Concept of Earthquake Resistant Design

Transcription

1 Concept of Earthquake Resistant Design Sudhir K Jain Indian Institute of Technology Gandhinagar November

2 Bhuj Earthquake of 2001 Magnitude 7.7, ~13,805 persons dead Peak ground acceleration ~0.60g at Anjar About 44 km from epicentre Earlier significant earthquakes in the region: 1819 Kachchh earthquake, ~M8.0, ~1,500 deaths 1956 Anjar earthquake, ~M7.0, ~115 deaths

3 Facts Severe earthquakes are rather infrequent Low probability of strong shaking during life time of the structure Structures to resist most severe ground shaking without damage are too expensive to build.

4 Objectives of EQ Resistant Design Should the structure be designed to withstand strong shaking without sustaining any damage? Such a construction will be too expensive. It may be more logical to accept some damage in case of strong but infrequent shaking. However, loss of life and contents in the structure must be protected even in case of strong shaking.

5 Objectives of EQ Resistant Design (contd ) Structures should be able to resist Minor (and frequent) shaking with No damage. Moderate shaking with No structural damage Some non-structural damage Severe (and infrequent) shaking with Structural damage, but without collapse

6 Implications of Design Objectives Design earthquake loads << maximum expected elastic loads during strong shaking. Design force may be as low as one-tenths of the expected maximum elastic force. Reliance placed on inelastic response of the structure Good detailing and quality of construction are more crucial than for ordinary construction To ensure adequate post-elastic response

7 Level of Design Force Level of earthquake protection to depend on consequences of damage Essential services (water, electricity, hospitals, schools, etc) Needed for post-earthquake management Must be provided with higher earthquake protection than the ordinary buildings

8 Level of Design Force (contd ) Dams, nuclear plants,... May cause another disaster if damaged Must be provided maximum level of protection

9 Nature of Aseismic Design Problem Civil Engineering Structures Large Unique (one-of-a kind; unlike aircrafts or cars) Expensive

10 Nature of Aseismic Design Problem (contd ) Response of structure Dynamic Cyclic about equilibrium Elastic behaviour upto yield Inelastic behaviour beyond yield

11 Cyclic Loads +P P=0 t -P Cyclic About Equilibrium (e.g. Seismic) P av P=0 t Cyclic About an Average Load (e.g. Wind)

12 Nature of Aseismic Design Problem (contd ) Civil Engineering Profession Limited time for design and development Limited funds

13 Nature of Aseismic Design Problem (contd ) Uncertainties in Input Motion When and where the next earthquake? On which fault? Of what magnitude (size)? Nature of ground shaking near source? Effect of travel path on shaking at a distance? Effect of local geology, topography and soil profile?

14 Nature of Aseismic Design Problem (contd ) Structural response depends on Input motion Structural properties

15 Nature of Aseismic Design Problem (contd ) Uncertainties in structural properties Natural periods/stiffness? Damping? Soil-foundation interaction? Post-yield behavior?

16 Implications Non-linear dynamic analysis desirable, but Complex, time consuming, and expensive Numerous uncertainties in input motion Requires parameters which are hard to specify accurately

17 Implications (contd ) Linear static analysis Considered adequate for most purposes With due consideration to inelastic dynamic behaviour Simple design approach to a complex problem With implicit consideration of some of the complexities

18 Loading: Force versus Displacement P Δ P P Δ P Applied Force Δ Applied Displacement Δ

19 Force-Controlled Systems Example: Gravity Loads Failure if Imposed force > Yield force P P Failure Δ

20 Displacement-Controlled Systems Example: Seismic Loads No failure even if Imposed displ. > Yield displ. Provided the system is ductile Δ P Δ

21 Earthquake Force It is an inertia force Given by mass times acceleration Acceleration of the mass Generated where the mass is located That is, at floors of the building Needs to be transferred safely to the ground

22 Ground Vibrations Random in magnitude and direction Two horizontal and one vertical component Vertical vibrations Vertical inertia force Adds and subtracts to the gravity force Generally not a problem due to factor of safety in gravity design

23 Vertical Vibrations Gravity Loads Vertical Component of EQ - Induced Inertia Force

24 Horizontal Vibrations Cause horizontal inertia force Need to provide adequate load transfer path for the force to be transferred to the ground Need adequate strength along the load transfer path.

25 Load Transfer Path and Elements

26 Single Degree of Freedom System Linear elastic system Natural frequency: m k m Natural period: 2 T 2 Damping: m k c 2m c Ground Motion k

27 Dynamic Response Response of linear elastic structure to the ground motion depends on Input motion Natural period (frequency) Damping

28 Response Spectrum Response Spectrum is a plot of maximum response versus natural period (for different values of damping) for a given input motion. By response we may mean force, displacement, velocity, acceleration, Maximum Response For different values of damping Natural Period

29 Maximum Velocity, in/sec Response Spectrum (contd ) Velocity response spectra for N-S component of 1940 El Centro record (damping values of 0, 2, 5 and 10%) Fig From Housner, 1970 Natural Period T (sec)

30 Elastic versus Inelastic Response Total Horizontal Force Elastic Inelastic, Ductile Brittle: Unacceptable Roof Displacement

31 Cyclic Behaviour Poor Desirable

32 Detailing versus Cyclic Response Fig. from Wakabayashi Poor detailing Desirable detailing

33 Force Deformation Response Force F y Idealized curve Actual curve Δ y Deformation Elasto-plastic system

34 Ductility F y Force Δ y Ductility Displacement Δ max Maximum max imumdisplacement Yield yielddispl displacement acement Δhkh max Δdfh y

