INTRODUCTION IN SEISMIC

Seismic design 

Is primarily concerned with structural safety during major earthquakes, however the serviceability and the economic loss are also concern, depend on the size of the earthquake which the book divide them as follow:-

1-Minor → no damage

2-Moderate → some damage in nonstructural elements

3-Major→ some damage in structural elements

On the other hand, the distribution of forces and displacement resulting from earthquake influenced by three main factors:-

1-Properties of the structure

2-Properties of the foundation

3-The character of the earthquake it self

Building behavior 

The main idea is the inertial forces caused by vibration of the building mass are the main reason of building damages and the increase of the building mass may be has undesirable effects on earthquake design (F=m*a)

Where (m=building mass) (a=ground acceleration)

The magnitude of inertia force depends as we mentioned on:-

1-Building mass

2-The nature of foundation

3-Ground acceleration

Also the dynamic characteristics of the structure

So, 1-for the infinitely rigid buildings and it’s foundation it would have the same acceleration as the ground, in this case F=m*a

       2-for the buildings that deforms slightly it absorb some energy, in this case F<m*a

       3-for the tall buildings it’s more flexible than low rise buildings and much lower                                                                                        acceleration but it has much period that produce larger forces

Where (period=the length of a full cycle in second)

The magnitude of lateral force is not a function of the acceleration of the ground only, but also the response of the structure and its foundation and this relationship depends on the building period

The fundamental period for building is a function of its stiffness mass and damping characteristics and can vary from 0.05 to 0.30 times the number of stories

Influence of soil 

Harder soils and bedrock will transmit short-period vibrations and vice versa with softer soils, also the acceleration will be amplified if the fundamental period of the building coincides with the period of vibrations being transmitted through the soil, this amplified response called resonance

Damping 

Is the prevention of the building to oscillation and this depends on the building materials, connections and the effect of the nonstructural elements on the stiffness of the building, and the damping rations used in practice vary from 1% to 10% of critical damping

Where (critical damping=the minimum amount of damping necessary to prevent oscillation completely

Building drift

 In general is the total displacement of any point relative to the base, building joints must to permit adjoining buildings to respond independently to earthquake motion

Seismic design concept

1-select system that appropriate to the expected level of ground shaping, this include a redundant and continuous load path to ensure that the building responds as a unite

2-determining code forces and deformations

3-analys the building for the combined effects of gravity and seismic loads

4-providing details to assure the building has sufficient inelastic deformation ability to dissipate energy of the motion

Structural response to seismic

The resulting stresses and distortions in building are the same as if the base of the structure were to remain and horizontal forces are applied to the upper part of the building, these forces are the inertia forces equal F=m*a  where (m=w/g)

In general the building deforms in three dimensional manner (one vertical, two horizontal)

The inertia forces generated by the horizontal require greater consideration which the resistance to vertical seismic loads usually provided by the member capacities required for gravity loads

Load path

Seismic forces originated mostly in the heavy mass elements such as diaphragms, horizontal diaphragms distribute these forces to vertical force-resisting elements transfer the force into the foundation and the foundation transfer into soil

Irregularity

Typical building configuration deficiencies include an irregular geometry such as

1-A weakness story

2-Discontinuity in lateral system

3-A concentration of mass

These irregularities are defined in terms of strength, stiffness, geometry and mass and they can come with each other for example:- building that has a tall first story it has two of these terms (stiffness, strength)

Lateral loads resisting systems

1-Space frame resists the earthquake, the columns and beams act in bending, also this type has a large story drift but it may be accommodate without causing failure of columns or beams this system may be a poor economic risk unless special damage-control measure are taken

2-Shear wall system this more rigid than the previous, the story drift is relatively small, also it’s economical method to limit damage

This system excellent in these cases

1-Height to width ratio large enough to overturning problem

2-Soil is relatively soft

3-Dual system this when the frame alone can resist 25% of the lateral loads

4-Diaphragms this is the horizontal element (roof-floor) that distributed the lateral loads to the vertical structural elements

