INTRODUCTION IN SEISMIC

Seismic design 

Is primarily concerned with structural safety during major earthquakes, however the serviceability and the economic loss are also concern, depend on the size of the earthquake which the book divide them as follow:-

1-Minor → no damage

2-Moderate → some damage in nonstructural elements

3-Major→ some damage in structural elements

On the other hand, the distribution of forces and displacement resulting from earthquake influenced by three main factors:-

1-Properties of the structure

2-Properties of the foundation

3-The character of the earthquake it self

Building behavior 

The main idea is the inertial forces caused by vibration of the building mass are the main reason of building damages and the increase of the building mass may be has undesirable effects on earthquake design (F=m*a)

Where (m=building mass) (a=ground acceleration)

The magnitude of inertia force depends as we mentioned on:-

1-Building mass

2-The nature of foundation

3-Ground acceleration

Also the dynamic characteristics of the structure

So, 1-for the infinitely rigid buildings and it’s foundation it would have the same acceleration as the ground, in this case F=m*a

       2-for the buildings that deforms slightly it absorb some energy, in this case F<m*a

       3-for the tall buildings it’s more flexible than low rise buildings and much lower                                                                                        acceleration but it has much period that produce larger forces

Where (period=the length of a full cycle in second)

The magnitude of lateral force is not a function of the acceleration of the ground only, but also the response of the structure and its foundation and this relationship depends on the building period

The fundamental period for building is a function of its stiffness mass and damping characteristics and can vary from 0.05 to 0.30 times the number of stories

Influence of soil 

Harder soils and bedrock will transmit short-period vibrations and vice versa with softer soils, also the acceleration will be amplified if the fundamental period of the building coincides with the period of vibrations being transmitted through the soil, this amplified response called resonance

Damping 

Is the prevention of the building to oscillation and this depends on the building materials, connections and the effect of the nonstructural elements on the stiffness of the building, and the damping rations used in practice vary from 1% to 10% of critical damping

Where (critical damping=the minimum amount of damping necessary to prevent oscillation completely

Building drift

 In general is the total displacement of any point relative to the base, building joints must to permit adjoining buildings to respond independently to earthquake motion

Seismic design concept

1-select system that appropriate to the expected level of ground shaping, this include a redundant and continuous load path to ensure that the building responds as a unite

2-determining code forces and deformations

3-analys the building for the combined effects of gravity and seismic loads

4-providing details to assure the building has sufficient inelastic deformation ability to dissipate energy of the motion

Structural response to seismic

The resulting stresses and distortions in building are the same as if the base of the structure were to remain and horizontal forces are applied to the upper part of the building, these forces are the inertia forces equal F=m*a  where (m=w/g)

In general the building deforms in three dimensional manner (one vertical, two horizontal)

The inertia forces generated by the horizontal require greater consideration which the resistance to vertical seismic loads usually provided by the member capacities required for gravity loads

Load path

Seismic forces originated mostly in the heavy mass elements such as diaphragms, horizontal diaphragms distribute these forces to vertical force-resisting elements transfer the force into the foundation and the foundation transfer into soil

Irregularity

Typical building configuration deficiencies include an irregular geometry such as

1-A weakness story

2-Discontinuity in lateral system

3-A concentration of mass

These irregularities are defined in terms of strength, stiffness, geometry and mass and they can come with each other for example:- building that has a tall first story it has two of these terms (stiffness, strength)

Lateral loads resisting systems

1-Space frame resists the earthquake, the columns and beams act in bending, also this type has a large story drift but it may be accommodate without causing failure of columns or beams this system may be a poor economic risk unless special damage-control measure are taken

2-Shear wall system this more rigid than the previous, the story drift is relatively small, also it’s economical method to limit damage

This system excellent in these cases

1-Height to width ratio large enough to overturning problem

2-Soil is relatively soft

3-Dual system this when the frame alone can resist 25% of the lateral loads

4-Diaphragms this is the horizontal element (roof-floor) that distributed the lateral loads to the vertical structural elements

