V. AS4100 1998 - SHS section subject to compression
Verify the axial compression capacities of an SHS section beam per the AS 4100 1998 code.
Details
The member is 3.8 m in length, with pinned supports at both ends. The section is a 200 x 200 x 5.0 SHS of grade 250 steel. The member is subject to 1,030 kN in compression.
Section Properties
- Depth of section, b = d = 200 mm
- Thickness, t = 5 mm
- Cross-sectional area, Ag = 3,810 mm2
- Radius of gyration, rx = 79.2 mm
Material Properties
- E = 199,947 MPa
- G = 80,000 MPa
- Fy = 250 MPa
- Fu = 320 MPa
Validation
Nominal Section Capacity
Clear width: bcw = b - 2t = 200 - 2×5 = 190 mm
Effective width, be, for each compression element:
Use be = 190 mm
Effective area, Ae = 4×be×t = 4 × 190 × 5 = 3,800 mm2
Assume the net area, An, is equal to the gross area (i.e., no holes).
The nominal section capacity:
Axial Member Capacity
The effective length, le = Ke × L = 1 × 3,800 mm = 3,800 mm
The modified slenderness ratio:
Member section constant, ɑb, for shape of section, residual stress cold-formed (non-stress relieved) CHS category, and Kf = 1.0 from AS 4100 Table 6.3.3.(2): ɑb = -0.5.
From linear interpolation of Table 6.3.3(3), the slenderness reduction factor, ɑc = 0.913.
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Australia\AS4100 1998 - SHS section subject to compression.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-Mar-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3.80001 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE PMEMBER
1 PMEMBER 1
DEFINE MATERIAL START
ISOTROPIC STEEL
E 1.99947e+08
POISSON 0.3
DENSITY 76.8191
ALPHA 6.5e-06
DAMP 0.03
G 7.7221e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED AUSTRALIAN
1 TABLE ST 200X200X5.0SHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GX 1030 0
1 CON GX -1030 3.8
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
TRACK 2 PMEMB 1
SGR 0 PMEMB 1
CHECK CODE PMEMB ALL
FINISH
STAAD.Pro Output
**************************************************** MEMBER DESIGN OUTPUT FOR PMEMBER 1 DESIGN Notes ------------ 1. (*) next to a Load Case number signifies that a P-Delta analysis has not been performed for that particular Load Case; i.e. analysis does not include second-order effects. 2. ϕ = 0.9 for all the calculations [AS4100 Table 3.4] 3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per AS4100 1.4. DESIGN SUMMARY ===================================================================================== Designation: ST 200X200X5.0SHS (AUSTRALIAN COLDFORMED SECTIONS) Governing Load Case: 1* Governing Criteria: COMPRESSION Governing Ratio: 1.316 *(FAIL) SECTION PROPERTIES ===================================================================================== d: 200.0000 mm bf: 200.0000 mm tf: 5.0000 mm tw: 5.0000 mm Ag: 3809.9998 mm2 J: 37.8000E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 23.9000E+06 mm4 Sz: 277.0000E+03 mm3 (plastic) Zz: 239.0000E+03 mm3 (elastic) rz: 79.2021E+00 mm Iy: 23.9000E+06 mm4 Sy: 277.0000E+03 mm3 (plastic) Zy: 239.0000E+03 mm3 (elastic) ry: 79.2021E+00 mm MATERIAL PROPERTIES ===================================================================================== Material Standard : AS 1163 Nominal Grade : 250 Residual Stress Category : CF (Cold formed) E (#) :199947.000 MPa [AS 4100 1.4] G : 80000.000 MPa [AS 4100 1.4] fy, flange : 250.000 MPa [AS 4100 Table 2.1] fy, web : 250.000 MPa [AS 4100 Table 2.1] fu : 320.000 MPa [AS 4100 Table 2.1] SLENDERNESS ===================================================================================== Actual slenderness : 47.979 Allowable slenderness: 180.000 STAAD SPACE -- PAGE NO. 4 BENDING ===================================================================================== Section Bending Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm Z-Axis Section Slenderness: N/A Y-Axis Section Slenderness: N/A Zez = 0.0000E+00 mm3 Zey = 0.0000E+00 mm3 ϕMsz = 0.0000E+00 KNm ϕMsy = 0.0000E+00 KN[AS 4100 5.2.1] Member Bending Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Crtiical Segment/Sub-segment: Location (Type): 0.00 m(U )- 0.00 m(U ) Length: 0.00 m Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm kt = 0.00 [AS4100 Table 5.6.3(1)] kl = 0.00 [AS4100 Table 5.6.3(2)] kr = 0.00 [AS4100 Table 5.6.3(3)] le = 0.00 m [AS4100 5.6.3] αm = 0.000 [AS4100 5.6.1.1(a)(iii)] Mo = 0.0000E+00 KNm [AS4100 5.6.1.1(a)(iv)] αsz = 0.000 [AS4100 5.6.1.1(a)(iv)] ϕMbz = 0.0000E+00 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)] SHEAR ===================================================================================== Section Shear Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Vy* = 0.0000E+00 KN ϕVvy = 0.0000E+00 KN [AS 4100 5.11.2] ϕVvmy = 0.0000E+00 KN [AS 4100 5.12.3] Vz* = 0.0000E+00 KN ϕVvz = 0.0000E+00 KN [AS 4100 5.11.2] ϕVvmz = 0.0000E+00 KN [AS 4100 5.12.3] STAAD SPACE -- PAGE NO. 5 AXIAL ===================================================================================== Section Compression Capacity Critical Load Case: 1* Critical Ratio: 1.316 Critical Location: 0.317 m from Start. N* = 1.0300E+03 KN Ae = 3.8100E+03 mm2 [AS 4100 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 3.8100E+03 mm2 ϕNs = 857.2499E+00 KN [AS 4100 6.2.1] Member Compression Capacity Lz = 3.80 m Ly = 3.80 m Lez = 3.80 m Ley = 3.80 m αb = -0.50 [AS 4100 Table 6.3.3(1)/6.3.3(2)] λn,z = 47.979 [AS 4100 6.3.3] αa,z = 20.013 [AS 4100 6.3.3] λ,z = 37.972 [AS 4100 6.3.3] h ,z = 0.080 [AS 4100 6.3.3] x ,z = 3.533 [AS 4100 6.3.3] αc,z = 0.913 [AS 4100 6.3.3] ϕNcz = 0.7827E+3 KN [AS 4100 6.3.3] λn,y = 47.979 [AS 4100 6.3.3] αa,y = 20.013 [AS 4100 6.3.3] λ,y = 37.972 [AS 4100 6.3.3] h ,y = 0.080 [AS 4100 6.3.3] x ,y = 3.533 [AS 4100 6.3.3] αc,y = 0.913 [AS 4100 6.3.3] ϕNcy = 0.7827E+3 KN [AS 4100 6.3.3] ϕNc = N/A [AS 4100 6.3.3 / AS 4600 3.4.1(b)] Section Tension Capacity Critical Load Case: 1* Critical Ratio: 0.000 Critical Location: 0.000 m from Start. N* = 0.0000E+00 KN kt = 1.00 [User defined] An = 3.8100E+03 mm2 ϕNt = 857.2499E+00 KN [AS 4100 7.2] STAAD SPACE -- PAGE NO. 6 COMBINED BENDING AND AXIAL ===================================================================================== Section Combined Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A N* = 0.0000E+00 KN Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm ϕNs = 0.0000E+00 KN [AS 4100 8.3.1] ϕMsz = 0.0000E+00 KNm ϕMsy = 0.0000E+00 KNm ϕMrz = 0.0000E+00 KNm [AS 4100 8.3.2] ϕMry = 0.0000E+00 KNm [AS 4100 8.3.3] Member Combined Capacity - In-plane Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Member Combined Capacity - Out-of-plane(compression) Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Member Combined Capacity - Out-of-plane(tension) Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Member Combined Capacity - Biaxial(compression) Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Member Combined Capacity - Biaxial(tension) Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A STAAD SPACE -- PAGE NO. 7 ******************************************************************************** ************** END OF TABULATED RESULT OF DESIGN ************** 41. FINISH