基本板设计示例使用en 1993-1-8:2005, 在 1993-1-1:2005, 在 1992-1-1:2004, 和EN 1992-4:2018.
问题陈述:
Determine whether the designed column-to-base plate connection is sufficient for a Vy=5-kN 和 Vz=5-kN 剪力.
给定数据:
柱:
列部分: SHS 180x180x8
列区域: 5440 毫米2
列材料: S235
底盘:
基板尺寸: 350 毫米× 350 毫米
基板厚度: 12 毫米
底板材料: S235
灌浆:
灌浆厚度: 6 毫米
Grout material: ≥ 30 兆帕
具体:
混凝土尺寸: 350 毫米× 350 毫米
混凝土厚度: 350 毫米
混凝土材料: C25/30
破裂或无裂缝: 破裂
锚:
锚直径: 12 毫米
有效嵌入长度: 150 毫米
Embedded plate diameter: 60 毫米
嵌入式板厚度: 10 毫米
Anchor material: 8.8
Other information:
- Non-countersunk anchors.
- Anchor with cut threads.
- K7 factor for anchor steel shear failure: 1.0
- Degree of Restraint of Fastener: No restraint
焊缝:
焊接类型: Fillet Weld
Weld leg size: 8毫米
填充金属分类: E35
锚数据 (从 SkyCiv计算器):
定义:
负载路径:
的 SkyCiv 底板设计软件 跟随 在 1992-4:2018 for anchor rod design. 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.
锚群:
The software includes an intuitive feature that identifies which anchors are part of an anchor group for evaluating 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
我们假设 电压 shear load is resisted by the top and bottom welds, 而 你 shear load is resisted exclusively by the left and right welds.
To determine the weld capacity of the top and bottom welds, we first calculate their total weld lengths.
\(
L_{w,top\&底部} = 2 \剩下(b_{上校} – 2t_{上校} – 2r_{上校}\对)
= 2 \时代左(180 \,\文本{毫米} – 2 \次 8 \,\文本{毫米} – 2 \次 4 \,\文本{毫米}\对)
= 312 \,\文本{毫米}
\)
下一个, 我们计算 stresses in the welds.
Note that the applied Vz shear acts parallel to the weld axis, with no other forces present. This means the perpendicular stresses can be taken as zero, and only the shear stress in the parallel direction needs to be calculated.
\(
\sigma_{\人} = frac{ñ}{(L_{w,top\&底部})\,a\sqrt{2}}
= frac{0 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米} \次 sqrt{2}}
= 0
\)
\(
\你的_{\人} = frac{0}{(L_{w,top\&底部})\,a\sqrt{2}}
= frac{0 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米} \次 sqrt{2}}
= 0
\)
\(
\你的_{\平行} = frac{V_{与}}{(L_{w,top\&底部})\,一个}
= frac{5 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米}}
= 2.8329 \,\文本{兆帕}
\)
使用 在 1993-1-8:2005, 情商. 4.1, the design weld stress is obtained using the directional method.
\(
F_{w,Ed1} = sqrt{ (\sigma_{\人})^ 2 + 3 \剩下( (\你的_{\人})^ 2 + (\你的_{\平行})^2 对) }
= sqrt{ (0)^ 2 + 3 \时代左( (0)^ 2 + (2.8329 \,\文本{兆帕})^2 对) }
= 4.9067 \,\文本{兆帕}
\)
此外, the design normal stress for the base metal check, 每 在 1993-1-8:2005, 情商. 4.1, is taken as zero, 以来 no normal stress is present.
\(
F_{w,Ed2} = \sigma_{\人} = 0
\)
现在, let us assess the left and right welds. As with the top and bottom welds, we first calculate the 总焊接长度.
\(
L_{w,left\&对} = 2 \剩下(d_{上校} – 2t_{上校} – 2r_{上校}\对)
= 2 \时代左(180 \,\文本{毫米} – 2 \次 8 \,\文本{毫米} – 2 \次 4 \,\文本{毫米}\对)
= 312 \,\文本{毫米}
\)
We then calculate the components of the weld stresses.