The diaphragms act like a deep beam, the floor is the web that carrying the shear and the wall is the flange of the beam that resisting the bending

The diaphragms must have the following:-

1-Resist bending and shear tied to act as one unite

2-To be adequate to transfer loads to lateral system

3-Openenig or reentrant must properly places and adequately reinforced

Ductility 

The capability to absorb energy with acceptable deformations without failure and it depend on the building materials, systems and reinforcing details

The ductility is measured by the hysteric behavior of critical component such as columns-beam assembly of moment frame (refer to figure 2.9)

Continues load path 

Or preferably more than on path with adequate strength and stiffness should be provided from the origin of the load ‘’inertia forces generated in an element’’ to the final lateral load resisting elements

Redundancy

Is a crucial characteristics for a good lateral performance and this means that the failure of a single connection or element doesn’t negatively affect the lateral stability of the structure 

Configuration

Building with irregular configuration won’t perform as well as a building with regular configuration even if it meet all code requirements

There are two types of irregularity:- 

1-Vertival irregularities 

2-Plan irregularities

For example, the building that take shapes (I, L, H, X) this is a plan irregularities and these shapes have two problems in seismic performance:-

1-Differential vibrations

2-Torsion because the not coincidences of the center of mass and the center of rigidity

We can solve these problems by tie the buildings together at lines of stress concentration and locate seismic resisting element at the extremity of wings or separate the building with joints with adequate width that allow the building to behave independently

Dynamic analysis

Static method based on single mode response while appropriate for simple regular structures

The dynamic analysis is preferred for design of buildings with unusual or irregular geometry

Symmetrical buildings with non-irregularity features behave in a fairly predictable manners, while the buildings that are asymmetrical or with irregularities don’t behave with predictable manners

For such buildings the dynamic analysis is used to determine response characteristics such as

1-Effect of the structure’s dynamic characteristics on the vertical distribution of lateral forces

2-The increase of dynamic loads

3-The effect of higher modes, resulting in an increase in story shears and deformations

SDOF-MDOF 

Simple oscillators are represented by single-degree-of-freedom system

Complex oscillators are represented by multi-degree-of-freedom system

SDOF the idealized system represent two kinds of structure

1-Single column with relatively large mass at its top

2-Single story frame with flexible columns and rigid beam

If the mass is deflected and then suddenly released, it will vibrate at a certain frequency that called fundamental frequency, the reciprocal of frequency is the period of vibration , it represent the time of the mass to move through one complete cycle, the period (T) is given by the following relation

T=2π*(M/K) ^0.5

Where (M=mass) (K=stiffness)

In an ideal system without damping the system will vibrate forever, but in the natural system and as the results of the damping effect the amplitude of the vibration will gradually decrease

The system will act in a similar manner if the instead of deflects the mass in the top, a sudden force hit the system to its base

MDOF the structure may be analyses as a multi degree of freedom by summing the story masses at intervals along the length of vertical pole

During the vibration each mass will behave differently, for higher modes of vibrations some masses may have in opposite directions or all masses may simultaneously deflect in the same direction as in the fundamental mode

The idealized of MDOF system has a number of modes equal a number of masses

When the ground motion is applied to a multi mass system, the deflects shape of the system is a combination of all mode shapes

For modes that have periods near predominated period of the motion will affect more than the other modes

Each mass presented by a single mass system having a generalized value (M) and (K), this values represent the equivalent combined effect of story masses and stiffness 

Building with irregularities is complicated not only the method of dynamic analysis, but also the method of combine the modes, so for building with regular and symmetrical shape, two dimensional model is sufficient

Note when the plan of the building aspect ratio (length/width) is large, torsion response may be predominate so it is required 3D analysis

For most building inelastic response can be expected to occur during a major earthquakes, that is mean that the inelastic analysis is more proper for design, but due to its difficulties and because it is expensive, in practice typically use linear procedures based on the response spectrum method

