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 30 kN tension load, 3 kN Vy shear load, 和 6 kN Vz shear load.

给定数据:

柱:

列部分: W14x30
列区域: 5709.7 毫米²
列材料: A992

底盘:

基板尺寸: 12 在x 12 在
基板厚度: 1/2 在
底板材料: A36

灌浆:

灌浆厚度: 0 毫米

具体:

混凝土尺寸: 300 毫米× 500 毫米
混凝土厚度: 500 毫米
混凝土材料: 20.7 兆帕
破裂或无裂缝: 破裂

锚:

锚直径: 16 毫米
有效嵌入长度: 400 毫米
Anchor Ending: Circular Plate
嵌入式板直径: 70 毫米
嵌入式板厚度: 10 毫米
Steel Material: A325N
Threads in Shear Plane: Included

焊缝:

焊缝尺寸: 1/4 在
填充金属分类: E70XX

锚数据 (从 SkyCiv计算器):

注意:

The purpose of this design example is to demonstrate the step-by-step calculations for capacity checks involving concurrent shear and axial loads. Some of the required checks have already been discussed in the previous design examples. Please refer to the links provided in each section.

分步计算:

检查一下 #1: 计算焊接容量

To determine the weld capacity under simultaneous loading, we first need to calculate the weld demand due to the shear load and the weld demand due to the tension load. You may refer to this 链接 for the procedure to obtain the weld demands for shear, and this 链接 for the tension weld demands.

For this design, 的 weld demand at the web due to the tension load is found to be as follows, where the stress is expressed as 单位长度力.

\(r_{ü,\文本{普拉特桁架和普拉特桁架设计的技术研究}} = frac{T_{ü,\文本{锚}}}{由使用公式计算的最小值控制{\文本{效果}}} = frac{5\ \文本{千牛}}{93.142\ \文本{毫米}} = 0.053681\ \文本{千牛/毫米}\)

此外, 的 weld stress at any part of the column section due to the shear load is determined as:

\(v_{你} = frac{v_y}{L_{\文本{焊接}}} = frac{3\ \文本{千牛}}{1250.7\ \文本{毫米}} = 0.0023987\ \文本{千牛/毫米}\)

\(v_{到} = frac{v_z}{L_{\文本{焊接}}} = frac{6\ \文本{千牛}}{1250.7\ \文本{毫米}} = 0.0047973\ \文本{千牛/毫米}\)

Since there is a combination of tension and shear loads at the 普拉特桁架和普拉特桁架设计的技术研究, we need to obtain the resultant. Expressing this as force per unit length, 我们有:

\(r_u = sqrt{(r_{ü,\文本{普拉特桁架和普拉特桁架设计的技术研究}})^ 2 + (v_{你})^ 2 + (v_{到})^ 2}\)

\(r_u = sqrt{(0.053681\ \文本{千牛/毫米})^ 2 + (0.0023987\ \文本{千牛/毫米})^ 2 + (0.0047973\ \文本{千牛/毫米})^ 2}\)

\(r_u = 0.053949\ \文本{千牛/毫米}\)

为了 法兰, only shear stresses are present. 从而, the resultant is:

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

\(r_u = sqrt{(0.0023987\ \文本{千牛/毫米})^ 2 + (0.0047973\ \文本{千牛/毫米})^ 2} = 0.0053636\ \文本{千牛/毫米}\)

下一个, 我们计算 weld capacities. For the flange, we determine the angle θ 使用 电压 和 你 负载.

\( \theta = \tan^{-1}\!\剩下(\压裂{v_{你}}{v_{到}}\对) = \tan^{-1}\!\剩下(\压裂{0.0023987\ \文本{千牛/毫米}}{0.0047973\ \文本{千牛/毫米}}\对) = 0.46365\ \文本{工作} \)

所以, 的 kds factor and weld capacity are calculated using AISC 360-22 情商. J2-5 和 情商. J2-4.

\(钢底板设计欧洲规范{DS} = 1.0 + 0.5(\没有(\θ))^{1.5} = 1 + 0.5 \次 (\没有(0.46365\ \文本{工作}))^{1.5} = 1.1495\)

\(\phi r_{ñ,flg} = \phi\,0.6\,F_{EXX}\,E_w\,k_{DS} = 0.75 \次 0.6 \次 480\ \文本{兆帕} \次 4.95\ \文本{毫米} \次 1.1495 = 1.2291\ \文本{千牛/毫米}\)

For the web, we calculate the angle θ using a different formula. 注意 Vuy is used in the formula since it represents the load parallel to the weld axis.

