Seismic Design of Precast Concrete Structures · Seismic Design of Precast Concrete Structures ... 7- story building ... Where the diaphragm is required to transfer design seismic

Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 1

Seismic Design of Precast

Concrete Structures

S. K. Ghosh

S. K. Ghosh Associates Inc.

Palatine, IL and Aliso Viejo, CA


2015 NEHRP Provisions


Two Diaphragm-Related

Developments

FEMA P-1050, the 2015 NEHRP Provisions

includes two significant new items related to the

seismic design of precast diaphragms.


Two Aspects to Seismic Design

Seismic design is an exercise in tradeoff

between

Strength and

Inelastic deformability

Inelastic deformability is directly related to

design and detailing

Inelastic Required

Deformability Strength


New Items in the 2015 NEHRP

Provisions

Design Force Level Provision in Part 1 – modifies

ASCE 7-10 Section 12.10 Section 12.10.3 in ASCE

7-16

Design Force Level Provision in Part 3 – modifies

ASCE 7-10 Section 12.10

Precast Diaphragm Design Provision in Part 1 –

modifies ASCE 7-10 Section 14.2.4 Section 14.2.4

in ASCE 7-16

Resource Paper in Part 3


Alternative ASCE 7-16 Force Level

for Seismic Design of Diaphragms


Diaphragms, Chords, and Collectors

12.10.1.1 Diaphragm Design Forces. Floor

and roof diaphragms shall be designed to resist

design seismic forces from the structural

analysis, but not less than the following forces:

Where

Fpx = the diaphragm design force

Fi = the design force applied to Level i

wi = the weight tributary to Level i

wpx = the weight tributary to the diaphragm

at Level x


Diaphragm Design Forces

0

1

2

3

4

5

6

7

0 50 100 150 200

Fpx

Fx

Force (kips)

Flo

or

Lev

el

Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 9 p. 9 of Set 8

Each mode’s contribution is reduced by R

2

1

,n

i

j j j

i

F f w

a iS T

g R

Fj

j

j

j j

ASCE 7 Method

Fj wj

j Fpj

Floor Accelerations for Diaphragm Design

and

0 2 0 4 0 4

0 5

0 5 Acceleration "Magnification" 1 0

DS e px px DS e DS

e px px e

e e

PGA. S I F / w . S I but . S

g

PGA PGA. I F / w I

g g

or . I . I

SRSS


0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Peak ground acceleration (g)

Flo

or

mag

nif

icati

on

RC Frames n 5

RC Frames 5< n 10

RC Frames 10 < n 20

Walls 5 < n 10

Walls 10 < n 20

Steel Frames n 5

Steel Frames 5 < n 10

Steel Frames 10 < n 20

Steel Frames n > 20

Braced Frames n 5

Braced Frames 5 < n 10

Braced Frames 10 < n 20

Braced Frames n > 20

7-story building

Northridge Earthquake Data

Repaired PCI building

p. 10 of Set 8

? Floor Accelerations for Diaphragm Design

ASCE 7 Method

ASCE 7 Range, Ie =1

05 Acceleration "Magnification" 10e e. I . I

The upper and lower limits in ASCE7 do not seem to be rational

The computation of floor acclerations based on the assumption that all modes

are equally reduced by plasticity does not seem rational

either

Northridge earthquake and shaketable test data


Diaphragm Design

In 2001 Rodriguez et al. noted that inelastic

response in multi-story buildings tended to

cause an important reduction in floor

accelerations contributed by the first mode of

response but had a much lesser effect on those

contributed by the higher modes of response.

They proposed the First Mode Reduced

method, in which the roof acceleration could be

determined by a square root sum of the squares

combination in which the first mode contribution

was reduced for inelasticity and the higher

modes were left unreduced.


