,\text{kip/in} \)

下一个, the weld capacity is calculated using AISC 360-22 情商. 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:

\( \phi r_n = phi 0.6 F_{EXX} E_w k_{DS} = 0.75 \次 0.6 \times 70\,\text{KSI} \times 0.177\,\text{在} \次 1 = 5.5755\,\text{kip/in} \)

It is also necessary to check the base metals, both the column and the base plate, 使用 AISC 360-22 情商. J4-4 to obtain the shear rupture strength. This gives:

\( \phi r_{nbm, 上校} = phi 0.6 F_{u\_col} t_{上校} = 0.75 \次 0.6 \times 58\,\text{KSI} \times 0.291\,\text{在} = 7.5951\,\text{kip/in} \)

\( \phi r_{nbm, BP} = phi 0.6 F_{u\_bp} t_{BP} = 0.75 \次 0.6 \times 58\,\text{KSI} \times 0.75\,\text{在} = 19.575\,\text{kip/in} \)

\( \phi r_{nbm} = \min\left( \phi r_{nbm, BP},\, \phi r_{nbm, 上校} \对) = min(19.575\,\文本{kip/in},\, 7.5951\,\文本{kip/in}) = 7.5951\,\text{kip/in} \)

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 充足的.

检查一下 #2: Calculate concrete breakout capacity due to Vy shear

Perpendicular Edge Capacity:

From the layout, 锚 1 和 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 单锚, 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:

\( V_{fa\perp} = frac{V_y}{n_a} = frac{2\,\文本{基普}}{6} = 0.33333\,\text{基普} \)

Let’s consider Anchor 1. The maximum projected area of a single anchor is calculated using ACI 318-19 情商. 17.7.2.1.3.

\( 一个_{压控振荡器} = 4.5 (C_{a1,s1})可以假设为 4.5 \次 (2\,\文本{在})^2 = 18\,\text{在}^ 2 \)

The actual projected area is then determined from the width and height of the projected failure cone.

\( b_{VC} = min(C_{剩下,s1},\, 1.5C_{a1,s1}) + \分(C_{对,s1},\, 1.5C_{a1,s1}) \)

\( b_{VC} = min(10\,\文本{在},\, 1.5 \times 2\,\text{在}) + \分(2\,\文本{在},\, 1.5 \times 2\,\text{在}) = 5\,\text{在} \)

\( H_{VC} = min(1.5C_{a1,s1},\, t_{浓}) = min(1.5 \times 2\,\text{在},\, 10\,\文本{在}) = 3\,\text{在} \)

\( 一个_{VC} = B_{VC} H_{VC} = 5\,\text{在} \times 3\,\text{在} = 15\,\text{在}^ 2 \)

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.

\( V_{11} = 7 \剩下( \压裂{\分(l_e,\, 8D_A)}{D_A} \对)^{0.2} \sqrt{\压裂{D_A}{\文本{在}}} \lambda_a sqrt{\压裂{f'_c}{\文本{压力}}} \剩下( \压裂{C_{a1,s1}}{\文本{在}} \对)^{1.5} \,\文本{磅力} \)

\( V_{11} = 7 \时代左( \压裂{\分(8\,\文本{在},\, 8 \times 0.5\,\text{在})}{0.5\,\文本{在}} \对)^{0.2} \次 sqrt{\压裂{0.5\,\文本{在}}{1\,\文本{在}}} \次 1 \次 sqrt{\压裂{3\,\文本{KSI}}{0.001\,\文本{KSI}}} \时代左( \压裂{2\,\文本{在}}{1\,\文本{在}} \对)^{1.5} \times 0.001\,\text{基普} \)

\( V_{11} = 1.1623\,\text{基普} \)

\( V_{b2} = 9 \lambda_a sqrt{\压裂{f'_c}{\文本{压力}}} \剩下( \压裂{C_{a1,s1}}{\文本{在}} \对)^{1.5} \,\文本{磅力} \)

\( V_{b2} = 9 \次 1 \次 sqrt{\压裂{3\,\文本{KSI}}{0.001\,\文本{KSI}}} \时代左( \压裂{2\,\文本{在}}{1\,\文本{在}} \对)^{1.5} \times 0.001\,\text{基普} = 1.3943\,\text{基普} \)

\( V_b = \min(V_{11},\, V_{b2}) = min(1.1623\,\文本{基普},\, 1.3943\,\文本{基普}) = 1.1623\,\text{基普} \)

下一个, 的 breakout capacity parameters are determined. 的 breakout edge effect factor is calculated according to ACI 318-19 条款 17.7.2.4, 和 thickness factor is calculated according to 条款 17.7.2.6.1.

