STRUCTURAL design

1. Unit three
Earthquake Load
ES EN 1998-1:2014

2. Introduction
 An earthquake is the vibration of earth produced by the rapid
release of accumulated energy in elastically strained rocks.
 It is the earth’s natural means of releasing stress
 Energy released radiates in all directions from its source, the
focus;
 Energy propagates in the form of seismic waves;
 Their time of occurrence is not exactly predictable
 However earthquake prone areas can be identified
 Resulting from a rupture or a sudden movement along an
existing fault in the earth’s crust
2

3. Types of Earthquakes
1. Tectonic Earthquakes:
occur when rocks in the earth's crust break due to geological
forces created by movement of tectonic plates
2. Volcanic Earthquakes:
occur in conjunction with volcanic activity
3. Collapse Earthquakes:
are small earthquakes in underground mines
4. Explosion Earthquakes:
 result from the explosion of nuclear and chemical devices
 About 90% of all earthquakes result from tectonic events,
primarily movements on the faults
 Two distinct mechanisms cause earthquakes and major cases are:
 Volcanic eruption;
 Tectonic movements of the earth’s crust

4. 4
 The most damaging effects a direction parallel to the ground surface
 focus is point inside the earth where the earthquake started
 Epicenter is point on the surface of the earth directly above the
focus

5. How does an earthquake damage buildings?
1. Ground Shaking
 This is the most common and the principal cause of
earthquake–induced damage.
 As the earth vibrates the building on the ground starts
responding to the vibration in varying degrees depending upon
how these have been designed and constructed.
2. Ground Failure
There are four types of ground failures i.e.,
 fault,
 landslides,
 settlement and
 soil liquefaction 5

6. 6
 Fault is a fracture along which the blocks of crust on either side
have moved relative to one another parallel to the fracture
 Landslides includes a wide range of ground movement, such as
rock falls, deep failure of slopes, and shallow debris flows
 Settlement can displace, tilt, stretch, twist, buckle or a
combination of all
 Soil Liquefaction is a phenomenon where low density saturated
sands of relatively uniform size starts behaving like a jelly with
no strength to hold a building up, and the building just sinks in or
gets tilted on one side.

7.  The phenomenon of liquefaction is particularly important for
dams, bridges, underground pipelines and buildings close to river
banks, sea shore or large lakes.
3. Tsunamis
These are waves and are generally produced by a sudden
movement of the ocean floor
The water waves rush towards land suddenly and with
great velocity causing destruction on coastal areas
7

8. Body waves
8
 Two seismic wave types

9. Behavior of a building during an earthquake
9

10. 4. Fire
 Earthquake does not itself cause fire, however structures
can catch fire as a consequence of damages
 In such cases often it is difficult to control
 Cause damage to water supply
 Cause traffic jams making access by fire fighting personnel
and equipment difficult
What is an earthquake resistant structure?
• It is a structure which does not collapse during an earthquake
,even though it may suffer damage
• The idea is to prevent the structure from collapsing
• So that lives and valuable kept in the structure are saved
• The damaged part can be repaired at a fraction of cost
10

11. Earthquake Resisting Structure
 Structures should not be brittle, ductile designing is
preferred and it should not collapse suddenly.
 It should be tough and be able to show inelastic
deformation
 Resisting elements such as bracing or shear walls must be
provided evenly throughout the building
 Highly integral structure is preferred so that separation of
parts will not occur during earthquake
 Materials used must be of good quality
 Care shall be taken on the proper foundation design
11

12. Measurement of Earthquakes
 There are two terms used to define the measurement of
earthquakes:
Magnitude: refers to a measure of its size in terms of energy
released and radiated in the form of seismic waves.
Intensity: The potential destruction of an earthquake at a
particular location. It depends on focal depth, epicenter distance,
local geology and structural characteristics in addition to the
magnitude of earthquake.
12

13. Ground Conditions And Seismic Action
 According to EBCS EN 1998-1:2014 there are five ground types
 Two additional soil profiles (S1 and S2) are also included
• For sites with ground conditions matching either one of these
ground types, special studies for the definition of the seismic
action are required
 Three parameters are used in the classification
• the value of the average shear wave velocity, vs,30
• the number of blows in the standard penetration test (NSPT)
• the undrained cohesive resistance (cu)

