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CE 31D STRUCTURAL DESIGN II

EARTHQUAKE-RESISTANT DESIGN

OUTLINE OF TOPICS(3 No. Sessions at 2 hrs each)

by R. Clarke

Delivery Media:

Equipment:

Objective: To enable the earthquake-resistant design of regular RC space framebuildings.

Scope/Limitations: UBC-94; Regular Buildings; Special Ductile Moment-ResistingSpace Frames of Reinforced Concrete.

Primary Approach: Procedure-Based; Graphics-Based; Example-Based.

TOPICS

1.0 The Effects of Earthquakes on Buildings1.1 The Earthquake Cause-to-Effect Chain1.2 Typical Building Responses to Inertia (Framed Buildings)

2.0 Earthquake-Resistant Structural Design2.1 The Design Earthquake2.2 Earthquake Resistant Design Philosophy

3.0 Earthquake-Resisting Structural Systems

4.0 The Earthquake-Resistant Design of RC Special Ductile Moment-Resisting SpaceFrames

4.1 Load Combinations4.2 Beam Design4.3 Column Design

5.0 Example Design of a RC Special Ductile Moment-Resisting Space

Oral Blackboard Handouts Slides/Transpar-encies

Slide Projector TransparencyProjector

Internet

ComputerProjector

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1.0 The Effects of Earthquakes on Buildings

1.1 The Earthquake Cause-to-Effect Chain

In accordance with tectonic plate theory, the earth’s crust is divided into a number ofplates. These plates, which are composed of rock, are interlocked at their surface therebyforming fault lines. However, each plate is moving relative to the other so that over time,the interlocked plates develop strain and therefore potential energy is stored in the platesat the fault. When this strain reaches a limit, the plates slip and release the energy. Thisis the primary cause of an earthquake.

This release of energy generates two types of waves: body waves (P and S), which radiatefrom the sources of the slip, and surface waves (L and R), which are restricted to thesurface (Fig 1 items 1 to 3). The P wave propagates in the same direction as its motionand travels at about 5.6 km/s and is the first wave to arrive at a location. The S wavepropagates at right angles to its motion and travels at about 3.2 km/s. S waves inflictmore damage to a building since they transmit more energy. Surface waves travel moreslowly than body waves, and R waves generally travel slower that L waves. All thewaves are refracted and reflected at discontinuities, and reflected at the surface, so that atany point a complex combination of wave-forms arrives over a period greater than thattaken for the original disturbance.

The magnitude of an earthquake is an expression of the amount of energy released at thesource of the earthquake (called the hypocentre or focus) and is usually expressed using alogarithmic scale (e.g. Richter scale). The intensity of an earthquake is a measure of theactual ground shaking at a particular point on the surface of the ground. A qualitativemeasure of the intensity is the MM scale which ranges from I to XII and is a subjectiveassessment based on observation of the effects of the earthquake (e.g. an earthquake is ofMM intensity V if it is felt outdoors; sleepers are awakened; doors swing, etc). Acommon quantitative measure of earthquake intensity is the ground acceleration. This isrecorded on an accelerometer for the duration of the earthquake (Fig 1).

The ground shaking is a dynamic phenomenon in that it induces inertia forces on abuilding (Fig 1 item 4). The inertia forces are in a feedback relationship with thebuilding. This is because the magnitude of the inertia forces depends on the deformationof the building, which in turn depends on the magnitude of the inertia forces.

1.2 Typical Building Responses to Earthquakes (Framed Buildings)

The inertia forces are the applied loads on the building. The total inertia force isequivalent to the base shear, V of seismic design code formulae. The design engineermust know the values of the inertia forces in order to analyse and then design thebuilding. Although the inertia forces vary with time, the engineer is typically concernedwith the maximum inertia force applied at each floor.

The inertia force acting on a floor is applied through the CG of the floor (Fig 2).However, the CG of the floor does not coincide with the centre of stiffness or rigidity,CR, of the floor (Fig 3).