\( \psi_{编辑,V} = \min\left(1.0,\, 0.7 + 0.3 \剩下( \压裂{C_{a2,s1}}{1.5C_{a1,s1}} \对) \对) = \min\left(1,\, 0.7 + 0.3 \时代左( \压裂{2\,\文本{在}}{1.5 \times 2\,\text{在}} \对) \对) = 0.9 \)

\( \psi_{H,V} = \max\left( \sqrt{ \压裂{1.5C_{a1,s1}}{t_{浓}} },\, 1.0 \对) = \max\left( \sqrt{ \压裂{1.5 \times 2\,\text{在}}{10\,\文本{在}} },\, 1 \对) = 1 \)

最后, ACI 318-19 条款 17.7.2.1(一个) 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 ps.

\( \非V_{cb\perp} = phi 左( \压裂{一个_{VC}}{一个_{压控振荡器}} \对) \psi_{编辑,V} \psi_{C,V} \psi_{H,V} V_b \)

\( \非V_{cb\perp} = 0.65 \时代左( \压裂{15\,\文本{在}^ 2}{18\,\文本{在}^ 2} \对) \次 0.86 \次 1 \次 1 \times 1.1623\,\text{基普} = 0.56661\,\text{基普} \)

The calculated capacity for Vy shear 在里面 perpendicular direction is 0.56 ps.

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. 所以, 的 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; 因此, the anchors are treated as a group.

案件 1:

案件 2:

We refer to ACI 318-19 图. R17.7.2.1b for the different cases used when evaluating anchor groups. In this base plate design, welded plate washers are specifically used. 因此, 只要 案件 2 is checked.

The required load for the anchor group in Case 2 is taken as the total shear load.

\( V_{fa\parallel,case2} = V_y = 2\,\text{基普} \)

In calculating the capacity for the Case 2 failure, the anchors considered are the rear anchors. 结果是, 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 条款 17.7.2.1.2, the SkyCiv Base Plate software identified the support as narrow. 因此, 的 modified ca1 distance 用来, which is calculated to be 6.667 在.

The same steps as in the perpendicular case are followed: 计算 projected failure areas, 的 basic single-anchor breakout strength, 和 breakout parameters. The calculated values for each step are shown below.

\( 一个_{压控振荡器} = 4.5 (C_{‘a1,g2})可以假设为 4.5 \次 (6.6667\,\文本{在})^2 = 200\,\text{在}^ 2 \)

\( 一个_{VC} = B_{VC} H_{VC} = 14\,\text{在} \times 10\,\text{在} = 140\,\text{在}^ 2 \)

\( V_{11} = 7.0733\,\text{基普} \)

\( V_{b2} = 8.4853\,\text{基普} \)

\( V_b = \min(V_{11},\, V_{b2}) = min(7.0733\,\文本{基普},\, 8.4853\,\文本{基普}) = 7.0733\,\text{基普} \)

\( \psi_{编辑,V} = 1.0 \)

\( \psi_{H,V} = 1.0 \)

The equation for the parallel edge capacity differs from the perpendicular edge capacity. ACI 318-19 条款 17.7.2.1(C) is applied, where the breakout equation is multiplied by 2.

\( \非V_{cbg\parallel} = 2 \phi 左( \压裂{一个_{VC}}{一个_{压控振荡器}} \对) \psi_{编辑,V} \psi_{C,V} \psi_{H,V} V_b \)

\( \非V_{cbg\parallel} = 2 \次 0.65 \时代左( \压裂{140\,\文本{在}^ 2}{200\文本{在}^ 2} \对) \次 1 \次 1 \次 1 \times 7.0733\,\text{基普} = 6.4367\,\text{基普} \)

The calculated capacity for Vy shear 在里面 平行 direction is 6.43 ps.

We now assess the perpendicular and parallel failures separately.

• For the perpendicular edge failure, 以来 0.33 基普 < 0.56 基普, the design concrete shear breakout capacity is 充足的.
• For the parallel edge failure, 以来 2 基普 < 6.43 基普, the design concrete shear breakout capacity is 充足的.

检查一下 #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 ps 和 1.26 ps, 分别.

Perpendicular Edge:

Parallel Edge:

These capacities are then compared to the required strengths.

• For the perpendicular edge failure, 以来 2 基普 < 2.45 基普, the concrete shear breakout capacity is 充足的.
• For the parallel edge failure, 以来 0.33 基普 < 1.26 基普, the concrete shear breakout capacity is 充足的.

检查一下 #4: Calculate concrete pryout capacity

的 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. 因此, the anchors in the design must still be checked to determine whether they act 有一个 group or as 单锚 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, 的 nominal tensile breakout strength 锚群是 12.772 ps. With a pryout factor of kcp=2, the design pryout capacity is:

\( \非V_{cpg} = \phi k_{cp} N_{背景} = 0.65 \次 2 \次 12.772 \,\文本{基普} = 16.604\,\text{基普} \)

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.

