Seis Presentation

7 Reinforced Concrete By Peter W. Somers, S.E. Originally developed by Finley A. Charney, PhD, P.E.

Disclaimer Instru ctio nal Materials Complementi ng FEMA P-10 P-1051, 51, Design Examples

Reinforced Re inforced Concrete - 1

Top opic ic Overvi vervie ew

• • •

Concr on cre ete and re r einfo in forc rce ement behavi behavior or Reference stand s tanda ards rd s Requir qu ire ements by Seismi is mic c Design si gn Category

– Moment resisting frames – Shear walls

• •

Other topic s Design si gn Examples xamp les

Instru ctio nal Materials Complementi ng FEMA P-105 P-1051, 1, Design Examples



• • •

Concr on cre ete and re r einfo in forc rce ement behavi behavior or Reference stand s tanda ards rd s Requir qu ire ements by Seismi is mic c Design si gn Category


• •

Other topic s Design si gn Examples xamp les




• • •

Concr on cre ete and re r einfo in forc rce ement behavi behavior or Reference stand s tanda ard rds s Requ quir ire ements by Seis ismi mic c Desi sign gn Category


• •

Other topics topic s Desi sign gn Examp xamples les



Sum ummary mary of o f Con Concr cre ete Be Behavio havior r

•

Compre omp ressi ssive ve Ductili uct ility ty

– Strong in compression but brittle – Confinement improves ductility by • Maintaining concrete core integrity • Preventing longitudinal bar buckling

•

Flexur lexura al Ductili uct ility ty

– Longitudinal steel provides monotonic ductility at low reinforcement ratios

– Transverse steel needed to maintain ductility through reverse cycles and at very high strains (hinge development)



Topic Overview

• • •

Concrete and reinforcement behavior Reference standards Requirements by Seismic Design Category


• •

Other topics Design Examples

Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples

Reinforced Concrete - 5

Reference Standards 16



Modifications to Reference Standards



Con onte text xt in

NEHRP Recommended Provisions

Provisions

A SCE 7-16

A CI 318-14

ASCE A SCE 7-16 fo f o r Con Co n c r ete et e St r u c t u r al d es i g n c r i t er i a:

Ch ap . 12

St r u c t u r al an al y s i s p r o c ed u r es :

Ch ap . 12

Des i g n o f c o n c r et e s t r u c t u r es :

Sec . 14.2

Provisi rov isions ons modifi mod ifica catio tions ns to ASC ASCE 77-10 ASCE A SCE 7-16 mo m o d i f i c ati at i o n s t o A CI 318-14



Ref er en c e St an d ar d s ASCE A SCE 7-16: Define fin es syst s yste ems and classification classif ications s Provides rov ides desig design n coe co efficients ffi cients ACI A CI 318-14: Provides rov ides system sy stem desig design n and and deta detaili iling ng require requir ements cons co nsis istent tent wit w ith h AS A SCE 7-16 syst sy ste em crite cri teria ria Modif od ifii ed by ASCE ASCE 77-16



Us e o f Ref er en c e St an d ar d s

• ACI A CI 318 – Chapter 18, Earthquake-Resistant Earthquake-Resistant Structures

• ASCE A SCE 7-16 and an d Pro Pr o v i s i o n s Sect Sec t i o n 14.2 – Modifications to ACI 318 – Detailing requirements for concrete piles ASCE 7-1 7-10 0 • Provisions s u p er s ed e ASCE modifications



Det ai led Mod Modif ific ica ati tion ons s to t o AC A CI 318 pi ers and wall se s egme gm ents nt s • Wall pie • Membe mb ers not no t de d esign si gna ated as as part of o f the t he LRF LRFS walls • Columns supporting discontinuous walls nt erme rm edia di ate pre pr ecast walls • Inte • Plain lain concrete con crete struct str uctures ures A n c h o r i n g t o c o n c r ete et e • An • Foundations • Ac A c c ept ep t anc an c e cr c r i t eri er i a fo f o r v ali al i d ati at i o n t est es t i n g o f spe sp ecia ci al pre pr ecast walls



Topic Overview

• • •



• •




Design Coefficients Moment Resisting Frames Seismic Force Resisting System Special R/C Moment Frame Intermediate R/C Moment Frame Ordinary R/C Moment Frame

Deflection

Response Modification Coefficient, R

Amplification

8

5.5

5

4.5

3

2.5


Factor, Cd


Performance Objectives

•

Special Moment Frames

– Strong column • Avoid story mechanism

– Hinge development • Confined concrete core • Prevent rebar buckling • Prevent shear failure