The diaphragms act like a deep beam, the floor is the web that carrying the shear and the wall is the flange of the beam that resisting the bending

The diaphragms must have the following:-

1-Resist bending and shear tied to act as one unite

2-To be adequate to transfer loads to lateral system

3-Openenig or reentrant must properly places and adequately reinforced

Ductility 

The capability to absorb energy with acceptable deformations without failure and it depend on the building materials, systems and reinforcing details

The ductility is measured by the hysteric behavior of critical component such as columns-beam assembly of moment frame (refer to figure 2.9)

Continues load path 

Or preferably more than on path with adequate strength and stiffness should be provided from the origin of the load ‘’inertia forces generated in an element’’ to the final lateral load resisting elements

Redundancy

Is a crucial characteristics for a good lateral performance and this means that the failure of a single connection or element doesn’t negatively affect the lateral stability of the structure 

Configuration

Building with irregular configuration won’t perform as well as a building with regular configuration even if it meet all code requirements

There are two types of irregularity:- 

1-Vertival irregularities 

2-Plan irregularities

For example, the building that take shapes (I, L, H, X) this is a plan irregularities and these shapes have two problems in seismic performance:-

1-Differential vibrations

2-Torsion because the not coincidences of the center of mass and the center of rigidity

We can solve these problems by tie the buildings together at lines of stress concentration and locate seismic resisting element at the extremity of wings or separate the building with joints with adequate width that allow the building to behave independently

Dynamic analysis

Static method based on single mode response while appropriate for simple regular structures

The dynamic analysis is preferred for design of buildings with unusual or irregular geometry

Symmetrical buildings with non-irregularity features behave in a fairly predictable manners, while the buildings that are asymmetrical or with irregularities don’t behave with predictable manners

For such buildings the dynamic analysis is used to determine response characteristics such as

1-Effect of the structure’s dynamic characteristics on the vertical distribution of lateral forces

2-The increase of dynamic loads

3-The effect of higher modes, resulting in an increase in story shears and deformations

SDOF-MDOF 

Simple oscillators are represented by single-degree-of-freedom system

Complex oscillators are represented by multi-degree-of-freedom system

SDOF the idealized system represent two kinds of structure

1-Single column with relatively large mass at its top

2-Single story frame with flexible columns and rigid beam

If the mass is deflected and then suddenly released, it will vibrate at a certain frequency that called fundamental frequency, the reciprocal of frequency is the period of vibration , it represent the time of the mass to move through one complete cycle, the period (T) is given by the following relation

T=2π*(M/K) ^0.5

Where (M=mass) (K=stiffness)

In an ideal system without damping the system will vibrate forever, but in the natural system and as the results of the damping effect the amplitude of the vibration will gradually decrease

The system will act in a similar manner if the instead of deflects the mass in the top, a sudden force hit the system to its base

MDOF the structure may be analyses as a multi degree of freedom by summing the story masses at intervals along the length of vertical pole

During the vibration each mass will behave differently, for higher modes of vibrations some masses may have in opposite directions or all masses may simultaneously deflect in the same direction as in the fundamental mode

The idealized of MDOF system has a number of modes equal a number of masses

When the ground motion is applied to a multi mass system, the deflects shape of the system is a combination of all mode shapes

For modes that have periods near predominated period of the motion will affect more than the other modes

Each mass presented by a single mass system having a generalized value (M) and (K), this values represent the equivalent combined effect of story masses and stiffness 

Building with irregularities is complicated not only the method of dynamic analysis, but also the method of combine the modes, so for building with regular and symmetrical shape, two dimensional model is sufficient

Note when the plan of the building aspect ratio (length/width) is large, torsion response may be predominate so it is required 3D analysis

For most building inelastic response can be expected to occur during a major earthquakes, that is mean that the inelastic analysis is more proper for design, but due to its difficulties and because it is expensive, in practice typically use linear procedures based on the response spectrum method