Column Design

Lecture - Design of ColumnsCEN 347

Introduction

Types of Column

Strength of short or Slender Columns

0.70

0.65

Analysis and Design of “Short” Analysis and Design of “Short” ColumnsColumns

General Information

Vertical Structural membersTransmits axial compressive loads with or without momenttransmit loads from the floor & roof to the foundation

Column:


General Information

Column:


Tie spacing h (except for seismic)tie support long bars (reduce buckling)ties provide negligible restraint to lateral expose of core

Tie Columns - 95% of all columns in buildings are tied


Pitch = 1.375 in. to 3.375 in.spiral restrains lateral (Poisson’s effect)axial load delays failure (ductile)

Spiral Columns


Elastic Behavior Concrete creeps and shrinks, therefore we can not calculate the stresses in the steel and concrete due to “acting” loads using an elastic analysis.


Elastic Behavior An elastic analysis using the transformed section method would be:

stcc nAA

Pf

For concentrated load, P uniform

stress over section

cs nff

area steel area concrete

/

s

c

cs

AA

EEn


Elastic Behavior An elastic analysis does not work because creep and shrinkage affect the acting concrete compression strain as follows:


Elastic Behavior The change in concrete strain with respect to time will effect the concrete and steel stresses as follows:Concrete

stress

Steel stress


Elastic Behavior Therefore, we are not able to calculate the real stresses in the reinforced concrete column under acting loads over time. As a result, an “allowable stress” design procedure using an elastic analysis was found to be unacceptable. Reinforced concrete columns have been designed by a “strength” method since the 1940’s.

Creep and shrinkage do not affect the strength of the member.

Note:

Behavior, Nominal Capacity and Behavior, Nominal Capacity and Design under concentric Axial loadsDesign under concentric Axial loads

Initial Behavior up to Nominal Load - Tied and spiral columns.

1.


stystgc0 *85.0 AfAAfP

Factor due to less than ideal consolidation and curing conditions for column as compared to a cylinder. It is not related to Whitney’s stress block.

Let Ag = Gross Area = b*h Ast = area of long steel fc =concrete compressive strength fy = steel yield strength


Maximum Nominal Capacity for Design Pn (max)

2.

0maxn rPP

r = Reduction factor to account for accidents/bendingr = 0.80 ( tied )r = 0.85 ( spiral )


Reinforcement Requirements (Longitudinal Steel Ast)

3.

g

stg A

A

- ACI Code 10.9.1 requires

Let

08.001.0 g


3.- Minimum # of Bars ACI Code 10.9.2 min. of 6 bars in

circular arrangement w/min. spiral reinforcement.min. of 4 bars in rectangular arrangement

Reinforcement Requirements (Longitudinal Steel Ast)


3.ACI Code 7.10.5

Reinforcement Requirements (Lateral Ties)

# 3 bar if longitudinal bar # 10 bar # 4 bar if longitudinal bar # 11 bar # 4 bar if longitudinal bars are bundled

siz

e


3.Reinforcement Requirements (Lateral Ties)

16 db ( db for longitudinal bars ) 48 db ( db for tie bar ) least lateral dimension of column

Vertical spacing:

s s s


3.Reinforcement Requirements (Lateral Ties) Vertical spacing: Arrangement,

At least every other longitudinal bar shall have lateral support from the corner of a tie with an included angle 135o.No longitudinal bar shall be more than 6 in. clear on either side from “support” bar.

1.)

2.)


Examples of lateral ties.


ACI Code 7.10.4

Reinforcement Requirements (Spirals )

3/8 “ (3/8” smooth bar, #3 bar dll or wll wire)

- size- clear spacing:

1 in. 3 in.


Reinforcement Requirements (Spiral)

sDAc

sps

4Core of VolumeSpiral of Volume

Spiral Reinforcement Ratio, s

sDDA 41

:from 2c

csps

Behavior, Nominal Capacity and Behavior, Nominal Capacity and Design under concentric Axial loadsDesign under concentric Axial loadsReinforcement Requirements (Spiral)

y

c

c

gs *1

ff

AA

ACI Eqn. 10-6

psi 60,000 steel spiral ofstrength yield center) (center to steel spiral oftch spacing(pi

spiral of edge outside toedge outside :diameter core 4 area core

entreinforcem spiral of area sectional-cross

y

c

2c

c

sp

fs

D

DA

A

where

Behavior, Nominal Capacity and Behavior, Nominal Capacity and Design under concentric Axial loadsDesign under concentric Axial loads4.Design for Concentric Axial Loads

(a) Load Combination

wDLu

wLLDLu

LLDLu

3.19.07.17.14.1*75.0

7.14.1

PPPPPPP

PPP

Gravity:Gravity + Wind: and

Etc.


(b) General Strength Requirement

un PP = 0.7 for tied columns = 0.75 for spiral columns

where,


(c) Expression for Design

08.00.01 Code ACI gg

stg

AA

defined:


ucystcgn

steel85.0

concrete85.0 PffAfArP

or

ucygcgn 85.085.0 PfffArP


85.085.0 cygc

ug

fffr

PA

* when g is known or assumed:

cg

u

cyst 85.0

85.01 fA

rP

ffA

* when Ag is known or assumed:

Example: Design tied Column for Example: Design tied Column for concentric Axial Loadconcentric Axial Load

Design tied column for concentric axial loadPdl = 150 k; Pll =300 k; Pw = 50 kfc =4500 psi fy = 60 ksiDesign a square column aim for g =0.03. Select longitudinal transverse reinforcement.

Behavior under Combined Bending Behavior under Combined Bending and Axial Loadsand Axial Loads

Usually moment is represented by axial load times eccentricity, i.e.


Resultant Forces action at Centroid( h/2 in this case )

s2

positive is ncompressiocs1n TCCP

Moment about geometric center

2*22*2* 2s2c1s1n

hdTahCdhCM


Interaction Diagram Between Axial Load and Moment ( Failure Envelope )

Concrete crushes before steel yields

Steel yields before concrete crushes

Note: Any combination of P and M outside the envelope will cause failure.


Axial Load and Moment Interaction Diagram -General

Example: Axial Load vs. Moment Example: Axial Load vs. Moment Interaction DiagramInteraction Diagram

Column Design

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