V. AS4100 1998 - UPT Angle Section subject to Conc Load
Verify the capacity of a user-provided table single angle section per the AS 4100 - 1998 design code.
Details
The beam is a 1.6 m long simple span subject to a concentrated load of 165 kN at midspan. 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 200 mm ✕ 200 mm ✕ 26 mm angle. The material is grade AS 3678 300 steel.
Material Properties
- E = 200 GPa
- G = 80 GPa
- flange yield stress = web yield stress, fy = 280 MPa
- ultimate tensile strength, fu = 450 MPa
Validation
Section Properties
- gross area = net area,
- centroid of section:
- centroid of section:
- Moment of inertia, major axis:
- Moment of inertia, minor axis:
- Elastic section modulus, major axis:
- Plastic section modulus, major axis: Sz = 326.6 (10)3 mm3
- Elastic section modulus, minor axis:
- Plastic section modulus, major axis: Sy = 643.9 (10)3 mm3
- Radius of gyration about the major axis:
- Radius of gyration about the minor axis:
- Torsional constant:
- Warping constant:
Section Classification
Section slenderness
Flange slenderness:
Web slenderness:
Bending about the Z axis puts the bottom flange in uniform compression (table 5.2 of AS 4100). Thus, λef < λep_f = 8 < λey_f = 15. The ratio
Bending about the Z axis puts one end of the web in tension and the other in compression (table 5.2 of AS 4100). Thus, λep_w 8 < λew < λey_w = 22. The ratio
As the ratio for the flange is higher, the flange is the critical element per cl. 5.2.2. The section is considered "compact" (λef < λep_f.
Similarly, the section is "compact" in bending about the Y axis.
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 Y 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 = 1.6 m.
The maximum moment, Mm = M3 for symmetric loading conditions. Further, the quarter point moments, M2 and M4 are both equal to Mm/2 for a single point load at mid-span. Substituting these values into the equation in cl. 5.6.1.1(a)(iii), the moment modification factor for a simply-supported beam with a concentrated load at mid-span simplifies to:
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:
Shear Capacity
The shear area along the Z axis and Y axis:
The nominal shear capacity along the Z axis and Y axis:
(Cl. 5.11.4) |
The factored shear capacity:
The shear buckling capacity factor: , so Vvy = Vwy
Compression Capacity
The calculated effective bottom flange width and effective depth (cl. 6.2.1 of AS 4100):
- λef = 7.082 < λey_f = 16
- λew = 7.082 < λey_w = 35
Therefore, Ae = Ae (no reduction for the effective area); the form factor (cl. 6.2.2), kf = 1
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: no axial force so no reduction:
Uniaxial bending capacity about the Y axis: no axial force so no reduction:
Member combined capacity out-of-plane: no axial force so no reduction:
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
The nominal section moment capacity about Z axis (k·Nm) | 66.7 | 66.691 | negligible | |
The nominal section moment capacity about Y axis (k·Nm)
|
152.2 | 152.212 | negligible | |
The nominal member moment capacity (k·Nm) | 66.7 | 66.691 | negligible | |
Shear Capacity Z axis (kN) | 524.2 | 524.161 | negligible | |
Shear Capacity Y axis (kN)
|
524.2 | 524.161 | negligible | |
Nominal section compression capacity (kN) | 2,450 | 2.45(10)3 | none | |
Nominal Member compression capacity Z axis (kN) | 2,074 | 2.074(10)3 | none | |
Nominal Member compression capacity Y axis (kN) | 2,235 | 2.344(10)3 | negligible | |
Section Tension Capacity (kN)
|
2,450 | 2.45(10)3 | none | |
Uniaxial bending Capacity Z axis (k·Nm)
|
66.7 | 66.691 | negligible | |
Uniaxial bending Capacity Y axis (k·Nm)
|
152.2 | 152.212 | negligible | |
Member Combined Capacity Out-plane | 66.7 | 66.691 | negligible |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - UPT Angle Section subject to Conc Load.STD is typically installed with the program.
The following design parameters are used:
- The value of LHT 0 indicates a load applied at the shear center.
- The value of IST 4 indicates the section is lightly welded longitudinally steel per Table 5.2 of AS 4100 - 1998.