Hence this causes torsion of the floor, in addition to the direct inertia forces (Fig 4).Though we know the inertia and torsion forces on the floor, the building is typicallymodelled as a space frame. Therefore to analyse the building, the inertia and torsionforces his must be converted to point loads on the frames (Fig.5).

Analysis of the frame under the earthquake loads gives certain typical patterns of thedesign actions (moments, shears and axial loads) for the structural elements.

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Fig 6 to 8 shows typical bending moment and shearing force diagrams for beams. Fig 9shows typical axial load and bending moment diagrams for columns.

2.0 Earthquake-Resistant Structural Design

2.1 The Design Earthquake

In order to design buildings to resist earthquakes, the first question to be answered iswhat magnitude of force must the building resist. The design earthquake can be definedin terms of any effect resulting from the fault slip (e.g. ground acceleration, groundvelocity, ground motion spectra, etc) and that imposes stresses on the building. Hence,the design earthquake must be differentiated from the design event. It is common toexpress the design earthquake in terms of the ground acceleration.

The design earthquake is typically defined with respect to an event with a 90%probability of non-exceedence in a 50 year period. This corresponds to an earthquakewith a return period of 475 years. This is usually determined by seismologists throughstudy of the history of earthquakes for the area in question. The outcome of this study istypically an iso-acceleration contour map for the area. This describes the designearthquake in terms of a percentage of the acceleration due to gravity (e.g. 0.3g).Earthquakes of the order of 0.08g are considered minor earthquakes, and greater than0.3g are considered to be major earthquakes. It must be emphasised however that inaddition to the magnitude of ground shaking, building damage due to earthquakes is afunction of the duration of the earthquake, or number of cycles of vibration when thebuilding is in the inelastic range.

2.2 Earthquake Resistant Design Philosophy

The general philosophy of earthquake resistant building design is that:

(a) For minor earthquakes – there should be no damage(b) For moderate earthquakes – there may be minor, repairable, structural damage and

some non-structural damage(c) For major earthquakes - there may be major, unrepairable, structural and non-

structural damage but without collapse of the building.

Though the building can be designed to remain in the elastic range of material behaviourfor major earthquakes (as it must be for nuclear facilities), by international consensus, itis agreed that this approach is most economical.

This approach is called design by hysteretic damping. The objective is to allow thestructure to enter the inelastic range at certain points, and maximise the energy absorbedby plastic flow. To achieve this, any type of possible brittle failure (e.g. shear failure,bond failure, slip, etc) must be suppressed as much as possible.

This approach is therefore based on the need for ductility in the structural system chosento resist the earthquake. Some systems (materials plus geometric configuration) arenaturally more ductile than others. Each system has a ductility capacity. This capacity isdetermined, in the case of reinforced concrete and reinforced masonry, by thearrangement of the reinforcement. In the case of structural steel the ductility capacity isdetermined by the arrangement of the connections, and selection of the section types.Since the ductility demand on the structure is typically not calculated, it is important thatthe detailing be consistent with the force reduction factor used to determine the baseshear.

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GENERAL PROCESS FLOWCHART FOREARTHQUAKE-RESISTANT DESIGN OF BUILDINGS

1. Choose Structural System

3. Determine Base Shear, V, byELF

4. Distribute V vertically to eachfloor

5. Check if Dynamic Analysis (DA)is req’d (due to irregularity)

Is DA req’d?

6. Perform DA (Response Spectrumor Modal Analysis are typical; Time

History; Non-Linear Dynamicssometimes used).

7. Reduce Inertia Forces due toductility (except for non-linear dyn)

8. Compare with V from ELF anduse larger value

9. For each floor, distribute inertiaforces horizontally to each system

including torsion

2. Choose Earthquake Direction

11. Apply load combinations

All eq directionsconsidered ?

