使用CSA S16的底板设计示例:19 和CSA A23.3:19
问题陈述
确定设计的列板连接是否足够 您= 5-kn 和 vz = 5-kn 剪力.
给定数据
柱:
列部分: HP200x54
列区域: 6840.0 毫米2
列材料: 350w ^
底盘:
基板尺寸: 400 毫米× 400 毫米
基板厚度: 13 毫米
底板材料: 300w ^
灌浆:
灌浆厚度: 13 毫米
具体:
混凝土尺寸: 450 毫米× 450 毫米
混凝土厚度: 380 毫米
混凝土材料: 20.68 兆帕
破裂或无裂缝: 破裂
锚:
锚直径: 12.7 毫米
有效嵌入长度: 300 毫米
板垫圈厚度: 0 毫米
板垫圈连接: 没有
焊缝:
焊缝尺寸: 8 毫米
填充金属分类: E43xx
锚数据 (从 SkyCiv计算器):
SkyCiv 免费工具中的模型
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定义
负载路径:
The design follows the CSA A23.3:2019 standards and the recommendations of AISC 设计指南 1, 3RD版. 施加到色谱柱的剪切载荷通过焊缝转移到底板上, 然后通过 锚杆. 在此示例中不考虑摩擦和剪切凸耳, 由于这些机制在当前软件中不支持.
默认, 的 applied shear load is distributed to all anchors, either through the use of welded plate washers or by other engineering means. The load carried by each anchor is determined using the three (3) cases stated in CSA A23.3:2019 Clause D.7.2.1 and Figure D.13. Each anchor then transfers the load to the supporting concrete below. The load distribution in accordance with these references is also used when checking the anchor steel shear strength to ensure continuity in the load transfer assumptions.
作为备选, 该软件允许简化，更保守的假设, 在哪里 entire shear load is assigned only to the anchors nearest the loaded edge. 在这种情况下, 仅在这些边缘锚点上进行剪切能力检查, 确保保守解决潜在的剪切故障.
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 混凝土剪切突破 和 具体的剪切撬 失败.
一个 锚群 被定义为两个或多个锚，并具有重叠的预防阻力区域. 在这种情况下, 锚一起行动, 并且它们的组合电阻被检查针对该组的施加载荷.
一个 单锚 被定义为锚点，其投影阻力区域不会与其他任何. 在这种情况下, 锚独自行动, 并直接检查锚上施加的剪切力，以其单独的电阻检查.
在评估剪切相关的故障模式时.
分步计算
检查一下 #1: 计算焊接容量
第一步是计算 总焊接长度 可抵抗剪切. The total weld length, Lweld , is obtained by summing the welds on all sides.
\( L_{焊接} = 2b_f + 2(d_{上校} – 2T_F – 2r_{上校}) + 2(B_F – t_w – 2r_{上校}) \)
\( L_{焊接} = 2 \times 207,\text{毫米} + 2 \次 (204,\文本{毫米} – 2 \times 11.3,\text{毫米} – 2 \times 9.7,\text{毫米}) + 2 \次 (207,\文本{毫米} – 11.3,\文本{毫米} – 2 \times 9.7,\text{毫米}) = 1090.6,\text{毫米} \)
使用此焊接长度, Y中的施加力- 和z方向分配以确定平均值 单位长度的剪切力 在每个方向:
\( v_{风云} = frac{v_y}{L_{焊接}} = frac{5,\文本{千牛}}{1090.6,\文本{毫米}} = 0.0045846,\text{千牛/毫米} \)
\( v_{fz} = frac{v_z}{L_{焊接}} = frac{5,\文本{千牛}}{1090.6,\文本{毫米}} = 0.0045846,\text{千牛/毫米} \)
的 resultant shear demand per unit length is then determined using the square root of the sum of the squares (SRSS) 方法.
\( v_f = \sqrt{\剩下((v_{风云})^2\right) + \剩下((v_{fz})^2\right)} \)
\( v_f = \sqrt{\剩下((0.0045846,\文本{千牛/毫米})^2\right) + \剩下((0.0045846,\文本{千牛/毫米})^2\right)} = 0.0064836,\text{千牛/毫米} \)
下一个, 焊接容量是使用 CSA S16:19 条款 13.13.2.2, 将定向强度系数视为 kds=1.0 to be conservative. The weld capacity for an 8mm weld on both the flanges and web is:
\( v_r = 0.67\phi t_{w,法兰}X_u = 0.67 \次 0.67 \times 5.657,\text{毫米} \times 430,\text{兆帕} = 1.092,\text{千牛/毫米} \)
\( v_r = 0.67\phi t_{w,普拉特桁架和普拉特桁架设计的技术研究}X_u = 0.67 \次 0.67 \times 5.657,\text{毫米} \times 430,\text{兆帕} = 1.092,\text{千牛/毫米} \)
执政者 角焊缝产能 是:
\( v_{[R,fillet} = min(v_r, v_i) = min(1.092\,\文本{千牛/毫米}, 1.092\,\文本{千牛/毫米}) = 1.092\,\text{千牛/毫米} \)
For this welded connection, the electrode strength does not overmatch the base metal strengths. 因此, the base metal check is not governing and does not need to be performed.