– Member shear strength – Joint shear strength – Rebar development and splices (confined)




•

Intermediate Moment Frames

– Avoid shear failures in beams and columns – Plastic hinge development in beams and columns – Toughness requirements for two-way slabs without beams

•

Ordinary Moment Frames

– Minimum ductility and toughness – Continuous top and bottom beam reinforcement – Minimum column shear failure protection



Summary of Seismic Detailing for Frames Issue

Ordinary

Intermediate

Special

Hinge development and confinement

minor

full

Bar buckling

lesser

full

Member shear

lesser

full

minor

full

Joint shear

minor

Strong column

full

Rebar development

lesser

lesser

full

Load reversal

minor

lesser

full



Special Moment Frames

• • • • •

General detailing requirements Beams Joints Columns Example problem



Frame Mechanisms “ strong column – weak beam”

Story mechanism

Sway mechanism



Required Column Strength M nc1

M nb1

M

nc

 1.2 Mnb

M nb2

M nc2



Hinge Development

•

Tightly Spaced Hoops

– Provide confinement to increase concrete strength and usable compressive strain

– Provide lateral support to compression bars to prevent buckling

– Act as shear reinforcement and preclude shear failures

– Control splitting cracks from high bar bond stresses



ACI 318, Overview of SMF: Beam Longitudinal Reinforcement 200

f y







0.025

At least 2 bars continuous top & bottom Joint face Mn+ not less than 50% MnMin. Mn+ or Mn- not less than 25% max. Mn at joint face Splice away from hinges and enclose within hoops or spirals



ACI 318, Overview of SMF: Beam Transverse Reinforcement Closed hoops at hinging regions with “seismic” hook 135º hook, 6dh  3” extension Maximum spacing of hoops: d/4

6db

6”

Longitudinal bars on perimeter tied as if column bars 2h min

Stirrups elsewhere, s


 d/2


ACI 318, Overview of SMF: Beam Shear Strength 1.2D + 1.0L + 0.2S

Mpr1

Mpr2

n

Ve1

Ve



Ve2

Mpr 1  Mpr 2 n

If earthquake-induced shear force



w u n 2

 Ve

Mpr  Mn f s

with

 1.25f y ,   1.0

by analysis

 1V e 2

and Pu 

' g c

A f

then Vc = 0

20



ACI 318, Overview of SMF: Beam-Column Joint Vcol T

V j

 T  C  Vcol

C

V j

T  1.25f y A s, top C  1.25f y A s, bottom



ACI 318, Overview of SMF: Beam-column Joint

20   Vn  15  f 'c A j 12    • • • •

Vn often controls size of columns Coefficient depends on joint confinement To reduce shear demand, increase beam depth Keep column stronger than beam

Instru ctio nal Materials Complementin g FEMA P-1051, Design Examp les


ACI 318, Overview of SMF: Column Transverse Reinforcement at Potential Hinging Region hx

hx

14  h x   so  4     3  Spacing shall not exceed the smallest of: b/4 or 6 db or so (4” to 6”) Distance between longitudinal bas supported by hoops or cross ties, hx  14” Instru ctio nal Materials Complementin g FEMA P-1051, Design Examples


Topic Overview

• • •



• •




Design Coefficients Structural Walls (Bearing Systems) Seismic Force Resisting System

Special R/C Struc tural Walls Ordinary R/C Structural Walls Intermediate Precast

Response

Deflection

Modification

Amplification

Coefficient, R

Factor, Cd

5

5

4

4

4

4

3

3

Structural Walls

Ordinary Precast Walls




•

Special R/C structural walls

– Resist axial forces, flexure and shear – Boundary members • Where compression stress/strain is large, maintain capacity

– Development of rebar in panel – Ductile coupling beams

•

Ordinary R/C structural walls

– No seismic requirements, Ch. 18 does not apply



Design Philosophy

•

Flexural yielding will occur in predetermined flexural hinging regions

•

Brittle failure mechanisms will be precluded

– Diagonal tension – Sliding hinges – Local buckling – Shear failures in coupling beams



ACI 318, Overview of Special Walls: General Requirements w

t = parallel to shear plane hw

 = perpendicular to shear plane Shear plane, Acv = web thickness x length of wall



ACI 318, Overview of Special Walls: General Requirements

•

and

t

not less than 0.0025 unless

V u

 Acv

f 'c

then per Sec.11.6

• •

Spacing not to exceed 18 in. Reinforcement contributing to Vn shall be continuous and distributed across the shear plane