\( \theta = \cos^{-1}\!\剩下(\压裂{v_{你}}{r_u}\对) = \cos^{-1}\!\剩下(\压裂{0.0023987\ \文本{千牛/毫米}}{0.053949\ \文本{千牛/毫米}}\对) = 1.5263\ \文本{工作} \)

使用 AISC 360-22 情商. J2-5 和 情商. J2-4, 的 kds factor and the resulting weld capacity are determined in the same manner.

\(钢底板设计欧洲规范{DS} = 1.0 + 0.5(\没有(\θ))^{1.5} = 1 + 0.5 \次 (\没有(1.5263\ \文本{工作}))^{1.5} = 1.4993\)

\(\phi r_{ñ,普拉特桁架和普拉特桁架设计的技术研究} = \phi\,0.6\,F_{EXX}\,E_w\,k_{DS} = 0.75 \次 0.6 \次 480\ \文本{兆帕} \次 4.95\ \文本{毫米} \次 1.4993 = 1.603\ \文本{千牛/毫米}\)

最后, we perform base metal checks for both the column and the base plate, then obtain the governing base metal capacity.

\( \phi r_{NBM,上校} = \phi\,0.6\,F_{ü,上校}\,t_{上校,half} = 0.75 \次 0.6 \次 448.2\ \文本{兆帕} \次 3.429\ \文本{毫米} = 0.6916\ \文本{千牛/毫米} \)

\( \phi r_{NBM,BP} = \phi\,0.6\,F_{ü,BP}\,t_{BP} = 0.75 \次 0.6 \次 400\ \文本{兆帕} \次 12\ \文本{毫米} = 2.1595\ \文本{千牛/毫米} \)

\( \phi r_{NBM} = \min\big(\phi r_{NBM,BP},\ \phi r_{NBM,上校}\big) = min(2.1595\ \文本{千牛/毫米},\ 0.6916\ \文本{千牛/毫米}) = 0.6916\ \文本{千牛/毫米} \)

We then compare the fillet weld capacities 和 base metal capacities for the weld demands at the flanges and web separately.

以来 0.053949 千牛/毫米 < 0.6916 千牛/毫米, 焊接容量是 充足的.

检查一下 #2: 计算由于张力负载而导致的基本板弯曲屈服能力

A design example for the base plate flexural yielding capacity is already discussed in the Base Plate Design Example for Tension. Please refer to this link for the step-by-step calculation.

检查一下 #3: 计算锚杆拉伸能力

A design example for the anchor rod tensile capacity is already discussed in the Base Plate Design Example for Tension. Please refer to this link for the step-by-step calculation. Please refer to this link for the step-by-step calculation.

检查一下 #4: 计算张力的混凝土突破能力

A design example for the capacity of the concrete in tension breakout is already discussed in the Base Plate Design Example for Tension. Please refer to this link for the step-by-step calculation. Please refer to this link for the step-by-step calculation.

检查一下 #5: 计算锚推拉力

A design example for the anchor pull out capacity is already discussed in the Base Plate Design Example for Tension. Please refer to this link for the step-by-step calculation. Please refer to this link for the step-by-step calculation.

检查一下 #6: 计算嵌入板弯曲能力

A design example for the supplementary check on the embedded plate flexural yielding capacity is already discussed in the Base Plate Design Example for Tension. Please refer to this link for the step-by-step calculation.

检查一下 #7: 计算Y方向的侧面井喷容量

计算 Side-Face Blowout (SFBO) 容量, we first determine the total tension force on the anchors closest to the edge. For this check, we will evaluate the capacity of the edge along the Y-direction.

Since the failure cone projections of the SFBO along the Y-direction overlap, the anchors are treated as an 锚群.

