Arizona State UniversityStructural Engineering Program

CEE 536—Structural DynamicsInstructor: Keith D. Hjelmstad

Homework Problems

Homework 10

The multi-degree of freedom system shown at right ismade of masses and linear springs. The equations ofmotion for a system subjected to prescribed accelerationsat the support point (an earthquake) have the form

( ) ( ) ( )(0)(0)

g

o

o

t t t u+ + = −

==

M u Cu Ku M1u uu v

where M is the mass matrix, C is the damping matrix, Kis the stiffness matrix, �̈�𝑢𝑔𝑔 is the support acceleration, 1 isa column matrix of ones, uo is the initial displacementvector and vo is the initial velocity vector. Implement theearthquake excitation in your MATLAB code fromHW8 and HW9. Use an artificially generated earthquakeor a measured one (if you can find one on the internet).

1k

1m

2k 3k 4k

2m 3m

1u 2u 3u

A CB

1( )f t 2 ( )f t 3 ( )f t

System 1: “Bridge”

1k

1m

2k 3k

2m 3m

1u 2u 3u

A CB

1( )f t 2 ( )f t 3 ( )f t

System 2: “Building”

System 3: “Shear Building”

1m

1EI1f

nEI

nmnf

At this point your code should be able to do elasto-plastic response of the individual elements. Make surethat your earthquake is adjusted so that the groundvelocity is zero when the earthquake ends.

gu

t

© 2015 Keith D. Hjelmstad