V.NZS3404 1997-Simply Supported Beam With Overhang
Verify the design strength of an I section per the NZS3404 1997 code.
Reference
Kirke, Brian, and Iyad Hassan Al-Jamel. Steel Structures Design Manual to AS4100. 2004. p.124
Details
From the reference:
The 250UC89.5 beam in Grade 300 steel shown below is continuous over the supports at B and D and is free at A and E. The beam section is restrained against lateral deflection at B and D, fully restrained against twist rotation at B and D, and is unrestrained at A and E. A downward concentrated load of 5P* acts at C and a downward concentrated load of P* acts at A and E. These loads act at the top flange, and are free to deflect laterally with the beam. Determine the maximum value of P*.
Validation
Section Classification
Evaluate the slenderness effects of the flange:
Section classification of the flange is compact.
Evaluate the slenderness effects of the web:
Section classification of the web is compact
Section Bending Capacity About Z-Axis
Effective Section Modulus, Zez = 1.23×106 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 280× 1.23 ×10-6 = 344.4 kN·m
ϕMsz = 0.9×344.4 = 309.96 kN·m
Section Bending Capacity About Y-Axis
Effective Section Modulus, Zey = 575×103 mm3
The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey
Msy = 280× 575×10-3 = 161 kN·m
ϕMsy = 0.9×161 = 144.9 kN·m
Member Bending Capacity of Cantilevers
End restraint arrangement = FU
A twist restraint factor, Kt (SKT) = 1.00
Minor axis rotation restraints = Both
Lateral rotation restraint factor, Kr (SKR) = 1.0
Load Height factor, Kl, (LHT) = 2 [Ref : Table 5.6.3(2)]
Effective length = 1×1×2×4,000 = 8,000 mmThe alpha value for a cantilever is taken from Table 5.6.2 in the code.
[Ref. Table 5.6.2] |
Reference buckling moment, Mo
[Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsx ≤ Msx
Mbz = 1.25 × 0.643 × 344.4 = 276.8 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×276.8 = 249.1 kN·m
Member Bending Capacity of Main Span
End restraint arrangement = FF
A twist restraint factor, Kt (SKT) = 1.00
Minor axis rotation restraints = Both
Lateral rotation restraint factor, Kr (SKR) = 1.0
Load Height factor, Kl, (LHT) = 1.4 [Ref : Table 5.6.3(2)]
Effective length = 1×1×1.4×8,000 = 11,200 mmReference buckling moment, Mo
[Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsx ≤ Msx
Mbz = 1.655 × 0.528 × 344.4 = 300.95 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×300.95 = 270.9 kN·m
Maximum Load Determination
The moments over the supports due to the cantilevers, M1 = M2 = 4×P*
The maximum moment in the middle span occurs at the 5P load:
So the maximum value of P* is derived from setting Mmax = ϕMbz and solving for P*:
P* = ϕMbz/6 = 270.9 / 6 = 45.1 kN
Results
Result Type | Calculations | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕMsz (kN·m) | 309.96 | 309.96 | none | |
ϕMsy (kN·m) | 144.9 | 142.9313 | 1.4% | |
ϕMbz (kN·m) - Cantilever | 249.1 | 249.4725 | negligible | |
ϕMbz (kN·m) - Main span | 270.9 | 269.5 | negligible | |
P* (kN) | 45.1† | 44.9‡ | 0.5% |
†The reference gives a P* value of 44.33 kN (though to be noted this is also calculated for the AS 4100 code as opposed to the NZS 34043 1997 code).
‡For STAAD.Pro, the value of 44.9 kips gives a critical ratio of 1.00 for the member bending capacity.
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\New Zealand\NZS3404 1997-Simply Supported Beam With Overhang.std is typically installed with the program.