14. Groun
d type Description of stratigraphic profile
Parameters
vs,30
(m/s)
NSPT
(blows/30cm)
cu
(kPa)
A
Rock or other rock-like geological formation, including at
most 5m of weaker internal at the surface. >800 - -
B
Deposits of very dense sand, gravel, very stiff clay, at
least several tens of meters in thickness, characterized by
a gradual increase mechanical properties with depth. 360-800 >50 >250
C
Deep deposits of dense or medium- dense sand, gravel or
stiff clay with thickness from several tens to many
hundreds of meters. 180-360 15-50
70-
250
D
Deposits of 1oose-to-medium cohesionless soil (with or
without some soft cohesive layers), or of predominantly
soft-to-firm cohesive soil. <180 <15 <70
E
A soil profile consisting of a surface alluvium layer with
Vs values of type C or D and thickness varying between
about 5m and 20m, underlain by stiffer material with Vs
800m/s.
S1
Deposits consisting, or containing a layer at least 10m
thick, of soft clays/silts with a high plasticity index (PI>
40) and high water content <1000 - 10-20
S2
Deposits of liquefiable soils, of sensitive clays, or any
other soil profile not included in types A-E or SI

15. Performance Requirements And Compliance Criteria
 Fundamental Requirements
o No-collapse requirement
o Damage limitation requirement
 Compliance Criteria: to satisfy the fundamental requirements
the following limit states shall be checked
o ultimate limit states;
o damage limit states

16. Basic Representation of Seismic Action
 Within the scope of ES EN 1998-1:2014 the earthquake motion
represented by elastic ground acceleration response spectrum,
called elastic response spectrum
 Alternative representations of the seismic action
 Time - history representation
 Spatial model of the seismic action

17. Seismic Zone
 It depends on the local hazard
 The hazard is described in terms of a the value of the reference
peak ground acceleration on type A ground, agR
 The reference peak ground acceleration chosen for seismic zone
corresponds to a reference return period of 475 years (10%
probability of exceedance in 50 years).
 An importance factor γ equal to 1.0 is assigned to this reference
return period.
 For other return periods design ground acceleration on type A
ground ag is equal to agR times importance factor γ (ag= γ1.agR)
 In ES EN 1998-1:2014, five seismic hazard map zones,

18. Zone 5 4 3 2 1 0
αo = ag/g 0.20 0.15 0.10 0.07 0.04 0
Table D1: Bedrock acceleration Ratio 𝛂o

20. Horizontal Elastic Response Spectrum
 For the horizontal components of the seismic action the elastic
response spectrum Se(T) is defined by the following expressions
0≤ 𝑇 ≤ 𝑇𝐵 ∶ 𝑆𝑒(𝑇)=ag.S. 1 +
𝑇
𝑇𝐵
. (2.5𝜂 − 1
TB ≤ 𝑇 ≤ 𝑇𝐶 ∶
𝑆𝑒(𝑇)=2.5ag.S. 𝜂
TC ≤ 𝑇 ≤ 𝑇𝐷 ∶ 𝑆𝑒(𝑇)=2.5ag.S. 𝜂
𝑇𝐶
𝑇
TD ≤ 𝑇 ≤ 4𝑠 ∶ 𝑆𝑒(𝑇)=2.5ag.S. 𝜂
𝑇𝐶
𝑇𝐷
𝑇2
where
Se(T) is the elastic response spectrum;
T is vibration period of a linear single-degree-of-freedom system;
ag is the design ground acceleration on type A ground (ag =𝛾1. 𝑎𝑔𝑅);
TB is lower limit period of constant spectral acceleration branch;
Tc upper limit period of the constant spectral acceleration branch;
TD is value beginning of constant displacement response range of
spectrum;

21. S is the soil factor;
𝜂 is damping correction factor with a reference value of 𝜂 = 1 for
5% viscous damping
Figure 3.1: Shape of the elastic response spectrum

22. Table 3.2: Values of the parameters describing the recommended Type 1 elastic response spectra
Ground type S TB(s) TC(s) TD(s)
A 1.0 0.15 0.4 2.0
B 1.2 0.15 0.5 2.0
C 1.15 0.20 0.6 2.0
D 1.35 0.20 0.8 2.0
E 1.4 0.15 0.5 2.0
 If deep geology is not accounted, the recommended choice is the
use of two of spectra: Type 1 and Type 2
 surface-wave magnitude, Ms, not greater than 5.5, it is
recommended that the Type 2 spectrum

