Introduction

From the above explanation we found that originally this is a dynamic phenomenon when the acceleration and so the inertia forces change in each second. The interaction of the ground and structure is complicated so in a given time the acceleration of the structure depends on several components:

• ground acceleration (the seismic magnitude and its development on time),
• the elasticity of the structure,
• the mass and mass distribution of the structure,
• the connection between the structure and ground, namely soil type.

Another complicated problem is to define exact direction of the ground motion in the seismic investigation. Generally the ground movement is assumed as an arbitrary horizontal motion but the vertical motion also may cause problem to the structure. Fundamentally the calculation process can be divided into three methods:

Time history

This calculation is carried out as an ordinary forced vibration when the excitation is a time dependent acceleration function. These functions can be registered or simulated seismograms. Mathematically we always solve the differential equation system of the vibration by a suitable method (e.g. step-by-step method). From the results of the equation system (means the displacement of the structure) the internal forces can be calculated and the design can be performed.

Theoretically the method is exact, but several circumstances strongly constrain the usage:

• statistically the number of seismograms are insufficient,
• the calculation is very complicated and the runtime is long.

Because of the above mentioned difficulties, this method is not widespread and is not implemented in FEM-Design.

Modal analysis

Expected value of the maximal accelerations belongs to the individual periods which are prescribed in the national codes and named as acceleration response spectrum. The horizontal axis shows the frequency or vibration time of a single degree mass-spring system and the vertical axis shows the maximum corresponding acceleration. (In the Civil Engineering practice vibration period is used instead of frequency.)

The results which belong to the different ground motion directions and structural eigenfrequencies are summarized on the basis of the probability theory, which assumes that not all the effects appear in the same time. Most frequently used summation rule is the SRSS (Square Root of Sum of Squares).

Although the modal analysis is the most accepted method all over the world (as well as in EC8), it has some disadvantages. Some of them are listed as follows:

• the results which are calculated using the SRSS summation rule are not simultaneous. For example for a bending moment in a point of the structure we can’t show the simultaneous normal force in the same point, because the summation is carried out from component to component separately. Consequence of the summation rule, other calculations (second order application, stability analysis) are not interpreted,
• mainly from the application of the statistical method, the graphical results weakly can be followed compare to the results of statical calculation,
• in a lot of cases great number of vibration shapes should be calculated to reach reasonable results which require long calculation time.

Despite of all disadvantages of this method, we can expect most trustable results if the code requirements are fulfilled.

Lateral force method (Equivalent static load method)

The lateral force method partly eliminates the disadvantages of the previous method with simplification in certain cases. The method postulates that the dis- placement response of the structure for ground motion can be described with one (or both x', y' directions) mode shape. While this means generally a simplification or approximation, this method is suitable for a part of the structure (EC8 prescribes the condition of application). In this method the mode shape of the structure is a linear deviation or it is equivalent to the calculated fundamental vibration shape. In the case of linear deviation or mode shape the period also can be calculated by approximate formula.

The application of this method gives possibility to transform the seismic lateral forces to simple static loads and it is applicable as follows:

• these loads (seismic load cases) can be combined with other static loads,
• second order and stability analysis can be performed,
• it is also possible to use these loads for hand calculation, so the results can be checked easily.

This method is usable in FEM-Design with two options if the code permits:

• assumption of linear deviation shape when the period also can be defined by the user (Static, linear shape),
• application of the calculated fundamental vibration shape as the deformed shape of the structure and its period (Static, mode shape).

National codes

Supported national codes and methods:

Norwegian code differs from Eurocode in a few places, so they are reviewed together and the differences are marked separately.

2. Input data

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Dynamic calculations

Design spectrum

3. Calculations parameters and calculations steps

Calculation methods selection

Other setting possibilities

Combination rule, rotation and second order effects

Displacement calculation

4. The results of seismic calculation

5. Summation of static and seismic effects

Seismic loads in static load cases

Final results of seismic effect (Seismic max.) in load combination

Final results of seismic effect (Seismic max.) in load groups

6. Useful tips, which method to use?