V. CFST - Pipe - EQ Method

Verify the composite section properties of a round concrete-filled steel tube (CFST) using the equivelant steel section method.

References

“AISC Shapes Database v15.0” August, 2023. https://www.aisc.org/publications/steel-construction-manual-resources/15th-ed-steel-construction-manual/shapes-database-v15.0/
Stephen Timoshenko, James M. Gere. Mechanics of Materials. Van Nostrand Reinhold Co., 1972. p. 207.

Details

The section is an AISC HSS 6X.500 (HSS 152.4X12.7) round HSS. The steel has a modulus of elasticity, E_s = 205,000 MPa. The concrete core has a modulus of elasticity, E_c = 21,700 MPa.

HSS 6x.500 Section Properites (ref #1)

Outer diameter, D = 152.4 mm
Nominal thickness, t_nom = 2.7 mm
Design thickness, t_des = 11.8 mm
Cross-sectional area, A_x,s = 52.2 cm²
Moment of inertia, I_x,s = 1,300 cm⁴
Torsional moment of inertia, J_s = 2,600 cm⁴
D/t = 12.9

Calculations

The modular ratio for the composite section: .

Diameter of the concrete core:

ID = OD - 2×t_nom = 152 - 2×(12.7) = 127 mm

Cross Section Area

Area of the concrete core:

Area of core as equivelant steel area:

Total equivelant composite area: A_cfst = A_x,s + A_cs = 52.2 + 13.42 = 65.6 cm²

Shear Area

Shear correction factor for steel (circular hollow section), k_s (from ref. #2).

Since 0.5 < k_k < 0.89, k_s = k_k = 0.55.

Steel shear area, A_sv = k_sA_s = 0.55 × 52.2 = 28.8 cm²

Shear correction factor for concrete (circular section), k_c = 0.897 (from ref. #2).

Concrete shear area, A_cv = k_cA_cs = 0.897 × 13.42 = 12.04 cm²

Total equivelant composite shear area: A_v,cfst = A_sv + A_cv = 28.8 + 12.04 = 41.1 cm²

Moment of Inertia

Moment of inertia of the concrete core:

Equivelant moment of inertia of core:

Total equivelant composite moment of inertia: I_cfst = I_x,s + I_cs = 1,300 + 135.3 = 1,434 cm⁴

Section Modulus

Torsional Inertia

Torsional inertia of the concrete core:

Equivelant tosional inertia of core:

Total equivelant composite torsional inertia: J_cfst = J_s + J_cs = 2,600 + 270.6 = 2,868 cm⁴

Results

Table 1. Comparison of results
Criteria	Reference	STAAD.Pro	Difference
Composite cross-sectional area, A_cfst (cm²)	65.6	65.61	negligible
Composite shear area, A_v,cfst (cm²)	41.1	41.09	negligible
Composite moment of inertia, I_cfst (cm⁴)	1,434	1,433.93	negligible
Composite torsional inertia, J_cfst ( cm⁴)	2,868	2,867.86	negligible
Composite section modulus, S (cm³)	188.2	188.18	negligible

Input

The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \12 Composite Profiles\Property Calculation\CFST - Pipe - EQ Method.STD is typically installed with the program.

STAAD

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 7-May-2026
END JOB INFORMATION
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
5 0 10 10; 6 0 0 10;
MEMBER INCIDENCES
1 5 6;
START USER TABLE
TABLE 1
UNIT MMS NEWTON
PIPE
UPTPIPE
152.4 141.6 2493.8 2493.8
END
UNIT METER KN
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
G 7.7221e+07
TYPE STEEL
STRENGTH FY 248210 FU 399894 RY 1.5 RT 1.2
G 7.7221e+07
ISOTROPIC CONCRETE
E 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
G 9.28139e+06
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY 'US (AISC 2023).DB3'
1 TABLE 'HSS ROUND' CM 'HSS6X.500' CMAT CONCRETE EQ MR 9.43896
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
6 FIXED
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
JOINT LOAD
5 FY -100
5 FX 10
PERFORM ANALYSIS PRINT LOAD DATA
PRINT SUPPORT REACTION
PRINT MEMBER PROPERTIES ALL
PRINT MEMBER FORCES ALL
UNIT MMS NEWTON
PRINT MEMBER STRESSES ALL
FINISH

Output

   MEMBER PROPERTIES. UNIT - CM  
   -----------------

   MEMB   PROFILE              AX/          IZ/          IY/        IX/  
                               AY           AZ           SZ         SY


     1  CM  HSS6X.500         65.61      1433.93      1433.93     2867.86
                              41.09        41.09       188.18      188.18