twenty two concrete construction: http:// nisee.berkeley.edu/godden - - PowerPoint PPT Presentation

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twenty two concrete construction: http:// nisee.berkeley.edu/godden - - PowerPoint PPT Presentation

Jun 06, 2023 275 likes •637 views

A RCHITECTURAL S TRUCTURES : F ORM, B EHAVIOR, AND D ESIGN A RCH 331 D R. A NNE N ICHOLS S PRING 2019 lecture twenty two concrete construction: http:// nisee.berkeley.edu/godden materials & beams Concrete Beams 1 Architectural Structures

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SLIDE 1

F2018abn Concrete Beams 1 Lecture 22 Architectural Structures ARCH 331

lecture

twenty two

concrete construction:

materials & beams

http:// nisee.berkeley.edu/godden

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN ARCH 331

  • DR. ANNE NICHOLS

SPRING 2019

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SLIDE 2

F2018abn Concrete Beams 2 Lecture 22 Architectural Structures ARCH 331

Concrete Beam Design

  • composite of concrete and steel
  • American Concrete Institute (ACI)

– design for maximum stresses – limit state design

  • service loads x load factors
  • concrete holds no tension
  • failure criteria is yield of reinforcement
  • failure capacity x reduction factor
  • factored loads < reduced capacity

– concrete strength = f’c

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SLIDE 3

F2018abn Concrete Beams 3 Lecture 22 Architectural Structures ARCH 331

Concrete Construction

  • cast-in-place
  • tilt-up
  • prestressing
  • post-tensioning

http:// nisee.berkeley.edu/godden arch.mcgill.ca

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SLIDE 4

F2018abn Concrete Beams 4 Lecture 22 Architectural Structures ARCH 331

Concrete Beams

  • types

– reinforced – precast – prestressed

  • shapes

– rectangular, I – T, double T’s, bulb T’s – box – spandrel

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SLIDE 5

F2018abn Concrete Beams 5 Lecture 22 Architectural Structures ARCH 331

Concrete Beams

  • shear

– vertical – horizontal – combination:

  • tensile stresses

at 45

  • bearing

– crushing

http://urban.arch.virginia.edu

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SLIDE 6

F2018abn Concrete Beams 6 Lecture 22 Architectural Structures ARCH 331

Concrete

  • low strength to weight ratio
  • relatively inexpensive

– Portland cement

  • types I - V

– aggregate

  • course & fine

– water – admixtures

  • air entraining
  • superplasticizers
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SLIDE 7

F2018abn Concrete Beams 7 Lecture 22 Architectural Structures ARCH 331

Concrete

  • hydration

– chemical reaction – workability – water to cement ratio – mix design

  • fire resistant
  • cover for steel
  • creep &

shrinkage

jci-web.jp

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SLIDE 8

F2018abn Concrete Beams 8 Lecture 22 Architectural Structures ARCH 331

Concrete

  • placement (not pouring!)
  • vibrating
  • screeding
  • floating
  • troweling
  • curing
  • finishing
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SLIDE 9

F2018abn Concrete Beams 9 Lecture 22 Architectural Structures ARCH 331

Reinforcement

  • deformed steel bars (rebar)

– Grade 40, Fy = 40 ksi – Grade 60, Fy = 60 ksi - most common – Grade 75, Fy = 75 ksi – US customary in # of 1/8” 

  • longitudinally placed

– bottom – top for compression reinforcement

(nominal)

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SLIDE 10

F2018abn Concrete Beams 10 Lecture 22 Architectural Structures ARCH 331

Reinforcement

  • prestressing strand
  • post-tensioning
  • stirrups
  • detailing

– development length – anchorage – splices

http:// nisee.berkeley.edu/godden

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SLIDE 11

F2018abn Concrete Beams 11 Lecture 22 Architectural Structures ARCH 331

Composite Beams

  • concrete

– in compression

  • steel

– in tension

  • shear studs
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SLIDE 12

F2018abn

1 1 1

E y f E R    

2 2 2

E y f E R    

Concrete Beams 12 Lecture 22 Architectural Structures ARCH 331

Behavior of Composite Members

  • plane sections remain plane
  • stress distribution changes
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SLIDE 13

F2018abn Concrete Beams 13 Lecture 22 Architectural Structures ARCH 331

Transformation of Material

  • n is the ratio of E’s
  • effectively widens a material to get

same stress distribution

1 2

E E n 

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SLIDE 14

F2018abn

c transformed

My f I  

s transformed

Myn f I  

Concrete Beams 14 Lecture 22 Architectural Structures ARCH 331

Stresses in Composite Section

  • with a section

transformed to one material, new I

– stresses in that material are determined as usual – stresses in the other material need to be adjusted by n

concrete steel

E E E E n  

1 2

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SLIDE 15

F2018abn Concrete Beams 15 Lecture 22 Architectural Structures ARCH 331

Reinforced Concrete - stress/strain

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SLIDE 16

F2018abn Concrete Beams 16 Lecture 22 Architectural Structures ARCH 331

Reinforced Concrete Analysis

  • for stress calculations

– steel is transformed to concrete – concrete is in compression above n.a. and represented by an equivalent stress block – concrete takes no tension – steel takes tension – force ductile failure

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SLIDE 17

F2018abn Concrete Beams 17 Lecture 22 Architectural Structures ARCH 331

Location of n.a.

