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  3. 协会 7-16 地震荷载计算示例

协会 7-16 地震荷载计算示例

ASCE的一个完整的例子 7-16 使用等效侧向力程序计算地震载荷

SkyCiv Load Generator has recently added seismic load calculation in accordance with ASCE7-16. This involves integrating the USGS Seismic Data and processing it to generate the seismic base shear using Section 12.8 等效横向程序. 在这篇文章中, we will dive deeper into the process of calculating the seismic loads for a building using ASCE 7-16.

SkyCiv 现在集成了来自 USGS Web API 的现场地震数据. 试试我们的 SkyCiv负载生成器!

结构数据

在这个例子中, we will use the following data in calculating the seismic load:

桌子 1. Building data needed for our seismic load calculation.

位置 8050 西南比弗顿希尔斯代尔高速公路, 波特兰, 要么 97225, 美国
占用 Residential Building
方面 64 英尺 (4 bays) × 104 英尺 (6 bays) 计划中
Floor height 15 英尺
Roof height at elev. 75 英尺
Flat roof
柱: 20″x20
光束: 14″x20
大板: 8″ 厚度
载入中 Concrete unit weight : 156 pcf
叠加恒载 (on floor): 100 psf
叠加恒载 (on roof): 50 psf

数字 1. 地点坐标 (从Google地图).

协会 7-16 Seismic example structure

数字 2. Structure for this example.

美国地质勘探局地震数据

USGS has an open-source site seismic data which can be used from their Design Web Services API. 在这个计算中, we will only need the following data:

  • \({小号}_{D1}\) is the design spectral response acceleration parameters at a period of 1.0 s
  • \({小号}_{1}\) is the mapped maximum considered earthquake spectral response acceleration parameters
  • \({小号}_{DS}\)is the design spectral response acceleration parameter in the short period range
  • \({Ť}_{大号}\) is the long-period transition period

USGS Design Web Services

数字 3. USGS Seismic Design Web Services.

In order to request the data above we will need the following data:

  • Latitude, Longitude which we can get from Google Maps
  • Risk Category of the structure based on Section 1.5 ASCE的 7-16
  • Site Class based on Table 20.3-1 ASCE的 7-16

等效侧向力程序

抗震设计基础剪力可以使用公式计算 12.8-1 ASCE的 7-16:

\( V = {C}_{小号} w ^ \) (情商. 12.8-1)

在哪里:
\( V \) is the seismic design base shear
\( {C}_{s} \) is the seismic response coefficient based on Section 12.8.1.1
\( w ^ \) is the effective seismic weight as per Section 12.7.2

确定地震反应系数的公式为:

\( {C}_{s} = frac{{小号}_{DS}}{ \压裂 { [R }{ {一世}_{Ë} } } \) (情商. 12.8-2)

在哪里:
\( {小号}_{DS} \) is the design spectral response acceleration parameter in the short period range (来自美国地质调查局数据)
\( [R \) is the response modification factor as per Table 12.2-1
\( {一世}_{Ë} \) is the importance factor determined from Section 11.5.1

然而, 我们需要满足方程 12.8-3 至 12.8-6:

是屋檐到屋脊的水平距离 \({C}_{s}\) should not exceed 12.8-3 要么 12.8-4

对于 \( T ≤ {Ť}_{大号}\):

\({C}_{s,最高} = frac { {小号}_{D1}}{ \压裂{T R}{{一世}_{Ë}}} \) (情商. 12.8-3)

对于 \( Ť > {Ť}_{大号}\) :

\({C}_{s,最高} = frac { {小号}_{D1} {Ť}_{大号} }{ \压裂{ {Ť}^{2} [R}{{一世}_{Ë}}} \) (情商. 12.8-4)

此外, \( {C}_{s} \) shall not be less than Equation 12.8-5

\( {C}_{s,分} = 0.044 {小号}_{DS} {一世}_{Ë} ≥ 0.01 \) (情商. 12.8-5)

