Josh Plummer, S.E. - risa.com · for P-Delta effect by hand • Stability coeff gives a good “back of envelope” method of accounting for P-Delta by hand or for

Josh Plummer, S.E.

Director of Technical Support and Training

Analysis Requirements of the 2006 IBC

Fundamental Points of Discussion• Real Behavior will NOT exactly match

the assumed behavior• Is the cost (in time and effort) worth

the increase in accuracy?• What is the Standard of Care in the

Engineering community?• Is there a gap between the code

requirements and the standard of care?


Errors from Typical Analysis Assumptions

• Linear Elastic Materials– Materials are NOT elastic– Normally corrected by using adjusted

elastic properties (EI or EA)

• 1st Order Analysis– Lateral Stiffness can be significantly

affected by deflection for moment frames– Normally corrected by using a P-Delta or

2nd Order analysis


Requirements for Material Non-Linearity

AISC• Material Yielding

ACI • Cracking of Concrete

ASCE-7 • Material Yielding or Cracking

during seismic events


AISC – Chapter C (Stability)• Ignored in previous editions of the AISC

specifications• Section C1.1 requires “Member stiffness reduction

due to residual stresses.”• Accounted for by using the stiffness reduction

requirements of the Direct Analysis Method• May be ignored in many cases based on the

Chapter C Effective Length Method (ELM)– When investigating a braced frame– If a K > 1.0 is used for moment frames

Material Non-Linearity

(AISC)


Material Non-Linearity in the Direct Analysis Method (Appendix 7)

Axial Stiffness Reduction• 0.8EA – For Members Whose Axial

Stiffness Contributes To Lateral Stability of Structure

Flexural Stiffness Reduction• 0.8τbEI – For Members Whose Flexural

Stiffness Contributes To Lateral Stability of Structure

– Tau (τb) Varies Based on Axial Load


(AISC)


ACI 318 – 2005 Section 10.10.1• Material Nonlinearity• Cracking• Duration of Loads• Shrinkage• Creep• Interaction with Foundation• Member Curvature (P-Little Delta)• Lateral Drift (P-Big Delta)

ACI 318 – 2005 Section 10.11• Allowed as an alternate to the above

requirements


(ACI)


ACI 318 – 2005 Section 10.11.1(Magnified Moments)

• Section establishes the proper ELASTIC stiffness for considering P-Delta effects

• Icracked could be set for each member based on Ieffective (section 9.5.2.3)

Ie = (Mcr / Ma)3 Ig + [1- (Mcr / Ma)3 ]*Icr

• This Effective I value would have to be established through iteration

• This Effective I value would change with EVERY load combination


(ACI)


ACI 318 – 2005 Section 10.11.1(Alternative)

• I cracked (for Ultimate Level Loads) • 0.35 * Igross for beams• 0.70 * Igross for columns

• I cracked (for Service Level Loads) • 0.5 * Igross for beams• 1.0 * Igross for columns


(ACI)


ACI 318 – 2005 Section 10.11.1(Alternative)

• Axial stiffness (EA) doesn’t need to be modified

• Wall Stiffness • Assume same value as

columns (0.7*I gross)• If M > Mcrack then reduce

stiffness to 0.35*Igross

• Duration of Load Handled by dividing by (1 + bd) = 1.0 (for Lateral Forces)


(ACI)


ASCE-7 Section 12.7.3 (Structural Modeling)

• Stiffness of Concrete and Masonry elements SHALL consider effects of Cracked Sections

• For steel moment frame systems, the contribution of panel zone shear deformations to overall story drift shall be included


(ASCE)


ASCE-7 Panel Zone Shear• What is Panel Zone Shear Deformation?


(ASCE)


ASCE-7 Panel Zone Shear• What does “for contribution to overall story drift”

mean? – Implies that it may only be important for

Inelastic Drift and Building Separation– May not be required for P-Delta

• Does this refer to the elastic or in-elastic behavior of the panel zone?

– Inelastic Behavior and Capacity important for seismic design

• NEHRP 2003 commentary says– Panel Zone may be ignored if centerline

modeling is used – If clear span modeling is used, then panel

zones should be considered– See also commentary to AISC 341-05


(ASCE)


Errors from Typical Analysis Assumptions

• Linear Elastic Materials– Materials are NOT elastic– Normally corrected by using adjusted

elastic properties (EI or EA)

• 1st Order Analysis– Lateral Stiffness can be significantly

affected by deflection for moment frames– Normally corrected by using a P-Delta or

2nd Order analysis


Requirements for P-Delta or 2nd

Order Analysis2nd Order Effects (P-Delta)

• ASCE-7• AISC• ACI


Definition of P-D Effect P-Δ is the effect of story drift

P-d is the curvature effect

P-d is ignored in most cases


ASCE – 7 and P-Delta• P-D Required by Section 12.7.3• Calculations Governed by Section

12.8.7. • No attempt made to include (P-d)

• May be ignored when stability coefficient (θ) is less than 0.10

• Stability coefficient is not allowed to exceed:

θmax = 0.5 / (bCd) < 0.25

P-Delta Requirements

(ASCE)


Definition of Stability Coefficient θ• Stability Coefficient θ is the ratio of

increased shear to original story shear


(ASCE)

Moment = PΔo

Vi = PΔo / H

θ = PΔo/ (H Vo)

θ = Vi / Vo


Hand Calculation of P- Δ effect using θ• Incremental Deflection (due to Vi) = Δo* θ

• New Deflection = Δo + Δo θ = Δo(1 + θ)

• After amplifying the incremental deflections, the total deflection becomes an infinite series

ΔTotal =Δo(1 + θ + θ2 + θ3 + θ4 + ….)

