Column stack classification (concrete column: EC2)

Tekla Structural Designer
2022
Tekla Structural Designer

Column stack classification (concrete column: EC2)

Slenderness ratio

The slenderness ratio, λ of the restrained length about each axis is calculated as follows:

λ = l0 / i = l0 / √(I / A)

Where

l0 is the effective height of the stack,

i is the radius of gyration of the stack section about the axis under consideration,

I is the second moment of area of the stack section about the axis,

A is the cross-sectional area of the stack section.

The slenderness ratio λ is then checked against the limiting slenderness ratio λlim in each direction. If the slenderness is less than this limit, then the member is short and slenderness effects are ignored, otherwise it is slender.

Limiting slenderness ratio

λlim = 20 * A * B * C / √n

Where

A = 1 / (1 + (0.2 * φef)) ≥ 0.7

B = √(1 + (2 * ω)) ≥ 1.1

C = 1.7 - rm

Where

φef is the effective creep ratio,

ω = As * fyd / (Ac * fcd),

fyd is the design yield strength of the reinforcement,

fcd is the design compressive strength of the concrete,

As is the total area of longitudinal reinforcement,

n = NEd / (Ac * fcd),

NEd is the design axial force between restrained floor levels in this direction,

rm = M1.1 / M2.1

M1.1 and M2.1 are the first order moments at the ends of the stack about the axis being considered, with |M2.1| ≥ |M1.1|.

If M1.1 and M2.1 cause tension in the same side of the stack then rm is positive and C ≤ 1.7. If the converse is true then the stack is in double curvature, and it follows that rm is negative and C > 1.7.

For braced stacks in which the first order moments arise only from transverse loads (lateral loading is significant) or imperfections (Mimp.1 > |M2.1|), C must be taken as 0.7,

For

bracing stacks, C must be taken as 0.7,

For restrained lengths encompassing more than one stack, C is taken as 0.7.

The effective creep ratio, φef, is derived as follows:

fcm = fck + 8 (N/mm2)

h0 = 2 * Ag / u

Where

u is the section perimeter in contact with the atmosphere (assumed to be the full section perimeter),

Ag is the gross section area.

α1 = (35 / fcm)0.7

α2 = (35 / fcm)0.2

α3 = (35 / fcm)0.5

If fcm ≤ 35 N/mm2,

βH = (1.5 * (1 + (1.2 * RH))18 * h0) + 250 ≤ 1500

Else,

βH = (1.5 * (1 + (1.2 * RH))18 * h0) + (250 * α3) ≤ 1500 * α3

Where

RH is the relative humidity, which is set under Design parameters in the column properties.

βc( t , t0 ) = ((t - t0) / (βH + t - t0))0.3

βt0 = 1 / (0.1 + t00.2)

βfcm = 16.8 / √fcm

Where

t0 is the age of column loading and defaults to 14 days, if required it can be changed under Design parameters in the column properties.

If fcm ≤ 35 N/mm2,

φRH = 1 + ((1 - (RH / 100)) / (0.1 * h01/3))

Else,

φRH = (1 + (((1 - (RH / 100)) / (0.1 * h01/3)) * α1)) * α2

Then,

φ0 = φRH * βfcm * βt0

φ( ∞ , t0) = φ0 * βc( ∞ , t0 )

If φ( ∞ , t0) ≤ 2 and λ < 75 and Mmax.1 / NEd ≥ h and ω ≥ 0.25,

φef = 0

Else

φef = φ( ∞, t0) * RPL

Where

Mmax.1 is the largest first order moment in the restrained length in this direction,

NEd is the design axial force in the restrained length in this direction,

RPL is the permanent load ratio.

You are required to supply a value for the permanent load ratio which is located under Design parameters in the column properties. A default of 0.65 has been assumed, but you are advised to consider if this is appropriate and adjust as necessary.

Tekla Structural Designer assumes that t ∞ (t-infinity) is equal to 70 years (25550 days).

Pre-selection of Bracing Contribution

The significant parameter within the slenderness criteria is a choice of how a wall, or column, is contributing to the stability of the structure.

In-plane direction, a wall is usually considered to be a bracing member. Out-of-plane direction, a wall is usually considered to be braced by other stabilizing members. These are the default settings but can be edited.

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