以来 0.0064 千牛/毫米 < 1.092 千牛/毫米, the factored weld capacity is 充足的.
检查一下 #2: 计算由于Vy剪切的混凝土突破能力
垂直边缘容量:
Using the ca1 values of each anchor to project the failure cones, the software identified that the failure cones of these anchors overlap. 因此, we can treat them as an 锚群. Referring to CSA A23.3:19 图. D.13, because s<ca1 , 我们用 案件 3 to determine the resistance of the anchor group against shear breakout. 此外, the support was determined 不是 to be a narrow member, so the ca1 distance is used directly without modification.
案件 3:
The total force to be considered for Case 3 是个 full shear force along the Vy direction. This shear force is applied to the front anchors only.
\( V_{fa perp,case3} = V_y = 5\,\text{千牛} \)
To calculate the capacity of the anchor group, 我们用 CSA A23.3:19 Clause D.7.2. 的 maximum projected area for a single anchor is calculated using Equation D.34 with the actual ca dimension.
\( 一个_{压控振荡器} = 4.5(C_{a1,g1})可以假设为 4.5 \次 (180\,\文本{毫米})^2 = 145800\,\text{毫米}^ 2 \)
To get the actual projected area of the anchor group, 我们首先确定 width of the failure surface:
\( b_{VC} = min(C_{\文本{剩下},G1}, 1.5C_{a1,g1}) + (\分(s_{\文本{和},X,G1}, 3C_{a1,g1}(n_{X,G1} – 1))) + \分(C_{\文本{对},G1}, 1.5C_{a1,g1}) \)
\( b_{VC} = min(175\,\文本{毫米}, 1.5 \times 180\,\text{毫米}) + (\分(100\,\文本{毫米}, 3 \times 180\,\text{毫米} \次 (2-1))) + \分(175\,\文本{毫米}, 1.5 \times 180\,\text{毫米}) \)
\( b_{VC} = 450\,\text{毫米} \)
的 height of the failure surface 是:
\( H_{VC} = min(1.5C_{a1,g1}, t_{\文本{浓}}) = min(1.5 \times 180\,\text{毫米}, 380\,\文本{毫米}) = 270\,\text{毫米} \)
这给了 total area 作为:
\( 一个_{VC} = b_{VC}.H_{VC} = 450\,\text{毫米} \times 270\,\text{毫米} = 121500\,\text{毫米}^ 2 \)
然后我们使用 CSA A23.3:19 Equations D.35 and D.36 to obtain the basic single anchor breakout strength.
\( V_{br1} = 0.58\left(\压裂{\分(这, 8D_A)}{D_A}\对)^{0.2}\sqrt{\压裂{D_A}{毫米}}\phi\lambda_a\sqrt{\压裂{f'_c}{兆帕}}\剩下(\压裂{C_{a1,g1}}{毫米}\对)^{1.5}[R(ñ) \)
\( V_{br1} = 0.58 \时代左(\压裂{\分(300\,\文本{毫米}, 8 \times 12.7\,\text{毫米})}{12.7\,\文本{毫米}}\对)^{0.2} \次 sqrt{\压裂{12.7\,\文本{毫米}}{1\,\文本{毫米}}} \次 0.65 \次 1 \次 sqrt{\压裂{20.68\,\文本{兆帕}}{1\,\文本{兆帕}}} \时代左(\压裂{180\,\文本{毫米}}{1\,\文本{毫米}}\对)^{1.5} \次 1 \次0.001 ， text{千牛} \)
\( V_{br1} = 22.364\,\text{千牛} \)
\( V_{br2} = 3.75\lambda_a\phi\sqrt{\压裂{f'_c}{兆帕}}\剩下(\压裂{C_{a1,g1}}{毫米}\对)^{1.5}[R(ñ) \)
\( V_{br2} = 3.75 \次 1 \次 0.65 \次 sqrt{\压裂{20.68\,\文本{兆帕}}{1\,\文本{兆帕}}} \时代左(\压裂{180\,\文本{毫米}}{1\,\文本{毫米}}\对)^{1.5} \次 1 \次0.001 ， text{千牛} = 26.769\,\text{千牛} \)
The governing capacity between the two conditions is:
\( V_{br} = min(V_{\文本{br1}}, V_{\文本{br2}}) = min(22.364\,\文本{千牛}, 26.769\,\文本{千牛}) = 22.364\,\text{千牛} \)
下一个, we calculate the eccentricity factor, 边缘效应因子, and thickness factor using CSA A23.3:19 Clauses D.7.2.5, D.7.2.6, and D.7.2.8.