\( V_{做} = sqrt{(V_y)^ 2 + (V_z)^ 2} = sqrt{(2\,\文本{基普})^ 2 + (2\,\文本{基普})^ 2} = 2.8284\,\text{基普} \)

\( V_{做} = 左( \压裂{V_{做}}{n_a} \对) n_{一个,G1} = 左( \压裂{2.8284\,\文本{基普}}{6} \对) \次 6 = 2.8284\,\text{基普} \)

Since the total shear load is less than anchor group capacity, 2.82 ps < 18.976 ps, the design pryout capacity is 充足的.

检查一下 #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.

\( v_{做,和} = frac{V_y}{n_a} = frac{2\,\文本{基普}}{6} = 0.33333\,\text{基普} \)

\( v_{做,与} = frac{V_z}{n_a} = frac{2\,\文本{基普}}{6} = 0.33333\,\text{基普} \)

\( V_{做} = sqrt{(v_{做,和})^ 2 + (v_{做,与})^ 2} \)

\( V_{做} = sqrt{(0.33333\,\文本{基普})^ 2 + (0.33333\,\文本{基普})^ 2} = 0.4714\,\text{基普} \)

This gives the shear stress on the anchor rod 作为:

\( f_v = \frac{V_{做}}{一个_{杆}} = frac{0.4714\,\文本{基普}}{0.19635\,\文本{在}^ 2} = 2.4008\,\text{KSI} \)

Because a plate washer is present, 一个 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. 参考 AISC 设计指南 1, 3rd Edition Section 4.3.3.

\( e = 0.5 \剩下( \压裂{t_{pw}}{2} + t_{BP} \对) = 0.5 \时代左( \压裂{0.25\,\文本{在}}{2} + 0.75\,\文本{在} \对) = 0.4375\,\text{在} \)

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:

\( z_{杆} = frac{\pi}{32} (D_A)^3 = \frac{\pi}{32} \次 (0.5\,\文本{在})^3 = 0.012272\,\text{在}^ 3 \)

\( f_t = \frac{V_{做} Ë}{z_{杆}} = frac{0.4714\,\文本{基普} \times 0.4375\,\text{在}}{0.012272\,\文本{在}^ 3} = 16.806\,\text{KSI} \)

ACI Anchor Rod Shear Capacity:

Following ACI 318-19 条款 17.7.1, the design strength is then determined. 一个 0.8 reduction factor is applied due to the presence of grout pads. The design capacity is therefore:

\( \非V_{至,这里} = 0.8 \φ 0.6 一个_{我知道,v} F_{乌塔} = 0.8 \次 0.65 \次 0.6 \times 0.1419\text{在}^2 \times 90\text{KSI} = 3.9845\text{基普} \)

作为备选, 的 SkyCiv Base Plate software allows the 0.8 simplification to be disabled, and use the actual grout pad thickness in the calculations. 在这种情况下, 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:

第一, 的 nominal shear and tensile stresses are determined for an A325 rod.

\( F_{NV} = 0.45 F_{ü,无} = 0.45 \次 120\ \文本{KSI} = 54\ \文本{KSI} \)

\( F_{恩特} = 0.75 F_{ü,无} = 0.75 \次 120\ \文本{KSI} = 90\ \文本{KSI} \)

The AISC method uses AISC 360-22 情商. J3-3a, which may be expressed to include the effects of axial stress. This is carried out as follows.

\( F’_{NV} = min left( 1.3 F_{NV} – \剩下( \压裂{F_{NV}}{\phi f_{恩特}} \对) f_t,\; F_{NV} \对) \)

\( F’_{NV} = min left( 1.3 \次 54\ \文本{KSI} – \剩下( \压裂{54\ \文本{KSI}}{0.75 \次 90\ \文本{KSI}} \对) \次 16.806\ \文本{KSI},\; 54\ \文本{KSI} \对) = 54\ \文本{KSI} \)

The design shear capacity from the AISC method is then calculated as:

\( \φR_{ñ,\mathrm{aisc}} = \phi F’_{NV} 一个_{杆} = 0.75 \次 54\ \文本{KSI} \次 0.19635\ \文本{在}可以假设为 7.9522\)

To ensure both methods are covered, the governing capacity is taken as the lesser of the two, 这是 3.98 基普.

\( \phi V_n = \min \left( \非V_{至,这里},\; \φR_{ñ,\mathrm{aisc}} \对) = min (3.9845\ \文本{基普},\; 7.9522\ \文本{基普}) = 3.9845\ \文本{基普} \)

Since the shear load per anchor rod is less than the governing anchor rod capacity in shear, 0.47 基普 < 3.98 基普, the design anchor rod shear capacity is 充足的.

设计概要

的 SkyCiv底板设计软件 可以自动为此设计示例生成逐步计算报告. 它还提供了执行的检查及其结果比率的摘要, 一目了然地使信息易于理解. 以下是示例摘要表, 报告中包括.

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