Seismic Force Distribution 3

[Bh.Burhan]

Hello all,

Does the seismic force distribution change between the North-South direction and the East-West direction? If I have the same seismic resisting force system for the both directions in my building. The building is rectangular moment resisting frame without irregularities.

Thanks,

 

[Rabbit12]

Retired13, that's not the ASCE7 equation for approximation for fundamental period (I know you referenced the source). The ASCE7 equation is this:

T[sub]a[/sub]=C[sub]t[/sub]*h[sub]n[/sub][sup]x[/sup]

where h[sub]n[/sub] is the height of the structure in feet and C[sub]t[/sub] and x are constants based on the SFRS. So if you are using ASCE7 for design the approximate fundamental period is not dependent on the length of the building.

Josh,

I still am not seeing how ASCE7's ELF procedure is dependent on the period of the structure save for the maximum bound on C[sub]s[/sub]. S[sub]DS[/sub] is site specific and R is based on the SFRS so unless you hit the maximum bound on C[sub]s[/sub], there is no correlation between structure period and base shear.

spieng89,

I completely agree.

The OP stated he had the same SFRS is each direction. So based on that unless he isn't allowed to use the ELF procedure, and he didn't calculate T using something other than the approximation in ASCE7, his base shear in each direction would be identical.

 

[r13]

By Newton's Law? Just fun to open up discussion - why direction matters.
Another phenomenon to think about - a cantilever H beam (Ix ≠ Iy) subject to same magnitude forces in x and y axes, what is the resulting shear force at support in each direction?

 

[JoshPlumSE]

Rabbit,

Let's talk about two methods of calculating period.

1) simplified method which is based on height and system. In this case, you are correct, as long as you use the same type of system in each direction, the simplified period will be the same.

2) Rational method: Known as method "B" in the older codes where you do an analysis based on stiffness to get the period. Let's say you have a special concentrically braced steel frame in each direction. But, in one direction you have 4 frames that are braced an in the other direction you have 3 frames that are braced. You come up with different periods. The periods will be closer than a braced frame vs a moment frame, but they could still differ.

 

[r13]

Just a reminder, for simple harmonic motion, f = (1/2pi)*√(k/m), and T = 1/f. k = spring constant (stiffness).

 

[Blackstar123]

I still am not seeing how ASCE7's ELF procedure is dependent on the period of the structure save for the maximum bound on Cs.

From figure uploaded by josh, the relationship between Cs and time period is pretty clear. Here's another one. Same thing, but labelled with base shears and time periods as per ASCE7-10

As for the time period of the structure, JoshplumSE has nailed it again.

two methods of calculating period.
1) simplified method which is based on height and system. In this case, you are correct, as long as you use the same type of system in each direction, the simplified period will be the same.

2) Rational method: Known as method "B" in the older codes where you do an analysis based on stiffness to get the period.

 

[Blackstar123]

Retired, you're right that's how the period from method B is calculated. The equation given in UBC is driven from this basic equation.

for simple harmonic motion,
f = (1/2pi)*√(k/m), and
T = 1/f
k = spring constant (stiffness)

 

[r13]

Rabbit12,

Yes, your are correct. I only provide that equation to indicate different method in calculating fundamental period (see reference).

I personal don't believe there are two set of seismic reactions for the same structure, regardless of its geometry and flexibility; however, there are two set of structural responses (called base shear) that depend on structure's geometry and flexibility. It would be easier to see the difference and understand the concept, if we go through the development process of replacing ∝ = a/a[sub]g[/sub] (acceleration ratio, a simple constant) with Cs (seismic response coefficient, essentially a factor that takes into account of period and ...), that changes natural energy into design level energy, IMW.