23. Table 3.3: Values of the parameters describing the recommended Type 2 elastic response spectra
Ground type S TB(s) TC(s) TD(s)
A 1.0 0.05 0.25 1.2
B 1.35 0.05 0.25 1.2
C 1.5 0.10 0.25 1.2
D 1.8 0.10 0.30 1.2
E 1.6 0.05 0.25 1.2
Figure 3.2&3.3: Recommended Types elastic response spectra for ground types A to E (5% damping)
S
e
/a
g
S
e
/a
g
Type-1
Type-2

24.  The value of the damping correction factor η may be determined by:
η= 10/(5 + ξ) ≥ 0.55
 where; ξ is the viscose damping ratio of the structure, use 5% in
cases a viscous damping ratio
 The elastic displacement response spectrum, SDC(T), shall be
obtained by:
 direct transformation of the elastic acceleration response
spectrum, Se(T)
SDC T = Se(T)[
T2
2π
]……. for period of vibration not exceeding 4s

25. Vertical elastic response spectrum
 The vertical component of the seismic action shall be represented by
an elastic response spectrum, Sve(T):
0≤ 𝑇 ≤ 𝑇𝐵 ∶
𝑆𝑣𝑒(𝑇)=avg. 1 +
𝑇
𝑇𝐵
. (3𝜂 − 1
TB ≤ 𝑇 ≤ 𝑇𝐶 ∶
𝑆𝑣𝑒(𝑇)=3avg. 𝜂
TC ≤ 𝑇 ≤ 𝑇𝐷 ∶
𝑆𝑣𝑒(𝑇)=3avg. 𝜂
𝑇𝐶
𝑇
TD ≤ 𝑇 ≤ 4𝑠 ∶ 𝑆𝑣𝑒(𝑇)=3avg. 𝜂
𝑇𝐶
𝑇𝐷
𝑇2
Table 3.4: Recommended values of parameters describing the vertical elastic response spectra
spectrum avg/ag TB(S) TC(S) TD(S)
Type 1 0.90 0.05 0.15 1.0
Type 2 0.45 0.05 0.15 1.0

26. Design Ground Displacement
 The design ground displacement dg, corresponding to the design
ground acceleration,
Dg=0.025ag.S.TC.TD
Design Spectrum For Elastic Analysis
 For the horizontal components of the seismic action the design
spectrum, Sd(T):
0≤ 𝑇 ≤ 𝑇𝐵 ∶ 𝑆𝑑(𝑇)=ag.S.
2
3
+
𝑇
𝑇𝐵
. (2.5
𝑞
−
2
3
)
TB ≤ 𝑇 ≤ 𝑇𝐶 ∶
𝑆𝑑(𝑇)=ag.S.
2.5
𝑞
TC ≤ 𝑇 ≤ 𝑇𝐷 ∶
𝑆𝑑(𝑇)
=ag.S.
2.5
𝑞
𝑇𝐶
𝑇
≥ β . 𝑎𝑔

27. TD ≤ 𝑇: 𝑆𝑑(𝑇)
=ag.S.
2.5
𝑞
𝑇𝐶
𝑇𝐷
𝑇2
≥ β . 𝑎𝑔
 Where;
ag,S,TC and TD previously defined
Sd(T) is the design spectrum;
q is the behavior factor;
β is lower bound factor for horizontal design spectrum, β=0.2
 For the vertical component of the seismic action the design
spectrum is given in the previous slide
o avg replacing ag, S = 1.0, and other parameters as is it.
o behavior factor q up to 1.5 should generally be adopted for all
materials and structural systems.