\(
\sigma_{\人} = frac{ñ}{(L_{w,left\&对})\,a\sqrt{2}}
= frac{0 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米} \次 sqrt{2}}
= 0
\)
\(
\你的_{\人} = frac{0}{(L_{w,left\&对})\,a\sqrt{2}}
= frac{0 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米} \次 sqrt{2}}
= 0
\)
\(
\你的_{\平行} = frac{V_y}{(L_{w,left\&对})\,一个}
= frac{5 \,\文本{千牛}}{(312 \,\文本{毫米}) \次 5.657 \,\文本{毫米}}
= 2.8329 \,\文本{兆帕}
\)
使用 在 1993-1-8:2005, 情商. 4.1, we determine both the design weld stress and the design normal stress for the base metal check.
\(
F_{w,Ed1} = sqrt{ \剩下( \sigma_{\人} \对)^ 2 + 3 \剩下( \剩下( \你的_{\人} \对)^ 2 + \剩下( \你的_{\平行} \对)^2 对) }
\)
\(
F_{w,Ed1} = sqrt{ \剩下( 0 \对)^ 2 + 3 \时代左( \剩下( 0 \对)^ 2 + \剩下( 2.8329 \,\文本{兆帕} \对)^2 对) }
\)
\(
F_{w,Ed1} = 4.9067 \,\文本{兆帕}
\)
The next step is to identify the governing weld stress between the top/bottom welds and the left/right welds. Because the weld lengths are equal and the applied loads have the same magnitude, the resulting weld stresses are equal.
\(
F_{w,Ed1} = \max(F_{w,Ed1}, \, F_{w,Ed1})
= \max(4.9067 \,\文本{兆帕}, \, 4.9067 \,\文本{兆帕})
= 4.9067 \,\文本{兆帕}
\)
The base metal stress remains zero.
\(
F_{w,Ed2} = \max(F_{w,Ed2}, \, F_{w,Ed2}) = \max(0, \, 0) = 0
\)
现在, we calculate the weld capacity. 第一, the resistance of the 角焊缝 is computed. 然后, the resistance of the base metal is determined. 使用英文 1993-1-8:2005, 情商. 4.1, the capacities are calculated as follows:
\(
F_{w,Rd1} = frac{f_u}{\beta_w \left(\伽玛_{M2,weld}\对)}
= frac{360 \,\文本{兆帕}}{0.8 \次 (1.25)}
= 360 \,\文本{兆帕}
\)
\(
F_{w,Rd2} = frac{0.9 f_u}{\伽玛_{M2,weld}}
= frac{0.9 \次 360 \,\文本{兆帕}}{1.25}
= 259.2 \,\文本{兆帕}
\)
最后, we compare the weld stresses with the weld capacities, and the base metal stresses with the base metal capacities.
以来 4.9067 兆帕 < 360 兆帕 和 0 兆帕 < 259.2 兆帕, the capacity of the welded connection is 充足的.
检查一下 #2: Calculate concrete breakout capacity due to Vy shear
Following the provisions of 在 1992-4:2018, the edge perpendicular to the applied load is assessed for shear breakout failure. Only the anchors nearest to this edge are considered engaged, while the remaining anchors are assumed not to resist shear.
These edge anchors must have a concrete edge distance greater than the larger of 10·hef and 60·d, 哪里 有 is the embedment length and d is the anchor diameter. If this condition is not met, the thickness of the base plate must be less than 0.25·hef.
If the requirements in 在 1992-4:2018, 条款 7.2.2.5(1), are not satisfied, the SkyCiv software cannot proceed with the design checks, and the user is advised to refer to other relevant standards.
From the SkyCiv software results, the edge anchors act as 单锚, since their projected areas do not overlap. 为此计算, Anchor 1 will be considered.
To calculate the portion of the Vy shear load carried by Anchor 1, the total Vy shear is distributed among the anchors nearest to the edge. This gives the perpendicular force on Anchor 1.
\(
V_{\人} = frac{V_y}{n_{一个,s}}
= frac{5 \,\文本{千牛}}{2}
= 2.5 \,\文本{千牛}
\)
为了 parallel force, it is assumed that all anchors resist the load equally. 因此, the parallel component of the load is calculated as:
\(
V_{\平行} = frac{V_z}{n_{无}}
= frac{5 \,\文本{千牛}}{4}
= 1.25 \,\文本{千牛}
\)
的 total shear load on Anchor 1 is therefore:
\(
V_{埃德} = sqrt{ \剩下( V_{\人} \对)^ 2 + \剩下( V_{\平行} \对)^ 2 }
\)
\(
V_{埃德} = sqrt{ \剩下( 2.5 \,\文本{千牛} \对)^ 2 + \剩下( 1.25 \,\文本{千牛} \对)^ 2 } = 2.7951 \,\文本{千牛}
\)
The first part of the capacity calculation is to determine the alpha and beta factors. 我们使用 在 1992-4:2018, 条款 7.2.2.5, to set the lf dimension, 和 方程 7.42 和 7.43 to determine the factors.