10. Consider next earthquakedirection

12. Analyse structure to getmember design actions (M,V,P).

13. Check structure for if drift andoverturning are within limits.

Drift, OT areOK?

14. Design and detail each member;apply ductility rules.

Change system properties orChoose another system

y

n

y

y

n

n

END

- Typically(too often) notdone; structureassumed to beregular andtorsionnegligible

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This causes torsion of the floor that, ineffect, increases the lateral load on the floor.

a (ms-2)

t

Rock

Soil

1. Fault slip2. P and S waves propagated in rock and soil.

3. L and R surface waves

4. Inertia (dynamic) forces on each floor

Typical accelerogram

Inertia force ateach floor alwaysacts through CGof that floor

Roof slab CG

BUT,

Roof slab CR, Centre ofRigidity

CG and CR do notcoincide(due to asymmetry, inplan view, of thelocation, dimensions,and materials of theframe and/or walls)

Each floor has a centreof rigidity or stiffness ,(CR), relative to ahorizontal (lateral) loadacting at right angles tothe floor.

This is because each flooris supported by framesand/or walls that resistthe lateral load.

Fig. 1. The Cause-to-Effect chain ofearthquake forces on buildings.

Fig. 2. Distribution of Inertia Forcesto floors.

Fig. 3. The centre of rigidity concept.

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Inertial and torsional storey forcesdistributed to frames and/or walls inproportion to relative stiffness (for rigidfloors).

e, eccentricity

Inertia force plus torsion

F1 F2 F3 F4 F1 F2 F3 F4

Fig. 4. The generation of torsion on afloor.

Fig. 5. Horizontal Distribution ofInertial and Torsional forces toIndividual Frames or Walls.

E right

E left

Negative moment

Positive moment

Fig. 6. Beam Moments Under E only.

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Moments underD+L

Moments underE right

Moments underD+L+ E right

Fig. 7. Beam Moments Under D+L+E right atthe same time.

Shear underD+L

Shear under E Shear underD+L+ E

Fig. 8. Beam Shear Under D+L+E .

= ∆M/L

E right

E left

Typical columnaxial load (P)envelope.

Typical columnmoment (M)envelope under E.

Balance point

Under-reinforcedbehaviour

Over-reinforcedbehaviour

P/bh

M/bh2

Fig. 9. Column strength interaction curve (forsection x-x).

XX

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3.0 Earthquake Resistant Structural Systems1

A system is a unified collection of inter-connected parts. A system has a unique matrixof properties and behaviour (i.e. changes of properties) that defines it.

A structural system is a collection of structural elements intended to be the primaryvehicle in transferring loads on the structure from its source, to the soil.

An earthquake-resistant structural system is a structural system with properties andbehaviour that are favourable towards the objective of adequately resisting earthquakes.

Given that the main earthquake-resistant design philosophy is the use of the phenomenonof hysteretic damping to resist earthquakes, this implies that a main desirable property ofthe system is high ductility. Systems comprised of certain materials and methods ofconstruction, naturally possess better system ductilities than others. An overall measureof the system allowable or ultimate ductility is the Rw factor of the UBC-94 responsemodification factor. The larger the Rw value, the better the system ductility. See theattached table for examples.

Other desirable properties which promote high ductility and overall favourable seismicresponse of the structural system are: regularity; continuous load path; short load path;multiple load paths (redundancy), and strong connections.

These requirements translate into a set of do’s and dont’s with respect to the geometricconfiguration of the structural system. It is not that the dont’s will not work, but thereliability of the response calculations will be quite low. By experience, the do’s giveadequate performance. See the attached table for examples.

4.0 The Earthquake-Resistant Design of RC Special Ductile Moment-Resisting Space Frames

The following is an example of the desirable hinge mechanism for ductile moment-resisting frames.