28. o q greater than 1.5 in the vertical direction should be justified
through an appropriate analysis
 The design spectrum defined above is not sufficient for the design
of structures with base-isolation or energy-dissipation systems

29.  Respecting principles of conceptual design
• Lower additional costs for resistance to earthquakes
• Reduce problems of analysis and resistance checks
 Basic conceptual design of building against seismic hazard are:
Structural simplicity
Uniformity, symmetry and redundancy
Bidirectional resistance and stiffness
Torsional resistance and stiffness
Diaphragmatic action at story level
Adequate foundation
Concept of primary and secondary seismic members
Principles apply to building primary structure
Characteristics of Earthquake Resistant of Buildings

30. Consequence of structural regularity on seismic design ES EN
1998-1: 2014
30
Regularity allowed Simplification Behavior Factor
Plan Elevation Model Liner elastic Analysis (For Linear Analysis)
Yes Yes Planar Lateral force a
Reference value
Yes No Planar Modal Decreased value
No Yes Spatial b
Lateral force a
Reference value
No No Spatial Modal Decreased value
 a condition met Lateral force method of analysis
 b special regularity conditions are met
 For non-regular in elevation buildings the decreased values of the
behavior factor are given by the reference values multiplied by 0.8.

31. Regularity in Plan
 Symmetric in plan w.r.t. 2 orthogonal directions
 Compact outline in plan, enveloped by convex polygonal line
 Set-back (re-entrant corners or recesses), in plan don’t leave area up
to convex polygonal envelope >5 % area inside outline
 In-plane stiffness of floors sufficiently large compared to lateral
stiffness of vertical elements
 C, H, I, and X plan shapes should be carefully examined, notably as
concerns the stiffness of the lateral branches
 The slenderness λ =Lmax/Lmin<4, where Lmax and Lmin are
respectively the larger and smaller in plan dimension 31

32. Eccentricity eox < 0.3rx to be checked in both direction
eox is structural eccentricity
rx torsional radius (square root of the ratio between the torsional
stiffness and lateral stiffness)
 Torsional stiffness condition; rx >ls
ls is radius of gyration of the floor mass
Criteria For Regularity In Elevation
 All lateral load resisting systems run without interruption from
foundation to top
 Both lateral stiffness & mass of story's remain constant or reduce
gradually without abrupt changes
 Ratio of actual story resistance to resistance required by the
analysis should not vary disproportionately between adjacent
stories

33. ES EN 8

34. Short column
Partial floor-height panel infill
Failure pattern
Short column
Partial floor-height panel infill
Failure pattern

35. Figure: long section, olive view hospital
Note that shear walls stop on the third floor
Figure: cross section, olive view hospital
Showing the second floor plaza and the
discontinuous shear wall

36. Structural Analysis
Modeling
 Adequately represent the distribution of stiffness and mass
 Consider rigid or flexible diaphragms (diaphragms may be taken as
rigid if due to its deformation displacements do not vary more than
10%)
 For regular buildings, it is acceptable to use two separate plane
models, one for each main direction.
 In concrete, composite and in masonry buildings the stiffness of the
load bearing elements should take into account the effect of
cracking.
 Consider the deformability of the foundation

37. Structural analysis
Analysis methods
 Linear analysis
• Lateral force method (limits of application):
Regularity in elevation
𝑇1 ≤ (4𝑇𝐶, 2𝑠)
• modal response spectrum analysis (reference method):(Used
when lateral force method of analysis do not satisfy the
conditions)
 Non linear analysis
• Non-linear static (pushover) analysis
• Non-linear time-history analysis

38. Lateral Force Method of Analysis
Base shear force (Fb):
Fb=Sd(T1).m.λ
 Where:
Sd (T1 ) is the ordinate of the design spectrum at period T1
T1 is the fundamental period of vibration of the building
m is the total mass of the building, above the foundation or
above the top of a rigid basement
𝛌 is the correction factor, the value of which is equal to: λ = 0.85
if T1 < 2TC and the building has more than two stores, or λ = 1.0
otherwise.

39.  For buildings with heights of up to 40m the value of T1
 Fundamental period, T1 = Ct H3/4
 Where, H = Height of the building above the base in meter
Ct = 0.085 for steel moment resisting frames
= 0.075 for reinforced concrete moment resisting frames
and eccentrically braced steel frames
= 0.050 for all other structures
 Alternatively, the estimation of T1
𝑇1 = 2. 𝑑
 d is the lateral elastic displacement of the top of the building, in m,
due to the gravity loads applied in the horizontal direction

