Module 6

Question 1

mu

Answer 1

ductility capacity

mu = umax / uy

Question 2

ductility of different building types

Answer 2

• well detailed reinforced concrete and steel buildings: ‘ductile’
• unreinforced masonry buildings: ‘brittle’

Question 3

mu = 1

Answer 3

implies linear response - relates to zero structural damage

Question 4

mu = 10

Answer 4

implies structural collapse

Question 5

relationship of ductility and load capacity

Answer 5

ductile buildings can sustain larger loads than brittle buildings

Question 6

two parts to hysteresis curve

Answer 6

• backbone or virgin loading curve

- unloading and reloading curve

Question 7

‘backbone’ or ‘virgin loading’ curve

Answer 7

describes response of the material when subject to monotonic loading

Question 8

unloading and reloading rules

Answer 8

specify how the material responds when it is unloaded/reloaded

Question 9

two methods to predict non-linear dynamic response of a system

Answer 9

• solve equation of motion incrementally

- use empirical relationships between elastic spectral demands and inelastic response parameters

Question 10

Errors using tangent approximation to secant stiffness

Answer 10

1. tangent and secant stiffness differ greatly of a single time step
2. form cumulative errors over multiple time steps

Question 11

modified newton-raphson method

Answer 11

minimises errors by using an iterative procedure

- continue process until additional increments in displacement and/or residual force become acceptably small

Question 12

Original newton-raphson method

Answer 12

tangent recalculated at each iteration

• converges with fewer iterations
• BUT takes MUCH longer

Question 13

Ry

Answer 13

force reduction factor
- defines how much smaller the maximum inelastic force compared to the maximum elastic force
Ry = f0 / fy

Question 14

Cy

Answer 14

yield strength coefficient
- independent of elastic spectral demands - purely a characteristic of the building
Cy = Fy / mg

Question 15

Ry - mu - T relationships

Answer 15

• obtained by analysing a large number of SDOF systems to ground motions
• can use relationships to relate inelastic and elastic spectral demands

Question 16

two important trends when looking at umax/u0 vs T

Answer 16

• ratio umax/u0 broadly classified into two regions
  
  1. moderate/long periods (T >0.4) inelastic and elastic disp, are similar
  2. short periods, inelastic>elastic and ratio generally increases with decreasing T
• moderate/long T, umax/u0 insensitive to Ry
• short periods, umax/u0 increases with increasing Ry

Question 17

Equal displacement approximation

Answer 17

for moderate to long period structures

- inelastic and elastic disp similar (0.5

Question 18

Equal Energy approximation

Answer 18

short periods

Question 19

Sensitivity of R - mu - T

Answer 19

• hysteretic models with larger/fatter loops tend to have lower ratios
• lower magnitude events tend to generate longer ground motions

Question 20

P-delta effects

Answer 20

Fy,pdelta = Fy - ( P x delta / h)

Question 21

what happens when you consider P-delta

Answer 21

• tends to reduce equivalent lateral forces a structure can resist
• reduction in apparent system stiffness
• increase in system period of vibration
• reduce apparent acceleration demands
• increase apparent displacement demands, therefore typically non conservative to ignore P-delta