How do I approximate a portal frame to a pendulum?
EI Lumped mass
!--------!( o -> ) !
! ! !
!EI !EI !2EI
! ! !
- - -
Specific beam, column sections with mass and weight.
So, here are my concerns for some portal frames:
1)P.F.(portal frame) with 1 DOF;
2)P.F. with 1 DOF plus 1 lumped mass;
3)P.F. with 2 DOF
4)P.F. with 2 DOF plus 1 lumped mass acting on the top level;
5)P.F. with 2 DOF plus 2 lumped masses acting on every level;
The correspondance between the P.F. and the pendulum regarding the mom. of inertia (I) and modulus of elasticity (E)is given below:
P.F. Pendulum
1gld - 2I;
1gld+1lumped mass - 2I+2E;
2gld - 2I+2E;
2gld+1lumped mass - 2I+4E;
2gld+2lumped masses- 2I+4E;
In order to obtain similar fundamental periods (in the 1st mode of vibration) I had to do the up approximations.
I thought only a EI <=> 2EI approximation would be necessary, but as you can see sometimes I made EI <=> 4EI approx. Does this approx. depends on the number of DOFs?
EI Lumped mass
!--------!( o -> ) !
! ! !
!EI !EI !2EI
! ! !
- - -
Specific beam, column sections with mass and weight.
So, here are my concerns for some portal frames:
1)P.F.(portal frame) with 1 DOF;
2)P.F. with 1 DOF plus 1 lumped mass;
3)P.F. with 2 DOF
4)P.F. with 2 DOF plus 1 lumped mass acting on the top level;
5)P.F. with 2 DOF plus 2 lumped masses acting on every level;
The correspondance between the P.F. and the pendulum regarding the mom. of inertia (I) and modulus of elasticity (E)is given below:
P.F. Pendulum
1gld - 2I;
1gld+1lumped mass - 2I+2E;
2gld - 2I+2E;
2gld+1lumped mass - 2I+4E;
2gld+2lumped masses- 2I+4E;
In order to obtain similar fundamental periods (in the 1st mode of vibration) I had to do the up approximations.
I thought only a EI <=> 2EI approximation would be necessary, but as you can see sometimes I made EI <=> 4EI approx. Does this approx. depends on the number of DOFs?