Diaphragm Design

Fpx = Cpxwpx/Rs

≥ 0.2SDS Ie wpx

Cpx comes from Cp0, Cpi, and Cpn

Note: Cpi is not used in the 2015 NEHRP

Provisions


Diaphragm Design

2015 NEHRP

Provisions


Diaphragm Design

ASCE 7-16


Diaphragm Design

Cp0 = 0.4 SDS Ie

Cpn= m10CS2

+ m2CS22

≥ Cpi

Note: The lower-bound limit on Cpn is in ASCE

7-16 only, not in the 2015 NEHRP Provisions.


Diaphragm Design

• m1 = 1 + 0.5zS (1 – 1/N)

• m2 = 0.9zS (1 – 1/N) 2

where zS = modal contribution coefficient

modifier dependent on seismic force-resisting

system.


Diaphragm Design

Values of mode shape factor zs

• 0.3 for buildings designed with Buckling Restrained

Braced Frame systems

• 0.7 for buildings designed with Moment-Resisting

Frame systems

• 0.85 for buildings designed with Dual Systems with

Special or Intermediate Moment Frames capable of

resisting at least 25% of the prescribed seismic

forces

• 1.0 for buildings designed with all other seismic force-

resisting systems


Diaphragm Design

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 5 10 15 20 25

Γm1

Number of levels, ne

Eq. 3.1 zs = 1

Eq. 3.1 zs = 0.7

Wall buildings

Frame buildings

Number of levels, n


Diaphragm Design

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25

Γm2

Number of levels, ne

Eq. 3.1 zs = 1

Eq. 3.1 zs = 0.7

Wall buildings

Frame buildings

Number of levels, n


Diaphragm Design

Cpi is the greater of values given by:

Cpi = 0.8Cp0

Cpi = 0.9 m10CS


Diaphragm Design

CS = V/W or Vt/W

CS2 = minimum of:

(0.15N + 0.25) Ie SDS

Ie SDS

Ie SD1/[0.03(N-1)] for N ≥ 2 or 0 for

N = 1


Consistent Look into the Design

Spectra CsR

For the “Second mode”, R = 1

CS(T2) = min(0.15N+0.25, 1)IeSDS

≤ IeSD1/ [0.03(N-1)]

N: number of levels above ground,

N≥ 2


Diaphragm Capacity

Why have we not been seeing inadequate

performance of diaphragms in seismic events?


Inertial Forces in Diaphragms

Existing diaphragms may carry seismic inertial

forces through:

(a) inherent overstrength in the floor system,

including the floor plate and framing elements,

that permit the transfer of higher than code

design forces,


Inertial Forces in Diaphragms

or

(b) inherent ductility or plastic redistribution

qualities within the diaphragm (or at the

boundaries of the diaphragm) that limit the

amount of inertial forces that can develop,

without significant damage or failure.


Diaphragm Force Reduction

Factor, Rs

Elastic diaphragm design force level divided by

a diaphragm force reduction factor, Rs, to

account for overstrength, ductility, or both.

Reduction factors are different for flexure-

controlled and shear-controlled diaphragms.


Diaphragm Design

Flexure-controlled diaphragm: Diaphragm

with a well-defined flexural yielding mechanism,

which limits the force that develops in the

diaphragm.

The factored shear resistance shall be greater

than the shear corresponding to flexural

yielding.


Diaphragm Design

Shear-controlled diaphragm: Diaphragm

that does not meet the requirements of a

flexure-controlled diaphragm.


Diaphragm Design (NEHRP

Provisions)

Diaphragm System Shear Control Flexure Control

CIP Concrete 1.5 2

Precast concrete

EDO 1.0 0.7

BDO 1.0 1.0

RDO 1.0 1.3

Untopped Steel

Deck

Ductile 3.0 NA

Low ductility 2.0 NA

Topped Steel Deck

Reinforced topped

Steel Deck with

shear stud

connection to

framing

2.0

2.5

Other topped Steel

Deck with structural

concrete fill

1.5

2.0

Wood Typical 3.0 NA

When Rs is greater than 1, such a diaphragm should have a well-defined, ductile shear yielding mechanism which limits the force that develops in the diaphragm.