此外, for structures located where \( {小号}_{1} ≥ 0.6g\):

\( {C}_{s,分} = 0.5 \压裂 {{小号}_{1}} { \压裂{[R}{{一世}_{Ë}}} \) (情商. 12.8-6)

在哪里
\( {小号}_{D1} \) is the design spectral response acceleration parameter at period of 1.0 s (来自美国地质调查局数据)
\( Ť \) is the fundamental period of the structure
\( {Ť}_{大号} \) is the long period transition period (来自美国地质调查局数据)
\( {小号}_{1} \) is the mapped maximum considered earthquake spectral response acceleration parameter (来自美国地质调查局数据)

Once we calculate the value of the seismic design base shear \( V \), we need to distribute the forces along the height of the structure using Section 12.8.3 ASCE的 7-16. 在这个例子中, we will assume that the structure has no vertical or horizontal irregularities.

\( {F}_{X} ={C}_{vx} V \) (情商. 12.8-11)

\( {C}_{vx} = frac {{w}_{X}{{H}_{X}}^{ķ}} { \sum_{i = 1}^n{w}_{一世}{{H}_{一世}}^{ķ}} \) (情商. 12.8-12)

在哪里
\( {C}_{vx} \) is the vertical distribution factor
\( {w}_{一世} \) 和 \( {w}_{X} \) is the portion of the total effective seismic weight of the structure \( w ^ \) located or assigned to level 一世 要么 X
\( {H}_{一世} \) 和 \( {H}_{X} \) is the height from the base to level 一世 要么 X
\( ķ \) is defined as the following:

  • \( k = 1 \) for structures with \( T ≤ 0.5 s\)
  • \( k = 2 \) for structures with \( T ≥ 2.5 s\)
  • linear interpolation of \( ķ \) 对于 \( 0.5 < Ť < 2.5 s \)

此外, floor and roof diaphragm forces can be determined using Section 12.10.1 ASCE的 7-16. The design force can be calculated using Equations 12.10-1 至 12.10-3:

\( {F}_{像素} = 分数 { \sum_{i=x}^n {F}_{一世}} { \sum_{i=x}^n {w}_{一世} }{w}_{像素} \) (情商. 12.10-1)

\( {F}_{像素,分} = 0.2 {小号}_{DS}{一世}_{Ë}{w}_{像素} \) (情商. 12.10-2)

\( {F}_{像素,最高} = 0.4 {小号}_{DS}{一世}_{Ë}{w}_{像素} \) (情商. 12.10-3)

在哪里
\( {F}_{像素} \) is the diaphragm design force at level X
\( {F}_{一世} \) is the design force applied at level 一世
\( {w}_{一世} \) is the weight tributary to level 一世
\( {w}_{像素} \) is the weight tributary to diaphragm at level X

We will dive deeper into these parameters below and apply the concept to our structure.

 

重要性因子, \( {一世}_{Ë} \)

重要因素, \( {一世}_{Ë} \), 对于结构可以从部分确定 11.5.1 指向表 1.5-2 ASCE的 7-16.

° N

数字 4. 桌子 1.5-2 ASCE的 7-16 indicating importance factor values per Risk Category.

Since the structure falls under Risk Category II, the corresponding importance factor \( 一世_{Ë} \) 等于 1.0 基于表 1.5-2.

\( {一世}_{Ë} = 1.0 \)

响应修正因子, \( [R \)

The response modification factor, \( [R \), 雪地装载 12.2-1 取决于使用的结构系统. 在这个例子中, we will assume that the structural system used is Special Reinforced Concrete Moment Framesfor both X and Z directions. 由此, we can determine that value of \( [R \) 等于 8 根据表 12.2-1.

数字 5. Truncated values of Table 12.2-1 ASCE的 7-16 indicating Response Modification Coefficient, \( [R \), per structural system.

