Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engineering هندسة الزلازل & Assc.Prof Nasser El-Shafey)

Lecture (4)
Prepared by
Assc. Prof. Dr. Nasser. El-Shafey
Feb. 2017

1.Symmetry: The structure is almost symmetrical in plan along
two orthogonal directions regarding the lateral stiffness and
mass distribution.
2.Recesses: shall not exceed 5% of the floor area.
3.Aspect Ratio: Lx / Ly <4.0.
4.Torsional regularity: eccentricity between C.M. & C.R.
< 15% Li for each direction (Li=Lx &Ly for x & y directions).
Plan Regularity
Simplified Modal Response Spectrum Method

Elevation Regularity
All lateral force resisting elements such as cores, shear walls or
frames should be continuous from foundation up to the last
floor or setback or recess level.
Stiffness and mass regularity: Difference between two
successive floors does not exceed 75% for Lateral stiffness and
50% for mass.
Vertical geometric regularity.

Sub Soil Class S TB TC TD
A 1 0.05 0.25 1.2
B 1.35 0.05 0.25 1.2
C 1.5 0.1 0.25 1.2
D 1.8 0.1 0.3 1.2
Type 1 Response Spectrum
Response Spectrum analysis

Type 2 Response Spectrum
Sub Soil Class S TB TC TD
A 1 0.15 0.4 2
B 1.2 0.15 0.5 2
C 1.15 0.2 0.6 2
D 1.35 0.2 0.8 2

➢To get:- S, TB, TC, TD
(Depends on subsoil class & type)
Where
H: Height of structure, in meters, from top foundation
C t = 0.085 for space steel Frames
0.075 for RC framed structures
0.05 for shear wall structures or combined structures
➢The Fundamental Period (T)
For structures of heights up to 60.0m:
Or use computer modal analysis
from tables
T = Ct H3/4
T ≤ 4.0 Tc or T ≤ 2.0 second

γI Importance Factor (γI) (code 8-7-6):
Type of building Factor “γI”
I. Emergency facilities: hospitals, fire stations,
power plants, etc.
1.40
II. High occupancy buildings: schools, assembly
halls, etc.
1.20
III. Ordinary buildings. 1.00
IV. Buildings of minor importance for public safety. 0.80

Structural system Factor, R
1.Bearing walls; flexural walls-R.C. 4.5
2.Ordinary frames; flexural walls-R.C. 5.0
3. Moment resisting frames; R.C. with adequate ductility. 7.0
4. Moment resisting frames; R.C. with limited ductility.
5. Dual systems, moment frames walls with adequate
ductility.
6.0
6. Dual systems, moment frames walls with limited
ductility.
5.0
7. Other
Structures.
Water Tanks (framed) 2.0
Towers. 3.0
Minaret, chimneys, silos. 3.5
Response Modification Factor, R
5.0

- Sd (T) Ordinate of the elastic design spectrum at period T
T fundamental period of vibration of the structure
in the direction considered.
λ Correction factor (For structures has >two stories)
λ = 0.85
λ = 1.0
if T ≤ 2Tc
If T > 2Tc
Fb= Sd (T). λ .W/g
Ultimate Base Shear Force

Structural design load (W) (code 8-7-1-7)
Building weight above foundation
= Σ D.L+ (Factor) Σ L.L
W= D.L.+ 0.25 L.L for residential buildings.
W= D.L.+ 0.5 L.L. for common buildings, malls, schools
W= D.L.+ L.L. for silos, tanks, stores, libraries, garages
■ Wu = 1.4 D.L + 1.6 L
■ Wu = 0.9 D.L + EQ
■ Wu = 1.12 D.L + α L.L + EQ Where:
α = 0.25 for residential buildings
= 0.50 for public structures (Schools, hospitals,.)
= 1.0 for tanks, main stores, …
Design Combinations (The bigger of)

