Lecture 7

Seismic Codes: Theory and Practice
Lecture 7

Arch 721, Structural Design for Dynamic Loads, University of Virginia
Copyright © 1996-2004 Kirk Martini.

Today's topics

The theoretical basis of seismic codes.
- Approximating a building as a single degree of freedom system.
- The equivalent lateral force procedure.
  - Inelastic design response spectra.
  - Redistribution of forces for height
Practical aspects of codes
- Configuration
  - Plan irregularities.
  - Vertical irregularities.

The Theoretical Basis of Seismic Codes

Response Spectra

A response spectrum shows the maximum response of a single degree of freedom oscillator to a praticular ground motion. the figures below show the acceleration response spectra for three different ground motions, using elastic oscillators with 5% critical damping.

[Arcade demo]

The equivalent lateral force procedure

The multi-step code approach for calculating the Seismic Response Coefficient (C_s in NEHRP), is essentially a way of constructing a smoothed average response spectrum that accounts for the damping and ductility characteristics of the building, as well as the regional seismicity and underlying soil of the site.

Compare an elastic response spectrum for a Northridge 1994 earthquake motion, with a code design response spectrum developed with the NEHRP provisions.

Why the big gap?

[Arcade demo]

0.2 Second spectral acceleration

1.0 Second spectral acceleration

The code spectrum is an approximation of an elastic response spectrum, scaled down by two factors:

It is reduced by the factor of safety used in allowable stress design to account for the fact to achieve the given yield strength, allowable stress design must aim at a lower strength. (for this case, F_s = 1.5)
It is reduced by the R factor to account for damping and ductility. This reduction creates an inelastic spectrum which accounts for the effect of ductility in limiting force levels. (for this case, R=6.5)

Redistribution for Height

In particular, the levels of acceleration are not constant throughout the structure.

Example: Assume total building weight W = 3000 kips, and seismic coefficient C_s = 0.10 (i.e. 10% gravity), so the base shear V = C_sW = 300 K.

Level	w_x (K)	h_x (ft)	w_xh_x (Kft)	(w_xh_x)/sum(w_ih_i)	F_x (K)
3	1000 K	30 ft	30,000	0.50	150 = 0.50*300
2	1000 K	20 ft	20,000	0.33	100 = 0.33*300
1	1000 K	10 ft	10,000	0.17	50 = 0.17*300
TOTAL	3000 K		60,000 Kft	1.0	300 K

The code formula for redistribution distributes the base shear force so that levels with more mass (w) and more height (h) receive more load.

Performance and Configuration

The NEHRP commentary identifies four levels of performance.

Operational
Immediate occupancy.
Life safety.
Near Collapse.

The Provisions define three Seismic Use Groups requiring different levels of performance (NEHRP 1997, section 1.3)

Group	Description.
III	Essential facilities for post-earthquake recovery. Fire, police, medical, emergency, aviation control towers, toxic material storage, etc.
II	Structures that pose a substantial hazard due to occupance or use. Assembly halls > 300 people, All structures with a capacity greater than 5000 people, power generation, water treatment.
I	All other structures.

Combining Seismic Use Groups with regional seismicity, NEHRP defines Seismic Design Categories (NEHRP 2000, section 4.2) which indicate the level of attention required for seismic design.

Category	Description.
A	Low seismicity, any Seismic Use Group.
B	Moderate seismicity, Seismic Use Groups I and II.
C	Moderate Seismicity, Seismic Use Group III, or High seismicity, Seismic Use Group I or II.
D	High Seismicity, Seismic Use Group III, or Very high seismicity, any Seismic Use Group.
E	Extremely high seismicity, Seismic Use Group I or II.
F	Extremely high seismicity, Seismic Use Group III.

Plan Irregularities per 2000 NEHRP Provisions
1.	Torsional Irregularity – to be considered when diaphragms are not flexible Torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.2 times the average of the story drifts at the two ends of the structure. Action: D,E,F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2) C,D,E,F: Magnify torsional moment.(5.4.4) Extreme Torsional Irregularity – to be considered when diaphragms are not flexible Extreme torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.4 times the average of the story drifts at the two ends of the structure. Action: D, E, and F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2) C, D, E, and F: Magnify torsional moment.(5.4.4) E and F: Prohibited. (5.2.6.5.1)	[Arnold 1989]
2.	Re-entrant Corners Plan configurations of a structure and its lateral-force-resisting system contain re-entrant corners where both projections of the structure beyond a re-entrant corner are greater than 15 percent of the plan dimension of the structure in the given direction. Action: D,E,F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2)	[BSSC 1995b]
3.	Diaphragm Discontinuity Diaphragms with abrupt discontinuities or variations in stiffness including those having cutout or open areas greater than 50 percent of the gross enclosed diaphragm area or changes in effective diaphragm stiffness of more than 50 percent from one story to the next. Action: D,E,F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2)	[BSSC 1995b]
4.	Out-of-Plane Offsets Discontinuities in a lateral force resistance path such as out-of-plane offsets of the vertical elements. Action: D,E,F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2) B,C,D,E, and F: Design columns for extra load (5.2.6.2.10)	[Arnold 1981]
5.	Nonparallel Systems The vertical lateral-force-resisting elements are not parallel to or symmetric about the major orthogonal axes of the lateral-force-resisting system. Action: C,D,E, and F: Consider critical directions. (5.2.5.2)	[Arnold 1989]

Vertical Irregularities per 2000 NEHRP Provisions
1.	Stiffness Irregularity – Soft Story A soft story is one in which the lateral stiffness is less than 70 percent of that in the story above or less than 80 percent of the average stiffness of the three stories above. Action: D,E, and F: Must use dynamic analysis (5.2.5.1) Stiffness Irregularity – Extreme Soft Story An extreme soft story is one in which the lateral stiffness is less than 60 percent of that in the story above or less than 70 percent of the average stiffness of the three stories above. D, E, and F E and F Action: D: Must use dynamic analysis 5.2.5.1) E and F: Not permitted (5.2.6.5.1)	[Arnold 1989]
2.	Weight (Mass) Irregularity Mass irregularity shall be considered to exist where the effective mass of any story is more than 150 percent of the effective mass of an adjacent story. A roof that is lighter than the floor below need not be considered. Action: D,E,F: Must use dynamic analysis (5.2.5.1)	[Arnold 1989]
3.	Vertical Geometric Irregularity Vertical geometric irregularity shall be considered to exist where the horizontal dimension of the lateral force- resisting system in any story is more than 130 percent of that in an adjacent story. Action: D,E, and F: Must use dynamic analysis (5.2.5.1)	[Arnold 1989]
4.	In-Plane Discontinuity in Vertical Lateral-Force Resisting Elements An in-plane offset of the lateral-force-resisting elements greater than the length of those elements or a reduction in stiffness of the resisting element in the story below. Action: D,E,F: Dynamic analysis (5.2.5.1) D,E,F: Increase connector strength by 25% for diaphragms to vertical and collectors. (5.2.6.4.2) B,C,D,E,F: Design columns for extra load (5.2.6.2.10)	[Arnold 1989]
5.	Discontinuity in Capacity – Weak Story A weak story is one in which the story lateral strength is less than 80 percent of that in the story above. The story strength is the total strength of all seismic-resisting elements sharing the story shear for the direction under consideration. Action: B,C,D,E,F: No more than 2 stories or 30 feet if weak story is 65% less than story above. (5.2.6.2.3) D,E,F: Dynamic analysis (5.2.5.1) E,F: Not permitted. (5.2.6.5.1)	[Arnold 1989]