INTRODUCTION IN THE POST TENSION

Post tensionning

Types of prestressing

1-Post tensioning

• The prestressing steel is either placed in a duct or sleeve before the concrete is cast

• After the concrete is being casted and gained adequate strength, a stressing jack pulls the steel strands while reacting against the body of concrete member

• Over time, a friction of the initial force in the concrete is lost due to creep and shrinkage of the concrete and relaxation of the steel

2-Pretensioning

• The prestressing steel is first stressed and anchored against external bulkheads, concrete is then casted over the stressed steel

• Once the concrete has developed adequate strength, the tendons are released from the bulkheads

• The tendency of the stretched tendons to shorten pre-compresses the concrete

Advantages of post tensioned construction

1-Less steel

• Using higher tensile strength of prestressing steel provides four and half times the capacity of the conventional steel 

• The codes require a minimum amount of reinforcement in slabs to control shrinkage and temperature

• The codes require a minimum amount of reinforcement to be distributed through the slab in both directions, so that the slab will have the necessary in plan strength for diaphragm action

• The pre-compression imported by tendons spread rapidly through the slab from the anchorages and is sufficient to prevent cracking from shrinkage and temperature changes

• The pre-compression provided by tendons under service condition is generally more than the minimum reinforcement required for diaphragm action, thus eliminating the requirement of adding reinforcement

2-Thnner slabs “less concrete”

• Once span length exceed 5m, a post tensioned slab will be approximately one third thinner than the reinforced concrete slabs designed for the same loading

3-Large spans

• Post tensioned slabs can span greater than conventional slabs of the same thickness 

4-Simple forms “eliminating of beams”

• Application of post tensioning can allow beam to be eliminated, that will reduce the cost of forming as much as one-third of other system’s cost

5-Ability to better span irregular support arrangement

• Post tensioned slabs don’t have to rely on the beam-and-slab framing common in conventional slabs, thus post tensioned slabs are particularly adaptable to irregular geometry

6-Lighter concrete forms “lower seismic demand”

• The post tensioned concrete frame is generally one-third lighter than a conventionally reinforced

• The supports and foundation tank the advantaged of the lighter floor system

7-Shorter concrete frames “reduce floor height”

• Reducing slab thickness and elimination of beams results in shorter floor-to-floor height, and consequently, a reduction in the total height of the building

• The shorter building have lower arm for the overturning moment created by seismic or wind

8-Greater ability to resist concentrated forces

• The post tensioned acts as active load system, the applied force from post tensioning is generally configured to counteract the externally applied force, this reducing their undesirable effects

• The tendons can be profiled to apply on upward force from that when combined with pre-compression from the tendons will counteract the applied force without undue deflection or need for local cracking

9-Reduce deflection

• Post tensioning provides an upward force that balances a high friction of floor self-weight, thus reducing the net downward force that causes deflection

• Post tensioned floors have greater flexure stiffness

10-Reduce cracks

• Because the (ACI 318) imposes a low limit on the allowable tensile stresses, two way post tensioned floor slabs will be essentially crack-free under service conditions

• When using the (EC2) the designer selects the extend of allowable cracking and a design crack width based on the anticipated in-service conditions of floor system

• The designer choice becomes the amount of cracking and design crack width, as opposed to the elimination of cracking that results when using (ACI 318)

11-Improve resistance to water penetration

• Because the post tensioned slabs have fewer cracks, thus provides a greater resistance to water penetration

12-Preception and acceptability of vibration

• Foot fall on large areas supported on thin slabs can trigger unacceptable vibrations; cracking will exacerbate the problem because it lowers the natural frequency of the slab

• Post tensioned slabs are generally thinner than their  conventionally reinforced counterparts and have longer spans, thus they are more prone to unacceptable vibrations

• Two benefits of post tensioning help to reduce susceptibility of post tensioned floor to objectionable vibration

• One is the reduction of weight (mass), the other is a larger relative stiffness because of less cracking, both features help to increase the natural frequency of vibration and improve the design