px

px px

s

CF = w

R


Diaphragm Design (ASCE 7-16)

Diaphragm System Shear-

Controlled

Flexure-

Controlled

Cast-in-place concrete designed in

accordance with Section 14.2 and ACI 318 - 1.5 2

Precast concrete designed in accordance

with Section 14.2.4 and ACI 318

EDO 1 0.7 0.7

BDO 2 1.0 1.0

RDO 3 1.4 1.4

Wood sheathed designed in accordance

with Section 14.5 and AF&PA (now AWC)

Special Design Provisions for Wind and

Seismic

- 3.0 NA

1. EDO is precast concrete diaphragm Elastic Design Option.

2. BDO is precast concrete diaphragm Basic Design Option.

3. RDO is precast concrete diaphragm Reduced Design Option.


Transfer Diaphragms

ASCE 7-10 Section 12.10.1.1, 4th paragraph

Where the diaphragm is required to transfer design seismic

forces from the vertical resisting elements above the diaphragm

to other vertical resisting elements below the diaphragm due to

offsets in the placement of the elements or changes in relative

lateral stiffness in the vertical elements, these forces shall be

added to those determined from Eq. 12.10-1. The redundancy

factor, ρ, applies to the design of diaphragms in structures

assigned to Seismic Design Category D, E, or F. For inertial

forces calculated in accordance with Eq. 12.10-1, the

redundancy factor shall equal 1.0. For transfer forces, the

redundancy factor, ρ, shall be the same as that used for the

structure.


Transfer Diaphragms


Transfer Diaphragms


All diaphragms shall be designed for the inertial forces

determined from Eq. 12.10-1 through 12.10-3 and for all

applicable transfer forces. For structures having a horizontal

structural irregularity of Type 4 in Table 12.3-1, the transfer

forces from the vertical seismic force-resisting elements above

the diaphragm to other vertical seismic force-resisting elements

below the diaphragm shall be increased by the overstrength

factor of Section 12.4.3 prior to being added to the diaphragm

inertial forces. For structures having other horizontal or vertical

structural irregularities of the types indicated in Section 12.3.3.4,

the requirements of that section shall apply.


Transfer Diaphragms

12.10.3.3 Transfer Forces in Diaphragms

All diaphragms shall be designed for the inertial forces

determined from Eq. 12.10.3-1 and 12.10.3-2 and for all

applicable transfer forces. For structures having a horizontal

structural irregularity of Type 4 in Table 12.3-1, the transfer

forces from the vertical seismic force-resisting elements above

the diaphragm to other vertical seismic force-resisting elements

below the diaphragm shall be increased by the overstrength

factor of Section 12.4.3 prior to being added to the diaphragm

inertial forces. For structures having other horizontal or vertical

structural irregularities of the types indicated in Section 12.3.3.4,

the requirements of that section shall apply.


Transfer Diaphragms


ASCE 7-16 Section 12.10.3.3,

Exception: One- and two-family dwellings of light

frame construction shall be permitted to use Ω0 = 1.0.


Collectors

12.10.3.4 Collectors - Seismic Design Categories C

through F

In structures assigned to Seismic Design Category C, D, E, or

F, collectors and their connections including connections to

vertical elements shall be designed to resist 1.5 times the

diaphragm inertial forces from Section 12.10.3.2 plus 1.5

times the design transfer forces.

EXCEPTION: 1. Any transfer force increased by the

overstrength factor of Section 12.4.3 need not be further

amplified by 1.5.


