earthquake effect on building

7/30/2019 earthquake effect on building

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ANALYSIS OF EARTHQUAKE GROUND

MOTIONS : STATIC ANALYSIS

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ANALYSIS OF EARTHQUAKE GROUND

MOTIONS I: STATIC ANALYSIS

Requirements of Earthquake Resistant

Design

Seismic Coefficient Method

Torsion due to Eccentricities

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orey r a cu a ons

Appendages

Numerical Examples

Requirements of Earthquake Resistant

Design

Earthquake can cause damage not only on

also due to other chain effects like landslides,

floods, fires and disruption to communication.

Therefore it is important to take necessary

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structures so that they are safe against such

secondary effects also.

6.1.1 The Characteristics (intensity,

duration, etc) of Seismic Ground

Vibrations expected

epen s on

Magnitude of EQ

Depth of Focus Distance from Epicenter

Characteristics of the Path through which seismic waves

travel

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Soil strata on which the structure stands


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6.1.2 Response of Structures to Ground

Vibrations is a Function of ---

Nature of Foundation Soil

, ,

Structures

Duration and Characteristics of Ground Motions

IS 1893(Part I): 2002 specifies design forces for structures

standing on Rocks or soils which do not settle, liquefy or

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slide due to loss of strength during ground vibrations.

6.1.3 Design Approach:

Structure should-

Possess at least a minimum strength to withstand minorEQs (= required


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6.3.2 Design Horizontal EQ Load

When the Lateral Load resisting elements are oriented

along orthogonal horizontal directions the structure shall

be designed for the effects due to full Design EQ Load in

one horizontal direction at time.

When the lateral load resisting elements are not oriented

along the orthogonal horizontal directions, the structure

shall be desi ned for the effects due to full desi n EQ

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load in one horizontal direction plus 30 % of the design

EQ load in the other direction

7.5 Design Lateral Force:

The Design Lateral Force shall first be computed for the

buildin as a whole..

This Design Lateral Force shall then be distributed to the

various floor levels.

The overall design seismic force thus obtained at each

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floor level, shall then be distributed to individual Lateral

Load Resisting elements depending on the floor

diaphragm action.

7.5.3 Design Seismic Base Shear

Total Design Lateral Force or Design Seismic BaseShear (Vb) along any principal direction shall be

determined by

Vb = Ah * W

Where,

Ah = Design Horizontal acceleration spectrum using thefundamental natural Period Ta , as per the considereddirection of vibration

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W = Seismic weight of the building.

7.6 Fundamental Natural Period (Tn)

The Approximate Fundamental Natural Period of Vibration (Tn), in seconds, of a Moment-Resisting FrameBuilding Without Brick Infill Panels may be estimated bythe empirical expression

Tn = 0.075 * h0.75 for RC Frame Building

= 0.085 * h0.75 for Steel Frame Building

Where, h Height of Building in m, excludes the basementstoreys, where basement walls are connected with the

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ground floor deck or fitted between the building columns.


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7.6.2 Tn For all Other Buildings

For Moment-Resisting Frame Buildings with the infill

anels

Tn = 0.09 * h / (d)

Where, h height of building

d Base dimension of the building at the Plinth Level, in

m, along the considered direction of the Lateral Force

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6. 4 Design Spectrum

6.4.2 The Design Horizontal Seismic Coefficient Ah for a

structure

Ah = (Z * I * Sa) / (2 * R * g)

= (Z/2)*(I/R)*(Sa/g)

Provided that for any structure with T


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7.4 Seismic Weight

7.4.1 Seismic Weight of Floors

DL + % of LL

the Weight of Columns and Walls in any storey shall be

equally distributed to the floors above and below the

storey.

7.4.2 Seismic Weight of Building

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.

7.4.3 Any Weight supported in between the storeys shall

be distributed to the floors above and below in Inverse

proportion to its distance from the floors.

7.7 Distribution of Design Force

7.7.1 Vertical Distribution of Base Shear to Different

Floor Levels

Qi = (Vb) * (Wi * hi^2)/( Wi * hi^2)

Qi Design Lateral Force at Floor I,

Wi Seismic Weight of Floor I,

hi Height of Floor I measured from Base,

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n num er o oreys n e u ng s e num er of levels at which the masses are located

7.9 Torsion

7.9.1 Provision shall be made in all buildings for Increase in SF on the Lateral Force ResistingElements resulting from the Horizontal Torsional

of Mass and Centre of Rigidity. However, the NegativeTorsional Shear shall be neglected.

7.9.2 Design Eccentricity ( whichever gives the moresevere effect) e di static eccentricty, distancebetween CM and CR

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Bi Floor Plan dimension perpendicular to thedirection of Force.

b0.05-eORb0.05e*1.5e isiisidi +=

7.11 Deformations

7.11.1 Storey Drift Limitation

The storey drift in any storey due to minimum specified

design lateral force with partial factor of 1.0 shall not

exceed 0.004 times the storey height. No drift l imit for

single storey building which has been designed to

accommodate storey drift.