• On the other hand, the longer spans used in post tensioned structure tend to lower the nature frequencies and aggravate the perception of vibration 

• The vibration of post tensioned slabs under foot fall should generally be investigated where spans are relatively large

Application of post tensioning in building construction 

1-Floor system “flat slab construction”

a. Application in regions of high seismic risk, high wind forces

• Because of lower weight and height and the improved of diaphragm action that results from pre-compression

b. General building applications

• Optimum design in residential and commercial building flat slabs have spans between (8m to 10m)

2-Floor system “beam and slab construction”

• When the aspect ratio of a slab panel exceeds two, it’s often more economical to use this system

3-Podium slabs in low rise building

• For building up to five levels, post tensioned podium slab resists concentrated loads from posts and walls of the upper levels without requiring a support immediately below each load

• Podium slabs are used in building which the lower level require a support layout that is different from the levels above

4-Transfer slabs

• For high rise building where open space is required at the ground floor, one solution is to terminate the supports of upper levels on a transfer slab that received the loads from supports of super structure and transfer them to a limit number of generally widely spaced supports

5-Mat (raft) foundation

• Post tensioned mat is used when the allowable bearing pressure is not adequate to resist peak stresses below walls and columns, but the total area of the soil below the foot print of structure is large enough to resist the total load

• A well designed post tensioned mat can be as much as 40% thinner than a conventional reinforced concrete

6-Industrial ground support slab

• In industrial storage areas, it’s necessary to provide a smooth ride for forklift and other loading equipment, a conventionally reinforced slab besides being subject to shrinkage cracks cannot accommodate the changes in the underlying soil with the flexibility of post tensioned alternative

• Construction of post tensioned ground support slab

a) Covering the upper layer of underlying soil with two large of plastic sheets

b) The tendons are laid out

c) The concrete is casted

d) The tendons are stressed

7-Slab-on-grade “SOG for residential and light industrial”

• SOG used to limit the effect of seasonal changes on building by limiting the shallow foundation movement

• The objective is generally to limit the deformation in the structure to an amount that doesn’t impair it’s serviceability

8-Retrofit through external post tensioning

• Post tensioning has been used effectively to correct strength and deflection deficiencies in building

• When post tensioning is applied judiciously, its active force can configure the probable failure mode of structure, thus enhancing the structure’s level of safety

9-Post tensioning to restore geometry in seismic frames

• In region of high seismic risk, building are designed to undergo post-elastic deformation, this helps dissipate the seismic energy and reduces the demand on resistance from the building frames

• While building are designed to prevent collapse under anticipated seismic forces, they are expected to sustain damage

• Observation from an earthquake revealed that multi story buildings that have experienced post-elastic deformation may not return to their original plumb position

• Post tensioning can be used to restore a building closer to its original position after post elastic deformation from an earthquake

• This is done by directing and controlling the post elastic deformation to designed location and using the force of prestressing tendons to restore the building to its original plumb position

10-Post tensioning in walls

• When the lateral forces along the length of the wall are large and the vertical axial force is not adequate to prevent the wall from excessive tension, the wall possibly overturning

• Post tensioning along the height of the wall in the vertical direction can be used to reduce tension and keep the wall in position

11-Post tensioning in column

• When the column is subjected to significant bending, post tensioning reduces the axial capacity of the column

Post tensioning material and hardware

• Types of post tensioning tendons systems

a. Unbonded

• The prestressing steel is coated with a corrosion inhibiting grease, then encased in aplastic 

Marking and recording of tendons position

• Recording the as-installed location of the tendons is necessary to modify the structure in the future

• This helps to identify where repair or drilling will require special precautions

A. Marking of tendons on finished floors

 One way is to spray paint the location on the formwork before the concrete is cast, the paint mark will be transferred to slab soffit

 Another option is to paint the tendons location on the slab soffit after removing the forms

B. Photo\video recording of reinforcement

 Recording the position of reinforcement through photographs or videos and file the record as  part of the as-built documents of the construction 

