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4. MACHADOS 7-16 Exemplo de cálculo de carga sísmica

# MACHADOS 7-16 Exemplo de cálculo de carga sísmica

## Um exemplo totalmente trabalhado de ASCE 7-16 Cálculo de Carga Sísmica usando o Procedimento de Força Lateral Equivalente

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 Procedimento Lateral Equivalente. Neste artigo, we will dive deeper into the process of calculating the seismic loads for a building using ASCE 7-16.

SkyCiv agora integrou os dados sísmicos do site da USGS Web API. Experimente o nosso SkyCiv Load Generator!

Neste exemplo, we will use the following data in calculating the seismic load:

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

 Localização 8050 SW Beaverton Hillsdale Hwy, Portland, OU 97225, EUA Ocupação Residential Building Dimensões 64 ft (4 bays) × 104 ft (6 bays) No planoFloor height 15 ftRoof height at elev. 75 ftFlat roofColuna: 20″x20″Feixe: 14″x20″Laje: 8″ grossura Carregando Concrete unit weight : 156 pcfCarga morta sobreposta (on floor): 100 psfCarga morta sobreposta (on roof): 50 psf

Figura 1. Localização do site (do Google Maps).

Figura 2. Structure for this example.

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

• $${S}_{D1}$$ is the design spectral response acceleration parameters at a period of 1.0 s
• $${S}_{1}$$ is the mapped maximum considered earthquake spectral response acceleration parameters
• $${S}_{DS}$$is the design spectral response acceleration parameter in the short period range
• $${T}_{eu}$$ is the long-period transition period

Figura 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 de ASCE 7-16
• Site Class based on Table 20.3-1 de ASCE 7-16

## Procedimento de Força Lateral Equivalente

O cisalhamento de base de projeto sísmico pode ser calculado usando a Equação 12.8-1 de ASCE 7-16:

$$V = {C}_{S} C$$ (Eq. 12.8-1)

Onde:
$$V$$ is the seismic design base shear
$${C}_{s}$$ is the seismic response coefficient based on Section 12.8.1.1
$$C$$ is the effective seismic weight as per Section 12.7.2

A fórmula para determinar o coeficiente de resposta sísmica é:

$${C}_{s} = frac{{S}_{DS}}{ \fratura { R }{ {eu}_{e} } }$$ (Eq. 12.8-2)

Onde:
$${S}_{DS}$$ is the design spectral response acceleration parameter in the short period range (dos dados do USGS)
$$R$$ is the response modification factor as per Table 12.2-1
$${eu}_{e}$$ is the importance factor determined from Section 11.5.1

Contudo, precisamos satisfazer as equações 12.8-3 para 12.8-6:

é a distância horizontal do beiral ao cume $${C}_{s}$$ should not exceed 12.8-3 ou 12.8-4

Pra $$T ≤ {T}_{eu}$$:

$${C}_{s,max} = frac { {S}_{D1}}{ \fratura{T R}{{eu}_{e}}}$$ (Eq. 12.8-3)

Pra $$T > {T}_{eu}$$ :

$${C}_{s,max} = frac { {S}_{D1} {T}_{eu} }{ \fratura{ {T}^{2} R}{{eu}_{e}}}$$ (Eq. 12.8-4)

além disso, $${C}_{s}$$ shall not be less than Equation 12.8-5

$${C}_{s,min} = 0.044 {S}_{DS} {eu}_{e} ≥ 0.01$$ (Eq. 12.8-5)

Além disso, for structures located where $${S}_{1} ≥ 0.6g$$:

$${C}_{s,min} = 0.5 \fratura {{S}_{1}} { \fratura{R}{{eu}_{e}}}$$ (Eq. 12.8-6)

Onde
$${S}_{D1}$$ is the design spectral response acceleration parameter at period of 1.0 s (dos dados do USGS)
$$T$$ is the fundamental period of the structure
$${T}_{eu}$$ is the long period transition period (dos dados do USGS)
$${S}_{1}$$ is the mapped maximum considered earthquake spectral response acceleration parameter (dos dados do USGS)

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 de ASCE 7-16. Neste exemplo, we will assume that the structure has no vertical or horizontal irregularities.

$${F}_{x} ={C}_{vx} V$$ (Eq. 12.8-11)

$${C}_{vx} = frac {{C}_{x}{{h}_{x}}^{k}} { \sum_{i=1}^n{C}_{eu}{{h}_{eu}}^{k}}$$ (Eq. 12.8-12)

Onde
$${C}_{vx}$$ is the vertical distribution factor
$${C}_{eu}$$ e $${C}_{x}$$ is the portion of the total effective seismic weight of the structure $$C$$ located or assigned to level eu ou x
$${h}_{eu}$$ e $${h}_{x}$$ is the height from the base to level eu ou x
$$k$$ 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 $$k$$ pra $$0.5 < T < 2.5 s$$

