V. AS4100 1998 - UPT I Section with UDL and Axial Compression
Verify the capacity of a user-provided table I section per the AS 4100 - 1998 design code.
Details
The beam is a 12 m long, simple span. The member is subjected to 1,000 kN axial compressive force and a 300 kN/m distributed load along the length of the member. Assume that the load is applied at the section shear center and that the load restrains against twist and lateral rotation.
The profile is used is a 1,510 mm deep, doubly-symmetric I section. The web is 32 mm thick. The flanges are 450 mm ✕ 50 mm. The material is grade AS 3678 350 steel. Assume that the flanges are heavily welded to the web.
Material Properties
- E = 200 GPa
- G = 80 GPa
- flange yield stress = web yield stress, fy = 340 MPa (plate thicknesses all within 20 mm to 80 mm)
- ultimate tensile strength, fu = 450 MPa
Validation
Section Properties
- height of web,
- area of the web,
- area of the flanges,
- gross area = net area,
- centroid of section (wrt bottom):
- Moment of inertia, major axis:
- Moment of inertia, minor axis:
- Elastic section modulus, major axis:
- Elastic section modulus, minor axis:
- Plastic neutral axis (wrt bottom):
- Plastic section modulus, major axis: Sz = 488.75 (10)6 mm3
- Plastic section modulus, major axis: Sy = 5.423 (10)6 mm3
- Radius of gyration about the major axis:
- Radius of gyration about the minor axis:
- Torsional constant:
- Distance between flange centroids:
- Moment of inertia about y of the compression flange:
- Warping constant:
Design Forces
Design maximum moment:
- Max. moment, M*: at mid-span
- Moment at ¼ point = Moment at ¾ point:
Design axial force:
- N* = 1,000 kN (compression)
Section Slenderness Ratio
Flange section slenderness parameter:
Hence, the flanges are compact.
Web section slenderness parameter:
Hence, the web is compact.
Bending Capacity
The section bending capacity about the major axis (cl. 5.2 of AS 4100) is determined using the section modulus as:
The nominal section capacity about the Z axis:
The factored section capacity about the Z axis:
The section bending capacity about the minor axis (cl. 5.2 of AS 4100) is determined using the section modulus as:
The nominal section capacity about the Y axis:
The factored section capacity about the Z axis:
The section bending capacity against lateral torsional buckling is checked per cl. 5.6.1 of AS 4100. The twist restraint factor, load height factor, and lateral rotation restraint factor are all equal to unity (1.0). Thus, le = L×ktklkr = L = 12 m.
The moment modification factor is given as:
(cl. 5.6.1.1(a)(iii) ) |
The reference buckling moment:
(Eqn. 5.6.1.1(3) ) |
= | ||
= | ||
= |
The slenderness reduction factor per AS 4100 Eq. 5.6.1.1(2):
The nominal member capacity:
The factored section capacity about the Z axis:
Shear Capacity
The shear area along the Z axis:
The nominal shear capacity along the Z axis:
(Cl. 5.11.4) |
The factored shear capacity:
The shear area along the Y axis:
(Cl. 5.11.2) |
Thus, shear buckling does not control (i.e., Vu = Vw).
The nominal shear capacity along the Z axis:
(Cl. 5.11.4) |
The factored shear capacity:
Compression Capacity
The plate element yield slenderness limits for heavily welded flanges = 14, webs = 35 (Table 6.2.4 of AS 4100 1998)
The calculated effective bottom flange width and effective depth (cl. 6.2.1 of AS 4100):
- λef = 4.88 < λey_f = 14
- λew = 51.4 > λey_w = 35
Therefore, the effective area is not reduced for the flanges; but it is reduced for the web:
The effective area:
The form factor (cl. 6.2.2), kf = 75,720 / 90,120 = 0.840
The nominal section compression capacity:
The factored section compression capacity:
The member compression capacity about the Z axis.
