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(1)

lecture

twenty six

concrete construction:

columns & frames

Brenton Hardee

A

RCHITECTURAL

S

TRUCTURES

:

F

ORM,

B

EHAVIOR, AND

D

ESIGN

A

RCH 331

HÜDAVERDİ TOZAN

(2)

Concrete in Compression

• crushing

• vertical cracking

– tension

• diagonal cracking

– shear

•

c

f

http://www.bam.de

(3)

Columns Reinforcement

• columns require

– ties or spiral reinforcement

to “confine” concrete

(#3 bars minimum)

– minimum amount of longitudinal steel

(4)

Slenderness

• effective length in monolithic with

respect to stiffness of joint:

& k

• not slender when

22

r

kL

u

(5)

Effective Length (revisited)

• relative rotation

b

c

l

EI

l

EI

(6)
(7)

Column Design

•

c

= 0.65 for ties,

c

= 0.75 for spirals

• P

o

– no bending

• P

u

c

P

n

– ties: P

n

= 0.8P

o

– spiral: P

n

= 0.85P

o

• nominal axial capacity:

– presumes steel yields

– concrete at ultimate stress

st

y

st

g

c

o

f

A

A

f

A

P

0

.

85

(

)

(8)

Columns with Bending

• eccentric loads can cause moments

• moments can change shape and induce

more deflection

(P-

)

P

(9)

Columns with Bending

• for ultimate strength behavior, ultimate

strains can’t be exceeded

– concrete 0.003

– steel

• P reduces

with M

s

y

E

f

(10)

Columns with Bending

• need to consider

combined

stresses

• linear strain

• steel stress at or

below f

y

• plot interaction

(11)

Design Methods

• calculation intensive

– handbook charts

(12)

Design Considerations

• bending at both ends

– P-

maximum

• biaxial bending

• walls

– unit wide columns

– “deep” beam shear

Referanslar

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