40. Distribution of the Horizontal Seismic Forces
 The seismic action effects shall be determined by applying, to the
two planar models, horizontal forces Fi to all stores
𝐹𝑖 = 𝐹𝑏.
𝑆𝑖
.𝑚𝑖
𝑠𝑗
.𝑚𝑗
 When the fundamental mode shape is approximated by horizontal
displacements increasing linearly along the height, the horizontal
forces Fi
𝐹𝑖 = 𝐹𝑏.
𝑧𝑖
.𝑚𝑖
𝑧𝑗
.𝑚𝑗
where
Fi is the horizontal force acting on story i
Fb is the seismic base shear
Si, Sj are the displacements of masses mi, mj
mi,mj are the story masses
zi, zj are the heights of the masses mi mj

41.  Accidental torsion effect (eai=±0.05𝐿𝑖)
 Accidental torsion effect when using two planar models:
 Multiplication of the seismic internal forces in all elements by
Symmetrical building 𝛿 = 1 + 0.6.
𝑥
𝐿𝑒
Other situations 𝛿 = 1 + 1.2.
𝑥
𝐿𝑒
 Where:
eai is accidental eccentricity of story mass i
Li is floor-dimension perpendicular to direction of Seismic action
x-distance of the element to the center of mass
Le-distance between two outermost lateral load resisting element

42. Importance Classes and Importance Factors (𝜸𝟏)
 Buildings are classified in 4 importance classes, depending on:
• the consequences of collapse for human life,
• their importance for public safety and civil protection in the
immediate post-earthquake period
• the social and economic consequences of collapse
Table 1.2.1 Importance classes and recommended values for importance factors for buildings
class Buildings 𝜸𝟏
I Buildings of minor importance for public safety, e.g. agricultural
buildings, etc.
0.8
II Ordinary buildings, not belonging in the other categories. 1.0
III Buildings whose seismic resistance is of importance in view of the
consequences associated with a collapse, e.g. schools, assembly halls,
cultural institutions etc.
1.2
IV Buildings whose integrity during earthquakes is of vital importance for
civil protection, e.g. hospitals, fire stations, power plants, etc.
1.4

43. ductility classes
 Depending on the required hysteretic dissipation energy
DCL (low ductility)
• structures designed and dimensioned according to ES EN 2
• recommended only for low seismicity cases
DCM (medium ductility)
• specific provisions for design and detailing to ensure inelastic
behavior of the structure without brittle failure
• concrete class  C16/20
DCH (high ductility)
• special provisions for design and detailing to ensure stable
mechanisms with large dissipation of hysteretic energy
• concrete class  C20/25

44. Behavior Factors for Horizontal Seismic Actions
 Behavior Factor (q) to account for energy dissipation capacity
 shall be derived for each design direction as follows:
q=qoKw >1.5
 where
• qo is basic value of the behavior factor
• kw is factor reflecting the prevailing failure mode in structural
systems with walls
Table 5.1: Basic value of the behavior factor, qo, for systems regular in elevation
STRUCTURAL TYPE DCM DCH
Frame system, dual system, coupled wall system 3.0𝛼o/𝛼1 4.5𝛼o/𝛼1
Uncoupled wall system 3.0 4.0𝛼o/𝛼1
Torsionally flexible system 2.0 3.0
Inverted pendulum system 1.5 2.0

45.  For buildings which are not regular in elevation, the value of qo
should be reduced by 20%
 factor 𝛼o/𝛼1 for regular in plan can be evaluated
a. Frames or frame-equivalent dual systems.
• One- story buildings: 𝛼o/𝛼1 =1.1
• multistory, one-bay frames: 𝛼o/𝛼1 =1.2
• multistory multi-bay frames or frame-equivalent dual structures:
𝛼o/𝛼1 = 1.3
b. Wall- or wall-equivalent dual systems.
• wall systems with only two uncoupled walls per horizontal
direction: 𝛼o/𝛼1 =1.0
• other uncoupled wall systems: 𝛼o/𝛼1 =1.1
• wall-equivalent dual, or coupled wall systems: 𝛼o/𝛼1 =1.2

46.  For buildings which are not regular in plan, 𝛼o/𝛼1 equal to the
average of 1.0 and the value given in previous slide
 The factor kw
1.0 𝑓𝑜𝑟 𝑓𝑟𝑎𝑚𝑒 𝑎𝑛𝑑 − 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑑𝑢𝑎𝑙 𝑠𝑦𝑠𝑡𝑒𝑚
𝑘𝑤 =
1 + 𝛼𝑜
3
≤ 1, > 0.5, 𝑓𝑜𝑟 𝑤𝑎𝑙𝑙 − 𝑒𝑞𝑢𝑖𝑣𝑎𝑙𝑒𝑛𝑡 𝑎𝑛𝑑 𝑡𝑜𝑟𝑠𝑖𝑜𝑛𝑎𝑙𝑙𝑦 𝑓𝑙𝑒𝑥𝑖𝑏𝑙𝑒 𝑠𝑦𝑠𝑡𝑒𝑚𝑠
𝛼𝑜 =
ℎ𝑤𝑖
𝑙𝑤𝑖
 where
 hWi is the height of wall i; and
 lWi is the length of the section of wall i.