\(
l_f = \min(H_{ef}, \, 12d_{无})
= min(150 \,\文本{毫米}, \, 12 \次 12 \,\文本{毫米})
= 144 \,\文本{毫米}
\)
\(
\alpha = 0.1 \剩下(\压裂{l_f}{C_{1,s1}}\对)^{0.5}
= 0.1 \时代左(\压裂{144 \,\文本{毫米}}{50 \,\文本{毫米}}\对)^{0.5}
= 0.16971
\)
\(
\beta = 0.1 \剩下(\压裂{d_{无}}{C_{1,s1}}\对)^{0.2}
= 0.1 \时代左(\压裂{12 \,\文本{毫米}}{50 \,\文本{毫米}}\对)^{0.2}
= 0.07517
\)
The next step is to calculate the initial value of the characteristic resistance of the fastener. 使用 在 1992-4:2018, 方程 7.41, the value is:
\(
V^{0}_{检查锚容量,C} = k_9 \left( \压裂{d_{无}}{\文本{毫米}} \对)^{\α}
\剩下( \压裂{l_f}{\文本{毫米}} \对)^{\由使用公式计算的最小值控制}
\sqrt{ \压裂{F_{钢底板设计欧洲规范}}{\文本{兆帕}} }
\剩下( \压裂{C_{1,s1}}{\文本{毫米}} \对)^{1.5} ñ
\)
\(
V^{0}_{检查锚容量,C} = 1.7 \时代左( \压裂{12 \,\文本{毫米}}{1 \,\文本{毫米}} \对)^{0.16971}
\时代左( \压裂{144 \,\文本{毫米}}{1 \,\文本{毫米}} \对)^{0.07517}
\次 sqrt{ \压裂{20 \,\文本{兆帕}}{1 \,\文本{兆帕}} }
\时代左( \压裂{50 \,\文本{毫米}}{1 \,\文本{毫米}} \对)^{1.5}
\次 0.001 \,\文本{千牛}
\)
\(
V^{0}_{检查锚容量,C} = 5.954 \,\文本{千牛}
\)
然后, 我们计算 reference projected area of a single anchor, 下列的 在 1992-4:2018, 方程 7.44.
\(
一个_{C,V}^{0} = 4.5 \剩下( C_{1,s1} \对)^ 2
= 4.5 \时代左( 50 \,\文本{毫米} \对)^ 2
= 11250 \,\文本{毫米}^ 2
\)
在那之后, 我们计算 actual projected area of Anchor 1.
\(
b_{C,V} = min(C_{剩下,s1}, \, 1.5C_{1,s1}) + \分(C_{对,s1}, \, 1.5C_{1,s1})
\)
\(
b_{C,V} = min(300 \,\文本{毫米}, \, 1.5 \次 50 \,\文本{毫米}) + \分(50 \,\文本{毫米}, \, 1.5 \次 50 \,\文本{毫米}) = 125 \,\文本{毫米}
\)
\(
H_{C,V} = min(1.5C_{1,s1}, \, t_{浓}) = min(1.5 \次 50 \,\文本{毫米}, \, 200 \,\文本{毫米}) = 75 \,\文本{毫米}
\)
\(
一个_{C,V} = H_{C,V} b_{C,V} = 75 \,\文本{毫米} \次 125 \,\文本{毫米} = 9375 \,\文本{毫米}^ 2
\)
We also need to calculate the parameters for shear breakout. 我们使用 在 1992-4:2018, 方程 7.4, to get the factor that accounts for the disturbance of stress distribution, 方程 7.46 for the factor that accounts for the member thickness, 和 方程 7.48 for the factor that accounts for the influence of a shear load inclined to the edge. These are calculated as follows:
\(
\psi_{s,V} = min left( 0.7 + 0.3 \剩下( \压裂{C_{2,s1}}{1.5C_{1,s1}} \对), \, 1.0 \对)
= min left( 0.7 + 0.3 \时代左( \压裂{50 \,\文本{毫米}}{1.5 \次 50 \,\文本{毫米}} \对), \, 1 \对)
= 0.9
\)
\(
\psi_{H,V} = max left( \剩下( \压裂{1.5C_{1,s1}}{t_{浓}} \对)^{0.5}, \, 1 \对)
= max left( \剩下( \压裂{1.5 \次 50 \,\文本{毫米}}{200 \,\文本{毫米}} \对)^{0.5}, \, 1 \对)