Site Class

To calculate for our seismic load, the location we will be using is at Raleigh Hills, 波特兰, 要么, 美国 based on Seismic Loads: Guide to the Seismic Load Provisions of ASCE 7-16 (Charney et al., 2020) 分类为 Site Class C.

美国地质勘探局地震数据

.The USGS Seismic Data for the location are the following:

SkyCiv 现在集成了来自 USGS Web API 的现场地震数据. 试试我们的 SkyCiv负载生成器!

数字 6. Site seismic data from USGS Web Services.

\({小号}_{D1} = 0.402 \)
\({小号}_{1} = 0.402 \)
\({小号}_{DS} = 0.708 \)
\({Ť}_{大号} = 16 s \)
\({Ť}_{0} = 0.114 \)

Seismic Design Category

部分 11.6 ASCE的 7-16 details how the procedure in determining the Seismic Design Category of the structure based on the Risk Category and Site Class for the structure.

  • 对于 \({小号}_{1} ≥ 0.75 \) and Risk Category I, II, or III, the Seismic Design Category shall be assigned to Seismic Design Category E
  • 对于 \({小号}_{1} ≥ 0.75 \) and Risk Category IV, the Seismic Design Category shall be assigned to Seismic Design Category F
  • 除此以外, 桌子 11.6-1 和表 11.6-2 shall be used, whichever is more severe.

 

数字 7. Seismic design category from Section 11.6 ASCE的 7-16.

对于这种结构, with Risk Category II, \({小号}_{D1} = 0.402 \), 和 \({小号}_{DS} = 0.708 \) the Seismic Design Category is D based on both tables 11.6-1 和 11.6-2 ASCE的 7-16. The Seismic Design Category will be used for redundancy factor \( ρ \) in calculating diaphragm design forces.

Fundamental Period of the Structure \( Ť \)

结构的基本周期可以从结构的模态分析中确定. 协会 7-16 允许使用截面近似结构的基本周期 12.8.2.1.

\( {Ť}_{一个} = {C}_{Ť} {{H}_{ñ}}^{X} \)

在哪里 \( {H}_{ñ} \) is the structural height of the structure (基础至结构抗震系统最高层的垂直距离), 和 \( {C}_{Ť} \) 和 \( X \) 雪地装载 12.8-2.

Approximate Period Parameters Ct and x

数字 8. 的价值 \( {C}_{Ť} \) 和 \( X \) 从表 12.8-2 ASCE的 7-16.

Since the structure is a concrete moment-resisting frame:

\( {C}_{Ť} = 0.016\)
\( x = 0.9\)

因此, using structure height \( {H}_{ñ} \) 我们将插入已知值 75 ft., the approximate fundamental period of the structure \( {Ť}_{一个} \) 可以确定:

\( {Ť}_{一个} = {C}_{Ť} {{H}_{ñ}}^{X} = (0.016) {(75)}^{0.9}\)
\( T = {Ť}_{一个} = 0.7792 s\)

Seismic Response Coefficient \({C}_{s}\)

因为屋顶轮廓是山墙或双坡, we can already calculate for Seismic Response Coefficient \({C}_{s}\):

\( {C}_{s} = frac{ {小号}_{DS} }{ \压裂 {[R}{{一世}_{Ë}} } = frac{ 0.402 }{ \压裂 {8}{1.0} } \)
\( {C}_{s} = 0.0885\)

以来 \( T ≤ {Ť}_{大号}\):

\({C}_{s,最高} = frac { {小号}_{D1}}{ \压裂{T R}{{一世}_{Ë}}} = frac { (0.402)}{ \压裂{(0.7792)(8)}{(1.0)}} \)
\({C}_{s,最高} = 0.0645 \)

此外, the minimum value of \( {C}_{s} \) 不得少于:

\( {C}_{s,分} = 0.044 {小号}_{DS} {一世}_{Ë} ≥ 0.01 \)
\( {C}_{s,分} = 0.044 (0.402) (1.0) ≥ 0.01 \)
\( {C}_{s,分} = 0.0312 \)

The final value of \( {C}_{s} \) to be used in calculation shall be:

\( {C}_{s} = 0.0645\)

Effective Seismic Weight \( w ^ \)

在这个例子中, we will calculate the effective seismic weight using the dead and superimposed dead load applied to floors. External and internal walls are assumed to be incorporated in the superimposed floor dead load equal to 100 psf. Using concrete unit weight equal to 156 lb/cu.ft.:

For typical floor level (excluding ground and roof levels):

柱: Typical story height x cross-sectional area x unit weight of concrete x total no. of columns = 15 ft x 156 lb/cu.ft. X (20″x20″) X 35 = 227.5 ps
大板: Floor area x thickness x unit weight of concrete = 64ft (104 英尺) x 8″ X 156 lb/cu.ft. = 692.224 ps
横梁: Total length x cross-sectional area x unit weight of concrete = 968 ft x 156 lb/cu.ft. X (14″x20″) = 293.627 ps
叠加恒载: Floor area x load= 64ft (104 英尺) X 100 psf= 665.6 ps
Total dead load per level: 1878.951 ps

For roof level:

柱: Typical story height x cross-sectional area x unit weight of concrete x total no. of columns = 7.5 ft x 156 lb/cu.ft. X (20″x20″) X 35 = 113.75 ps
大板: Floor area x thickness x unit weight of concrete = 64ft (104 英尺) x 8″ X 156 lb/cu.ft. = 692.224 ps
横梁: Total length x cross-sectional area x unit weight of concrete = 968 ft x 156 lb/cu.ft. X (14″x20″) = 293.627 ps
叠加恒载: Floor area x load= 64ft (104 英尺) X 50 psf= 332.8 ps
Total dead load at roof level: 1432.401 ps

综上所述:

楼层 海拔, 英尺 重量, wx, ps
屋顶 75 1432.401
5th level 60 1878.951
4th level 45 1878.951
3rd level 30 1878.951
2nd level 15 1878.951
Effective Seismic Weight, w ^ 8948.203

\( 是屋檐到屋脊的水平距离 8949.203 基普)

Seismic Base Shear \( V \)

使用方程式 12.8-1 ASCE的 7-16, the seismic base shear can be calculated:

\( V = {C}_{小号} 是屋檐到屋脊的水平距离 (0.0645)(8948.203) \)
\( V = 577.159 ps \)

Vertical Distribution of Seismic Forces \( {F}_{X} \)

We need to distribute the seismic load throughout the structure. Since the fundamental period of the structure is \( T = {Ť}_{一个} = 0.7792 s\), 因此:

\( k = 1.1396\)

To calculate the seismic force \( {F}_{X} \) per level, the best approach is to tabulate the seismic weights per level:

楼层 \( {w}_{X} \) ps \( {H}_{X} \) 英尺 \( {w}_{X} {{H}_{X}}^{ķ} \) \( {C}_{vx} \)
\( {F}_{X} \) ps
屋顶 1432.401 75 196303.644 0.2923 168.6950
5th level 1878.951 60 199681.715 0.2973 171.5980
4th level 1878.951 45 143865.010 0.2142 123.6315
3rd level 1878.951 30 90631.141 0.1349 77.8845
2nd level 1878.951 15 41135.482 0.0612 35.3501
Σ = 671616.992 \( V \) = 577.1591

Diaphragm Forces \( {F}_{像素} \)

The calculation of the diaphragm forces are shown below. Since we assumed there are no irregularities, the redundancy factor \( ρ \) 设定为 1.0. This parameter shall be multiplied to \( {F}_{像素} \):

