G1 EE - ELASTIC AND INELASTIC RESPONSE SPECTRA:

A. MULTIPLE DEGREE OF FREEDOM SYSTEMS (MDOF) B.

elastic and inelastic response spectra

are used to represent the maximum response of structures to ground motion, but they differ in how they handle structural behavior under seismic loads.

Elastic Response Spectrum

assumes that the structure remains within its elastic limit. it will return to its original shape after the earthquake stops. The spectrum shows maximum responses like displacement, velocity, or acceleration as functions of frequency or period.

Inelastic Response Spectrum

assumes that the structure may undergo permanent deformations due to high seismic forces. Here, some parts of the structure yield, but it can still carry loads through its remaining, undamaged parts. In inelastic analysis, the spectrum accounts for energy dissipation due to material yielding, which reduces the overall structural response compared to elastic analysis.

MULTIPLE DEGREE OF FREEDOM (MDOF) SYSTEM

refers to buildings or other structural systems that have multiple independent ways of moving or deforming in response to seismic forces. Each degree of freedom represents a unique mode of vibration or displacement, such as lateral movement of each floor, twisting, or vertical movement.

mode shapes

In dynamic analysis, practical structures can vibrate in multiple distinct patterns, known as ______, each with its own unique frequency.

matrix methods

In modal analysis for shear buildings, we use ______ to model all vibration modes simultaneously

LIQUEFACTION

happens when loose, wet soil turns into a quicksand-like mush during an earthquake. The shaking causes the water in the soil to push the particles apart, making it weak and unstable. This can lead to buildings and roads sinking, tilting, or even collapsing because the ground can 't support them properly.

HAPPENS DUE TO LIQUEFACTION

1. Buildings constructed on loose soil pitch and tilt easily when liquefaction occurs,

2. When loose saturated sands, silts, or gravel are shaken, the material consolidates, reducing the porosity and increasing pore water pressure.

1. 1964 Niigata, Japan earthquake

2. 1995 Kobe, Japan, earthquake,

3. 1999 Kocaeli, Turkey earthquake

4. 1989 Loma Prieta, California earthquake

EXAMPLE OF LIQUEFACTION

soil deposit

consists of an assemblage of individual soil particles.

CAUSES OF LIQUEFACTION

a. Soil grains in a soil deposit.

b. The length of the arrows represent the size of the contact forces between individual soil grains.

trapped

the water is “______” and prevents the soil particles from moving closer together. This is accompanied by an increase in water pressure which reduces the contact forces between the individual soil particles, therby softening and weakening the soil deposit.

1. Building failure

2. Foundation crack

3. Damage to pile foundation

4. Retaining wall failure

5. Slope Erosion

6. Damage to utilities

7. Sand Boiling

7 EFFECTS OF LIQUEFACTION

1. Building failure

- In soil liquefaction, the bearing capacity of soil is being reduced.

- The combination of liquefaction and earthquake forces causes the buildings to lose their equilibrium. This causes buildings on affected land to sink into the ground.These dangers do not provide sufficient time for evacuation, resulting in a catastrophic loss of life and property.

2. Foundation crack

- The uneven settlement of a raft foundation may damage the foundation.

- A cracked foundation fails to distribute the load evenly on the ground. - Liquefaction can also cause the overlying ground to spread and crack as the liquid sediment forces its way to the surface

3. Damage to pile foundation

- The pile foundation acts as a column that transfers the structural load to the deeper strata. The liquefied soil exerts lateral stress to the pile that causes buckling. The pile may distort, and its load-carrying capacity decreases.

4. Retaining wall failure

- A retaining wall fails by sliding, tilting, or overturning. The liquefied soil exerts an additional force on the retaining wall that causes it to fail.

5. Slope Erosion

- Liquefaction destroys the soil slopes

-The soil flows down and settles on the flat ground. The sliding soil causes a large fissure formation on the slopes.

6. Damage to utilities

-Utilities like water lines, sewers, gas lines, etc., are distrubed due to liquefaction. The sewer manholes vertically uplift in the liquefaction phenomenon.

7. Sand Boiling

-When liquefaction happens under a tightly compacted crust, the water pressure beneath the surface causes the water to escape in the form of a bubble. These result in the formation of boiling water