Slenderness ratio

Since the wall panel has a rectangular plan shape, the above calculation can be simplified:

In-plane,

Slenderness, l_y = l_0,y / i_y

Where

Radius of gyration, i_y = l_w/(12)^0.5

l_0,y is the effective length,

l_w is the length of wall panel

Out-of-plane,

Slenderness, l_z = l_0,z / i_z

Where

Radius of gyration, i_z = h_w/(12)^0.5

l_0,z is the effective length

h_w is the thickness of wall panel

Limiting slenderness ratio

λ_lim = 20 * A * B * C / √n

Where

A = 1 / (1 + (0.2 * φ_ef)) ≥ 0.7

B = √(1 + (2 * ω)) ≥ 1.1

C = 1.7 - r_m

Where

φ_ef is the effective creep ratio,

ω = A_s * f_yd / (A_c * f_cd),

f_yd is the design yield strength of the reinforcement,

f_cd is the design compressive strength of the concrete,

A_s is the total area of longitudinal reinforcement,

n = N_Ed / (A_c * f_cd),

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

r_m = M_1.1 / M_2.1

M_1.1 and M_2.1 are the first order moments at the ends of the stack about the axis being considered, with |M_2.1| ≥ |M_1.1|.

If M_1.1 and M_2.1 cause tension in the same side of the stack then r_m is positive and C ≤ 1.7. If the converse is true then the stack is in double curvature, and it follows that r_m 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 (M_imp.1 > |M_2.1|), 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, φ_ef, is derived as follows:

f_cm = f_ck + 8 (N/mm²)

h₀ = 2 * A_g / u

Where

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

A_g is the gross section area.

α₁ = (35 / f_cm)^0.7

α₂ = (35 / f_cm)^0.2

α₃ = (35 / f_cm)^0.5

If f_cm ≤ 35 N/mm²,

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

Else,

β_H = (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.

β_c( t , t₀ ) = ((t - t₀) / (β_H + t - t₀))^0.3

β_t0 = 1 / (0.1 + t₀ ^0.2)

β_fcm = 16.8 / √f_cm

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 f_cm ≤ 35 N/mm²,

φ_RH = 1 + ((1 - (RH / 100)) / (0.1 * h₀ ^1/3))

Else,

φ_RH = (1 + (((1 - (RH / 100)) / (0.1 * h₀ ^1/3)) * α₁)) * α₂

Then,

φ₀ = φ_RH * β_fcm * β_t0

φ( ∞ , t₀) = φ₀ * β_c( ∞ , t₀ )

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

φ_ef = 0

Else

φ_ef = φ( ∞, t₀) * R_PL

Where

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

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

R_PL 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.