Além disso, floor and roof diaphragm forces can be determined using Section 12.10.1 de ASCE 7-16. The design force can be calculated using Equations 12.10-1 para 12.10-3:

$${F}_{px} = frac { \sum_{i=x}^n {F}_{eu}} { \sum_{i=x}^n {C}_{eu} }{C}_{px}$$ (Eq. 12.10-1)

$${F}_{px,min} = 0.2 {S}_{DS}{eu}_{e}{C}_{px}$$ (Eq. 12.10-2)

$${F}_{px,max} = 0.4 {S}_{DS}{eu}_{e}{C}_{px}$$ (Eq. 12.10-3)

Onde
$${F}_{px}$$ is the diaphragm design force at level x
$${F}_{eu}$$ is the design force applied at level eu
$${C}_{eu}$$ is the weight tributary to level eu
$${C}_{px}$$ is the weight tributary to diaphragm at level x

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

### Fator de Importância, $${eu}_{e}$$

O fator de importância, $${eu}_{e}$$, para a estrutura pode ser determinada na Seção 11.5.1 que aponta para a Tabela 1.5-2 de ASCE 7-16.

Figura 4. Mesa 1.5-2 de ASCE 7-16 indicating importance factor values per Risk Category.

Since the structure falls under Risk Category II, the corresponding importance factor $$Outro exercício útil é observar tudo isso considerando a fórmula geral do círculo de momento de inércia{e}$$ é igual a 1.0 baseado na tabela 1.5-2.

$${eu}_{e} = 1.0$$

### Fator de modificação de resposta, $$R$$

The response modification factor, $$R$$, cargas de neve no painel solar também devem ser consideradas 12.2-1 dependendo do sistema estrutural usado. Neste exemplo, we will assume that the structural system used is Special Reinforced Concrete Moment Framesfor both X and Z directions. Deste, we can determine that value of $$R$$ é igual a 8 conforme Tabela 12.2-1.

Figura 5. Truncated values of Table 12.2-1 de ASCE 7-16 indicating Response Modification Coefficient, $$R$$, per structural system.

### Classe do Site

To calculate for our seismic load, the location we will be using is at Raleigh Hills, Portland, OU, EUA based on Seismic Loads: Guide to the Seismic Load Provisions of ASCE 7-16 (Charney et al., 2020) que é classificado como Site Class C.

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

SkyCiv agora integrou os dados sísmicos do site da USGS Web API. Experimente o nosso SkyCiv Load Generator!

Figura 6. Site seismic data from USGS Web Services.

$${S}_{D1} = 0.402$$
$${S}_{1} = 0.402$$
$${S}_{DS} = 0.708$$
$${T}_{eu} = 16 s$$
$${T}_{0} = 0.114$$

### Seismic Design Category

Seção 11.6 de ASCE 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.

• Pra $${S}_{1} ≥ 0.75$$ and Risk Category I, II, or III, the Seismic Design Category shall be assigned to Seismic Design Category E
• Pra $${S}_{1} ≥ 0.75$$ and Risk Category IV, the Seismic Design Category shall be assigned to Seismic Design Category F
• De outra forma, Mesa 11.6-1 e mesa 11.6-2 shall be used, whichever is more severe.

Figura 7. Seismic design category from Section 11.6 de ASCE 7-16.

Para esta estrutura, with Risk Category II, $${S}_{D1} = 0.402$$, e $${S}_{DS} = 0.708$$ the Seismic Design Category is D based on both tables 11.6-1 e 11.6-2 de ASCE 7-16. The Seismic Design Category will be used for redundancy factor $$ρ$$ in calculating diaphragm design forces.

### Fundamental Period of the Structure $$T$$

O período fundamental de uma estrutura pode ser determinado a partir da análise modal da estrutura. MACHADOS 7-16 permite a aproximação do período fundamental de uma estrutura usando a Seção 12.8.2.1.

$${T}_{uma} = {C}_{t} {{h}_{n}}^{x}$$

Onde $${h}_{n}$$ is the structural height of the structure (distância vertical da base ao nível mais alto do sistema de resistência à força sísmica da estrutura), e $${C}_{t}$$ e $$x$$ cargas de neve no painel solar também devem ser consideradas 12.8-2.

Figura 8. Valores de $${C}_{t}$$ e $$x$$ da mesa 12.8-2 de ASCE 7-16.

Since the structure is a concrete moment-resisting frame:

$${C}_{t} = 0.016$$
$$x = 0.9$$

Portanto, using structure height $${h}_{n}$$ Caso de carga A 75 ft., the approximate fundamental period of the structure $${T}_{uma}$$ pode ser determinado:

$${T}_{uma} = {C}_{t} {{h}_{n}}^{x} = (0.016) {(75)}^{0.9}$$
$$T = {T}_{uma} = 0.7792 s$$

### Seismic Response Coefficient $${C}_{s}$$

Dos valores acima, we can already calculate for Seismic Response Coefficient $${C}_{s}$$:

$${C}_{s} = frac{ {S}_{DS} }{ \fratura {R}{{eu}_{e}} } = frac{ 0.402 }{ \fratura {8}{1.0} }$$
$${C}_{s} = 0.0885$$