Though ductility is typically stated as the key requirement for earthquake resistantstructural systems (designed by the hysteretic damping concept), it must be emphasizedthat this is due to the high energy absorption under dynamic conditions that results whenthe system has high ductility. Therefore to be more specific, the primary parameter is the 1 Excerpted and modified from Earthquake Resistant Design For Engineers and Architects 2nd Edition,Wiley-Interscience, by David J. Dowrick, Earthquake Design Practice, Thomas Telford,London, by DavidKey, and The Seismic Design Handbook, Chapman and Hall, Edited by Farzad Naeim.

µ = (xu - xy)/ xy

= ductility

xu = Ultimate deflection

x

xy = Yield deflection

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energy absorption. This is displayed by the load-deflection hysteresis loops of thestructural system as it undergoes the dynamic motion. A typical example for regularstructural steelwork ductile moment-resisting space frames is as follows. This systemdisplays the maximum possible energy absorption of all present available earthquakeresistant structural systems. The energy absorption is equivalent to the total area of thehysteresis loops. The shape of the typical loop shown is called the “spindle” shape, andis considered the ideal loop shape.

General Comments

• All frame elements must be detailed so that they can respond to strong earthquakes ina ductile fashion. Any elements which are necessarily incapable of ductile behaviourmust be designed to remain elastic at ultimate load conditions.

• Non-ductile modes such as shear and bond failures must be avoided. This impliesthat anchorage and splices of rebars should not be done in areas of high concretestress, and a high resistance to shear should be provided.

• Rigid elements should be attached to the structure with ductile or flexible fixings.• As many zones of energy-absorbing ductility as possible should be provided before a

failure mechanism is created. For framed structures this means that the yieldingshould occur first in the beams, then in the columns (weak beam-strong column).

• Movement joints should be provided at discontinuities so that pounding is avoided.

Summary of Factors Affecting Ductility of Reinforced Concrete Members:-

For practical values of section size and reinforcement:

Section ductility capacity is increased for:

• An increase in the compression reinforcement• An increase in concrete compressive strength• An increase in ultimate concrete strain

Section ductility capacity is decreased for:

• An increase in tensile steel reinforcement• An increase in steel yield strength• An increase in axial load

General Materials Requirements:-

Concrete Quality:

• The minimum recommended characteristic cylinder crushing strength is 20 MPa butless than 27 MPa for lightweight concrete

P

∆

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Reinforcement Quality:

• Suitable quality must be ensured by both specification and testing.• An adequate minimum yield stress may be ensured by specifying steel to an

appropriate standard, such as BS4449 or ASTM A615 or A706.• The actual yield stress should not exceed the minimum specified yield stress by more

than 124 MPa.• Grades of steel with characteristic strength in excess of 415 MPa should not be used.

4.1 Load Combinations (ACI-83)

U = 1.4D + 1.7LU = 0.75[ 1.4D + 1.7L ± 1.87E]U = 0.9D ± 1.43E

U = Ultimate Load (or its effects)D = Dead Load (or its effects)L = Live Load (or its effects)E = Earthquake load (or its effects)

4.2 Beam Design

Rules:

1. b/h shall not be less than 0.3 (b, total beam width; h, total beam depth).2. b shall not be less than 250mm.3. b shall not be greater the column width plus 0.75h on each side.4. The minimum longitudinal steel content as a fraction of the gross cross-sectional area

of the web shall be 1.4/fy (N/mm2) or 200/fy (psi).5. The maximum longitudinal steel content as a fraction of the gross cross-sectional area

of the web shall be 0.0256. The positive moment strength at the beam-column joint face shall not be less than

one-half of the negative moment strength provided.7. At any section in the beam span, neither the negative nor the positive moment

strength shall be less than a quarter of the maximum moment provided at the face ofeither beam-column joint.

8. Lap splices shall not be used: within joints; within 2h from the face of the beam-column joint, at locations of potential plastic hinging.

9. Lap splices where used shall be confined by hoops or spiral reinforcement with amaximum spacing or pitch of d/4 or 100mm (d, effective depth to main steel).