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7.11.2 Deformation Compatibility of Non-Seismicstructures

For buildings located in seismic zones IV and V, it shallbe ensured that the structural components that are notpart of the seismic Force Resisting System in thedirection under consideration, do not lose their verticalload-carrying capacity under the induced moments

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storey displacements calculated.

7.12.2 Cantilever Projections

7.12.2.1 Vertical Projections

, , ,Other Vertical cantilever projections attached to buildingsand projecting above the roof shall be designed andchecked for stability forFIVE times the design horizontalseismic coefficient Ah. In the analysis of the building, theweight of these projecting elements will be lumped withthe roof weight.

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7.12.2.2 Horizontal Projections

All Horizontal Projections like cornices and balconies

shall be designed and checked for stability for FIVE

7.12.2.3 The increased Design Forces are ONLY for

designing the projecting parts and their connections with

the main structures. For the design of the main structure,

such increase NEED not be considered.

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Calculation of Design Seismic Force by

Static Analysis

Problem Statement:

Consider G+3 Storey building. The building is located in

seismic zone III. The soil conditions are medium stiff. The

R.C. frames are infilled with brick masonry. The lumped

weight due to dead loads is 10 KN/m2 on floors and on

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roof. The floors carry live load of 5 KN/m on floors and

roof.


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Cases considered for the analysis

(a) Only Building.

(b) Building + Vertical Projection --- Water Tank placed concentrically

(c) Building + Vertical Projection --- Water Tank placed eccentrically.

(d) Analysis of cantilever portions --- Vertical & horizontal projections.

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3.0

3.0

PLAN AND ELEVATION OF A BUILDING

3.0

5 @ 5m c/c

3.0

3.0

PLAN

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3.0

3.0

5 @ 5m c/c

ELEVATION

Case a): Analysis of G + 3 BUILDING

Design Parameters:

For seismic zone III, z= 0.16 (Table 2 of IS:1893)

mpor ance ac or = . esponse e uc on ac or =

Seismic Weights:

Floors: Roof:

Floor area= 25 X 9 = 225 m2 W4 = 225 x 10

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W1 = W2 = W3 = 225 X (10+0.5 X 5) = 2250 KN

= 3750 KN

Total Seismic weight of the structure, W = Wi = 3 X 3750+2250 = 13500 KN

Fundamental Period:

EQ in X-direction:

T = 0.09h/d = 0.09 X 12/25 = 0.216 sec.

Ah = (Z / 2) X (I/R) X (Sa/g) = (0.16/2) X (1/5) X 2.5 = 0.04

Vb = Ah X W = 0.04 X 13500 = 540 KN.

EQ in Y-direction:

T = 0.09h/d = 0.09 X 12/9 = 0.36sec

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Ah = (Z / 2) X (I/R) X (Sa/g) = (0.16/2) X (1/5) X 2.5 = 0.04

Vb = Ah X W = 0.04 X 13500 = 540 KN.

Seismic Force is same in both directions.


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Lateral force distribution along height by

Static Analysis

Storey

Level Wi (KN)

hi

(m) Wi hi2 Wihi/(Wihi2

Lateral Force at ith Level

for EL in X & Y-direction

(KN)

4 2250 12 324 0.40678 219.66

3 3750 9 303.75 0.381356 205.93

2 3750 6 135 0.169492 91.52

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1 3750 3 33.75 0.042373 22.88

796.5 1 540

VERTICAL PROJECTION (WATER TANK) CONCENTRICALLY

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Case b): Building + Vertical Projection --- Water

Tank placed concentrically

DL on floors = 10 KN/m2 , LL on floors = 5 kN/m2

seismic zone III z = 0.16 ; I = 1 : R = 5

Seismic Weight calculations:

L = 9m ; b = 25m ; floor area = 225 sq.m

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LL >= 5KN/sqm , 50% LL need to be considered on all floors except roof.

Seismic weight on floors :

w1 = 225(10 + 0.5 x 5) = 2812.5 KN = w2 = w3

Seismic weight on roof:w4 = DL + wt. of tank

wt. of tank :

a) Roof slab = 0.120 x 5.2 x 3.2 x 25 =49.92 = 50 KN

b)Walls - 0.2 x 16 x 2 x 25 = 160 KN

c)Bottom slab = 0.2 x 5.2 x 3.2 x 25 = 83.2KN

4)Beams = 0.6 x 0.3 x (5 x 2 + 3 x 2) x 25 = 72 KN

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5)Staging 4-columns 4 x 0.3 x 0.3 x 2.1 = 18.9 = 19 KN

Total wt. of tank = 384.2 KN ; Total wt. on roof = 2634.2 KN

Total wt.of structure = 11071.7 KN


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Lateral force distribution along height bystatic method.