For stability: Highest value of
WU = 0.9 D + 1.3 W
= 0.9 D+ S
Where:
WU =ultimate load, D=dead load,
L= live load, W=wind load, EQ=seismic load
Working stress design method:
o If seismic or wind loads are considered, then allowable
stresses may be increased by 15%.
o Wind loads and seismic loads should not be combined. (only,
the higher of the two loads is to be considered)

1.Determine W, γI and λ
2.Determine the location of the building and get ag
3.Calculate the fundamental period T1
4.Specify soil type and city in which building located,
determine the type of response spectrum (Type 1 or
2) and get S, TA, TB, TC.
5.Get the value of Sd (T).
6.Substitute in the equation of Fb
Summary of the procedure for Base
Shear calculation

Distribution of the Horizontal Seismic Forces

➢First Method:
ET  E (Fx )  0.3E(Fy )
ET  0.3E(Fx )  E(Fy )
To be used in each direction
➢Second Method:
Horizontal Components of the Seismic Action.

Structural Modeling Modification Factors

The horizontal forces Fb shall be distributed to the
lateral resisting elements assuming rigid floors.
(Diaphragms)

Floor slab acts like a beam
resisting horizontal rather
than vertical forces and
possessing span-to-depth
ratio smaller than that of a
typical beam. Just like
simply supported beam the
diaphragm bends under
the influence of the
horizontal inertia forces,
spanning not between
piers or posts, but between
two structural walls

➢C.G. or Center of Mass is the location where the earthquake
force acts. It depends on the shape of the floor in plan.
➢C.R. or Center of Rigidity is the location of the resultant of
the forces that resist the earthquake force. It depends on the
distribution of the elements that resist the earthquake force.
Center of Gravity and Center of Rigidity
If the C.G. is not coincide with C.R., torsional moment will
develop. The torsional moment depend on Eccentricity.

Eccentricity
Center of
Resistance
Center of
Mass
Good systems (Symmetric) Bad System (big ecc.)

Shear Wall Structures
Non-twisting wall Systems
C.R. is located on the
C.M. (No eccentricity)
Eccentricity
Center of
Resistance
Center of
Mass
Twisting wall Systems
C.R. is NOT located on the
C.M. (eccentricity)

(EI )j
- Take an origin as a
reference.
∑(EI)j = the flexural rigidities for all walls parallel to the Y
axis at level j.
(EI.x)j = the sum of the first moment of the flexural
rigidities about a chosen reference point
1 2 3
x1
x2
x3
c3
c2
c1
x Center of twisting (C.R.)
To get C.R. location
(EI.x)j
X 

1) Non-twisting wall Systems
At any floor, the external shear force Qj and
external moment Mj will be distributed between
the walls in the ratio of their flexural rigidities.

requires consideration of accidental torsion by
increasing the design straining actions on element by
a factor δ.
Where:
X = distance from the element to the C.G.
Le = distance between the outermost elements
resisting EQ measured in a direction ┴ to EQ load.
For Symmetrical structures, the Egyptian code

Accidental torsion effects(code item 8-7-2)
In addition to actual eccentricity, to cover uncertainties in
location of masses, calculated center of mass at each floor
i shall be considered displaced from its nominal location
in each direction by an additional accidental eccentricity:
eli= ± 0.05 Li
Where:
eli :accidental eccentricity of storey mass i from its
nominal location, applied in the same direction at all
floors,
Li: floor-dimension perpendicular to the direction of
the seismic action.

Forces due to lateral loads are
Force due to direct shear

Twisting wall Systems
At any floor, the external shear force Qj and
external moment Mj will be increased due to torsion
Center of wall
rigidities
Structure twisting
about C

In case of structures have walls with and perpendicular
to the load direction:
The torsion effect will be resisted by all walls
(with and perpendicular to the load direction
Get (C.R.):
X
Y Perpendicular walls
(EI )j
(EI.x)j
X 
(EI )j
(EI.y)j
Y 

X
Y
Perpendicular walls
C.R.
c1
c2
d2
d1
c3
In that case the translation effect will be resisted by
walls parallel to the load direction only, but the
effect of twisting will be resisted by all WALLS