10. Transverse reinforcement in beams must satisfy requirements associated with theirdual function as confinement reinforcement and shear reinforcement.

11. Confinement reinforcement in the form of hoops is required: over a distance 2d fromthe column face, over distances 2d on both sides of sections within the span whereflexural yielding may occur due to earthquake loading.

12. The first hoop shall be 50mm from the column face and the maximum hoop spacingshall be the smallest of d/4; 8 times the diameter of the smallest longitudinal bar; 24times the diameter of the hoop bar, or 300mm.

13. Where hoops are not required, the hoop spacing shall be less than d/2.14. Shear reinforcement is to be provided so as to preclude shear failure prior to the

development of plastic hinges at the beam ends. Design shears for determining shearreinforcement are to be based on a condition where plastic hinges occur at beam endsdue to the combined effects of lateral displacement and factored gravity loads. Theprobable flexural strength associated with a plastic hinge is to be computed using astrength reduction factor of 1.0 and assuming a stress in the tensile reinforcement of1.25 fy. Note that the hoop reinforcement may satisfy the shear steel requirementsand vice versa.

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15. In determining the required shear reinforcement, the contribution of the concrete is tobe neglected if the shear associated with the probable flexural strengths at the beamends is greater than one-half the total design shear, and the factored axial compressiveforce including earthquake effects, is less than Agfc/20.

4.3 Column Design

Rules:

1. The shorter cross-sectional dimension shall be greater than or equal to 300mm.2. The ratio of shorter dimension to the perpendicular dimension shall be greater than or

equal to 0.4.3. The maximum and minimum longitudinal steel content as a fraction of the gross

cross-sectional area shall be 0.06 and 0.01.4. For all members framing into a beam column joint, the sum of the flexural strength of

the columns (for the relevant axial load level) must be greater than 1.2 times the sumof the flexural strength of the beams.

5. Lap splices are to be used only in the middle half of the column.6. As in beams, transverse reinforcement in columns must be provide confinement to the

concrete core and lateral support to the longitudinal bars, as well as shear resistance.In columns however, the transverse reinforcement must all be in the form of closedhoops or continuous spiral reinforcement. Sufficient reinforcement should beprovided to satisfy the requirements for confinement or shear, whichever is larger.

7. Confinement requirements:

For spiral reinforcement or circular hoop reinforcement, the volumetric ratio must begreater than,

0.12 fc’/ fyh or

0.45[(Ag/Ach) – 1] (fc’/ fyh)

fyh is the specified yield strength of transverse reinforcement, Ach is the core area ofcolumn section measured to the outside of transverse the transverse reinforcement in in2.

For rectangular hoop reinforcement total cross-sectional area within spacing s, must begreater than,

0.12shc fc’/ fyh or

0.3 shc [(Ag/Ach) – 1] (fc’/ fyh),

hc = cross-sectional dimension of column core, measured centre-to-centre of confiningreinforcement.

8. The maximum hoop spacing shall be the smallest of: quarter the smaller cross-sectional dimension, or 100mm.

9. The hoop reinforcement is to be provided over a length l0 from each joint face, wherel0 is the largest of: d, one-sixth the clear span of the member, or 450mm

10. Transverse reinforcement for shear in columns is to be based on the shear associatedwith the largest nominal moment strengths at the column ends (using fy and φ = 1)corresponding to the factored axial compressive force resulting from the largestmoment strengths.

11. Generally, it will be necessary to provide multiple stirrups, or stirrups and cross-ties,in order to give satisfactory confinement and restraint to main column reinforcement.Generally, overlapping hoops are to be preferred. In either case, one stirrup shouldsurround the whole of the main reinforcement. Where restrained bars are less than200mm apart, it is not necessary to restrain intermediate bars.

As an exercise, the student should examine ACI-315 on the seismic detailing rules forreinforced concrete elements.