The total tension demand of the anchor group is calculated as:

\(N_{做} = 左(\压裂{n_x}{n_{一个,Ť}}\对) n_{和,G1} = 左(\压裂{30\ \文本{千牛}}{6}\对) \次 3 = 15\ \文本{千牛}\)

下一个, 我们确定 边缘距离:

\(C_{与,\分} = min(C_{\文本{剩下},G1},\ C_{\文本{对},G1}) = min(100\ \文本{毫米},\ 200\ \文本{毫米}) = 100\ \文本{毫米}\)

\(C_{和,\分} = min(C_{\文本{最佳},G1},\ C_{\文本{底部},G1}) = min(150\ \文本{毫米},\ 150\ \文本{毫米}) = 150\ \文本{毫米}\)

Using these edge distances, 我们计算 anchor group capacity in accordance with ACI 318-19 情商. (17.6.4.1).

\(N_{作为} = 左(\压裂{1 + \dfrac{C_{和,\分}}{C_{与,\分}}}{4} + \压裂{s_{和,和,G1}}{6\,C_{与,\分}}\对)\次 13 \时代左(\压裂{C_{与,\分}}{1\ \文本{毫米}}\对)\次 sqrt{\压裂{一个_{brg}}{\文本{毫米}^ 2}}\ \lambda_a sqrt{\压裂{f_c}{\文本{兆帕}}}\次 0.001\ \文本{千牛}\)

\(N_{作为} = 左(\压裂{1 + \dfrac{150\ \文本{毫米}}{100\ \文本{毫米}}}{4} + \压裂{200\ \文本{毫米}}{6\次 100\ \文本{毫米}}\对)\次 13 \时代左(\压裂{100\ \文本{毫米}}{1\ \文本{毫米}}\对)\次 sqrt{\压裂{3647.4\ \文本{毫米}^ 2}{1\ \文本{毫米}^ 2}}\次 1 \次 sqrt{\压裂{20.68\ \文本{兆帕}}{1\ \文本{兆帕}}}\次 0.001\ \文本{千牛}\)

\(N_{作为} = 342.16\ \文本{千牛}\)

In the original equation, a reduction factor is applied when the anchor spacing is less than 6ca₁, assuming the headed anchors have sufficient edge distance. 然而, in this design example, 以来 ca₂ < 3ca₁, the SkyCiv calculator applies an additional reduction factor to account for the reduced edge capacity.

最后, 的 design SFBO capacity 是:

\(\φN_{作为} = \phi\,N_{作为} = 0.7 \次 342.16\ \文本{千牛} = 239.51\ \文本{千牛}\)

以来 15 千牛 < 239.51 千牛, the SFBO capacity along the Y-direction is 充足的.

检查一下 #8: 计算Z方向的侧面井喷容量

Following the same approach as in 检查一下 #7, the total tension demand of the anchor group for the anchors closest to the Z-direction edge is:

\(N_{做} = 左(\压裂{n_x}{n_{一个,Ť}}\对)n_{与,G1} = 左(\压裂{30\ \文本{千牛}}{6}\对)\次 2 = 10\ \文本{千牛}\)

的 边缘距离 are calculated as:

\(C_{和,\分} = min(C_{\文本{最佳},G1},\ C_{\文本{底部},G1}) = min(150\ \文本{毫米},\ 350\ \文本{毫米}) = 150\ \文本{毫米}\)

\(C_{与,\分} = min(C_{\文本{剩下},G1},\ C_{\文本{对},G1}) = min(100\ \文本{毫米},\ 100\ \文本{毫米}) = 100\ \文本{毫米}\)

的 nominal SFBO capacity is then determined as:

\(N_{作为} = 左(\压裂{1 + \dfrac{C_{与,\分}}{C_{和,\分}}}{4} + \压裂{s_{和,与,G1}}{6\,C_{和,\分}}\对)\次 13 \时代左(\压裂{C_{和,\分}}{1\ \文本{毫米}}\对)\次 sqrt{\压裂{一个_{brg}}{\文本{毫米}^ 2}}\ \lambda_a sqrt{\压裂{f_c}{\文本{兆帕}}}\次 0.001\ \文本{千牛}\)

\(N_{作为} = 左(\压裂{1 + \dfrac{100\ \文本{毫米}}{150\ \文本{毫米}}}{4} + \压裂{100\ \文本{毫米}}{6\次 150\ \文本{毫米}}\对)\次 13 \时代左(\压裂{150\ \文本{毫米}}{1\ \文本{毫米}}\对)\次 sqrt{\压裂{3647.4\ \文本{毫米}^ 2}{1\ \文本{毫米}^ 2}}\次 1 \次 sqrt{\压裂{20.68\ \文本{兆帕}}{1\ \文本{兆帕}}}\次 0.001\ \文本{千牛}\)

\(N_{作为} = 282.65\ \文本{千牛}\)

Since the edge distance ca₂ is still less than 3ca₁, the same modified reduction factor is applied.