Desde a $$T ≤ {T}_{eu}$$:

$${C}_{s,max} = frac { {S}_{D1}}{ \fratura{T R}{{eu}_{e}}} = frac { (0.402)}{ \fratura{(0.7792)(8)}{(1.0)}}$$
$${C}_{s,max} = 0.0645$$

Além disso, the minimum value of $${C}_{s}$$ não deve ser menor que:

$${C}_{s,min} = 0.044 {S}_{DS} {eu}_{e} ≥ 0.01$$
$${C}_{s,min} = 0.044 (0.402) (1.0) ≥ 0.01$$
$${C}_{s,min} = 0.0312$$

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

$${C}_{s} = 0.0645$$

### Effective Seismic Weight $$C$$

Neste exemplo, 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):

Coluna: 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 kips
Laje: Floor area x thickness x unit weight of concrete = 64ft (104 ft) x 8″ x 156 lb/cu.ft. = 692.224 kips
feixes: Total length x cross-sectional area x unit weight of concrete = 968 ft x 156 lb/cu.ft. x (14″x20″) = 293.627 kips
Carga morta sobreposta: Floor area x load= 64ft (104 ft) x 100 psf= 665.6 kips

For roof level:

Coluna: 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 kips
Laje: Floor area x thickness x unit weight of concrete = 64ft (104 ft) x 8″ x 156 lb/cu.ft. = 692.224 kips
feixes: Total length x cross-sectional area x unit weight of concrete = 968 ft x 156 lb/cu.ft. x (14″x20″) = 293.627 kips
Carga morta sobreposta: Floor area x load= 64ft (104 ft) x 50 psf= 332.8 kips

Resumindo:

 Térreo Elevação, ft Peso, wx, kips Cobertura 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, C 8948.203

$$é a distância horizontal do beiral ao cume 8949.203 kips) ### Seismic Base Shear \( V$$

Usando Equação 12.8-1 de ASCE 7-16, the seismic base shear can be calculated:

$$V = {C}_{S} é a distância horizontal do beiral ao cume (0.0645)(8948.203)$$
$$V = 577.159 kips$$

### 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 $$T = {T}_{uma} = 0.7792 s$$, Portanto:

$$k = 1.1396$$

To calculate the seismic force $${F}_{x}$$ por nível, the best approach is to tabulate the seismic weights per level:

 Térreo $${C}_{x}$$ kips $${h}_{x}$$ ft $${C}_{x} {{h}_{x}}^{k}$$ $${C}_{vx}$$ $${F}_{x}$$ kips Cobertura 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 $${F}_{px}$$

The calculation of the diaphragm forces are shown below. Since we assumed there are no irregularities, the redundancy factor $$ρ$$ está configurado para 1.0. This parameter shall be multiplied to $${F}_{px}$$:

 Térreo $${C}_{px}$$ kips $$Σ {C}_{eu}$$ $$Σ {F}_{eu}$$ $${F}_{px,min}$$ $${F}_{px,max}$$ $${F}_{px}$$ Projeto $${F}_{px}$$ Cobertura 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

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, Classe do Site, and Project Address are defined. Note that the parameters $${S}_{D1}$$, $${S}_{1}$$, $${S}_{DS}$$, e $${T}_{eu}$$ should have values in order to proceed with the Seismic Load Calculation.

Figura 9. Parameters needed to get the USGS Seismic data for the location.

Figura 9. Results from USGS Seismic data.

Os usuários podem modificar os parâmetros obtidos do USGS Web Services para obter a carga sísmica mais adequada para a estrutura.

Na guia Dados da Estrutura, you just need to define the standard building data: Roof Profile, Comprimento do edifício, Largura do Edifício, Altura média do telhado, and Roof Pitch Angle.

Figura 10. Building data input.

### Seismic Data

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

• Sistema de estrutura – para determinar os valores de $${C}_{t}$$ e $$x$$ que será utilizado no cálculo do período fundamental aproximado da estrutura $${T}_{uma}$$
• Período fundamental aproximado da estrutura $${T}_{uma}$$ – pode ser definido pelo usuário para cálculo de carga sísmica mais apropriado
• Fator de modificação de resposta $$R$$ – valor padrão é 8.5 e ser modificado para resultados sísmicos mais apropriados
• fator de redundância, $$ρ$$ – valor padrão é 1.0 e pode ser modificado. Usado no cálculo das forças do diafragma
• Pesos de Piso – usado para a distribuição vertical de cisalhamento de base e para forças de diafragma. Os dados por nível exigidos são: Nível (para designação), Elevação, e Peso

Figura 11. Seismic parameters required for the seismic calculation.

The output of the calculation is the seismic parameters used and the calculated seismic base shear $$V$$, seismic forces per level, e forças de diafragma por nível.

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

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

Upon generating the results, Usuários de conta profissional e aqueles que compraram o módulo gerador de carga autônomo 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 link.

Take advantage of this feature by signing up for a Professional Account or by purchasing the Módulo gerador de carga autônomo!

Para recursos adicionais, Nossa solução personalizada para painel solar criada para MT Solar usando a API SkyCiv:

Patrick Aylsworth Garcia
Engenheiro estrutural, Desenvolvimento de Produto
MS Engenharia Civil