(cl. 6.3.3) |
= | ||
= | ||
= | ||
= | ||
= | ||
= | ||
= | ||
= |
The factored member compression capacity about the Z axis:
The member compression capacity about the Y axis:
(cl. 6.3.3) |
= | ||
= | ||
= | ||
= | ||
= | ||
= |
The factored member compression capacity about the Y axis:
Tension Capacity
Assume an end connection which provides uniform force distribution (i.e., kt = 1.0)
The factored tension capacity:
Check Against Combined Actions
Uniaxial bending capacity about the Z axis:
(Cl. 8.3.2 b) |
, therefore
Uniaxial bending capacity about the Y axis:
(Cl. 8.3.3 a) |
, therefore
Member bending capacity: in-plane about the Z axis:
(Cl. 8.4.2.2) |
Member bending capacity: in-plane about the Y axis:
(Cl. 8.4.2.2) |
Member combined capacity out-of-plane:
(Cl. 8.4.4.1) |
Ratio for biaxial bending: here, ϕMcz = the minimum of ϕMiz and ϕMoz
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
The nominal section moment capacity about Z axis (k·Nm) | 14,920 | 14.9190(10)3 | negligible | |
The nominal section moment capacity about Y axis (k·Nm)
|
1,557 | 1.557(10)3 | none | |
The nominal member moment capacity (k·Nm) | 7,795 | 7.7905(10)3 | negligible | |
Shear Capacity Z axis(kN) | 8,262 | 8.262(10)3 | none | |
Shear Capacity Y axis(kN)
|
8,284 | 8.284(10)3 | none | |
Nominal section compression capacity (kN) | 23,170 | 23.1742(10)3 | negligible | |
Nominal member compression capacity Z axis(kN) | 21,900 | 0.2185(10)5 | negligible | |
Nominal member compression capacity Y axis(kN) | 6,558 | 0.6448(10)4 | 1.7% difference | |
Section Tension Capacity(kN)
|
27,580 | 27.5767(10)4 | negligible | |
Uniaxial bending Capacity Z axis(k·Nm)
|
14,920 | 14.919(10)3 | negligible | |
Uniaxial bending Capacity Y axis(k·Nm)
|
1,557 | 1.557(10)3 | none | |
Member Capacity - In-plane Z axis(k·Nm)
|
14,240 | 14.2362(10)3 | negligible | |
Member Capacity - In-plane Y axis(k·Nm)
|
1,320 | 1.3155(10)3 | negligible | |
Member Capacity - Out-of-plane (k·Nm) |
6,606 | 6.5832(10)3 | negligible | |
Member Combined Capacity - Biaxial(compression) ratio
|
0.754 | 0.758 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - UPT I Section with UDL and Axial Compression.STD is typically installed with the program.
The following design parameters are used:
- The value of SGR 9 indicates that the steel grade is AS/NZS 3678 350.
- The value of IST 5 indicates that the section is heavily welded longitudinal steel per Table 5.2 of AS 4100 - 1998.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 02-Jan-23
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 4 12 0 0;
MEMBER INCIDENCES
1 1 4;
DEFINE PMEMBER
1 PMEMBER 1
START USER TABLE
TABLE 1
UNIT METER KN
ISECTION
816X350X28
0.816 0.01 0.816 0.35 0.028 0.3 0.028 0.1 0.1 0.1
1510X450X50
1.51 0.032 1.51 0.45 0.05 0.45 0.05 0.04512 0.045 0
END
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
1 UPTABLE 1 1510X450X50
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
4 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -300
1 CON GX -1000 12
1 CON GX 1000 0
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
SGR 9 PMEMB 1
IST 5 PMEMB 1
TRACK 2 PMEMB 1
CHECK CODE PMEMB ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - ( AS4100-1998 ) V2.3 **************************************************** 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 1510X450X50 (UPT) Governing Load Case: 1* Governing Criteria: AS-8.4.4.1 Governing Ratio: 0.820 (PASS) SECTION PROPERTIES ===================================================================================== d: 1510.0000 mm bf: 450.0000 mm tf: 50.0000 mm tw: 32.0000 mm Ag: 90120.0000 mm2 J: 52.9010E+06 mm4 Iw: 406.7227E+12 mm6 Iz: 31.4651E+09 mm4 Sz: 48.7548E+06 mm3 (plastic) Zz: 41.6757E+06 mm3 (elastic) rz: 590.8867E+00 mm Iy: 763.2253E+06 mm4 Sy: 5.4235E+06 mm3 (plastic) Zy: 3.3921E+06 mm3 (elastic) ry: 92.0271E+00 mm MATERIAL PROPERTIES ===================================================================================== Material Standard : AS 3678 Nominal Grade : 350 Residual Stress Category : HW (Heavily welded longitudinally) E (#) :199947.000 MPa [AS 4100 1.4] G : 80000.000 MPa [AS 4100 1.4] fy, flange : 340.000 MPa [AS 4100 Table 2.1] fy, web : 340.000 MPa [AS 4100 Table 2.1] fu : 450.000 MPa [AS 4100 Table 2.1] SLENDERNESS ===================================================================================== Actual slenderness: 130.396 Allowable slenderness: 180.000 STAAD SPACE -- PAGE NO. 4 BENDING ===================================================================================== Section Bending Capacity Critical Load Case: 1* Critical Ratio: 0.362 Critical Location: 6.000 m from Start. Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm Z-Axis Section Slenderness: Compact Y-Axis Section Slenderness: Compact Zez = 48.7548E+06 mm3 Zey = 5.0882E+06 mm3 ϕMsz = 14.9190E+03 KNm ϕMsy = 1.5570E+03 KN[AS 4100 5.2.1] Member Bending Capacity Critical Load Case: 1* Critical Ratio: 0.693 Critical Location: 6.000 m from Start. Crtiical Segment/Sub-segment: Location (Type): 0.00 m(F )- 12.00 m(F ) Length: 12.00 m Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm kt = 1.00 [AS4100 Table 5.6.3(1)] kl = 1.00 [AS4100 Table 5.6.3(2)] kr = 1.00 [AS4100 Table 5.6.3(3)] le = 12.00 m [AS4100 5.6.3] αm = 1.166 [AS4100 5.6.1.1(a)(iii)] Mo = 10.1273E+03 KNm [AS4100 5.6.1.1(a)(iv)] αsz = 0.448 [AS4100 5.6.1.1(a)(iv)] ϕMbz = 7.7905E+03 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)] SHEAR ===================================================================================== Section Shear Capacity Critical Load Case: 1* Critical Ratio: 0.181 Critical Location: 1.000 m from Start. Vy* = 1.5000E+03 KN ϕVvy = 8.2840E+03 KN [AS 4100 5.11.2] ϕVvmy = 8.2840E+03 KN [AS 4100 5.12.3] Vz* = 0.0000E+00 KN ϕVvz = 8.2620E+03 KN [AS 4100 5.11.2] ϕVvmz = 8.2620E+03 KN [AS 4100 5.12.3] STAAD SPACE -- PAGE NO. 5 AXIAL ===================================================================================== Section Compression Capacity Critical Load Case: 1* Critical Ratio: 0.155 Critical Location: 1.000 m from Start. N* = 1.0000E+03 KN Ae = 75.7325E+03 mm2 [AS 4100 6.2.3 / 6.2.4] kf = 0.840 [AS 4100 6.2.2] An = 90.1200E+03 mm2 ϕNs = 23.1742E+03 KN [AS 4100 6.2.1] Member Compression Capacity Lz = 12.00 m Ly = 12.00 m Lez = 12.00 m Ley = 12.00 m αb = 1.00 [AS 4100 Table 6.3.3(1)/6.3.3(2)] λn,z = 21.993 [AS 4100 6.3.3] αa,z = 8.117 [AS 4100 6.3.3] λ,z = 30.110 [AS 4100 6.3.3] h ,z = 0.054 [AS 4100 6.3.3] x ,z = 5.209 [AS 4100 6.3.3] αc,z = 0.943 [AS 4100 6.3.3] ϕNcz = 0.2185E+5 KN [AS 4100 6.3.3] λn,y = 141.212 [AS 4100 6.3.3] αa,y = 13.525 [AS 4100 6.3.3] λ,y = 154.736 [AS 4100 6.3.3] h ,y = 0.460 [AS 4100 6.3.3] x ,y = 0.747 [AS 4100 6.3.3] αc,y = 0.278 [AS 4100 6.3.3] ϕNcy = 0.6448E+4 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 = 90.1200E+03 mm2 ϕNt = 27.5767E+03 KN [AS 4100 7.2] STAAD SPACE -- PAGE NO. 6 COMBINED BENDING AND AXIAL ===================================================================================== Section Combined Capacity Critical Condition: Cl 8.3.2 Critical Load Case: 1* Critical Ratio: 0.362 Critical Location: 6.000 m from Start. N* = 1.0000E+03 KN Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm ϕNs = 23.1742E+03 KN [AS 4100 8.3.1] ϕMsz = 14.9190E+03 KNm ϕMsy = 1.5570E+03 KNm ϕMrz = 14.9190E+03 KNm [AS 4100 8.3.2] ϕMry = 1.5570E+03 KNm [AS 4100 8.3.3] Member Combined Capacity - In-plane Critical Load Case: 1* Critical Ratio: 0.379 Critical Location: 6.000 m from Start. N* = 1.0000E+03 KN Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm ϕNcz = 21.8513E+03 KN [AS 4100 8.4.2.2] ϕMiz = 14.2362E+03 KNm [AS 4100 8.4.2.2] ϕNcy = 6.4482E+03 KN [AS 4100 8.4.2.2] ϕMiy = 1.3155E+03 KNm [AS 4100 8.4.2.2] Member Combined Capacity - Out-of-plane(compression) Critical Load Case: 1* Critical Ratio: 0.820 Critical Location: 6.000 m from Start. N* = 1.0000E+03 KN Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm ϕMbz = 7.7905E+03 KNm ϕNcy = 6.4482E+03 KN ϕMozc = 6.5823E+03 KNm [AS 4100 8.4.4.1] 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: 1* Critical Ratio: 0.758 Critical Location: 6.000 m from Start. N* = 1.0000E+03 KN Mz* = -5.4000E+03 KNm My* = 0.0000E+00 KNm ϕMcz = 6.5823E+03 KNm [AS 4100 8.4.5.1] ϕMiy = 1.3155E+03 KNm [AS 4100 8.4.5.1] Member Combined Capacity - Biaxial(tension) Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A STAAD SPACE -- PAGE NO. 7 ********************************************************************************