Presented by: Civil Engineering Academy

Columns Presented by: Civil Engineering Academy

Concrete Columns (CERM Ch. 52)

Steel Columns (CERM Ch. 61 & 62)

Do to their slenderness, the design strength of

steel columns is based on buckling. There are

two types of buckling: ◦ Global

◦ Local

The AISC column design provisions for global

buckling are based on Euler column buckling

behavior. The Euler column assumes the

column ends are pinned (K=1). The critical

buckling load for the Euler column is: Pcr =

𝜋²𝐸𝐼

𝐿²

Or in terms of stress using the radius of gyration (r):

The L/r portion of the equation is called the

slenderness ratio and is a measure of a

column’s susceptibility to buckling. You’ll

notice that the slenderness ratio is squared –

meaning that if you double the columns

length you will decrease its buckling capacity

by 4.

The slenderness ratio (L/r) should preferable

not exceed 200. The CERM outlines that the

slenderness ratio also includes a K factor

based on Table 61.1. This is critical.

K = the effective length factor from CERM

Table 61.1

L = the column length

r = radius of gyration = (I/A)1/2

For intermediate columns that fail by inelastic

buckling, the design stress is:

For long columns that fail by elastic buckling, use:

Compare the design strength, ϕPn, to the

required strength. ϕPn = 0.90FcrAg (LRFD, Eq. 61.10(b))

CERM Ex. 61.1

There are two types of concrete columns –

tied and spiral. Tied columns have close

stirrup reinforcement at specified intervals.

The ties contain the longitudinal

reinforcement and prevent it from buckling

out of the column.

For both types of columns, there are a couple of common equations. The common capacity equation is developed from the Euler buckling load.

A common reinforcement ratio provision is

𝜌𝑔𝑟𝑜𝑠𝑠 =

𝐴𝑠𝑡

𝐴𝑔

0.85 (1 )gross gross grosso c yP A f f Eq. 52.11

Eq. 52.12

Problems involving tied columns involve mostly detailing requirements and not a lot of calculations.

For tie spacing use the smallest of:

◦ 16 x longitudinal bar diameter ◦ 48 x tie bar diameter ◦ smallest gross dimension of column

Use no. 3 bars if longitudinal bars are no. 10 or smaller; otherwise use no. 4

bars. The cover should be 1.5 in minimum.

Use a minimum of four longitudinal bars, one in each corner of a square

or rectangular column.

Design the axial load strength.

The 70% is the capacity reduction factor and the 80% is for eccentricity.

(0.80)(0.70)ult oP P

For spiral columns, use a minimum of six

longitudinal bars, spiral ties no smaller than no.

3, spaced 1 in to 3 in apart. Also, check the

following code provision for the spiral

reinforcement ratio.

The 75% is the capacity reduction factor, and

the 85% is for eccentricity.

CERM Ex. 52.1

Column exam-type problems.

Slabs!