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Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend vertical reinforcements |
Long column Column fails in lateral buckling. |

See test picture from web-site below |
See picture from web-site below |

For frame braced against side sway: | For Frame not braced against side sway: |

Long column if kl_{u}/r
> 34-12(M_{1}/M_{2}) or 40 |
Long column if kl_{u}/r
> 22 |

Where k is slenderness factor, *l*_{u} is
unsupported length, and r is radius of gyration. M1 and
M2 are the smaller and larger end moments. The value, (M_{1}/M_{2})
is positive if the member is bent in single curve, negative if
the member is bent in double curve.

The slender factor, k should be determined graphically from the Jackson and Moreland Alignment charts.

(Charts will be added later)

where y
= å (E_{c}I_{c}/*l*_{c})
of column /å (E_{b}I_{b}/*l*_{b})
of beam, is the ratio of effective length factors.

E_{c} and E_{c} are
younger modulus of column and beams.

*l*_{c} and *l*_{c }are
unbraced length of column and beams.

The cracked moment of inertia, I_{c} is
taken as 0.7 times gross moment of column and I_{b} is
taken as 0.35 times gross moment of inertia of beam.

Alternatively, k can be calculated as follows:

k can be taken as the smaller value of the two equations below.

k = 0.7 + 0.05 (y_{A}+y_{B}) £
1,

k = 0.8 + 0.05 (y_{min}) £
1

y_{A} and y_{B} are
the y at
both ends, y_{min} is
the smaller of the two y values.

For y_{m } <
2

k = [(20- y_{m})/20] Ö(1+y_{m})

For y_{m } ³
2

k = 0.9 Ö(1+y_{min})

y_{m} is
the average of the two y values.

k = 2.0 + 0.3 y

y is the effective length factor at the restrained end.

Beam information:

Beam size: b = 18 in, h = 24 in

Beam unsupported length: *l*_{b} =
30 ft

Concrete strength: 4000 psi

Young's modulus, E_{b} =
57 Ö4000
= 3605 ksi

Moment of inertia of beam: I_{b} =
0.35bh^{3}/12 = 7258 in^{4}.

Column information:

Square Column: D = 18 in, unsupported length *l*_{c} =10
ft

Concrete strength: 5000 psi

Young's modulus: E_{c} =
57 Ö5000
= 4030 ksi

moment of inertia of column: I_{c} =
0.7D^{4}/12 = 6124 in^{4}.

Column top condition:

There are beams at both sides of column at top of column, no column stop above the beams

The effective length factor: y_{A} =
(E_{c}I_{c}/*l*_{c})
/[2 (E_{b}I_{b}/*l*_{b})]
= 1.4

Column bottom condition:

There are beams at both sides of column at bottom of column and a column at bottom level

The effective length factor: y_{A} =
[2 (E_{c}I_{c}/*l*_{c})]
/ [2 (E_{b}I_{b}/*l*_{b})]
= 2.8

From chart:

If the column is braced: k » 0.84

If the column is unbraced: k » 1.61

From equation

If the column is braced:

k = 0.7 + 0.05 (y_{A}+y_{B}) =
0.91

k = 0.8 + 0.05 (y_{min}) =
0.92

If the column is unbraced: y_{m} = (y_{A}+y_{B})/2
= 2.12

k = 0.9 Ö(1+y_{min})
= 1.6

Short column | Long non-sway column & Long sway columns |

1. Column shall be designed to resist factored axial compressive load and factored moments. 2. Column strength shall be determined based on strain compatibility analysis. |
1. Column shall be designed to resist factored axial compressive load. Factored moment shall be magnified with magnification factors. 2. Column strength shall be determined based on strain compatibility analysis. |

- No. 3 ties for longitudinal reinforcement no. 10 bars or less, no. 4 ties for no. 11 bars or larger and bundled bars.
- Tie spacing shall not exceed 16 diameter of longitudinal bars, 48 diameters of tie bars, nor the least dimension of column.
- Every corner bar and alternate bars shall have lateral tie provide the angle shall not exceed 135 degree.
- No longitudinal bar shall be spacing more than 6 inches without a lateral tie.

- Sprial shall be evenly space continuous bar or wire, no. 3 or larger.
- Sprial spacing shall not exceeds 3 in, nor be less than 1 in.
- Anchorage of spiral shall be provided by 1-1/2 extra turn.