# Calculating the Seismic Design Force and Seismic Base Shear for a Building Using the Simplified Analysis Procedure

September 7, 2017 Abdul Siraj, P.E.

### Problem Description

The problem statement states,

Compute the seismic design force, seismic shear force, and check the lateral deformation for a structure given the following information:

Building Material – Reinforced Concrete
Nature of Building Occupancy – Minor Storage Facility
Basic Seismic Force Resisting System – Ordinary Reinforced Shear Wall System
Number of Stories – 2
Height of Each Floor – 12 ft
Weight of Each Floor – 40 Kips
Seismic Design Category – D
Soil Type – Soft Rock
Design Spectral Response Acceleration Coefficient for Short Period – 1.35g

### Step 1 – Identify Seismic Risk Category

The first step is to identify the risk category of the reinforced concrete building. The risk category is based on Section 1604.5 of the International Building Code (IBC) 2012. The title of Table 1604.5 is “Risk Category of Buildings and Other Structures”. According to this table, the risk category for minor storage facilities is 1.

### Step 2 – Identify Site Classification

The second step is to identify the site classification of our building based on the soil type. The problem statement tells us that the soil type is soft rock. Using Table 20.3-1 of ASCE 7-10, we see that a site with soft rock is considered to be class C.

### Step 3 – Check if the Simplified Analysis Procedure is Applicable

To simplify our analysis, we can use what’s known as the simplified analysis procedure as outlined in Section 12.14 of ASCE 7-10. In order to use this approach, we must ensure that our structure satisfies the following conditions:

The risk classification of the structure based on the nature of occupancy can only be risk category 1 or 2.

The site class cannot be class E or F.

The maximum height of the structure above grade cannot be greater than 3 stories.

The seismic force resisting system that is utilized must either be a bearing wall system or building fame system.

The structure should have a minimum of two lines of lateral resistance in each of two major axis directions.

Our structure has a risk category of 1, is less than 3 stories high, and utilizes a bearing wall system to resist the seismic force. Therefore, we may use the simplified analysis procedure as outlined in ASCE 7-10.

### Step 4 – Identify Response Modification Factor

The fourth step is to choose the appropriate response modification factor, R, using Table 12.14-1 of ASCE 7-10. Under the bearing wall system section, we find that the response modification factor is equal to 4 for a ordinary reinforced concrete shear wall.

### Step 5 – Compute Effective Seismic Weight

The fifth step is to compute the effective seismic weight of the structural building. For this example, it is equal to the summation of the floor weights for the whole building.

### Step 6 – Compute Seismic Base Shear

The sixth step is determine the seismic base shear, V. Per Equation 12.14-11 of ASCE 7-10, it is equal to the design spectral response acceleration coefficient for short period times the effective seismic weight times “F” divided by the response modification factor. For a two-story building, “F” can be taken as 1.1 per Section 12.14.8.1 of ASCE 7-10.

### Step 7 – Calculate Seismic Lateral Force for Each Level, FX

The seventh step is to calculate the lateral force, Fx, for each level. Per Equation 12.14-12 of ASCE 7-10, it is equal to the seismic base shear times the weight of the given level divided by the total effective seismic weight.

### Step 8 – Calculate Seismic Story Shear, VX

The eighth step is to compute seismic story shear, Vx, per Equation 12.8-13 of ASCE 7-10.

### Step 9 – Calculate Overturning Moment, MX

The ninth step is to determine the overturning moment, Mx, at each level.

### Step 10 – Calculate Seismic Lateral Story Drift

The tenth step is to determine the seismic lateral story drift. Since we are using the simplified analysis procedure, we are allowed to take the seismic lateral story drift as 1% of the the story height per Section 12.14.8.5.

### Step 11 – Check Seismic Lateral Story Drift

The eleventh step is to check the seismic lateral story drift. The allowable story drift can be found from Table 12.12-1 of ASCE 7-10. The allowable story drift should be greater than or equal to the design story drifts for each floor level.