35 Ductility (contd ) Overall structural ductility Base shear versus roof displacement Storey ductility Storey shear versus storey drift Member ductility Displacement ductility Rotation ductility Section ductility Curvature ductility

36 Ductility versus Response Force F max Force F y Δ max Displacement Linear Elastic System Δ y Δ max Displacement Elasto-plastic System

37 Ductility Reduction Factor Ductility Reduction Factor (R µ ) is ratio of maximum elastic force and the yield force Fmax R f, T F y It gives reduction in yield force on account of ductility. If ductility (μ) is assured, the structure can be designed to yield at a reduced force of (F max /R μ )

38 Ductility Reduction Factor (R μ ) Force Force Displacement Short Period Structures (T<0.4 sec) Displacement Intermediate / Large Period structures (T>0.4 sec) R 2 1 R

39 Overstrength Overstrength factor (Ω) is the ratio of yield force of the structure and the design force. Overstrength ( ) Yield Force(F Design Force(F y ) d )

40 Overstrength contributed by Partial Safety Factors Partial safety factor on seismic loads Partial safety factor on gravity loads Partial safety factor on materials

41 Overstrength contributed by (contd ) Material Properties Member size or reinforcement larger than required Strain hardening in materials Confinement of concrete improves its strength Higher material strength under cyclic loads

42 Overstrength contributed by (contd ) Strength contribution of non-structural elements Special ductile detailing adds to strength also Redundancy in the structure

43 Total Horizontal Load Response Reduction Factor Δ Maximum force if structure remains elastic Maximum Load Capacity Load at First Yield F el F y F s Linear Elastic Response First Significant Yield Non linear Response Due to Ductility Total Horizontal Load Due to Overstrength Design force F des 0 Δ w Δ y Δ max Roof Displacement (Δ)

44 Response Reduction Factor Response Reduction Factor (R) = Ductility Reduction factor (R μ ) R= R μ Ω Overstrength (Ω) Design Force = Max. Elastic Force (F max) R R= 10 to 12 for special ductile frames!

45 Design Spectrum Design specification in terms of response spectrum Accounts for ductility, overstrength,... Smooth As against peaks and valleys in response spectrum Specified concurrently with Damping to be used Procedure for calculation for natural period Permissible stresses/strains, load factors, etc.

46 Typical Design Spectrum Period (sec)

47 Fundamental Period of Building Due to uncertainty in calculating the period of a building, modern codes now require one of the following safeguards: Enforce an upper bound on the period that can be used for calculating design seismic force. The upper bound is based on empirical period (e.g., NEHRP). Place a lower bound on design base shear based on empirical period (e.g., UBC).

48 Lateral Stiffness Low lateral stiffness leads to Large deformations/strains, and hence more damage in inelastic response. Significant P- effect. Damage to non-structural elements Due to large deformations Discomfort during vibrations

49 Acceleration Spectrum Period (sec)

50 Displacement Spectrum Period (sec)

51 Lateral Stiffness (contd ) Even though low force for high natural period, stiff structures perform better during earthquakes. Codes specify limit on lateral displacement to ensure adequate stiffness.

52 Structural Configuration Simple, direct load transfer path gives better performance Regular configuration preferred Even distribution of mass and stiffness in building plan and with building height In buildings with irregular configuration Simple code expressions not valid Ductility demand gets concentrated in a few storeys or elements

53 Importance of Configuration To quote Late Henry Degenkolb, the well-known earthquake engineer in California: If we have a poor configuration to start with, all the engineer can do is to provide band-aid improve a basically poor solution as best as he can. Conversely, if we start off with a good configuration and a reasonable framing system, even a poor engineer can t harm its ultimate performance too much.

54 Irregular Buildings End Wall Conditions for Imperial Services County Building damaged in 1979 earthquake

55 Irregular Buildings (contd ) Seismic codes discourage buildings with irregular distribution of mass or stiffness in plan or in elevation. Requires a good understanding of structural behaviour by the architect, and A good coordination between the architect and the structural engineer.

56 Soils and Foundations Main Effects Effect of local soil-type on input ground motion Soil-structure interaction Effect of travel path on dissipation energy Differential settlement

57 Response Spectra Average Acceleration Spectra for different site conditions

58 Response Spectra (contd ) Normalized Response Spectra for 5% Damping

59 Capacity Design Concept Brittle Link Ductile Link The chain has both ductile and brittle elements. To ensure ductile failure, we must ensure that the ductile link yields before any of the brittle links fails.

60 Capacity Design Concept (contd ) Assess required strength of chain from code. Apply suitable safety factors on load and material Design/detail ductile element(s). Assess upper-bound strength of the ductile element Design brittle elements for upper-bound load Ensures that brittle elements are elastic when the ductile elements yield.

61 Capacity Design Concept (contd ) For instance, in a RC member Shear failure is brittle Flexural failure can be made ductile Element must yield in flexure and not fail in shear Beams can be made ductile more easily than the columns Beams should yield and not the columns Weak beam strong column philosophy

62 Non-Traditional Methods Base isolation systems Energy dissipation devices

63 To Summarise In case of strong shaking, some damage is acceptable. Design seismic force only a fraction of the maximum expected elastic force. Horizontal acceleration is of more serious concern as compared to vertical acceleration. Structure should have adequate Lateral strength Lateral stiffness Ductility Structural configuration