的 偏心率因子 是:
\( \psi_{欧共体,V} = min 左(1.0, \压裂{1}{1 + \压裂{2和’_N}{3C_{a1,g1}}}\对) = min 左(1, \压裂{1}{1 + \压裂{2\times0}{3\times180\,\text{毫米}}}\对) = 1 \)
的 边缘效应因子 是:
\( \psi_{编辑,V} = min 左(1.0, 0.7 + 0.3\剩下(\压裂{C_{a2,g1}}{1.5C_{a1,g1}}\对)\对) = min 左(1, 0.7 + 0.3 \时代左(\压裂{175\,\文本{毫米}}{1.5 \times 180\,\text{毫米}}\对)\对) = 0.89444 \)
的 厚度因子 是:
\( \psi_{H,V} = max left(\sqrt{\压裂{1.5C_{a1,g1}}{t_{\文本{浓}}}}, 1.0\对) = max left(\sqrt{\压裂{1.5 \times 180\,\text{毫米}}{380\,\文本{毫米}}}, 1\对) = 1 \)
最后, the breakout strength of the anchor group, 计算使用 CSA A23.3:19 Clause D.7.2.1, 是:
\( V_{cbg\perp} = 左(\压裂{一个_{VC}}{一个_{压控振荡器}}\对)\psi_{欧共体,V}\psi_{编辑,V}\psi_{C,V}\psi_{H,V}V_{br} \)
\( V_{cbg\perp} = 左(\压裂{121500\,\文本{毫米}^ 2}{145800\,\文本{毫米}^ 2}\对) \次 1 \次 0.89444 \次 1 \次 1 \times 22.364\,\text{千牛} = 16.669\,\text{千牛} \)
The calculated capacity for Vy shear in the perpendicular direction 是 16.669 千牛.
平行边缘容量:
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 involved are different due to the new failure cone projection. 基于下图, 的 failure cone projections overlap; 因此, the anchors are again treated as an 锚群.
案件 3:
The Case to use is still 案件 3 since s<ca1. 因此, the load taken by this anchor group is the full Vy shear load.
\( V_{fa perp,case3} = V_y = 5\,\text{千牛} \)
We then follow the same steps as for the perpendicular capacity.
The failure surface for an individual anchor 是:
\( 一个_{压控振荡器} = 4.5(C_{a1,g1})可以假设为 4.5 \次 (175\,\文本{毫米})^2 = 137810\,\text{毫米}^ 2 \)
的 actual failure surface 锚群是:
\( b_{VC} = min(C_{\文本{底部},G1}, 1.5C_{a1,g1}) + (\分(s_{\文本{和},和,G1}, 3C_{a1,g1}(n_{和,G1} – 1))) + \分(C_{\文本{最佳},G1}, 1.5C_{a1,g1}) \)
\( b_{VC} = min(180\,\文本{毫米}, 1.5 \times 175\,\text{毫米}) + (\分(90\,\文本{毫米}, 3 \times 175\,\text{毫米} \次 (2-1))) + \分(180\,\文本{毫米}, 1.5 \times 175\,\text{毫米}) \)
\( b_{VC} = 450\,\text{毫米} \)
\( H_{VC} = min(1.5C_{a1,g1}, t_{\文本{浓}}) = min(1.5 \times 175\,\text{毫米}, 380\,\文本{毫米}) = 262.5\,\text{毫米} \)
\( 一个_{VC} = b_{VC}H_{VC} = 450\,\text{毫米} \times 262.5\,\text{毫米} = 118130\,\text{毫米}^ 2 \)
相似地, 的 basic single anchor breakout 优势 are calculated as follows:
\( V_{br1} = 0.58\left(\压裂{\分(这, 8D_A)}{D_A}\对)^{0.2}\sqrt{\压裂{D_A}{毫米}}\phi\lambda_a\sqrt{\压裂{f'_c}{兆帕}}\剩下(\压裂{C_{a1,g1}}{毫米}\对)^{1.5}[R(ñ) \)