•

Two curtains of reinforcing required if:

V u •

 2 Acv

f 'c

Design shear force determined from lateral load analysis




•

Shear strength:

V n

 Acv  c

f 'c

  t f y

 c = 3.0 for hw/ w1.5  c = 2.0 for hw/ w2.0 Linear interpolation between

•

Walls must have reinforcement in two orthogonal directions




•

For axial load and flexure, design like a column to determine axial load – moment interaction P M



ACI 318, Overview of Special Walls: Boundary Elements For walls with a high compression demand at the edges – special boundary elements are required

Widened end with confinement Extra confinement and/or longitudinal bars at end Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


ACI 318: Overview of Special Walls Boundary Elements Two options for determining need for boundary elements

•

Strain-based: Determined using wall deflection and associated wall curvature

•

Stress-based: Determined using maximum extreme fiber compressive



ACI 318, Overview of Special Walls: Boundary Elements—Strain

•

Boundary elements are required if: c

w

1.5 u 600 



 hw 

= Design displacement = Depth to neutral axis from strain compatibility analysis with loads causing u

u

c



ACI 318, Overview of Walls: Boundary Elements—Strain

•

Where required, boundary elements must extend up the wall from the critical section a distance not less than the larger of:

w

or

Mu /4Vu



ACI 318: Overview of Walls Boundary Elements—Stress

•

Boundary elements are required where the maximum extreme fiber compressive stress calculated based on factored load effects, linear elastic concrete behavior and gross section properties, exceeds 0.2f’ c

•

Boundary element can be discontinued where the compressive stress is less than 0.15f’ c



ACI 318: Overview of Walls Boundary Elements—Detailing •

Boundary elements must extend horizontally not less than the larger of c /2 or c -0.1 w

• •

Width of boundary elements, b > h u /16 or 12”

•

Transverse reinforcement must extend into the foundation

•

Horizontal reinforcement shall extend into the core of boundary and anchored to develop fy.

In flanged walls, boundary element must include all of the effective flange width and at least 12 in. of the web



ACI 318: Overview of Walls Coupling Beams Requirements based on aspect ratio and shear demand n

/h 4

n

/ h  2 and V u

Design as Special Moment Frame beam

Other cases

4

f 'c Acw

Reinforce with 2 intersecting groups of diagonal bars Standard or diagonal



Topic Overview

• • •



• •




Members Not Part of LFRS

•

In frame members not designated as part of the lateral-force-resisting system in regions of high seismic risk:

– Must be able to support gravity loads while subjected to the design displacement

– Transverse reinforcement increases depending on: Forces induced by drift Axial force in member



Precast Concrete: Performance Objectives

Field connections at points of low stress

Field connections must yield

Strong connections

Ductile connections

•

•

Configure system so that hinges occur in factory cast members away from field splices

Inelastic action at field splice



Topic Overview

• • •



• •

Other topics Design Examples from FEMA P-751



IK5

Special Moment Frame Example A

A’

B

C

C’

N

D 1

• Located in Berkeley, California • 12-story concrete building • N-S direction: SMF • E-W direction: dual system • Seismic Design Category D

2

’ 0 1 2 = ’ 0 3 @ 7

3 4 5 6

• Modal Analysis Procedure

7 5 @ 20’ = 100’

8

Typical Floor Plan Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Slide 47 IK5

Update required. Insung Kim, 8/4/2016

Frame Elevations

Grid Lines 3 to 6

Grid Lines 2 and 7



Story Shears: E-W Loading



Layout of Reinforcement #4 stirrup 4

#8 bar, assumed

” 5 . 8 2

” ” 5 . 2 9 3 2

24” 30” Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Design Strengths Design Aspect

Strength Used

Beam flexure

Design strength

Beam shear

Maximum probable strength

Beam-column joint


Column flexure

1.2 times nominal beam strength

Column shear




Bending Moment Envelopes: Frame 1 Beams, 7th Floor



Beam Reinforcement: Longitudinal Design for Negative Moment at the Face of the Interior Support (Grid A’): Mu = 1.46(-602) + 0.5(-278) + 1.0(-3,973) = -4,976 inch-kips One #7 bars in addition to the four #8 bars required for minimum steel: As = 4(0.79) + 1(0.60) = 3.76 in^2 a = 3.76 (60)/[0.85 (5) 24] = 2.21 inches Mn = 0.9(3.76)60(29.5 – 2.21/2) = 5,765 inch-kips > 4,976 inch-kips . Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Beam Reinforcement: Longitudinal (continued) Check additional requirements: Minimum of two bars continuous top and bottom:

OK (three #8 bars continuous top OK (four #8 bars continuous top and bottom)

Positive moment strength greater than 50 percent negative moment strength at a joint:

OK (at all joints)

Minimum strength along member greater than 0.25 maximum strength:

OK (As provided = four #8 bars is more than 25 percent of reinforcement provided at joints)



Beam Reinforcement: Layout

1

4

4

Instru ctio nal Materials Complementin g FEMA P-1051, Design Examples


Determine Beam Design Shear

B

Assumed hinging mechanism

C

6,841

Probable moment strength, Mpr (k-in) Vu,grav = 34.1 kips

7,929 20’ – 30” = 17’-6”=210”

V e



M pr 1  M pr 2 n

 V u , grav 

7,929  6,841 210

 34.1  104.4 kips



Loading

Beam Shear Force

Hinge locations A

A'

7,042

B

C 7,042

7,042

7,042

(a) Seismic moment (tension side) in.-kips

5,519

5,519

5,519

Beam moments

5,519

210" 15"

15"

240"

58.1

58.1

58.1 (b) Seismic shear positive

Seismic shear

kips 58.1

58.1

33.8

32.9

58.1

33.3

33.3

33.3

33.3

(c) Gravity shear (1.42 D + 0.5 L) positive kips

91.4

91.9 24.8

25.2

91.4 24.8 (d) Design shear seismic + gravity

24.3 91.0

91.4

Factored gravity shear

24.8

24.8 91.4

Design shear

positive kips



Beam Reinforcement: Transverse Vseismic > 50% Vu therefore take Vc = 0

Use 4 legged #4 stirrups smax



 Av f y d V e



0.75(0.8)(60)(29.5) 104.4

 10.2 in.

At ends of beam s = 6 in. (near midspan, s = 6.0 in. w/ 2 legged stirrup)



Beam Reinforcement: Transverse

•

Check maximum spacing of hoops within plastic hinge length (2h)

– d/4 = 7.4 in. – 6db = 6.0 in. – 6 in. Therefore, 6.0 in. spacing at ends is adequate At beam rebar splices, s = 4.0 in.



Joint Shear Force

V j

Vcol T

 T  C  V col

C

T  1.25 f y As , top

V j

C  1.25 f y As , bottom But how to compute Vcol? Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Joint Shear Force V col

V col

 M  M   V  V  h  pr , R R L  pr , L 2  

h

lc

At 7th Floor, Column C:

V col

7,929  6,841  70.3  70.3   156

30  2

  108.2 kips

V e,L

M pr,R

c

l

V e,R

M pr,L

V col



Joint Shear Force 108 282

237

411

T  1.25 f y As ,top

 282 kips C  1.25 f y As ,bot  237 kips V j  T  C  V col  411 kips  15 f c' A j  15 5,000 (30) 2  955  V n  0.85  955  811 kips  411 kips

V n



Frame 1 Column Design Column:

then:

Pu

f 'c Ag



A

A'

10

 M

nc

 1.2 M nb

B

P L = 78 kips Includes P D = 367 kips level 7 " 2 3

" 0 ' 3 1

Level 7

30" " 2 3

Design column using standard P-M interaction curve

20'-0"


Level 6

20'-0"


Column Design Moments Design for strong column based on nominal beam moment strengths

A

A'

B

6,406

Beam moments (Level 7)

 M

5,498

nc

 1.2 M nb

1.25,498  6,406   14,285 k - ft 7,142 7,142

Column moments (Level 7), assume uniform distribution top and bottom



Column Transverse Reinforcement

nl: number of longitudinal bars that are laterally supported by the corner of hoops or by seismic hooks



Column Transverse Reinforcement Maximum spacing is smallest of: h/4 = 30/4 = 7.5 in. 6db = 6*1.0 = 6.0 in. (#8 bars) so calculated as follows: 14  h x so  4  3

for 12 #8 vertical bars and #4 hoops, hx = 8.33 in. and so = 5.72 in. Next, check confinement requirements……



