Module 2_spring 2020.pdf

CE 412: Introduction to Structural Dynamics and
Earthquake Engineering
MODULE 2
(Concepts related to Earthquake engineering)

Seismic Risk
Seismic hazard depend on the geology of site and, therefore, cannot be controlled.
Seismic vulnerability belong to structures and, therefore, can be reduced by
appropriate design and construction
Seismic Risk can be minimized by reducing seismic vulnerability of
structures
5

Some basic considerations for seismic design
6

Effect of relative stiffness on lateral forces distribution
The lateral force is distributed (at a particular story level) in proportion to the relative
stiffness of the resisting members.
The applied forces are “attracted to” and concentrated at the stiffer elements of the
building. Hence, if two elements (two frames, walls, braces, or any combination) are
forced to deflect the same amount, and if one is stiffer, that one will take more of the
load.
7

In the figure the columns have the same cross-section, but the short column is half the
length of the long one.
Effect of relative stiffness on forces distribution
8
450 lb
Mathematically, the stiffness of a column
varies approximately as the cube of its length.
Therefore, the short column will be eight times
stiffer (23) instead of twice as stiff and will be
subject to eight times the horizontal load of the
long column.
Stiffness, k= coefficient x EL/L3

H.Assignment 2.1
10 k
10 ft 15 ft
Fig. 1
10 k
10 ft 15 ft
8 ft
Fig. 2
Draw S.F.D and B.M.D of given frames. Assume:
1. EI= Constant in coulmns in all cases
2. Beams are infinitely stiff in flexure. i.e. beam-column joints act as fixed supports

Torsional Forces
The center of mass, or center of gravity, of an object is the point at which it could be
exactly balanced without any rotation resulting.
If the mass (or weight) of a building is uniformly distributed (in plan), the result is that
the plan's geometric center (centroid) will coincide with the center of mass.
In a building, the main lateral force is contributed by the weight of the floors, walls,
and roof, and this force is exerted through the center of mass, usually the geometric center
of the floor (in plan).
If the mass within a floor is uniformly distributed, then the resultant force of the
horizontal acceleration of all its particles is exerted through the floor's geometric center
11

12
Torsional Forces
Centre of mass and rigidity
Centre of rigidity
The distance between the center of mass and the center of rigidity, C.R. (or
center of stiffness) is referred as eccentricity. This eccentricity makes a
building subjected to ground motion rotate around its center of rigidity,
creating torsion - a twisting action in plan, which results in undesirable and
possibly dangerous concentrations of stress

In a building in which the mass is approximately evenly distributed in plan (typical
of a symmetrical building with uniform floor, wall and column masses) the ideal
arrangement is that the earthquake resistant elements should be symmetrically placed,
in all directions
In practice, some degree of torsion is always present, and the building code makes
provision for this.
13
Torsional Forces

Non structural components
Structure (left), nonstructural components and systems (right). 14
In most modern buildings, the nonstructural components account for 60 to 80
percent of the value of the building

Non structural components
The nonstructural elements (such as parapet walls, furniture video 1 start at 4:00 , video 2) if
not properly anchored can impose serious threat to human lives.
The nonstructural components or systems may modify the structural response in
ways detrimental to the safety of the building. Examples are the placing of heavy
nonstructural partitions in locations that result in severe torsion and stress
concentration, or the placement of nonstructural partitions between columns in such a
way as to produce a short column condition (video start at 1:00). This can lead to column
failure, distortion, and further nonstructural damage.
15

Common construction issues affecting seismic resistance
of structures.
16

Four serious configurations conditions
Four configuration conditions (two vertical and two in plan) that originate in the
architectural design and that have the potential to seriously impact seismic
performance are:
1. Soft stories
2. Discontinuous shear walls
3. Variations in perimeter strength and stiffness
4. Re-entrant corners
17

1. Soft-story effect
The most prominent of the problems caused by severe stress concentration is that of the
“soft” story.
The term “soft-story” refers to one level of a building that is significantly more flexible
or weak in lateral load resistance than the stories above it and the floors or the foundation
below it (70% or greater reduction from one floor to the next according to the modern,
International Building Code (IBC) definition).
The soft first story failure mechanism. 18

Lower story columns were collapsed in a hotel at
Balakot, 2005 Kashmir earthquake
Avoid soft-storey ground floors!
20
Permanent plastic deformation in the ground floor of a
building under construction. Soft story effect almost provoked
a collapse (Friaul, Italy 1976).

Avoid soft-storey Upper floors!
Intermediate story columns are completely
collapsed
Bagh, 2005 Kashmir earthquake
21
Kobe, Japan 1995.

