基本板设计示例使用en 1993-1-8-2005, 在 1993-1-1-2005 和EN 1992-1-1-2004
问题陈述:
确定设计的列板连接是否足够 50-kN tension load, 4-kN Vy shear load, 和 2-kN Vz shear load.
给定数据:
柱:
列部分: CHS193.7×10
列区域: 5770.0 mm²
列材料: S460
底盘:
基板尺寸: 300mm x 300mm
基板厚度: 18毫米
底板材料: S235
灌浆:
灌浆厚度: 0 毫米
具体:
混凝土尺寸: 350mm x 350mm
混凝土厚度: 400 毫米
混凝土材料: C35/45
破裂或无裂缝: 破裂
锚:
锚直径: 16 毫米
有效嵌入长度: 350 毫米
嵌入式板直径: 70 毫米
嵌入式板厚度: 10 毫米
锚材料: 4.8
焊缝:
焊接类型: 鱼片
焊缝尺寸: 7毫米
填充金属分类: E42
锚数据 (从 SkyCiv计算器):
笔记:
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
The full tensile load is resisted by the entire weld section, 而 shear load components are distributed only to a portion of the total weld length. This portion is determined by projecting a 90° 扇区 from the center of the column to its circumference. 因此, 只要 half of the total circumference is designed to resist the shear load.
We first compute the 总焊接长度 和 portion of the weld within the 90° projection.
\(L_{焊接,full} = \pi d_{上校} = \pi \times 193.7\ \文本{毫米} = 608.53\ \文本{毫米}\)
\(L_{焊接} = frac{\pi d_{上校}}{2} = frac{\pi times 193.7\ \文本{毫米}}{2} = 304.26\ \文本{毫米}\)
下一个, 我们计算 resultant shear load.
\(V_r = \sqrt{(v_y)^ 2 + (v_z)^ 2} = sqrt{(4\ \文本{千牛})^ 2 + (2\ \文本{千牛})^ 2} = 4.4721\ \文本{千牛}\)
We then compute the 普通的 和 shear stresses, taking into account the assumed load distribution.
\( \sigma_{\人} = frac{n_x}{L_{焊接,full}\,a\,\sqrt{2}} = frac{40\ \文本{千牛}}{608.53\ \文本{毫米} \次 4.95\ \文本{毫米} \次 sqrt{2}} = 9.39\ \文本{兆帕} \)
\( \你的_{\人} = frac{n_x}{L_{焊接,full}\,a\,\sqrt{2}} = frac{40\ \文本{千牛}}{608.53\ \文本{毫米} \次 4.95\ \文本{毫米} \次 sqrt{2}} = 9.39\ \文本{兆帕} \)
\( \你的_{\平行} = frac{V_r}{L_{焊接}\,一个} = frac{4.4721\ \文本{千牛}}{304.26\ \文本{毫米} \次 4.95\ \文本{毫米}} = 2.9693\ \文本{兆帕} \)
在那之后, 我们计算 综合压力 使用 在 1993-1-8:2005 情商. (4.1).
\(F_{w,ED1} = sqrt{(\sigma_{\人})^ 2 + 3\big((\你的_{\人})^ 2 + (\你的_{\平行})^2\big)}\)
\(F_{w,ED1} = sqrt{(9.39\ \文本{兆帕})^ 2 + 3\big((9.39\ \文本{兆帕})^ 2 + (2.9693\ \文本{兆帕})^2\big)}\)
\(F_{w,ED1} = 19.471\ \文本{兆帕}\)
与此同时, 我们确定 stress on the base metal using the same equation.
\(F_{w,ED2} = \sigma_{\人} = 9.39\ \文本{兆帕}\)
下一个, 我们计算 weld capacity. We first determine the ultimate tensile strength (fu) 的 weaker material, and then use 在 1993-1-8:2005 情商. (4.1) to obtain the fillet weld resistance 和 base metal resistance.