ΔTotal =Δo / (1 – θ)

• Amplify original story shear by 1 / (1-θ) to account for P-Delta effect by hand

• Stability coeff gives a good “back of envelope” method of accounting for P-Delta by hand or for verifying your analysis program results


(ASCE)


ASCE-7 and P-Delta (cont...)Important Notes or Inconsistencies

1. Stability coefficient inherently ignores P-Little Delta

2. P-Big Delta can be performed with elastic deflections!

3. Implies that P-D can be performed with strength level lateral forces, but service level gravity forces


(ASCE)


ASCE-7 (explained in FEMA 450-2)Why not use inelastic deflections Cd * Δe?

1. Dynamic / Inertial nature of seismic forces. By the time Δ is observed ground motion may be moving to stabilize the structure.

2. Typical over strength of structures required to control drift. This is more of a factor in higher seismic zones

3. Few stability related failures in past Seismic events don’t justify the tremendous additional cost associated with using inelastic deflections for P - Δ.


(ASCE)


AISC and P-Delta• P-Δ (Big Delta) Analysis

Always Required• P-δ (little delta) Analysis

Can Be Ignored If αPr < 0.15PeL

Watch For:– Weak Axis Frames– Members w/ Similar Bending Properties

About Both Axis (i.e. Tubes & Pipes)– Cantilever Columns


(AISC)


AISC and P-DeltaExample: W12x65 Column (L = 15’)Strong Axis in Plane of Bending

PeL = 4704 kips Py = 955 kipsΦPn = 662 kips → 0.14PeL

Weak Axis in Plane of BendingPeL = 1539 kips Py = 955 kipsΦPn = 662 kips → 0.43PeL


(AISC)


P-Little Delta “Benchmark” ProblemsP-Delta Requirements

(AISC) Case 1

Case 2

Benchmark – Case 1P-Delta Requirements

(AISC)


Zero Joints

One Joint

Three Joints


(AISC) Case 1: Deflection Amplification

1.00

1.50

2.00

2.50

3.00

3.50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Axial Force Normalized by Euler Buckling Load, P/Pe

Am

plifi

catio

n Fa

ctor

, Ym

a

RISA (1 Node) RISA (3 Nodes) RISA (10 Nodes) AISC Benchmark



(AISC) Case 1: Moment Amplification

1.00

1.50

2.00

2.50

3.00

3.50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Axial Force Normalized by Euler Buckling Load, P/Pe

Am

plifi

catio

n Fa

ctor

, Mm

a

RISA (1 Node) RISA (3 Nodes) RISA (10 Nodes) AISC Benchmark



ACI 318 - 2005• P-D Governed by 10.11 ~ 10.13

10.11 Magnified Moments - General10.12 Magnified Moments – Non-sway 10.13 Magnified Moments - Sway

• Section 10.11 Gives criteria for establishing an effect elastic stiffness due to cracking

• Slenderness effects may be ignored when:KL / r ≤ 34 – 12 (M1 / M2) (Non-sway)KL / r ≤ 22 (Sway)KL / r > 100 NOT allowed (10.11.5)

• A frame may be considered non-sway if:Q = θ ≤ 0.05 (10.11.4.2)


(ACI)


ACI 318 – Nonsway frames• When slenderness effects must be

considered:• P-δ is accounted for using an amplified

moment Mc

Mc = M2 * Cm / (1 – (Pu / 0.75 Pc) ≥ M2

• Similar to B1 factor for steel or the old H1-1 equation for Green Book

• Main difference is in derivation of EI for elastic buckling


(ACI)


ACI 318 – Nonsway framesEI = (0.2EcIg + EsIse) / (1 + bd)

or

EI = 0.4EcIg / (1 + bd)

• When you assume 0.6 = bd (ratio of sustained load to max load) equal

EI = 0.25EcIg

• Also, it defines an minimum M2 value to use if no moment occurs

M2 = Pu (0.6 + 0.03h)


(ACI)


ACI 318 –Sway frames• Second Order Analysis required by

Section 10.13.4.1• Must use Reduced stiffnesses for 2nd

order analysis 10.11.1 (0.35 and 0.7 Igross)

• P-δ is ignored unless:Lu / r > 35 / √ ( Pu / f’cAg)

• When required P-δ is again accounted for using an amplified moment Mc

Mc = M2 * Cm / (1 – (Pu / 0.75 Pc) ≥ M2


(ACI)


In Review:• Linear Elastic Materials

– Materials are NOT elastic– AISC and ACI correct for this by using

adjusted elastic properties (EI or EA) • 1st Order Analysis

– Lateral Stiffness can be significantly affected by deflection for moment frames

– Normally corrected by using a P-Big Delta or 2nd Order analysis. This can be easily verified by hand calculations.

– P-Little Delta is usually ignored (ASCE, ACI, and even AISC) except for very slender elements.


ACI 318, Building Code Requirements and Commentary, 2005AISC 360, Specification for Structural Steel Buildings, 2005AISC, Seismic Design Manual, 1st Edition, 2006ASCE-7, Minimum Design Loads for Buildings and Other Structures, 2005FEMA 450, NEHRP, 2003Griffis and White, Stability Design of Steel Buildings, AISC Design Guide (unpublished)Naeim, Design for Drift and Lateral Stability, Seismic Design Hanbook, 2nd Edition, 2001SEAOC, Recommended Lateral Force Requirements and Commentary, 7th Edition, 1999

References:

Josh Plummer, S.E.(949) 951-5815

[email protected]

Documents

Josh Plummer, S.E. - risa.com · for P-Delta effect by hand • Stability coeff gives a good “back of envelope” method of accounting for P-Delta by hand or for