Column Transverse Reinforcement Assume 4 in. hoop spacing: f c' < 10,000 psi and Pu< 0.3 f c'Ag Equation (c) was not required. Ash

 f 'c  Ag    (4)(27) 5  900  1   0.63 in 2     0.3 sbc   1 0 . 3        60  729    f yt  Ach  

and Ash

 0.09sbc

f 'c f yt

5    0.09(4)(27)   0.81 in 2  60 

Therefore, use #4 bar hoops with 4 legs Ash = 0.80 in2 Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Determine Column Shear Based on probable moment strength of columns and can be limited by probable moment strength of beams

Mpr,1

Mpr,2

Mpr,top Vseismic

n

Mpr,3

Mpr,4

Vseismic Mpr,bottom



Column Shear Design Based on column moments: Mpr,col = 14,940 k-in (12 #8 vert and Pmax)

V e



2(14,940)

For Pmin

(124)



 241 kips

f 'c Ag

20



5(30)(3) 20

 225 kips,

Vc can be included in shear calculation



Column Shear Design Assume 6 in. max hoop spacing at mid-height of column

V c V s

2 

f 'c bd  2 5,000 (30)(27.5)  117 kips

Av f y d



0.8(60)(27.5)

 220 kips

s 6  V n   (V c  V s )  0.75(117  220)  252 kips  241 kips OK

Hoops:

4 legs #4 s = 6 in. max



Column Reinforcement A'

•

Confinement length, l o , greater of:

• • •

Level 7 " 2 3 " 2

h = 30 in. Hc/6 = (156-32)/6 = 20.7 in.

" 4 t a

(12) #8 bars

7

#4 hoops +

+

" 0 3

" 6 t a 7

18 in.

30" " 4 t a 7

– Therefore, use 30 in.

" 2

" 2 3

Level 6

" 4 t a 7

" 2

30"



Structural Wall Example A

• Same building as moment

A’

B

C

C’

1

frame example

• 12-story concrete building • N-S direction: SMF • E-W direction: dual system • Seismic Design Category D • Modal Analysis Procedure

N

D

2

’ 0 1 2 = ’ 0 3 @ 7

3 4 5 6 7

Shear wall @ grid 3-6

8

5 @ 20’ = 100’

Typical Floor Plan Instru ctio nal Materials Complementin g FEMA P-1051, Design Examp les


Structural Wall

17’-6”=210”

16” 30” x 30” column

Shear wall cross section

Ag = (16)(210)+2(30)(30) = 5,160 sq in Acv = 16[(210)+2(30)] = 4,320 sq in



Shear Panel Reinforcement  V n

  Acv



'

f c

  t f y

Vu = 769 kips (below level 2)

l

Panel

to A cv

f’c = 5,000 psi, f y = 60 ksi α

= 2.0

 = 0.6 (per ACI 9.3.4(a))

A cv

t

Req’d  t = 0.0019 Min  (and t) = 0.0025 Use #5 @ 12” o.c. each face:  t= 0.0032 and  Vn = 869 kips Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Axial-Flexural Design At ground floor: shear and moment determined from the lateral analysis and axial load from gravity load run down. All are factored forces.

• • •

Mu = 30,641 kip-ft Pu,max = 6,044 kips Pu,min = 2,460 kips



Axial and Flexural Design P-M interaction Wall reinforcement: #5 @12” o.c. Boundary reinforcement: 12 #9 each end



Boundary Element Check Use stress-based procedure (ACI 18.10.6.3). Boundary Elements required if max stress > 0.2 f’c Ground level axial load and moment are determined based on factored forces. Pu Ag



M u S



6,044 5,160



30,641(12) 284,444

 2.46ksi  0.49 f c'

Need confined boundary element (extend up to below 9th floor where max stress <


0.15f’c) Reinforced Concrete - 77

Boundary Element Length Length = larger of c/2 or c-0.1Lw From P-M interaction, max c = 72.6 in. So, c/2 = 38.8 and c-0.1Lw = 50.6 in Since length > column dimension, either

• •

Extend boundary into wall panel Increase f’c = reduce boundary element length

For this example, assume f’c = 7,000 psi, Then req’d boundary element length is 28.7 in. Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Boundary Element Confinement Transverse reinforcement in boundary elements is to be designed essentially like column transverse reinforcement. Assume #5 ties and 4 in. spacing Ash

 0 .09 sb c

'

f c

f y

7    0 .09 ( 4 )( 27 )    1 . 13 in 2  60 

#5 with 4 legs, Ash = 1.24 in2

Width of the flexural compression zone, b > 12in. or h u/16 Instru ctio nal Materials Complementi ng FEMA P-1051, Design Examples


Questions



Seis Presentation

Recommend Documents