- The value of SGR 11 indicates that the steel grade is AS/NZS 3678 300.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-Jan-23
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 1.6 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE PMEMBER
1 PMEMBER 1
START USER TABLE
TABLE 1
UNIT METER KN
ANGLE
200X200X26
0.2 0.2 0.026 0.0390814 0.00346667 0.00346667
END
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
G 7.88462e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY
1 UPTABLE 1 200X200X26
CONSTANTS
BETA 135 ALL
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -165
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
LHT 0 PMEMB 1
IST 4 PMEMB 1
SGR 11 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 200X200X26 (UPT) Governing Load Case: 1* Governing Criteria: AS-8.3.4 Governing Ratio: 1.006 *(FAIL) SECTION PROPERTIES ===================================================================================== d: 200.0000 mm bf: 200.0000 mm tf: 26.0000 mm tw: 26.0000 mm Ag: 9724.0000 mm2 J: 2.1911E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 14.8520E+06 mm4 Sz: 326.6270E+03 mm3 (plastic) Zz: 176.4321E+03 mm3 (elastic) rz: 39.0814E+00 mm Iy: 56.9470E+06 mm4 Sy: 643.9328E+03 mm3 (plastic) Zy: 402.6760E+03 mm3 (elastic) ry: 76.5267E+00 mm MATERIAL PROPERTIES ===================================================================================== Material Standard : AS 3678 Nominal Grade : 300 Residual Stress Category : LW (Lightly welded longitudinally) E (#) :204999.984 MPa [AS 4100 1.4] G : 80000.000 MPa [AS 4100 1.4] fy, flange : 280.000 MPa [AS 4100 Table 2.1] fy, web : 280.000 MPa [AS 4100 Table 2.1] fu : 430.000 MPa [AS 4100 Table 2.1] SLENDERNESS ===================================================================================== Actual slenderness: 40.940 Allowable slenderness: 400.000 STAAD SPACE -- PAGE NO. 4 BENDING ===================================================================================== Section Bending Capacity Critical Load Case: 1* Critical Ratio: 0.700 Critical Location: 0.800 m from Start. Mz* = 46.6690E+00 KNm My* = -46.6690E+00 KNm Z-Axis Section Slenderness: Compact Y-Axis Section Slenderness: Compact Zez = 264.6481E+03 mm3 Zey = 604.0139E+03 mm3 ϕMsz = 66.6913E+00 KNm ϕMsy = 152.2115E+00 KN[AS 4100 5.2.1] Member Bending Capacity Critical Load Case: 1* Critical Ratio: 0.700 Critical Location: 0.800 m from Start. Crtiical Segment/Sub-segment: Location (Type): 0.00 m(F )- 1.60 m(F ) Length: 1.60 m Mz* = 46.6690E+00 KNm My* = -46.6690E+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 = 1.60 m [AS4100 5.6.3] αm = 1.388 [AS4100 5.6.1.1(a)(iii)] Mo = 1.4344E+03 KNm [AS4100 5.6.1.1(a)(iv)] αsz = 1.009 [AS4100 5.6.1.1(a)(iv)] ϕMbz = 66.6913E+00 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)] SHEAR ===================================================================================== Section Shear Capacity Critical Load Case: 1* Critical Ratio: 0.111 Critical Location: 0.133 m from Start. Vy* = -58.3363E+00 KN ϕVvy = 524.1605E+00 KN [AS 4100 5.11.2] ϕVvmy = 524.1605E+00 KN [AS 4100 5.12.3] Vz* = -58.3363E+00 KN ϕVvz = 524.1605E+00 KN [AS 4100 5.11.2] ϕVvmz = 524.1605E+00 KN [AS 4100 5.12.3] STAAD SPACE -- PAGE NO. 5 AXIAL ===================================================================================== Section Compression Capacity Critical Load Case: 1* Critical Ratio: 0.000 Critical Location: 0.000 m from Start. N* = 0.0000E+00 KN Ae = 9.7240E+03 mm2 [AS 4100 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 9.7240E+03 mm2 ϕNs = 2.4504E+03 KN [AS 4100 6.2.1] Member Compression Capacity Lz = 1.60 m Ly = 1.60 m Lez = 1.60 m Ley = 1.60 m αb = 0.50 [AS 4100 Table 6.3.3(1)/6.3.3(2)] λn,z = 43.327 [AS 4100 6.3.3] αa,z = 19.188 [AS 4100 6.3.3] λ,z = 52.921 [AS 4100 6.3.3] h ,z = 0.129 [AS 4100 6.3.3] x ,z = 2.132 [AS 4100 6.3.3] αc,z = 0.846 [AS 4100 6.3.3] ϕNcz = 0.2074E+4 KN [AS 4100 6.3.3] λn,y = 22.127 [AS 4100 6.3.3] αa,y = 8.231 [AS 4100 6.3.3] λ,y = 26.242 [AS 4100 6.3.3] h ,y = 0.042 [AS 4100 6.3.3] x ,y = 6.625 [AS 4100 6.3.3] αc,y = 0.957 [AS 4100 6.3.3] ϕNcy = 0.2344E+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 = 9.7240E+03 mm2 ϕNt = 2.4504E+03 KN [AS 4100 7.2] STAAD SPACE -- PAGE NO. 6 COMBINED BENDING AND AXIAL ===================================================================================== Section Combined Capacity Critical Condition: Cl 8.3.4 Critical Load Case: 1* Critical Ratio: 1.006 Critical Location: 0.800 m from Start. N* = 0.0000E+00 KN Mz* = 46.6690E+00 KNm My* = -46.6690E+00 KNm ϕNs = 2.4504E+03 KN [AS 4100 8.3.1] ϕMsz = 66.6913E+00 KNm ϕMsy = 152.2115E+00 KNm ϕMrz = 66.6913E+00 KNm [AS 4100 8.3.2] ϕMry = 152.2115E+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: 1* Critical Ratio: 0.700 Critical Location: 0.800 m from Start. N* = 0.0000E+00 KN Mz* = 46.6690E+00 KNm My* = -46.6690E+00 KNm ϕMbz = 66.6913E+00 KNm ϕNt = 2.4504E+03 KN [AS 4100 8.4.4.2] ϕMozt = 66.6913E+00 KNm [AS 4100 8.4.4.2] 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: 1* Critical Ratio: 0.798 Critical Location: 0.800 m from Start. N* = 0.0000E+00 KN Mz* = 46.6690E+00 KNm My* = -46.6690E+00 KNm ϕMtz = 66.6913E+00 KNm [AS 4100 8.4.5.2] ϕMry = 152.2115E+00 KNm [AS 4100 8.4.5.2] STAAD SPACE -- PAGE NO. 7 ********************************************************************************