= 1
\)
\(
\α_{V} = \tan^{-1} \剩下( \压裂{V_{\平行}}{V_{\人}} \对)
= \tan^{-1} \剩下( \压裂{1.25 \,\文本{千牛}}{2.5 \,\文本{千牛}} \对)
= 0.46365 \,\文本{工作}
\)
\(
\psi_{\α,V} = max left(
\sqrt{ \压裂{1}{(\cos(\α_{V}))^ 2 + \剩下( 0.5 \, (\没有(\α_{V})) \对)^ 2 } }, \, 1 \对)
\)
\(
\psi_{\α,V} = max left(
\sqrt{ \压裂{1}{(\cos(0.46365 \,\文本{工作}))^ 2 + \剩下( 0.5 \times \sin(0.46365 \,\文本{工作}) \对)^ 2 } }, \, 1 \对)
\)
\(
\psi_{\α,V} = 1.0847
\)
One important note when determining the alpha factor is to ensure the perpendicular shear and parallel shear are identified correctly.
最后, 我们计算 breakout resistance of the single anchor using 在 1992-4:2018, 方程 7.1.
\(
V_{检查锚容量,C} = V^0_{检查锚容量,C} \剩下(\压裂{一个_{C,V}}{A^0_{C,V}}\对)
\psi_{s,V} \psi_{H,V} \psi_{欧共体,V} \psi_{\α,V} \psi_{检查锚容量,V}
\)
\(
V_{检查锚容量,C} = 5.954 \,\文本{千牛} \时代左(\压裂{9375 \,\文本{毫米}^ 2}{11250 \,\文本{毫米}^ 2}\对)
\次 0.9 \次 1 \次 1 \次 1.0847 \次 1
= 4.8435 \,\文本{千牛}
\)
Applying the partial factor, the design resistance is 3.23 千牛.
\(
V_{路,C} = frac{V_{检查锚容量,C}}{\伽玛_{检查锚容量}}
= frac{4.8435 \,\文本{千牛}}{1.5}
= 3.229 \,\文本{千牛}
\)
以来 2.7951 千牛 < 3.229 千牛, the shear breakout capacity for Vy shear is 充足的.
检查一下 #3: Calculate concrete breakout capacity due to Vz shear
The same approach is used to determine the capacity on the edge perpendicular to the Vz shear.
Because of the symmetric design, the anchors resisting Vz shear are also identified as 单锚. Let’s consider Anchor 1 again for the calculations.
计算 perpendicular load on Anchor 1, we divide the Vz shear by the total number of anchors nearest to the edge only. 计算 parallel load on Anchor 1, we divide the Vy shear by the total number of anchors.
\(
V_{\人} = frac{V_{与}}{n_{一个,s}}
= frac{5 \,\文本{千牛}}{2}
= 2.5 \,\文本{千牛}
\)
\(
V_{\平行} = frac{V_{和}}{n_{无}}
= frac{5 \,\文本{千牛}}{4}
= 1.25 \,\文本{千牛}
\)
\(
V_{埃德} = sqrt{ \剩下( V_{\人} \对)^ 2 + \剩下( V_{\平行} \对)^ 2 }
\)
\(
V_{埃德} = sqrt{ \剩下( 2.5 \,\文本{千牛} \对)^ 2 + \剩下( 1.25 \,\文本{千牛} \对)^ 2 }
= 2.7951 \,\文本{千牛}
\)
Using a similar approach to Check #2, the resulting breakout resistance for the edge perpendicular to Vz shear is:
\(
V_{路,C} = frac{V_{检查锚容量,C}}{\伽玛_{检查锚容量}}
= frac{4.8435 \,\文本{千牛}}{1.5}
= 3.229 \,\文本{千牛}
\)
以来 2.7951 千牛 < 3.229 千牛, the shear breakout capacity for Vz shear is 充足的.
