1

F2009abn

twenty two

concrete construction:

materials & beamsConcrete 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

F2008abnConcrete 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

F2008abnConcrete Beams 3

Lecture 22

Foundations Structures

ARCH 331

Concrete Construction

• cast-in-place

• tilt-up

• prestressing

• post-tensioning

http:// nisee.berkeley.edu/goddenarch.mcgill.ca

F2008abnConcrete 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

2

F2008abnConcrete 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

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Concrete

• low strength to weight ratio

• relatively inexpensive

– Portland cement

• types I - V

– aggregate

• course & fine

– water

– admixtures

• air entraining

• superplasticizers

F2008abnConcrete 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

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Concrete

• placement (not pouring!)

• vibrating

• screeding

• floating

• troweling

• curing

• finishing

3

F2008abnConcrete 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)

F2008abnConcrete Beams 10

Lecture 22

Foundations Structures

ARCH 331

Reinforcement

• prestressing strand

• post-tensioning

• stirrups

• detailing

– development length

– anchorage

– splices

http:// nisee.berkeley.edu/godden

F2008abnConcrete Beams 11

Lecture 22

Foundations Structures

ARCH 331

Composite Beams

• concrete

– in compression

• steel

– in tension

• shear studs

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• plane sections remain plane

• stress distribution changes

11 1

E yf E

R 2

2 2

E yf E

R

Concrete Beams 12

Lecture 22

Foundations Structures

ARCH 331

Behavior of Composite Members

4

Concrete Beams 13

Lecture 22

Foundations Structures

ARCH 331

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Transformation of Material

• n is the ratio of E’s

• effectively widens a material to get

same stress distribution

1

2

E

En

F2008abnConcrete 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

En

1

2

c

transformed

Myf

I

s

transformed

Mynf

I

Concrete Beams 15

Lecture 22

Foundations Structures

ARCH 331

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Reinforced Concrete - stress/strain

Concrete Beams 16

Lecture 22

Foundations Structures

ARCH 331

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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

5

Concrete Beams 17

Lecture 22

Foundations Structures

ARCH 331

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Location of n.a.

• ignore concrete below n.a.

• transform steel

• same area moments, solve for x

0)(2

xdnAx

bx s

Concrete Beams 18

Lecture 22

Foundations Structures

ARCH 331

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T sections

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

flangef f

bw

bw

hf hf

0)(22

xdnAhx

bhxh

xhb sf

wff

ff

F2008abnConcrete 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

F2008abnConcrete Beams 20

Lecture 22

Foundations Structures

ARCH 331

Reinforced Concrete Design

• stress distribution in bending

Wang & Salmon, Chapter 3

b

As

a/2

TTNA

CCc a=

1c

0.85f’c

actual stress Whitney stressblock

dh

6

F2008abnConcrete 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

40000.85 (0.05) 0.65

1000

cf

F2008abnConcrete 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

Ca=1c

0.85f’c

d

bf

fA

c

ys

85.00.25

* 0.65 ( ) 0.65(0.005 )

t y

y

F2008abnConcrete 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

Aρ 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

cs

f

baf.A

850

ys

u

fA

Mda

2

7

Concrete Beams 25

Lecture 22

Foundations Structures

ARCH 331

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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

2bd

MR nn

Concrete Beams 26

Lecture 22

Foundations Structures

ARCH 331

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Reinforcement

• min for crack control

• required

• not less than

• As-max :

• typical cover

– 1.5 in, 3 in with soil

• bar spacing

)(3

bdf

fA

y

c

s

)bd(f

Ay

s

200

cover

spacing

)d.(a 37501

F2008abnConcrete Beams 27

Lecture 22

Foundations Structures

ARCH 331

Shells

http:// nisee.berkeley.edu/godden

F2008abnConcrete Beams 28

Lecture 22

Foundations Structures

ARCH 331

Annunciation Greek Orthodox Church

• Wright, 1956

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

8

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

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Cylindrical Shells

• can resist tension

• shape adds “depth”

• not vaults

• barrel shells

F2008abnConcrete Beams 31

Lecture 22

Foundations Structures

ARCH 331

Kimball Museum, Kahn 1972

aasarchitecture.com

Concrete Beams 32

Lecture 22

Foundations Structures

ARCH 331

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Kimball Museum, Kahn 1972

• outer shell edges

9

Concrete Beams 33

Lecture 22

Foundations Structures

ARCH 331

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Kimball Museum, Kahn 1972

• skylights at peak

Concrete Beams 35

Lecture 22

Foundations Structures

ARCH 331

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Approximate Depths