Storey Lateral force at ith

Le

vel

Wi

(KN)

hi,

m

Wi hi2

x 1000

Wihi /

Wihi2level for EQx

and EQy (KN)

4 2634.0 12 379.3 0.520 229.0

3 2812.5 9 227.8 0.310 137.5

2 2812.5 6 101.3 0.140 61.1

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1 2812.5 3 25.3 0.034 15.3

= 733.7 1 442.9

VERTICAL PROJECTION (WATER TANK) AT ECCENTRICITY

3.0

3.0

3.0

5 @ 5m c/c

3.0

PLAN

2.1

2.0

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5 @ 5m c/c

3.0

3.0

3.0

ELEVATION

The lumped wt. of tank on roof causes a shift in center of mass of

roof level whereas the centre of rigidity remains at the geometrical

Case c): Building + Vertical Projection --- Water

Tank placed eccentrically.

center of roof. Thus an eccentricity in both directions is induced which

creates torsion & increases the shear.

EQ in X direction:-

T = 0.09h/d = 0.09 x 1225 = 0.216 Sec.

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Ah = (Z / 2) X( I / R) X (Sa/g) = 0.04

Design base shear = Ah x W = 442.868 KN

EQ in Y direction:-Ah = 0.04,

Design base shear = Ah x W = 442.868 KN

The center of mass (CM) is calculated as follows

wt. of tank = 384.2 KN = 25.613 KN/m2

2 .

X= 11.55 m, Y= 4.782 m

CM (11.56 , 4.73) , CR (12.5, 4.5)

EQ.in x direction :

Calculatedeccentricit esi = 12.5 - 11.56= 0.94 m

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Design eccentricity edi = 1.5 x esi + 0.05b OR

edi = esi - 0.05b whichever gives more severe effect


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edi = 1.5 x 0.94+ 0.05 x 25 = 1.41 + 1.25 = 2.66 m OR

edi = 0.94 - 0.05 x 25 = 0.94 - 1.25 = -0.31m

edi = 2.66 m

EQX = 228.95 KN

Torsional moment T =(EQX) x (edi) = 609.007 KNm

Additional shear due to torsion is given as Vx = (T / Ip) x (y) x (Kxx)

2 2 3 4

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, , . ,

E = 25 X 106 KN/m2 , Kx = 7500 KN/m,

(Kx) x Y2 = 1923750, ( Ky) x X2 = 13125000, Ip = 15048750.

For,

Ist column line, Vx = 8.195 KN

2nd column line, Vx = 2.730 KN

3rd column line, Vx = - 2.731 KN

4th column line, Vx = - 8.195 KN

The -ve values are to be neglected while +ve shear to be added i.e. force is

not to be deducted as per IS 1893 2002.

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Similar calculations follow for Y direction .

Case d): Design of Projection (Tank- Column)

Design of container Column:

Wt. of container = 384.2 KN ; Wt.of water = 30 x 10 = 300 KN.

Total load = 384.2 + 300 = 684.2 KN

The projection is to be designed for 5 times Ah --- IS 1893 2002

= 5 x Ah = 5 x 0.04 = 0.2

Vb = Ah x W = 0.2 x 684.2 = 136.84 KN.

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. . .

Axial load = 684.2 / 4 = 171.05 KN

The column is to be checked for,

Axial load = 166.32 KN Moment = 139.713 KNm. along both directions.

Case e): Design considerations for horizontal projections

Design of horizontal projections for vertical earthquake acceleration.

= = . .

Consider a horizontal balcony 0f 1m x 1m with a parapet wall of ht = 1m

M 20 concrete ; Fe 415 Steel

L / d =7 M.F.= 1.3

d = 1000/7 x 1.3 = 109.89mm :

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D = 109.89 + 20 = 129.89 mm =130 mm (say)

d = 110 mm .


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Loading calculation :

1) DL = 25 x 0.130 + 1.5 = 4.75 kn/m2

Assume LL = 5 KN / m2

o a oa = . m

ultimate load = 1.5 x 9.75 = 14.635 KN/m2

Wt. of parapet wall = 1 x 0.1 x 25 = 2.5 KN

Design moment = WuL2 + Wu x L

= 14.635 x 1 x 1/ 2 + 2.5 x 1 = 9.82 KN m

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Section design ; for given material Ru = 2.76

dreq =.(9.82 x 106 / 2.76 x 1000) = 59.65 mm < provided. -- o.k.

For the seismic acceleration in vertical direction the stability is checked

Av = (2/3) Ah also these projections are designed for five times

the horizontal accn.hence Av = (10 / 3) x Ah = (10 / 3) x 0.04 = 0.133

The overturning moment is obtained for a critical or worst combination as

Mo = w1 (1 + Av)L / 2 + w2 (1+ Av)L

w1 = 1 x 1 x 0.130 x 25 + LL;

w2 = 2.5 KN ( Point load of the Parapet wall)

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