47. Safety Verifications
1. Ultimate limit states: safety against collapse (ULS) is ensured if
resistance, ductility, equilibrium, foundation stability and seismic
joint conditions are met.
A. Resistance condition
 Design action effects  design resistance; Ed  Rd
 Check second order (P-∆) effects:
 Inter story drift sensitivity coefficient (𝜃)=
𝑃𝑡𝑜𝑡
.𝑑𝑟
𝑉𝑡𝑜𝑡
.ℎ
< 0.1
 0.1 <   0.2  consider 2nd order effects by amplifying by
1/(1- )
  shall not exceed 0.3 47

48. Cont.…
B. Global and Local Ductility condition
 check that the structural elements and the structure as a whole
posses adequate ductility
 specific material related requirements shall be satisfied
C. Equilibrium condition
 bldg. should be stable against overturning and sliding
 additional SLS verification for bldgs. with sensitive
equipments
D. Resistance of horizontal diaphragms
 Horizontal diaphragms & bracings shall have sufficient over-
strength in transmitting lateral loads
 The above requirements are satisfied if the diaphragms can
resist, for brittle failure modes 1.3 and for ductile failure
modes 1.1 times forces obtained from analysis 48

49. E. Resistance of foundation
 Verification of foundations according to ES EN 1998-5:2015 and to
1997 -1:2015
 Action effects based on capacity design consideration, but shall not
exceed that of elastic behavior with q =1.
F. Seismic joint condition
 To check that there is no collision with adjacent structures
 For structurally independent units, do not belong to the same
property, if the distance from the property line to the potential
points of impact is not less than maximum horizontal
displacement
 For structurally independent units, belonging to the same
property, if the distance between them is not less than the
Square Root of the Sum- of the Squares (SRSS) of maximum
horizontal displacements
 When floor elevations of adjacent bldgs. are the same the max.
separation distance referred above can be reduced by a factor
of 0.7 49

50. Cont.…
2. Damage limitation: Limitation of damage requirement (SLS) is
satisfied if, under the design seismic action, the interstorey drifts
dr are limited to:
a. For bldgs. having non-structural elements of brittle materials
attached to the structure
dr v ≤ 0.005h
b. For bldgs. having non-structural ductile non structural
elements:
dr v ≤ 0.0075h
c. For buildings having non-structural elements fixed in a way
so as not to interfere with structural deformations, or without
non-structural elements:
dr v ≤ 0.010h
where h is the story height
50

51. 51
Example :
 A four storied building has an elevation shown in figure and is
located in Woldya. Determine the lateral forces and storey shears
on an inner frame due to earthquake using the following data.

52. 52
Bay width = 6 m center to center
Frame spacing = 5 m center to center
Height of ground floor = 4 m
Height of other floors = 3.5 m
Floor thickness including Finishes = 15 cm
Outer columns = 25 cm x 30 cm – 2 numbers
Inner columns = 25 cm x 40 cm – 3 numbers
Girder below floor slab = 25 cm x 40 cm
Live load = 3 kN/m2
Ordinary building
Design for earthquakes with MS>5.5
Soil deposits of very dense sand with vS,30=450m/s
Frame system in DCM design

53. 53
Solution
 Seismic zone (for Woldya=IV), αo = ag/g = 0.15
 Importance class II(For ordinary buildings) ⇒ 𝜸𝟏 = 𝟏
⇒ 𝒂𝒈 = 𝜸𝟏*agR = 1*0.15g = 1.47 m/s2
 Spectrum Type 1
 Ground type B: S=1.2 , TB=0.15s , TC=0.5s , TD=2.0s
 Behavior factor for multi story multi-bay frames:
𝛼o/𝛼1 = 1.3 & kw=1.0
qo=3.0𝛼o/𝛼1=3.0*1.3=3.9
⟹q=qokw =3.9* 1=3.9 >1.5,so take q=3.9