Solutions
Add columns Add bracing Add external buttresses
22

Solutions
This apartment house appears to have a soft first story (Figure A), but the lateral force-resisting system is a
strong internal shear wall box, in which the shear walls act as party walls between the dwelling units
(Figure B).
23
Fig A Fig B

2. Avoid discontinuous Shear Walls
When shear walls form the main lateral resistant elements of a structure, and
there is not a continuous load path through the walls from roof to foundation, the
result can be serious overstressing at the points of discontinuity. This
discontinuous shear wall condition represents a special, but common, case of the
“soft” first-story problem.
24

Long section, Olive View Hospital. Note that the shear walls stop at the third floor.
Cross section, Olive View hospital, showing the second-floor plaza and the discontinuous shear wall.
25

Olive View hospital, San Fernando earthquake, 1971, showing the extreme deformation of the
columns above the plaza level.
26

The solution to the problem of the discontinuous shear wall is to eliminate the shear
walls.
If the decision is made to use shear walls, then their presence must be recognized from
the beginning of schematic design, and their size and location made the subject of careful
architectural and engineering coordination early.
Solutions
27

This problem may occur in buildings whose configuration is geometrically regular and
symmetrical, but nonetheless irregular for seismic design purposes.
If there is wide variation in strength and stiffness around the perimeter, the center of
mass will not coincide with the center of resistance, and torsional forces will tend to
cause the building to rotate around the center of resistance.
3. Variations in Perimeter Strength & Stiffness
28

Left, the building after the earthquake. Right, typical floor plan showing the Center
of Mass (CM), Center of Resistance (CR), and Eccentricity (e) along the two axes.
29

A common instance of an unbalanced perimeter is that of open-front design in buildings, such
as fire stations and motor maintenance shops in which it is necessary to provide large doors for
the passage of vehicles.
Unbalanced perimeter resistance: storefronts and “wedges.” 30
Centre of rigidity

3. Variations in Perimeter Strength and Stiffness
Penney’s store, Anchorage, Alaska, earthquake, 1964. Left: Damage to the store: Right: Second-floor plan,
showing unbalanced perimeter resistance
31

Solutions
The solution to this problem is to reduce the possibility of torsion by endeavoring to
balance the resistance around the perimeter.
The opaque portion of the perimeter can be constructed of nonstructural cladding,
designed so that it does not affect the seismic performance of the frame. This can be done
either by using lightweight cladding or by ensuring that heavy materials, such as concrete
or masonry, are isolated from the frame (Figure A)
32

Solutions
A second approach is to increase the stiffness of the open facades by adding sufficient
shear walls, at or near the open face, designed to approach the resistance provided by the
other walls (Figure B).
33

Solutions
A third solution is to use a strong moment resisting or braced frame at the open front, which
approaches the solid wall in stiffness.
The ability to do this will depend on the size of the facades; a long steel frame can never
approach a long concrete wall in stiffness. This is, however, a good solution for wood frame
structures, such as small apartment buildings, or motels with ground floor garage areas, or
small store fronts, because even a comparatively long steel frame can be made as stiff as
plywood shear walls (Figure C).
34

4. Re-entrant Corners
The re-entrant corner is the common characteristic of building forms that, in plan, assume
the shape of an L, T, H, etc., or a combination of these shapes
Re-entrant corner plan forms.
35

There are two problems created by these shapes.
The first is that they tend to produce differential motions between different wings of the
building that, because of stiff elements that tend to be located in this region, result in local
stress concentrations at the re-entrant corner.
The second problem of this form is torsion. Which is caused because the center of mass and
the center of rigidity in this form cannot geometrically coincide for all possible earthquake
directions. The result is rotation. The resulting forces are very difficult to analyze and predict.
36

37
Re-entrant corner
Centre of rigidity

Differential deformation at the junction of two wings
38

Solutions
Separation
Stiff resistant elements
In case of separation building must be sufficiently away to ensure they do not pound
together and damage each other in an earthquake
40

41
Solutions
The use of splayed rather than right angle re-entrant corners lessens the stress
concentration
This is analogous to the way a tapered beam is
structurally more desirable than an abruptly
notched one.
Splayed re-entrant corners
Recommended ?
Shall be avoided ?

The space between columns is sometimes filled in by a rigid wall, leaving a short space
for a clerestory window (a high windows above eye level to bring outside light, fresh air,
or both into the inner space).
Such a simple act of remodeling may not seem to require engineering analysis, and a
contractor may be hired to do the work: often such work is not subject to building
department reviews and inspection. Serious damage has occurred to buildings in
earthquakes because of this oversight.
Avoid short columns!
42

Partial floor- height panel infill Start time 1:00 Failure pattern
43
inserting parapet walls into a frame led to a short column phenomenon. Owing to the good confinement of the
transverse reinforcement, no actual shear failure occurred, but an equally dangerous sway mechanism developed
(Friaul, Italy 1976).

44
The diagonal cracks and shear failures in the short columns of a multi-storey car park almost
caused collapse (Northridge, California 1994).