\(f_u = \min\!\剩下(F_{ü,\文本{上校}},\ F_{ü,\文本{BP}},\ F_{ü,w}\对) = \min\!\剩下(550\ \文本{兆帕},\ 360\ \文本{兆帕},\ 500\ \文本{兆帕}\对) = 360\ \文本{兆帕}\)
\(F_{w,Rd1} = frac{f_u}{\beta_w\,(\伽玛_{M2,\text{焊接}})} = frac{360\ \文本{兆帕}}{0.8 \次 (1.25)} = 360\ \文本{兆帕}\)
\(F_{w,Rd2} = frac{0.9\,f_u}{\伽玛_{M2,\text{焊接}}} = frac{0.9 \次 360\ \文本{兆帕}}{1.25} = 259.2\ \文本{兆帕}\)
以来 19.471 兆帕 < 360 兆帕, 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: 计算张力的混凝土突破能力
A design example for the capacity of the concrete in breakout due to tension load 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 #4: 计算锚推拉力
A design example for the anchor pullout 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 #5: 计算Y方向的侧面井喷容量
A design example for the side-face blowout capacity in Y-direction 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 #6: 计算Z方向的侧面井喷容量
A design example for the side-face blowout capacity in Z-direction 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: Calculate base plate bearing capacity at anchor holes (vy剪)
A design example for the base plate bearing capacity in the anchor holes for Vy shear is already discussed in the Base Plate Design Example for Compression and Shear. Please refer to this link for the step-by-step calculation.
检查一下 #8: Calculate base plate bearing capacity at anchor holes (VZ剪)
A design example for the base plate bearing capacity in the anchor holes for Vz shear is already discussed in the Base Plate Design Example for Compression and Shear. Please refer to this link for the step-by-step calculation.
检查一下 #9: Calculate concrete breakout capacity (vy剪)
A design example for the concrete capacity in breakout 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 #10: Calculate concrete breakout capacity (VZ剪)
A design example for the concrete capacity in breakout failure due to Vz 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
A design example for the concrete pryout 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 #12: 计算锚杆剪切能力
The effect of the tension load on the anchor rod capacity is considered in this check if the shear force acts with a lever arm. 然而, 在这个例子中, the shear acts without a lever arm. 因此, the interaction between shear and tensile stresses on the anchor rod will be evaluated separately in the interaction check.
For the step-by-step calculation of the shear capacity without a lever arm, 请参考此链接.
The SkyCiv Base Plate Design software can perform all the necessary checks to determine whether the shear load acts with or without a lever arm. 你可以 try out the free tool 今天.
检查一下 #13: Calculate anchor steel interaction check
我们使用 在 1992-4:2018 桌子 7.3 情商. (7.54) 评估 interaction between the shear and tensile stresses on the anchor rod. By substituting the tensile stress and capacity as well as the shear stress and capacity into the equation, 结果 interaction value 是:
\(一世_{int} = 左(\压裂{N_{埃德}}{N_{路,s}}\对)^ 2 + \剩下(\压裂{V_{埃德}}{V_{路,s}}\对)^2)
\(一世_{int} = 左(\压裂{10\ \文本{千牛}}{49.22\ \文本{千牛}}\对)^ 2 + \剩下(\压裂{1.118\ \文本{千牛}}{38.604\ \文本{千牛}}\对)可以假设为 0.042117\)
以来 0.042 < 1.0, the anchor rod steel failure interaction check is 充足的.
检查一下 #14: Calculate concrete failure interaction check
SkyCiv 还使用一些参数自动计算地面雪荷载 interaction check is required for concrete failures under simultaneous shear and tensile loading. 为了这, 我们用 在 1992-4:2018 桌子 7.3 情商. (7.55) 和 情商. (7.56).
Here are the resulting ratios for all tensile checks.
Here are the resulting ratios for all shear checks.
第一, we check using 情商. (7.55) and compare the result to the maximum interaction limit of 1.0.
\(一世_{\文本{case1}} = 左(\剩下(\压裂{N_{埃德}}{N_{路}}\对)^{1.5}\对) + \剩下(\剩下(\压裂{V_{埃德}}{V_{路}}\对)^{1.5}\对)\)
\(一世_{\文本{case1}} = 左(\剩下(\压裂{40}{45.106}\对)^{1.5}\对) + \剩下(\剩下(\压裂{4.1231}{14.296}\对)^{1.5}\对) = 0.99\)
下一个, we check using 情商. (7.56) and compare the result to the maximum interaction limit of 1.2.
\(一世_{\文本{案例2}} = frac{N_{埃德}}{N_{路}} + \压裂{V_{埃德}}{V_{路}} = frac{40}{45.106} + \压裂{4.1231}{14.296} = 1.1752\)
以来 0.99 < 1.0 和 1.175 < 1.2, 的 concrete failure interaction check 是 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.
SkyCiv样本报告
单击此处下载示例报告.
购买基板软件
单独购买基本板设计模块的完整版本，而没有任何其他SkyCiv模块. 这为您提供了底板设计的完整结果, 包括详细报告和更多功能.