- The shear and moment in a wall i at level J
(Eccentricity in one direction)
Where: c = the distance of wall i from the C.R.
Effect of translation Effect of twisting

ij ij
For walls parallel to load Direction(eccentricity in Two direction)
ij j j
j
ij ij
ij j j
j
(EI ) (EI .c)
(EI) (EI .c)
Q Q (Q e)
(EI ) (EI .c2
)  (EI .d 2
)
M M (M e)
(EI ) (EI .c2
)  (EI .d 2
)
ij j
j
ij j
j
(EI .d )
(EI .d )
e) ij
Q  (Q .e) ij
(EI .c 2
)  (EI .d 2
)
M  (M
(EI .c2
)  (EI .d 2
)
For walls perpendicular to load direction
Effect of
Twisting
ONLYj
j
j
jj
j

Guide I for System selection
Simple symmetric and rectangular plans are preferable.
Buildings with articulated plans such are T, L and other
unsymmetrical shapes should be avoided as possible
and may be subdivided into simple forms

Guide II for System selection:
Symmetry of floor plans should be provided as possible because
lack of symmetry induces significant torsion effect (try to get the
center of rigidity coinciding with the center of mass).

Guide III for System selection
The infill walls alter lateral stiffness of frames and hence the
location of center of rigidity. Unsymmetrical infill wall can
cause significant torsion which should be accounted for in
design

Guide IV for System selection:
Regularity in building elevation in both geometry and storey
stiffness should be ensured. Abrupt changes in elevation may
result in concentration of straining actions at these locations.

Displacement Analysis: means maximum lateral movement of the
structure due to EQ forces, measured from the home situation.
Lateral Drift: is the relative movement between floors(difference between
the displacement of top floor and the displacement of the lower one)

ds = 0.7 R de
Where
:ds = Actual Displacement due to EQ forces
R = Ductility reduction factor
de = Computed displacement due to DEISGN
earthquake forces
0.7 = factor to get working displacement
(Note: earthquake force is ultimate load)

Requirements of Earthquake Separation

5.2.2 Code requirements for beam reinforcement
M+ at column face < 1/3 M- at column face
M+, M- at any section < 1/5 M- (max) at column face
c ) Lateral reinforcement :
1 - Maximum spacing between ties is the lesser of :
t/2 (beam depth)
200 mm
for earthquake design Maximum spacing is
8 φmin (longitudinal)
24 Φ stirrups
t/4 (beam depth)
for a distance from column face equal to: 2 t (beam depth)

Code requirements for column reinforcement
a ) Concrete dimensions :
1- Minimum dimensions of a column are 200 x 200 mm , and the minimum
column diameter is 200 mm.
For flat slabs the minimum column dimensions: L/20 h/15 300 mm
minimum column is 300 x 300 for ductile frames
b) Longitudinal reinforcement :
1- Minimum reinforcement :
1-1 Tied column :
A A
c gross
sc 
0.8
A A
cchosen
sc 
100
100
0.6
A
cchosen

100
1
(ductile frames)
1.2 Spiral column :
A
c gross
Asc 
100
1 A A
ccore
sc 
100
1.2

2- Maximum reinforcement :
4% For interior column. 4% (ductile frames)
5% For edge column.
6% For corner column.
c ) Lateral reinforcement :
Maximum spacing between ties is the lesser of :
15 φmin (longitudinal)
b (smaller dimension)
200 mm
for earthquake design Maximum spacing is 8 φmin (longitudinal)
24 φ stirrups b/2 (smaller dimension) 150 mm
for a distance from beam face equal to: h/6
t (larger dimension) 500 mm

Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engineering هندسة الزلازل & Assc.Prof Nasser El-Shafey)

Lec04 Earthquake Force Using Response Specturum Method (2) (Earthquake Engineering هندسة الزلازل & Assc.Prof Nasser El-Shafey)

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