Module 4

Question 1

examples of pulse loading

Answer 1

• impact of cars
• explosion loading
• impulsive types of earthquake loading

Question 2

impulsive force

Answer 2

very large force that acts for a very small time

Question 3

unit impulse has

Answer 3

• start at time t = tau
• duration e
• force p(t) = 1 / e

Question 4

damping and impulse

Answer 4

neglect effect of restoring and damping forces due to small displacement and velocity relative to acceleration, caused by infinitesimal duration of impulse

Question 5

Duhamel’s integral

Answer 5

provides a general result for evaluating the response of a LINEAR SDOF system to an arbitrary force

Question 6

pulse-like loading

Answer 6

important class of excitations fundamentally different from harmonic loading

• essentially consist of a single pulse
• can occur from blasts and explosions, or rapid impact

Question 7

fundamental difference between pulse load and harmonic load

Answer 7

• pulse loads never reach steady state conditions therefore effect of initial conditions must be considered

Question 8

two phases of pulse displacement solution

Answer 8

a) forced vibration phase

b) free vibration phase

Question 9

forced vibration phase

Answer 9

t

Question 10

free vibration phase

Answer 10

t > tp

Question 11

displacement solution for t

Answer 11

the same regardless of pulse duration

Question 12

effect of duration of pulse on dynamic amplitude

Answer 12

the larger the duration of the pulse, the larger the dynamic amplitude ( more energy imparted )

Question 13

maximum response (for a short pulse)

Answer 13

max response occurs in free vibration phase

Question 14

I

Answer 14

impulse

I = p(0) t(p)

Question 15

when is approximate pulse analysis considered accurate?

Answer 15

when tp / Tn

Question 16

effect of damping on pulse loads

Answer 16

effect of damping on amplitude of response is very small for pulse loads

• reason for lack of sensitivity is that max response occurs on first displacement cycle, after which time very little energy has been damped out
• in contrast by the time steady state for harmonic loading has been reached, many more displacement cycles have occured and so a significant amount of energy has been damped out

Question 17

two major drawbacks of Duhamel integral

Answer 17

• only applies for linear systems
• when p(tau) is not a ‘simple’ function, Duhamel integral must be solved numerically (particularly inefficient to solve)

Question 18

Most common numerical method used

Answer 18

Newmark-Beta Method

Question 19

two assumptions of Newmark-B method

Answer 19

• average constant acceleration

- linear acceleration

Question 20

Newmark-B derivation

Answer 20

1. draw accn assumption diagram
2. derive formula for accn
3. integrate to find velocity and disp
4. evaluate at tau = t(i+1)
5. Define incremental terms
6. apply these to eqautions from (4)
7. rearrange to find deltaaccn
8. substitute delta accn to find delta velocity
9. now have incremental formula so substitute into equation of motion

Question 21

Stability of Newmark-B method

Answer 21

• constant accn assumption unconditionally stable

- linear accn stable if time step is less than 0.551 times the shortest period of vibration in the system

Question 22

Accuracy of Newmark-B method

Answer 22

for sufficient accuracy, timestep

Question 23

preffered acceleration assumption

Answer 23

constant average acceleration - due to unconditional stability

Question 24

Effect of damping on Response Spectrum

Answer 24

• spectral amplitude decreases as damping ratio increases

- spectrum becomes less jagged with increasing damping

Question 25

is effect of damping on response spectra constant?

Answer 25

NO

• due to complexity of ground motion
• impulse much less sensitive than steady state to damping
• consider ground motion as sum of sine waves so amount of reduction depends on how response waves combine

Question 26

Effect of soil conditions on spectra demands

Answer 26

• softer soil leads to spectra with higher accn demands at longer periods
• rock sites have greater demands at short period range