Deflections under seismic loading

[fracture_point]

The NBCC (Canadian building code) allows us to reduce the base shear by multiplying by a factor of I_E/R_DR_O. The code then specifies that for deflections, the values should be multiplied by R_DR_O/I_E. My question is, should we be multiplying the reduced base shear values by this factor, to bring the deflections back up to an elastic base shear, or should we be multiplying deflections using the original elastic base shear, to increase them (by approximately 2 for RdRo = 1.5 x 1.3).

I think the latter, as this increase in deflections captures the deflections possible due to the inelastic behaviour expected in an earthquake. My colleague feels that it should be the former, where we are increased the reduced base shear back up to the original elastic base shear for deflections.

 

[Agent666]

Not familiar with your code specifically, but the approach is usually consistent with factoring the reduced base shear (reduced due to ductility/inelastic behaviour) at your design basis level event back up to the equivalent elastic level drift/deflections. EDIT - 2nd way over estimates this response.

 

[fracture_point]

My concern was that if we are allowing the structure to perform inelastically in an earthquake, how do the deflections from the elastic (unreduced) base shear correlate to this? The inelastic behaviour will reduce stiffness. Are the increased deflections from this inelasticity adequately represented by the increased design force back to elastic conditions? Is there any additional reading you recommend on this?

Cheers

 

[Shu Jiang PEng SE]

Reduced shear is used to check strength and deflection (base shear divided by RdR0). Structure strength is to be guaranteed by structure detailing design per the structure types (connection or end of beam yield to dissipate energy). Calculated deflection (elastic analysis) per reduced base shear has to be adjusted by RdR0 to consider the possible deflection amplification due to possible structure inelastic behavior.

 

[WARose]

Are the increased deflections from this inelasticity adequately represented by the increased design force back to elastic conditions?

At least in ASCE 7, you divide by the Response modification factor (R) to reflect the post-elastic response of the structure (based on type), i.e. the forces. And you multiply by the deflection amplification factor (Cd) to get real world deflections in the event.

In many cases, R & Cd are pretty close......but in others (especially more flexible systems with good energy dissipation systems, like special moment frames), R is significantly higher than Cd.

 

[PROFR]

The NBCC worded it very clearly. You should multiply the "lateral deflections" obtained from linear analysis by Rd Ro/ IE to give realistic values of the anticipated deflections.

You then have to compare it with the code limits.

 

[Agent666]

fracture_point, read up on equal energy principle and equal displacement principle in relation to seismic response spectra. Depending on which one governs is linked to the period of the structure.

There is some discussion in this report regarding these aspects that might help to explain things (in a NZ context at least), codes generally follow similar concepts around the world with varying scaling factors applied meant to allow for these effects.