Eurocode 4

In EC4 [1], there are two methods for designing composite columns in braced or non-sway

frames. The first method is “General Design Method”. This method is used for composite

columns with non-symmetrical or non-uniform cross-section over the column length. It is also

used for composite columns when the second method is not applicable. The second method is

“Simplified Design Method”. The second method is used for doubly symmetrical and uniform

cross-section over the column height. In this method, the load carrying capacity of short CFST

columns are calculated as plastic strength of concrete and steel modified by enhancement factor

for concrete strength to include the confining effect provided by steel tube to the concrete core.

Strength of steel tube is also modified by reduction factor to include the effect of biaxial stress

state. Since the columns in the present study are satisfying the requirement of the second method

so this method will be explained and adopted for analysis. The limits of applicability of the this

method are:

The steel contribution ratio, ρ, must satisfy the following condition:

0.2 ≤ ρ ≤ 0.9. If ρ is less than 0.2, the column may be designed as a reinforced concrete column.

If ρ is larger than 0.9, the concrete contribution is ignored and the column is designed as a steel

column. Where ρ is defined as :

ρ =����

��

Where, �� is design yield stress of steel tube �� is design nominal plastic resistance of concrete

filled steel tube (design nominal squash load) calculated as: [1]

�� = ���� + ����� + ����� for rectangular and square cross-section

�� = ɳ����� + ����� + �1 + ɳ��

�

��

���� ����

� for circular cross-section

Where Ar is the area of reinforcement bars, if any, fyr is design yield stress of reinforcement bar,

��� is design characteristics compressive strength of concrete ɳ� and ɳ� are confinement

parameters for steel tube and concrete core. ɳ�reduces the strength of steel section due to biaxial

stress effect while ɳ� increases the strength of concrete section due to triaxial stress effect. ɳ�

and ɳ� depend on relative slenderness ratio, λ̄ . Where λ̄ calculated as [1]:

� = ���

���

Where �� is the plastic resistance of the composite cross-section to compression calculated using

the nominal yield strength of steel tube and reinforcement bars and nominal compressive strength

of concrete cylinder:

�� = ���� + ����� + �����

��� is the Euler buckling load:

��� =�������

��

EIeff is the effective elastic flexural stiffness of the composite column calculated as:

����� = ���� + ���� + 0.6�����

Er and Ir are modulus of elasticity and yield stress of reinforcement bars and Ecm is the secant

modulus of elasticity for structural concrete calculated as [2]:

��� = 22000����

10�

�.�

Where ��� is mean compressive strength of concrete at 28 days age and calculated as [2]:

��� = ��� + 8(���)

For columns having e/d <10: [1]

ɳ� = 0.25�3 + 2�� ≤ 1.0

ɳ� = 4.9 − 18.5� + 17��

≥ 0

The squash load of composite columns in axial compression is calculated as:

�� = ���

Where �� is the squash load of CFST columns and � is reduction factor to account buckling

effect.

� = �

ɸ��ɸ������.�

ɸ = 0.5 ∗ (1 + ��� − 0.2� + ��)

Where � is imperfection factor has been taken as 0.34 as recommended by [3].

The maximum relative slenderness, λ̄ , of the composite column should not be more than

2.

The maximum amount of longitudinal reinforcement that can be considered in the

analysis is 6% of the concrete area. However, if design for fire resistance is not needed,

no minimum amount of reinforcement is normally necessary within composite columns.

(i.e.: 0% ≤��

��≤ 6.0%).

To prevent premature local buckling, the ratio between the width to the wall thickness of

steel tube cross-section in compression must satisfy the following limits:

D/t ≤ 52 ����

�� for rectangular and square CFST

D/t ≤ 90 ×���

�� for circular CFST