54.  Fundamental period,
Ct = 0.075 for reinforced concrete moment resisting frames
H = 14.5 m
T1 = Ct H3/4 =0.075 (14.5) ¾ = 0.56 sec
T1 = 0.56s ≤ (4TC, 2s)=(4*0.5=2s,2s)…………ok!
 Design Spectrum
 Horizontal component design spectrum[Sd(T1)]
T1= 0.56sec ⇒ TC < T1 < TD
Sd(T1)=TC ≤ T1 ≤ TD; Sd(T1)
=ag.S.
2.5
q
TC
T
=1.47∗1.2∗
2.5
3.9
(
0.5
0.56
)=1.01
≥ β . ag = 0.2 ∗ 1.47 = 0.294
 So take Sd(0.56) =1.01m/s2

55.  Base shear force (Fb):
Fb=Sd(T1).m.λ
𝛌 = 0.85, for T1=0.56 < 2TC=2∗0.5=1
 Total structure mass
 Weight at first floor
At any floor, half of the weight of walls and columns below it and half
of that above it are lumped at this level along with the weight of the
floor and girder.
Density of concrete = 25 kN/m3
Weight of floor slab = 0.15 * 24 * 5 * 25 = 450 kN
Weight of Longitudinal Girder = 4*0.25 * 0.4 *6* 25 = 60 kN
Weight of Transverse Girder = 5*0.25 * 0.4 * 5 * 25 = 62.5 kN

56. 56
Weight of outer columns = 2*0.25 * 0.3 * {(4 + 3.5)/2}* 25
= 14.1 kN
Weight of inner columns = 3*0.25 * 0.4 * {(4 + 3.5)/2}* 25
= 28.125 kN
Total = 614.725 kN
 Weight at second floor
Weight of floor slab = 0.15 * 24 * 5 * 25 = 450 kN
Weight of Longitudinal Girder = 0.25 * 0.4 * 24 * 25 = 60 kN
Weight of Transverse Girder = 5*0.25 * 0.4 * 5 * 25 = 62.5 kN
Weight of outer columns = 0.25 * 0.3 * 3.5 * 25 * 2 = 13.1 kN
Weight of inner columns = 0.25 * 0.4 * 3.5 * 25 * 3 = 26.25 kN
Total = 611.875 kN

57. 57
 Weight at third floor =Weight at second floor = 611.875 kN
 Weight at roof
Weight of roof slab = 0.15 * 24 * 5 * 25 = 450 kN
Weight of Longitudinal Girder = 0.25 * 0.4 * 24 * 25 = 60 kN
Weight of Transverse Girder =5 *0.25 * 0.4 * 5 * 25 = 62.5 kN
Weight of outer columns = 2*0.25 * 0.3 * 3.5/2 * 25 = 6.6 kN
Weight of inner columns = 0.25 * 0.4 * 3.5/2 * 25 * 3 = 13.125 kN
Total = 592.188 kN
Weight of the columns in the foundation
= (2 * 2 * 0.25 * 0.3 * 25) + (2 * 3 * 0.25 * 0.4 * 25) = 22.5 kN
Total weight of the building per frame
W = 614.725 + 2* 611.875 + 592.188 + 22.5 = 2453.163 kN

58.  Total mass (m)=
W
g
=
2453.163kN
9.81m/s2 =250068kg
⟹ Fb=Sd(T1).m.λ=1.01m/s2*250068kg*0.85=214.683kN
 Horizontal force acting on story I
𝐹𝑖 = 𝐹𝑏.
𝑧𝑖
.𝑚𝑖
𝑧𝑗
.𝑚𝑗
= 𝐹𝑏.
𝑧𝑖
.𝑊𝑖
𝑧𝑗
.𝑊𝑗
Stories Fb W z ziwi Story Shear
G+0 214.683 22.5 0 0 0
G+1 214.683 614.725 4 2458.9 23.603
G+2 214.683 611.875 7.5 4589.063 44.05
G+3 214.683 611.875 11 6730.625 64.607
Roof 214.683 592.188 14.5 8586.726 82.423
zj wj 22365.314

59. 59
Story Shear Distribution
82.423kN
64.607kN
44.05kN
23.603kN