Avoid strong beam- weak column
45
Strong beam-weak column joint simulates fixed
support, resulting in larger moments at joint
Ground floor of an under construction commercial
plaza (Muzzafarabad, 2005)

Inadequate lap of longitudinal bars in a collapsed column. (Abbotabad,2005)
Provide Adequate Anchorage
46

Separate adjacent buildings by joints!
Building must have sufficient separation to ensure they do not pound together and damage each
other in an earthquake. Generally if framed buildings are separated by at least 0.01 H, pounding
will not be a problem. (e.g. two 6-metre tall buildings should be separated by 60mm.)
47

Separate adjacent buildings by joints!
48

Use closely spaced transverse reinforcement with 135° hooks in
structural walls and columns!
Effect of confinement ( by decreasing ties spacing) spacing on the compressive strength of plain concrete
specimens

50
90o hooks open up at relatively smaller force as compared to 135o hooks

51
Largely spaced rings resulted in failure of column (due to spalling of concrete from rings) in a building
at Abbotabad during 2005 Kashmir earthquake

Closely spaced rings avoided collapse of column.
Left (Muzaffarabad secretariat,2005. Right (Taiwan, 1999)
52

53
Anchor free standing parapets walls & other elements
attached to the structure!
Out-of-plane overturning of freely standing masonry infills in reinforced concrete frames in
Muzaffarabad during 2005 Kashmir earthquake

54
Typical failure of boundary walls (left, Abbotabad) and overturning of a slender parapet prevented by proper
bracing across the length (right, Garhi Habibullah). 2005 Kashmir earthquake.

55
Water tanks fallen from supporting masonry piers due to their tensile failure Abbotabad &
Mansehra during 2005 Kashmir earthquake. Tanks, properly anchored to R.C. Columns through
steel reinforcement could have avoided this situation

Various mechanisms to dissipate energy imparted to a
structure by an earthquake
56

Response of a building with no base isolation is shown in Figure a. Where, response of the
building with base isolation can be simulated by Figure b, where the rollers move during
ground shaking but the building above does not move and no force is transferred to the
building due to shaking.
Base Isolation
(a) (b)
57

Base isolation is carried out, mostly, by using
i. Laminated rubber bearing (LRB)
ii. Spherical Sliding Isolation Systems
Lead-rubber bearings (LRB) are among the frequently-used types of base isolation
bearings. (See figure on next slide)
An LRB is made from layers of rubber sandwiched together with layers of steel. In
the middle of the bearing is a solid lead "plug." On top and bottom, the bearing is
fitted with steel plates which are used to attach the bearing to the building and
foundation. The bearing is very stiff and strong in the vertical direction, but flexible in
the horizontal direction.
Base Isolation
58

The bearing is very stiff
and strong in the vertical
direction, but flexible in the
horizontal direction.
a) Laminated rubber bearing (LRB).
Lead-Rubber Bearing
Lead plug in the middle of bearing experiences the same deformation as the rubber. However, it also generates heat as it
does so. In other words, the lead plug reduces, or dissipates, the energy of motion--i.e., kinetic energy--by converting that
energy into heat
Base Isolation
59

a) Laminated rubber bearing (LRB).
Experiments and observations of base-isolated buildings in earthquakes have been shown
to reduce building accelerations video1, video 2 to as little as 1/4 of the acceleration of
comparable fixed-base buildings, Increase or decrease in acceleration proportionally
increases or decreases inertial force as inertial forces are directly related to acceleration (FI =
ma).
Base Isolation
60
Building resting directly on ground Building base isolated with LRB (large displacements and acc. In

Lead-rubber bearings are just one of a number of different types of base isolation bearings
which have now been developed. Spherical Sliding Isolation Systems are another type of base
isolation. The building is supported by bearing pads that have a curved surface and low friction.
Spherical Sliding Isolation Bearing
b) Spherical Sliding Isolation Systems .
Base Isolation
61

62
The force needed to move the building upwards limits the horizontal or lateral forces
(Transformation of K.E into P.E & vice versa) which would otherwise cause building
deformations.
b) Spherical Sliding Isolation Systems .
Base Isolation
It should be noted that base isolation is not suitable for tall high rise buildings or
buildings located on soft soil.
Base isolation is most effective for short to medium rise buildings located on hard
soil.

Under a simple harmonic load, one can show that the main mass can be kept completely
stationary when the natural time period (of the attached absorber is chosen to be (or tuned
to) the time period of excitation .
During an earthquake or wind , TMD will move against the direction of main structural
vibration and an inertia force will be acted on the structure to reduce the response of the
structure .
TMD are effective in controlling wind induced excessive vibration in high rise buildings
due to one specific value of time period of tuned mass. However, multiple tuned mass
dampers have also been devised to control vibration during earthquake corresponding to
important modes
Tuned Mass Damper (TMD)
63

64
Assignment 2.2
1. How we can reduce the seismic risk of an existing building stock?
2. What will be your strategy as a design engineer to avoid soft story effect at a floor
(other than ground floor) without providing any wall?
3. How you will cope, as a design engineer, where you cannot avoid short columns?
4. How you will handle a situation as a design engineer where you cannot change the
x-sectional dimensions of a very stiff beam connected to a flexible column?

Module 2_spring 2020.pdf

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Module 2_spring 2020.pdf