A REPORT

ON

DESIGN OF EARTHQUAKE RESISTANT STRUCTURES

By

SRICHARAN G 2007A2PS609P

RAVI KIRAN P 2007A2PS586P

At

BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, PILANI

MARCH ,2010

DESIGN OF EARTHQUAKE RESISTANT STRUCTURES

INTRODUCTION:

Earthquakes are caused by faulting, a sudden lateral or vertical movement of rock along a rupture (break) surface.

The surface of the Earth is in continuous slow motion. This is plate tectonics--the motion of immense rigid plates at the surface of the Earth in response to flow of rock within the Earth. The plates cover the entire surface of the globe. Since they are all moving they rub against each other in some places, sink beneath each other in others, or spread apart from each other. At such places the motion isn't smooth--the plates are stuck together at the edges but the rest of each plate is continuing to move, so the rocks along the edges are distorted (what we call "strain"). As the motion continues, the strain builds up to the point where the rock cannot withstand any more bending. With a lurch, the rock breaks and the two sides move. An earthquake is the shaking that radiates out from the breaking rock.

Unfortunately, timing of this natural phenomenon cannot be predicted scientifically .Historical records reveal the tendency of earthquakes to revisit regions after an interval of time. This random time interval is called RETURN PERIOD. This is the basis of the seismic zonation.

There are four zones in the country and they are denoted as II,III,IV and V. Zone I which existed in the earlier versions of the code, has been upgraded to Zone II or higher. The higher the zone, the more vulnerable is that region to a major earthquake.

The size of an earthquake is measured by the strain energy released along the fault. It is expressed as MAGNITUDE. The commonly used scale for expressing the magnitude is the Richter Scale. Every unit increase in magnitude implies an increase of about 31 times the energy.

LIST OF MAJOR EARTHQUAKES IN INDIA

Uttarkashi (1991) Latur (1993) Jabalpur (1997) Bhuj (2001) Sumatra and Andaman (2004) Kashmir (2005)

DEFICIENCIES IN MASONRY & CONCRETE BUILDINGS DURING BHUJ EARTHQUAKE

A Heavy roof made of stones attracts large forces Absence of plinth,sill,lintel and roof bands causes collapse of

the walls Absence of supporting cross walls causes long walls to

collapse Corners of walls collapse due to high stresses and lack of

integrity. Inadequate frames to resist seismic forces. A frame consisits

of beams and columns with foundation. Faulty detailing of reinforcing bars and poor quality of

construction. A ground storey without walls can cave in , leading to

collapse of the building Weak beams and columns without proper amount of

anchorage of reinforcing bars lead to failure. Tilting or overturning of the building due to liquefaction of

sandy soil during an earthquake.

GROUND SHAKING EFFECTS ON STRUCTURES

INERTIA FORCES

Buildings are fixed to the ground as shownin Fig 2.1(a). As the base of a building movesthe superstructure including its contentstends to shake and vibrate from the positionof rest, in a very irregular manner due to the inertia of the masses.When the base of the building suddenly moves to the right, the building moves to the left relative the base, Fig 2.1(b), as if it was being pushed to the left by an unseen force which we call .Inertia Force.. Actually, there is no push at all but, because ofits mass, the building resists any motion. The process is much more complex because the ground moves simultaneously in three mutually perpendicular directions during an earthquake as shown in Fig 2.1 (b), (c), and (d).

It is not possible to determine precisely the size or direction of forces exerted on a structure due to earthquake-induced motion.The total seismic force that a structure must resist may be written as

V=C WWhere : V= Total lateral load to be resisted,often called “base shear”

C= Seismic coefficient written as a percentage of the weight of the structure expressed as a decimal.W = Weight of the structure conntributing to the seismic force

There are basically two methods for the mathematical determination of this seismic coefficient C to be used for the seismic design of buildings :static and dynamic analysis

STATIC ANALYSIS

The static analysis method relies on the determination of a seismic coefficient, using a building code formula to determine the lateral forces that must be used in designing buildings.

The static analysis approach is simple.The determination of the magnituide of the earthquake load simply utilizesa formula from the code.

V = Z I K C S W

Where: V = Total seismic force to be resisted (Base Shear)

Z = A numerical coefficient based upon the zone

I = The occupancy importance factor.