Diaphragm Design Force Level

Comparisons


4-Story Perimeter Wall Precast Concrete

Parking Structure (SDC C, Knoxville)

16'

10'-6"

10'-6"

10'-6"

47'-6"

204'


4-Story Perimeter Wall Precast Concrete

Parking Structure (SDC C, Knoxville)


4-Story Interior Wall Precast Concrete

Parking Structure (SDC D, Seattle)


4-Story Interior Wall Precast Concrete

Parking Structure (SDC D, Seattle)


8-Story Precast Concrete Moment Frame

Office Building


8-Story Precast Concrete Moment Frame

Office Building


8-Story Precast Concrete Shear Wall Office

Building


8-Story Precast Concrete Shear Wall Office

Building


Precast Concrete Diaphragm

Design


Diaphragm Design Options

Elastic Design Option (EDO)

Basic Design Option (BDO)

Reduced Design Option (RDO)

Diaphragm remains elastic in DBE and

MCE

Highest diaphragm design force

Connections can include LDE, MDE

and HDE

Diaphragm remains elastic in DBE but Not Necessarily in MCE

Lower diaphragm design force than

EDO

Connections can include MDE and

HDE

Some Diaphragm yielding in DBE,

significant in MCE

Lowest diaphragm design force

Connections must be High Deformation Elements (HDE)

Shear overstrength factor is needed

No shear overstrength needed since elastic

design

Shear overstrength factor is needed

SEAOH 2015 (C. Naito)

Deformation Category

Ten

sion F

OR

CE

LDE – Low Deformability Element

MDE – Moderate Deformability Element

HDE – High Deformability Element

OPENING DISPLACEMENT

LDE MDE HDE

48

7.5 mm

(0.3 in.) 15 mm

(0.6 in.)


Diaphragm Seismic Design Level (DSDL)

• Step 1B: Determine Diaphragm Seismic Design Level (DSDL)

0

1

2

3

4

5

6

7

8

0 50 100 150 200

Nu

mb

er o

f S

tori

es,

n

Diaphragm Span, L [ft]

DSDL: Low

DSDL:

Moderate

DSDL: High

Seismic Design

Category

B or C D, E or F Diaphragm

Seismic Design Level:

LOW

IS DSDL LOW &

AR>2.5? Diaphragm Seismic

Design Level: MODERATE

Diaphragm Seismic

Design Level: HIGH

DSDL Moderate

IS DSDL HIGH & AR<1.5?

YES

YES

NO

NO

49


Seismic Design Option

• Step 2A: Determine Diaphragm Design Option

Diaphragm Seismic

Design Level: LOW

Diaphragm Seismic

Design Level: MODERATE

Diaphragm Seismic

Design Level: HIGH

Design Option Diaphragm Seismic Demand level

Low Moderate High

Elastic Recommended With Penalty* Not Allowed

Basic Alternative Recommended With Penalty*

Reduced Alternative Alternative Recommended

Penalty* = Diaphragm design force shall be increased by 15%.

Choose Design Option: Elastic / Basic / Reduced

50


Precast Concrete


FEMA P-1051 Chapter 6 Overview

• Introduction

• Alternative ASCE 7-16 Force Level for

Seismic Design of Diaphragms

• Step-by-Step Determination of Traditional

Diaphragm Seismic Design Force

• Step-by-Step Determination of Alternative

Diaphragm Seismic Design Force

• Diaphragm Design Force Level Comparisons

• Connector Qualification Protocol


Precast Concrete


Requirements for Precast Concrete

Systems: Design Examples

• The examples in Section 11.1 illustrate the design of untopped

and topped precast concrete floor and roof diaphragms of three

five-story masonry buildings (SDC B, C, D)

• The example in Section 11.2 illustrates the design of an

intermediate precast concrete shear wall building in a region of

low or moderate seismicity. The precast concrete walls in this

example resist the seismic forces for a three-story office

building.

• The example in Section 11.3 illustrates the design of a special

precast concrete shear wall for a single-story industrial

warehouse building.

• The example in Section 11.4 is a partial example for the design

of a special moment frame constructed using precast concrete

per ACI 318 Section 18.9.