最后, 的 design SFBO capacity 是:

\(\φN_{作为} = \phi\,N_{作为} = 0.7 \次 282.65\ \文本{千牛} = 197.86\ \文本{千牛}\)

以来 10 千牛 < 197.86 千牛, the SFBO capacity along the Z-direction 是 充足的.

检查一下 #9: Calculate breakout capacity (vy剪)

A design example for the concrete breakout capacity in Vy shear is already discussed in the Base Plate Design Example for Shear. Please refer to this link for the step-by-step calculation.

检查一下 #10: Calculate breakout capacity (VZ剪)

A design example for the concrete breakout capacity in Vy shear is already discussed in the Base Plate Design Example for Shear. Please refer to this link for the step-by-step calculation.

检查一下 #11: Calculate pryout capacity (vy剪)

A design example for the capacity of the concrete against pryout failure due to Vy shear is already discussed in the Base Plate Design Example for Shear. Please refer to this link for the step-by-step calculation.

检查一下 #12: Calculate pryout capacity (VZ剪)

A design example for the capacity of the concrete against pryout failure due to Vy shear is already discussed in the Base Plate Design Example for Shear. Please refer to this link for the step-by-step calculation.

检查一下 #13: 计算锚杆剪切能力

A design example for the anchor rod shear capacity is already discussed in the Base Plate Design Example for Shear. Please refer to this link for the step-by-step calculation.

检查一下 #14: Calculate anchor rod shear and axial capacity (AISC)

To determine the capacity of the anchor rod under combined shear and axial loads, 我们用 AISC 360-22 情商. J3-3A. In this calculator, the equation is rearranged to express the result as the modified shear strength instead.

的 shear demand 被定义为 shear load per anchor.

\(V_{做} = V_{做} = 2.5\ \文本{千牛}\)

的 tension demand is expressed as the tensile stress in the anchor rod.

\(F_{ut} = frac{N_{做}}{一个_{杆}} = frac{5\ \文本{千牛}}{201.06\ \文本{毫米}^ 2} = 24.868\ \文本{兆帕}\)

的 modified shear capacity of the anchor rod is then calculated as:

\(f’_{NV} = \min\!\剩下(1.3\,F_{NV} – \剩下(\压裂{F_{NV}}{\phi f_{恩特}}\对) F_{ut},\; F_{NV}\对)\)

\(f’_{NV} = \min\!\剩下(1.3\次 232.69\ \文本{兆帕} – \剩下(\压裂{232.69\ \文本{兆帕}}{0.75\次 387.82\ \文本{兆帕}}\对)\次 24.868\ \文本{兆帕},\; 232.69\ \文本{兆帕}\对) = 232.69\ \文本{兆帕}\)

We then multiply this strength by the anchor area 使用 AISC 360-22 情商. J3-2.

\(\φR_{ñ,\文本{AISC}} = phi f’_{NV} 一个_{\文本{杆}} = 0.75 \次 232.69\ \文本{兆帕} \次 201.06\ \文本{毫米}可以假设为 35.09\ \文本{千牛}\)

以来 2.5 千牛 < 35.09 千牛, the anchor rod capacity is 充足的.

检查一下 #15: Calculate interaction checks (ACI)

When checking the anchor rod capacity under combined shear and tension loads using ACI, a different approach is applied. For completeness, we also perform the ACI interaction checks in this calculation, which include other concrete interaction checks 以及.

Here are the resulting ratios for all ACI tension checks:

And here are the resulting ratios for all ACI shear checks:

We get the check with the largest ratio and compare it to the maximum interaction ratio using ACI 318-19 情商. 17.8.3.

\(一世_{int} = frac{N_{做}}{\phi N_n} + \压裂{V_{做}}{\phi V_n} = frac{30}{47.749} + \压裂{6}{17.921} = 0.96308\)

以来 0.96 < 1.2, the interaction check is 充足的.

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