\( V_{br1} = 0.58 \时代左(\压裂{\分(300\,\文本{毫米}, 8 \times 12.7\,\text{毫米})}{12.7\,\文本{毫米}}\对)^{0.2} \次 sqrt{\压裂{12.7\,\文本{毫米}}{1\,\文本{毫米}}} \次 0.65 \次 1 \次 sqrt{\压裂{20.68\,\文本{兆帕}}{1\,\文本{兆帕}}} \时代左(\压裂{175\,\文本{毫米}}{1\,\文本{毫米}}\对)^{1.5} \次 1 \次0.001 ， text{千牛} \)
\( V_{br1} = 21.438\,\text{千牛} \)
\( V_{br2} = 3.75\lambda_a\phi\sqrt{\压裂{f'_c}{兆帕}}\剩下(\压裂{C_{a1,g1}}{毫米}\对)^{1.5}[R(ñ) \)
\( V_{br2} = 3.75 \次 1 \次 0.65 \次 sqrt{\压裂{20.68\,\文本{兆帕}}{1\,\文本{兆帕}}} \时代左(\压裂{175\,\文本{毫米}}{1\,\文本{毫米}}\对)^{1.5} \次 1 \次0.001 ， text{千牛} = 25.661\,\text{千牛} \)
的 governing strength 是:
\( V_{br} = min(V_{\文本{br1}}, V_{\文本{br2}}) = min(21.438\,\文本{千牛}, 25.661\,\文本{千牛}) = 21.438\,\text{千牛} \)
然后我们计算 偏心率因子 和 厚度因子:
\( \psi_{欧共体,V} = min 左(1.0, \压裂{1}{1 + \压裂{2和’_N}{3C_{a1,g1}}}\对) = min 左(1, \压裂{1}{1 + \压裂{2\times0}{3\times175\,\text{毫米}}}\对) = 1 \)
\( \psi_{H,V} = max left(\sqrt{\压裂{1.5C_{a1,g1}}{t_{\文本{浓}}}}, 1.0\对) = max left(\sqrt{\压裂{1.5 \times 175\,\text{毫米}}{380\,\文本{毫米}}}, 1\对) = 1 \)
为了 突破边缘效应因子, we take it as 1.0 per CSA A23.3:19 Clause D.7.2.1c. 此外, the value of the breakout capacity for the perpendicular edge is taken as twice the calculated value using Equation D.33 (for an anchor group).
的 归纳 breakout capacity of the anchor group 是:
\( V_{cbgr\parallel} = 2\left(\压裂{一个_{VC}}{一个_{压控振荡器}}\对)\psi_{欧共体,V}\psi_{编辑,V}\psi_{C,V}\psi_{H,V}V_{br} \)
\( V_{cbgr\parallel} = 2 \时代左(\压裂{118130\,\文本{毫米}^ 2}{137810\,\文本{毫米}^ 2}\对) \次 1 \次 1 \次 1 \次 1 \times 21.438\,\text{千牛} = 36.752\,\text{千牛} \)
- 为了 perpendicular edge 失败, 以来 5 千牛 < 16.7 千牛, 混凝土剪切突破能力是 充足的.
- 为了 parallel edge 失败, 以来 5 千牛 < 36.8 千牛, 混凝土剪切突破能力是 充足的.
计算由于VZ剪切而导致的混凝土突破能力
The base plate is also subjected to Vz shear, so the failure edges perpendicular and parallel to the Vz shear must be checked. 使用相同的方法, 垂直和平行容量计算为 16.6 kN and 37.3 千牛, 分别.
垂直边缘:
平行边缘:
然后将这些能力与所需的优势进行比较.
- 为了 perpendicular edge 失败, 以来 5 千牛 < 16.6 千牛, the factored concrete shear breakout capacity is 充足的.
- 为了 parallel edge failure, 以来 5 千牛 < 37.3 千牛, the factored concrete shear breakout capacity is 充足的.
检查一下 #4: 计算具体的撬动能力
The concrete cone for pryout failure is the same cone used in the tensile breakout check. 计算剪切撬能的能力, 的 标称拉伸突破强度 of the single anchors or anchor group must first be determined. Detailed calculations for the tensile breakout check are already covered in the 张力负载的SkyCiv设计示例 and will not be repeated here.