11.1

HORIZONTAL DIAPHRAGMS

11.1.1

Untopped Precast Concrete Units for Five-Story Masonry Buildings Assigned to Seismic Design Categories B and C

11.1.2

Topped Precast Concrete Units for Five-Story Masonry Building Assigned to Seismic Design Category D


11.1.1 Untopped Precast Concrete

Units for Five-Story Masonry

Buldings Assigned to SDC B and C

This example illustrates floor and roof

diaphragm design for five-story masonry

buildings in SDC B and in SDC C on soft rock.

The example in Section 13.2 provides design

parameters used. The floors and roofs of these

buildings are made of untopped 8-inch-thick

hollow-core precast, prestressed concrete

plank.


11.1 Horizontal Diaphragms

Hollow core plank floor plan for diaphragm examples

6'-0"

6'-

8"

Prestressed

hollow core

slabs

40'-0" 24'-0" 24'-0" 24'-0" 40'-0"

4'-0"

14'-

0"

24'-

0"

24'-

0"

24'-

0"

152'-0"

72'-

0"

8" concrete

masonry wall

A B C D E F

4

3

2

1


11.1 Horizontal Diaphragms

Building Elevation


This example illustrates floor and roof

diaphragm design using topped precast units in

the five-story masonry building when it is

assigned to SDC D. The topping thickness

exceeds the minimum of 2 in. The topping is

lightweight (115 pcf) concrete with f'c of 4,000

psi and is to act compositely with the 8-in.-thick

hollow-core precast, prestressed concrete

plank. Design parameters are provided in

Section 13.2.

11.1.2 Topped Precast Concrete Units for Five-Story Masonry Building Assigned to SDC D



11.2

THREE-STORY OFFICE BUILDING

WITH INTERMEDIATE PRECAST

CONCRETE SHEAR WALLS

11.3

ONE-STORY PRECAST SHEAR WALL

BUILDING


11.2 Three-story Office Building

with Intermediate Concrete

Shear Walls

This example illustrates the seismic design of

intermediate precast concrete shear walls.

These walls can be used up to any height in

SDCs B and C but are limited to 40 ft for SDCs

D, E, and F. An increase in structural height to

45 ft is permitted for “single story storage

warehouse facilities.”


11.2 Three-Story Office Building

with Intermediate Precast Concrete

Shear Walls

25'-0"25'-0"25'-0"25'-0"25'-0"25'-0"

150'-0"

40

'-0"

40

'-0"

40

'-0"

12

0'-

0"

15

'-0"

8'-0"

26 IT 28precast

beams

18" DT roof and floor

slabs (10 DT 18)

8" precast

shear walls

8'-

0"


11.3 One-Story Precast Shear Wall

Building

• This example illustrates the design of a precast

concrete shear wall for a single-story building

assigned to a high seismic design category.

• The precast concrete building is a single-story

industrial warehouse building (Risk Category II) on

Site Class C soils.

• The precast wall panels used in this building are

typical DT wall panels.

• Walls are designed using intermediate precast

structural walls.


11.3 One-Story Precast Shear Wall

Building 15 DT at 8'-0" = 120'-0"

48'-

0"

48'-

0"

12 D

T a

t 8'-

0"

= 9

6'-

0"

Steel tube

columns

Joist girder

(typical)

24

LH

03

at 4

'-0"

o.c

.

24L

H0

3at

4'-

0"

o.c

.

3 DT at 8'-0" =

24'-0"

16'-0"

O.H.

door

5 DT at 8'-0" = 40'-0" 3 DT at 8'-0" =

24'-0"

16'-0"

O.H.

door



11.4

SPECIAL MOMENT FRAMES

CONSTRUCTED USING PRECAST

CONCRETE


Precast Concrete

Instructional Slides developed by S. K. Ghosh, PhD


Precast Concrete

Instructional Slides developed by S. K. Ghosh, PhD,


Questions

Documents

Seismic Design of Precast Concrete Structures · Seismic Design of Precast Concrete Structures ... 7- story building ... Where the diaphragm is required to transfer design seismic