twenty two service loads x load factors concrete holds no tension - - PowerPoint PPT Presentation

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F2009abn

twenty two

concrete construction:

materials & beams

Concrete Beams 1 Lecture 22 Architectural Structures ARCH 331

lecture

http:// nisee.berkeley.edu/godden

ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN

ARCH 331

• DR. ANNE NICHOLS

SPRING 2018

F2008abn Concrete Beams 2 Lecture 22 Foundations 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

F2008abn Concrete Beams 3 Lecture 22 Foundations Structures ARCH 331

Concrete Construction

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

http:// nisee.berkeley.edu/godden arch.mcgill.ca F2008abn Concrete Beams 4 Lecture 22 Foundations 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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F2008abn Concrete Beams 5 Lecture 22 Foundations Structures ARCH 331

Concrete Beams

• shear

– vertical – horizontal – combination:

• tensile stresses

at 45

• bearing

– crushing

http://urban.arch.virginia.edu Concrete Beams 6 Lecture 22 Foundations Structures ARCH 331 F2008abn

Concrete

• low strength to weight ratio
• relatively inexpensive

– Portland cement

• types I - V

– aggregate

• course & fine

– water – admixtures

• air entraining
• superplasticizers

F2008abn Concrete Beams 7 Lecture 22 Foundations Structures ARCH 331

Concrete

• hydration

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

• fire resistant
• cover for steel
• creep &

shrinkage

jci-web.jp Concrete Beams 8 Lecture 22 Foundations Structures ARCH 331 F2008abn

Concrete

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

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F2008abn Concrete Beams 9 Lecture 22 Foundations 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)

F2008abn Concrete Beams 10 Lecture 22 Foundations Structures ARCH 331

Reinforcement

• prestressing strand
• post-tensioning
• stirrups
• detailing

– development length – anchorage – splices

http:// nisee.berkeley.edu/godden F2008abn Concrete Beams 11 Lecture 22 Foundations Structures ARCH 331

Composite Beams

• concrete

– in compression

• steel

– in tension

• shear studs

F2008abn

• plane sections remain plane
• stress distribution changes

1 1 1

E y f E R    

2 2 2

E y f E R    

Concrete Beams 12 Lecture 22 Foundations Structures ARCH 331

Behavior of Composite Members

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Concrete Beams 13 Lecture 22 Foundations Structures ARCH 331 F2008abn

Transformation of Material

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

same stress distribution

1 2

E E n 

F2008abn Concrete Beams 14 Lecture 22 Foundations 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

c transformed

My f I  

s transformed

Myn f I  

Concrete Beams 15 Lecture 22 Foundations Structures ARCH 331 F2008abn

Reinforced Concrete - stress/strain

Concrete Beams 16 Lecture 22 Foundations Structures ARCH 331 F2008abn

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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Concrete Beams 17 Lecture 22 Foundations Structures ARCH 331 F2008abn

Location of n.a.

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

) ( 2     x d nA x bx

s

Concrete Beams 18 Lecture 22 Foundations Structures ARCH 331 F2008abn

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

F2008abn Concrete Beams 19 Lecture 22 Foundations Structures ARCH 331

ACI Load Combinations*

*can also use old ACI factors

• 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

F2008abn Concrete Beams 20 Lecture 22 Foundations 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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F2008abn Concrete Beams 21 Lecture 22 Foundations 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           

F2008abn Concrete Beams 22 Lecture 22 Foundations 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

        

F2008abn Concrete Beams 23 Lecture 22 Foundations 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 Concrete Beams 24 Lecture 22 Foundations Structures ARCH 331 F2008abn

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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Concrete Beams 25 Lecture 22 Foundations Structures ARCH 331 F2008abn

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 

Concrete Beams 26 Lecture 22 Foundations Structures ARCH 331 F2008abn

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

 

F2008abn Concrete Beams 27 Lecture 22 Foundations Structures ARCH 331

Shells

http:// nisee.berkeley.edu/godden F2008abn Concrete Beams 28 Lecture 22 Foundations Structures ARCH 331

Annunciation Greek Orthodox Church

• Wright, 1956

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

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Concrete Beams 29 Lecture 22 Foundations Structures ARCH 331 F2008abn

Annunciation Greek Orthodox Church

• Wright, 1956

Concrete Beams 30 Lecture 22 Foundations Structures ARCH 331 F2008abn

Cylindrical Shells

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

F2008abn Concrete Beams 31 Lecture 22 Foundations Structures ARCH 331

Kimball Museum, Kahn 1972

aasarchitecture.com Concrete Beams 32 Lecture 22 Foundations Structures ARCH 331 F2008abn

Kimball Museum, Kahn 1972

• outer shell edges

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Concrete Beams 33 Lecture 22 Foundations Structures ARCH 331 F2008abn

Kimball Museum, Kahn 1972

• skylights at peak

Concrete Beams 35 Lecture 22 Foundations Structures ARCH 331 F2008abn

Approximate Depths