It is important to note that the anchor group determination for shear breakout is different from that for shear pryout. The anchors in the design must still be checked to determine whether they act as a group or as single anchors. The classification of the support as a narrow section must also be verified and should follow the same conditions used for tension breakout.
According to the SkyCiv software, the nominal tensile breakout strength of the anchor group is 60.207 千牛. 撬动因素 2.0, 的 factored pryout capacity 是:
\( V_{cpgr} 检查锚容量{cp}N_{CBR} = 2 \times 60.207\,\text{千牛} = 120.41\,\text{千牛} \)
所需的强度是 resultant of the applied shear loads. 由于所有锚都属于一个组, 将总剪切分配给组.
\( V_{fa} = sqrt{((v_y)^ 2) + ((v_z)^ 2)} = sqrt{((5\,\文本{千牛})^ 2) + ((5\,\文本{千牛})^ 2)} = 7.0711\,\text{千牛} \)
\( V_{fa} = 左(\压裂{V_{fa}}{N_A}\对)n_{一个,G1} = 左(\压裂{7.0711\,\文本{千牛}}{4}\对) \次 4 = 7.0711\,\text{千牛} \)
以来 7.07 千牛 < 120.4 千牛, the factored pryout capacity is 充足的.
检查一下 #5: 计算锚杆剪切能力
回想一下这个设计示例, 剪切分配给所有锚. 的 total shear load per anchor is therefore the resultant of its share of the Vy load and its share of the Vz load. We also consider the governing case used in the shear breakout checks.
For Vy shear, 案件 3 is governing.
\( V_{fa,和} = frac{v_y}{n_{与,G1}} = frac{5\,\文本{千牛}}{2} = 2.5\,\text{千牛} \)
相似地, for Vz shear, 案件 3 is governing.
\( V_{fa,与} = frac{v_z}{n_{和,G1}} = frac{5\,\文本{千牛}}{2} = 2.5\,\text{千牛} \)
这给了 shear force on the anchor rod 作为:
\( V_{fa} = sqrt{((V_{fa,和})^ 2) + ((V_{fa,与})^ 2)} = sqrt{((2.5\,\文本{千牛})^ 2) + ((2.5\,\文本{千牛})^ 2)} = 3.5355\,\text{千牛} \)
In this design example, grout is present. 因此, the anchor rod also experiences bending due to eccentric shear. 考虑到这一点, we can either apply the grout reduction factor per CSA A23.3:19 Clause D.7.1.3 要么 check shear–bending interaction using CSA S16:19 条款 13.12.1.4.
为此计算, we opted to use the 0.8 reduction factor from CSA A23.3. To allow for individual engineering judgment, 的 SkyCiv底板软件 provides the option to disable this reduction factor and instead use the shear–bending interaction check. This feature can be explored using the Base Plate Free Tool.
CSA A23.3 Anchor Rod Shear Capacity:
第一, we calculate the anchor rod shear capacity using CSA A23.3. 的 minimum tensile stress of the anchor rod is:
\( F_{乌塔} = min(F_{u _anc}, 1.9F_{y\_anc}, 860) = min(400\,\文本{兆帕}, 1.9 \times 248.2\,\text{兆帕}, 860.00\,\文本{兆帕}) = 400\,\text{兆帕} \)
的 factored anchor rod shear capacity, 计算使用 CSA A23.3:19 Equation D.31 and Clause D.7.1.3, 是:
\( V_{sar,a23} = 0.8A_{我知道,V}\phi_s0.6f_{乌塔}R = 0.8 \times 92\,\text{毫米}^2 times 0.85 \次 0.6 \times 400\,\text{兆帕} \次 0.75 = 11.258\,\text{千牛} \)
Note that the 0.8 reduction factor is applied here due to the presence of grout. This reduced shear capacity accounts for the additional bending in the anchor rod.
CSA S16 Anchor Rod Shear Capacity:
For the CSA S16 capacity, only the shear capacity is checked, since the bending due to eccentric shear has already been accounted for in the CSA A23.3 check.
的 factored shear capacity is calculated using CSA S16:19 条款 25.3.3.3.
\( V_{[R,s16} = 0.7\phi_m 0.6n A_{sr} F_{u _anc} = 0.7 \次 0.67 \次 0.6 \次 1 \times 126.68\,\text{毫米}^2 \times 400\,\text{兆帕} = 14.255\,\text{千牛} \)
To ensure both methods are considered, the governing capacity is taken as the lesser of the two values, 这是 11.258 千牛.
以来 3.54 千牛 < 11.258 千牛, the factored 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.
SkyCiv样本报告
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