楼层 \( {w}_{像素} \) ps \( Σ {w}_{一世} \)
\( Σ {F}_{一世} \) \( {F}_{像素,分} \) \( {F}_{像素,最高} \) \( {F}_{像素} \) 设计 \( {F}_{像素} \)
屋顶 1432.401 1432.401 168.6950 202.8279 405.6559 168.6950 202.8279
5th level 1878.951 3311.351 340.2930 266.0594 532.1188 193.0915 266.0594
4th level 1878.951 5190.302 463.9245 266.0594 532.1188 167.9461 266.0594
3rd level 1878.951 7069.253 541.8090 266.0594 532.1188 144.0085 266.0594
2nd level 1878.951 8948.203 577.1591 266.0594 532.1188 121.1923

266.0594

SkyCiv负载生成器

All these calculations are already incorporated in the SkyCiv Load Generator. Streamline your calculation using our Free Seismic Load Calculator for ASCE 7-16!

Site Seismic Data

The USGS Seismic Data can be obtained once the Risk Category, Site Class, and Project Address are defined. Note that the parameters \({小号}_{D1} \), \({小号}_{1} \), \({小号}_{DS} \), 和 \({Ť}_{大号} \) should have values in order to proceed with the Seismic Load Calculation.

Site tab input parameters数字 9. Parameters needed to get the USGS Seismic data for the location.

USGS Seismic data

数字 9. Results from USGS Seismic data.

Users can modify the parameters obtained from USGS Web Services to obtain the most appropriate seismic load for the structure.

结构数据

在结构数据选项卡上, you just need to define the standard building data: Roof Profile, 建筑长度, 建筑宽度, 平均屋顶高度, and Roof Pitch Angle.

 

Building data input

数字 10. Building data input.

Seismic Data

To proceed with the seismic calculations, the required are the following:

  • Structure systemfor determining the values of \({C}_{Ť} \) 和 \(X \) which will be used in calculating the approximate fundamental period of the structure \({Ť}_{一个} \)
  • Approximate fundamental period of the structure \({Ť}_{一个} \) – can be user-defined to more appropriate seismic load calculation
  • 响应修正因子 \( [R \) – default value is 8.5 and be modified for more appropriate seismic results
  • Redundancy factor, \( ρ \) – default value is 1.0 and can be modified. Used in diaphragm forces calculation
  • Floor Weightsused for the vertical distribution of base shear and for diaphragm forces. Data per level required are: 我们已经可以解决设计风速 (for designation), 海拔, and Weight

Seismic parameters

数字 11. Seismic parameters required for the seismic calculation.

结果

The output of the calculation is the seismic parameters used and the calculated seismic base shear \(V \), seismic forces per level, and diaphragm forces per level.

Seismic output and design base shear

数字 12. Input parameters and results for seismic load calculation.

Seismic forces

数字 13. Tabulated seismic forces per level including the diaphragm design forces.

详细报告

Upon generating the results, 专业帐户用户 和那些购买了 独立负载生成器模块 can generate a detailed seismic calculation. The report displays all the parameters and assumptions used in the seismic calculation to make it transparent to the user. The generated report for this example calculation can be accessed through this 链接.

Detailed seismic load report

数字 14. Detailed seismic load calculation of SkyCiv Load Generator.

Take advantage of this feature by signing up for a Professional Account or by purchasing the 独立的Load Generator模块!

有关其他资源, 你可以通过这个查看我们的 API 文档:

Patrick Aylsworth Garcia 结构工程师, 产品开发
帕特里克·艾尔斯沃斯·加西亚
结构工程师, 产品开发
土木工程硕士
领英

参考资料:

  • 美国土木工程师学会. (2017, 六月). 建筑物和其他结构的最小设计载荷和相关标准. 美国土木工程师学会.
  • Charney, F., Heausler, T., and Marshall, Ĵ. (2020). Seismic loads: Guide to the seismic load provisions of ASCE 7-16. 美国土木工程师学会.
  • 你可以通过这个查看我们的 API 文档
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