K = A numerical coefficient based on the type or arrangement of resisting elements

C = A numerical coefficient which is a function of the period of the structure

S = A numerical coefficient for site-structure resonance

W = The total dead load which contributes to the development of seismic forces

The horizontal force that has been calculated is distributed into the structure as given by the formula

CALCULATION OF DESIGN SEISMIC FORCE BY STATIC ANALYSIS

METHOD

PROBLEM STATEMENT:

Consider a four-storey reinforced concrete office building shown in Fig. 1.1. The building is located inShillong (seismic zone V). The soil conditions are medium stiff and the entire building is supported on a raftfoundation. The R. C. frames are infilled with brick-masonry. The lumped weight due to dead loads is 12kN/m2 on floors and 10 kN/m2 on the roof. The floors are to cater for a live load of 4 kN/m2 on floors and1.5 kN/m2 on the roof. Determine design seismic load on the structure as per new code.

DYNAMIC ANALYSIS

Dynamic analysis shall be performed to obtain the design seismic force, and its distribution to different

levels along the height of the building and to the various lateral load resisting elements, for the following buildings:

a) Regular buildings — Those greater than 40 m in height in Zones IV and ~ and those

greater than 90 m in height in Zones II and 111

b) irregular buildings — All framed buildings higher than 12m in Zones IV and V and those greater than 40m in height in Zones 11and III.

The analytical model for dynamic analysis of buildings with unusual configuration should be such that it

adequately models the types of irregularities present in the building configuration. Buildings with plan

irregularities, cannot be modelled for dynamic analysis by the method.

Dynamic analysis may be performed either by the Time History Method or by the ResponseSpectrum Method. For cases where a more refined design analysis is desired, response spectra are used as the means for determining lateral forces. A Response spectra for a particular earthquake shows in a relatively simple way the dynamic characteristics of a given earthquake.

RESPONSE SPECTRUM METHOD

The response spectrum method is suitable for irregular buildings. The calculations are based on the likely maximum values of the response quantities from the equations of motion. The method is applicable for all buildings , except those incorporating supplemental energy dissipation devices and some types of base isolation systems

This method is also known as the “modal analysis procedure” and can be performed in accordance with the requirements of clause 7.8.4,IS 1893:2002.The method is based on superposition of modes. Hence, free vibration modes are computed using eigenvalue analysis. The maximum value of a quantity termed as the modal response, is obtained for each mode. The number of modes to be used in the analysis should be such that the sum total of modal masses of all modes considered is at least 90 percent of the total seismic mass and missing mass correction beyond 33 percent. If modes with natural frequency beyond33 Hz are to be considered, modal combination shall be carried out only for modes upto 33 Hz. The effect of higher modes shall be included by considering missing mass correction following well established procedures. The peak response quantities ( for example, member forces, displacements, storey forces, storey shears and base reactions ) shall be combined as per Complete Quadratic Combination ( CQC ) method.

If the building has a few closely-spaced modes (see 3.2), then the

peak response quantity due to these modes shall be obtained as

where the summation is for the closely spaced modes only. This peak response quantity ( λ* )due to the closely spaced modes is then combined with those of the remaining well-separated modes

Buildings with regular, or nominally irregular plan configurations may be modelled as a system of masses lumped at the floor levels with each mass having one degree of freedom, that of lateral displacement in the direction under consideration. In such a case, the following expressions shall hold in the computation of the various quantities:

a) Modal Mass - The modal mass (Mk) ofmode k is given by

Where g = Acceleration due to gravity,i k φ = Mode shape coefficient at floor i inmode k, andWi = Seismic weight of floor i.

b) Modal Participation Factors - The modal participation factor (Pk) of mode k is given by:

c) Design Lateral Force at Each Floor in Each Mode -The peak lateral force(Qik) at floor i in mode k is given by

d) Storey Shear Forces in Each Mode – The peak shear force (Vik) acting in storey i in mode k is given by

e) Storey Shear Force due to All Modes Considered - The peak storey shear force (Vi) in storey i due to all modes considered is obtained by combining those due to each mode in accordance with 7.8.4.4.

f) Lateral Forces at Each Storey Due to All Modes Considered -The design lateral forces, F roof and F i, At roof and at floor i:

TIME HISTORY ANALYSIS

In this analysis ,the equations of motion representing the response of a building to ground motion are solved. From the solution , the variations of axial force, bending moment and shear force in a member can be noted . The maximum value of an internal force is selected for subsequent calculation of the demand under load combinations.

CALCULATION OF DESIGN SEISMIC FORCE BY DYNAMIC ANALYSIS METHOD

PROBLEM STATEMENT:

For the building of Example 1, the dynamic properties (natural periods, and mode shapes) for vibration in the X-direction have been obtained by carrying out a free vibration analysis (Table 2.1). Obtain the design seismic force in the X-direction by the dynamic analysis method outlined in cl. 7.8.4.5 and distribute it with building height.