Economics and material quantities

• The economy of post tensioned slab versus a conventionally reinforced slab is a function of span length, the span of (7m) is the cross-over point between the two options

• Compliance with different building codes and local practice can override the general case

• When (ACI 318) is used for the design of column-supported floor system, a minimum amount of prestressing is required and spacing between tendons is limited 

• These requirements do not exists in (EC2)

• These and other requirements such as allowable stresses, mean that the design quantities are often a function of the building code

• Engineering principles, local perception of good practice, can play a significant role in the quantities commonly used

1-Material quantities

A. Practice and project examples

 The quantities consists of concrete, prestressing strands and non-prestressing reinforcement

 The conversion to post tensioning reduce the total weight of reinforcement (combined PT and rebar ) by over 2.5 times

B. Base quantities for code compliance (ACI 318 AND EC2)

 The quantities used in each construction derive from two requirements

i. First, the reinforcement to comply with the in-service and safety requirements for the applicable code

ii. Second, the reinforcement for structural detailing used for crack control at discontinuities 

C. Reinforcement for detailing

2-Construction cost

• The bulk of the construction cost of a post tensioned floor consists of material, field labor, and equipment

A. Material cost

 Cost of rebar, purchased, bent, and placed

 Cost of prestressing material including hardware, placing, and stressing

B. Labor cost

 The benefits of post tensioned structures includes

i. Less reinforcement, which results in lower labor cost for handling and placing

ii. Simplification in construction, which reduces the cost of labor for forming 

iii. Shorter construction cycle

 The construction cycle is typically one week

 This includes stripping and re-shoring the previously cast concrete, moving the forms to next pour and installing them, placing rebar and prestressing tendons, inspection, placing concrete, and stressing tendons3

Repair, Retrofit, Maintenance, and life cycle

1-Floors reinforced with grouted tendons

• For slab with grouted tendons, the procedure for repair or remodeling are similar to conventionally reinforced slab

• The prestressing steel is bonded to the concrete the same way that non-prestressing reinforcement is, but there are some important differences

I. At the strength limit state (USL), prestressing strand is capable of developing three to more than four times the force of non-prestressing reinforcement of the same cross-sectional area, thus cutting a prestressing strand can be more detrimental than cutting a rebar of comparable size if the design relies on the full strength of the cut strand.

As a result, the loss of effectiveness of the strand extends over a longer distance from the location of the cut

II. Bonded strand provides local precompression that is beneficial to crack mitigation, this precompression is lost if a section of the strand is removed 

The precompression from each strand is dispersed into the slab when the strand is stressed, once the tendon is grouted, the precompression is locked into the floor system

When the tendon is cut, there will be a local reduction in precompression, but the precompression imported from the remainder of the strand will remain

• It is not necessary to re-stress and re-anchor a strand that has been cut, the grout that is injected into the duct, once hardened, locks the force into the tendon

2-Floors reinforced with unbonded tendons

• When an unbonded strand is cut, it losses it force a long its entire length, thus its contribution to both serviceability and safety of the structure is completely lost

The cut tendon’s contribution to the precompression in the floor system will be lost over the entire length of the tendon

• The loss of force and effectiveness of a tendon over its entire length require that the contribution of each tendon to be fully evaluated and, where necessary, compensated for the repair or retrofit

• The repair/retrofit procedure generally consists of 

1. Exposing the affected tendons 

2. Carefully cutting them

3. Re-stressing tem and re-anchoring them at the face of the cut

The sequencing of the work may vary depending on the number of tendons need to be cut and the location of the new opening or the repair 

• From the standpoint of a structure’s serviceability and safety, the loss of a single strand either inadvertently or by design, is usually not critical

Structural analysis for the effects of a lost tendon is often demonstrates that the structure has enough redundancy that it can lone one or more tendons without compromising its intended performance

• If it is necessary to replace a lost strand, one option is to extract the damaged portion of the strand and rethread the sheathing with a smaller diameter, but higher strength

The new strand is coupled to the existing strand and the tendon is restressed