  • ignore concrete below n.a.
  • transform steel
  • same area moments, solve for x

) ( 2     x d nA x bx

s

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SLIDE 18

F2018abn Concrete Beams 18 Lecture 22 Architectural Structures ARCH 331

T sections

  • n.a. equation is different if n.a. below

flange

f f

bw bw hf hf

   

) ( 2 2              x d nA h x b h x h x h b

s f w f f f f

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SLIDE 19

F2018abn Concrete Beams 19 Lecture 22 Architectural Structures ARCH 331

ACI Load Combinations*

  • 1.4D
  • 1.2D + 1.6L + 0.5(Lr or S or R)
  • 1.2D + 1.6(Lr or S or R) + (1.0L or 0.5W)
  • 1.2D + 1.0W + 1.0L + 0.5(Lr or S or R)
  • 1.2D + 1.0E + 1.0L + 0.2S
  • 0.9D + 1.0W
  • 0.9D + 1.0E

*can also use old ACI factors

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SLIDE 20

F2018abn Concrete Beams 20 Lecture 22 Architectural Structures ARCH 331

Reinforced Concrete Design

  • stress distribution in bending

Wang & Salmon, Chapter 3

b As a/2 T T NA C C c a= 1c 0.85f’c actual stress Whitney stress block d h

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SLIDE 21

F2018abn Concrete Beams 21 Lecture 22 Architectural Structures ARCH 331

Force Equations

  • C = 0.85 f´cba
  • T = Asfy
  • where

– f´c = concrete compressive strength – a = height of stress block – 1 = factor based on f´c – c = location to the n.a. – b = width of stress block – fy = steel yield strength – As = area of steel reinforcement a/2 T a=1c 0.85f’c C

1

4000 0.85 (0.05) 0.65 1000

c

f           

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SLIDE 22

F2018abn Concrete Beams 22 Lecture 22 Architectural Structures ARCH 331

  • T = C
  • Mn = T(d-a/2)

– d = depth to the steel n.a.

  • with As

– a = – Mu  Mn  = 0.9 for flexure* – Mn =  T(d-a/2) =  Asfy (d-a/2)

Equilibrium

a/2 T C a=1c 0.85f’c d

b f f A

c y s

 85 .

0.25 * 0.65 ( ) 0.65 (0.005 )

t y y

        

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SLIDE 23

F2018abn Concrete Beams 23 Lecture 22 Architectural Structures ARCH 331

  • over-reinforced

– steel won’t yield

  • under-reinforced

– steel will yield

  • reinforcement ratio

– – use as a design estimate to find As,b,d – max  is found with steel  0.004 (not bal) – *with steel  0.005,  = 0.9

Over and Under-reinforcement

bd A ρ

s

http://people.bath.ac.uk/abstji/concrete_video/virtual_lab.htm

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SLIDE 24

F2018abn Concrete Beams 24 Lecture 22 Architectural Structures ARCH 331

As for a Given Section

  • several methods

– guess a and iterate

  • 1. guess a (less than n.a.)

2.

  • 3. solve for a from Mu =  Asfy (d-a/2)
  • 4. repeat from 2. until a from 3. matches a in 2.

y c s

f ba f . A   85          

y s u

f A M d a  2

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SLIDE 25

F2018abn Concrete Beams 25 Lecture 22 Architectural Structures ARCH 331

As for a Given Section (cont)

  • chart method

– Wang & Salmon Fig. 3.8.1 Rn vs. 

  • 1. calculate
  • 2. find curve for f’c and fy to get 
  • 3. calculate As and a
  • simplify by setting h = 1.1d

2

bd M R

n n 

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SLIDE 26

F2018abn Concrete Beams 26 Lecture 22 Architectural Structures ARCH 331

Reinforcement

  • min for crack control
  • required
  • not less than
  • As-max :
  • typical cover

– 1.5 in, 3 in with soil

  • bar spacing

) ( 3 bd f f A

y c s

  ) bd ( f A

y s

200 

cover spacing

) d . ( a 375

1

 

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SLIDE 27

F2018abn Concrete Beams 27 Lecture 22 Architectural Structures ARCH 331

Shells

http:// nisee.berkeley.edu/godden

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SLIDE 28

F2018abn Concrete Beams 28 Lecture 22 Architectural Structures ARCH 331

Annunciation Greek Orthodox Church

  • Wright, 1956

http://www.bluffton.edu/~sullivanm/

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SLIDE 29

F2018abn Concrete Beams 29 Lecture 22 Architectural Structures ARCH 331

Annunciation Greek Orthodox Church

  • Wright, 1956
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SLIDE 30

F2018abn Concrete Beams 30 Lecture 22 Architectural Structures ARCH 331

Cylindrical Shells

  • can resist tension
  • shape adds “depth”
  • not vaults
  • barrel shells
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SLIDE 31

F2018abn Concrete Beams 31 Lecture 22 Architectural Structures ARCH 331

Kimball Museum, Kahn 1972

aasarchitecture.com

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SLIDE 32

F2018abn Concrete Beams 32 Lecture 22 Architectural Structures ARCH 331

Kimball Museum, Kahn 1972

  • outer shell edges
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SLIDE 33

F2018abn Concrete Beams 33 Lecture 22 Architectural Structures ARCH 331

Kimball Museum, Kahn 1972

  • skylights at peak
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SLIDE 34

F2018abn Concrete Beams 34 Lecture 22 Architectural Structures ARCH 331

Approximate Depths