检查一下 #4: Calculate concrete pryout capacity
The calculation for the shear pryout resistance involves determining the nominal capacity of the anchors against tension breakout. The reference for tension breakout capacity is 在 1992-4:2018, 条款 7.2.1.4. A detailed discussion of tension breakout is already covered in the SkyCiv Design Example with Tension Load and will not be repeated in this design example.
From the SkyCiv software calculations, the nominal capacity of the section for tension breakout is 44.61 千牛.
We then use 在 1992-4:2018, Equation 7.39a, to obtain the design characteristic resistance. 使用 k8 = 2, the capacity is 59.48 千牛.
\(
V_{路,cp} = frac{k_8 N_{背景}}{\gamma_c}
= frac{2 \次 44.608 \,\文本{千牛}}{1.5}
= 59.478 \,\文本{千牛}
\)
In the shear pryout check, all anchors are effective in resisting the full shear load. From the image generated by the SkyCiv software, all failure cone projections overlap with each other, making the anchors act as an 锚群.
因此, the required resistance of the anchor group is the total resultant shear load of 7.07 千牛.
\(
V_{res} = sqrt{(V_y)^ 2 + (V_z)^ 2}
= sqrt{(5 \,\文本{千牛})^ 2 + (5 \,\文本{千牛})^ 2}
= 7.0711 \,\文本{千牛}
\)
\(
V_{埃德} = 左(\压裂{V_{res}}{n_{无}}\对) n_{一个,G1}
= 左(\压裂{7.0711 \,\文本{千牛}}{4}\对) \次 4
= 7.0711 \,\文本{千牛}
\)
以来 7.0711 千牛 < 59.478 千牛, the shear pryout capacity is 充足的.
检查一下 #5: Calculate anchor rod shear capacity
The calculation of the anchor rod shear capacity depends on whether the shear load is applied with a moment arm. To determine this, 我们指的是 在 1992-4:2018, 条款 6.2.2.3, where the thickness and material of the grout, the number of fasteners in the design, the spacing of the fasteners, and other factors are checked.
的 SkyCiv底板设计软件 performs all the necessary checks to determine whether the shear load acts with or without a lever arm. For this design example, it is determined that the shear load is 不是 applied with a lever arm. 因此, 我们用 在 1992-4:2018, 条款 7.2.2.3.1, for the capacity equations.
We begin by calculating the characteristic resistance of the steel fastener using 在 1992-4:2018, 方程 7.34.
\(
V^0_{检查锚容量,s} = k_6 A_s f_{ü,无}
= 0.5 \次 113.1 \,\文本{毫米}^2 times 800 \,\文本{兆帕}
= 45.239 \,\文本{千牛}
\)
下一个, we apply the factor for the ductility of the single anchor or the anchor group, taking k7 = 1.
\(
V_{检查锚容量,s} = k_7 V^{0}_{检查锚容量,s}
= 1 \次 45.239 \,\文本{千牛}
= 45.239 \,\文本{千牛}
\)
We then obtain the partial factor for steel shear failure 使用 在 1992-4:2018, 桌子 4.1. For an anchor with 8.8 材料, the resulting partial factor is:
\(
\伽玛_{检查锚容量,剪力}
= max left( 1.0 \剩下( \压裂{F_{ü,无}}{F_{和,无}} \对), \, 1.25 \对)
= max left( 1 \时代 frac{800 \,\文本{兆帕}}{640 \,\文本{兆帕}}, \, 1.25 \对)
= 1.25
\)
Applying this factor to the characteristic resistance, the design resistance is 36.19 千牛.
\(
V_{路,s} = frac{V_{检查锚容量,s}}{\伽玛_{检查锚容量,剪力}}
= frac{45.239 \,\文本{千牛}}{1.25}
= 36.191 \,\文本{千牛}
\)
的 required shear resistance per anchor rod is the resultant shear load divided by the total number of anchor rods, which calculates to 1.77 千牛.
\(
V_{埃德} = frac{\sqrt{ (V_y)^ 2 + (V_z)^ 2 }}{n_{无}}
\)
\(
V_{埃德} = frac{\sqrt{ (5 \,\文本{千牛})^ 2 + (5 \,\文本{千牛})^ 2 }}{4}
= 1.7678 \,\文本{千牛}
\)
以来 1.7678 千牛 < 36.191 千牛, the anchor rod steel shear capacity is 充足的.
设计概要
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