STAAD PLANE
*
* INPUT FILE: NZS3404_Simply_Supported_Beam_with_Overhang.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF UC SHAPE PER
* THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 17-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 4 0 0; 3 12 0 0; 4 16 0 0;
*
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE PMEMBER
1 PMEMBER 1
2 PMEMBER 2
3 PMEMBER 3
*
*
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
*
MEMBER PROPERTY AUSTRALIAN
1 TO 3 TABLE ST UC250X89.5
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
2 PINNED
3 FIXED BUT FX MY MZ
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
*SELFWEIGHT Y -1
MEMBER LOAD
2 CON GY -224.5
JOINT LOAD
1 4 FY -44.9
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
TRACK 2 PMEMB 1 TO 3
SGR 2 PMEMB 1 TO 3
LHT 1 PMEMB 1 TO 3
PBRACE TOP 0 U 1 F PMEMB 1
PBRACE BOTTOM 0 U 1 F PMEMB 1
PBCRES ZZ 0 U 1 T PMEMB 1
PBCRES YY 0 U 1 T PMEMB 1
PBRACE TOP 0 F 1 U PMEMB 3
PBRACE BOTTOM 0 F 1 U PMEMB 3
PBCRES ZZ 0 T 1 U PMEMB 3
PBCRES YY 0 T 1 U PMEMB 3
CHECK CODE PMEMB 1 2 3
*
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0) ************************************************** AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE FOR Y UP :- STAAD.Pro NZS3404 Spec. Description --------- ------------- --------------- X/x Z/z Longitudinal axis of section Y/y Y/y Minor principal axis of section Z/z X/x Major Principal axis of section 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 [NZS3404 Table 3.4] 3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per NZS3404 1.4. DESIGN SUMMARY -------------- Designation: ST UC250X89.5 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.5.1 Governing Ratio: 0.720 (PASS) Governing Location: 4.000 m from Start. SECTION PROPERTIES ------------------ d: 260.0000 mm bf: 256.0000 mm tf: 17.3000 mm tw: 10.5000 mm Ag: 11400.0000 mm2 J: 1.0400E+06 mm4 Iw: 712.3514E+09 mm6 Iz: 143.0000E+06 mm4 Sz: 1.2300E+06 mm3 (plastic) Zz: 1.1000E+06 mm3 (elastic) rz: 111.9994E+00 mm Iy: 48.4000E+06 mm4 Sy: 575.0001E+03 mm3 (plastic) Zy: 378.1251E+03 mm3 (elastic) ry: 65.1584E+00 mm STAAD PLANE -- PAGE NO. 4 * MATERIAL PROPERTIES ------------------- Material Standard : AS/NZS 3679.1 Nominal Grade : 300 Residual Stress Category : HR (Hot-rolled) E (#) : 204999.984 MPa [NZS3404 1.4] G : 80000.000 MPa [NZS3404 1.4] fy, flange : 280.000 MPa [NZS3404 Table 2.1] fy, web : 320.000 MPa [NZS3404 Table 2.1] fu : 440.000 MPa [NZS3404 Table 2.1] SLENDERNESS: ACTUAL SLENDERNESS RATIO: 61.389 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 400.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.579 Critical Location : 4.000 m from Start. Mz* = 179.6000E+00 KNm Section Slenderness: Compact Zez = 1.2300E+06 mm3 ϕMsz = 309.9600E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. My* = 0.0000E+00 KNm Section Slenderness: Compact Zey = 567.1876E+03 mm3 ϕMsy = 142.9313E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.720 Critical Location : 4.000 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(U )- 4.00 m(F ) Mz* = 179.6000E+00 KNm kt = 1.00 [NZS3404 Table 5.6.3(1)] kl = 2.00 [NZS3404 Table 5.6.3(2)] kr = 1.00 [NZS3404 Table 5.6.3(3)] le = 8.00 m [NZS3404 5.6.3] αm = 1.250 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 399.9072E+00 KNm [NZS3404 5.6.1.1.1(d)] αsz = 0.644 [NZS3404 5.6.1.1.1(c)] ϕMbz = 249.4725E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] STAAD PLANE -- PAGE NO. 5 * SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.095 Critical Location : 0.000 m from Start. Vy* = -44.9000E+00 KN ϕVvmy = 471.7440E+00 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. Vz* = 0.0000E+00 KN ϕVvmz = 1.3393E+03 KN [NZS3404 5.12.2] STAAD PLANE -- PAGE NO. 6 * 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 = 11.4000E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 11.4000E+03 mm2 ϕNs = 2.8728E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. N* = 0.0000E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 4.00 m(T ) Lez = 8.80 m αb = 0.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 83.153 [NZS3404 6.3.3] λ,z = 83.153 [NZS3404 6.3.3] ε,z = 1.219 [NZS3404 6.3.3] αc,z = 0.659 [NZS3404 6.3.3] ϕNcz = 0.1892E+4 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. N* = 0.0000E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 4.00 m(T ) Ley = 8.80 m λn,y = 142.929 [NZS3404 6.3.3] λ,y = 142.929 [NZS3404 6.3.3] ε,y = 0.782 [NZS3404 6.3.3] αc,y = 0.318 [NZS3404 6.3.3] ϕNcy = 0.9146E+3 KN [NZS3404 6.3.3] 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 = 11.4000E+03 mm2 ϕNt = 2.8728E+03 KN [NZS3404 7.2] STAAD PLANE -- PAGE NO. 7 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.579 Critical Location : 4.000 m from Start. ϕMrz = 309.9600E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMry = 142.9313E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.466 Critical Location : 4.000 m from Start. γ = 1.400 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.579 Critical Location : 4.000 m from Start. ϕMiz = 309.9600E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMiy = 142.9313E+00 KNm [NZS3404 8.4.2] Member Out-of-plane Capacity (Tension) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. αbc = 0.00 ϕNoz = 0.0000E+00 KN [NZS3404 8.4.4.1.2] ϕMoz,t= 0.0000E+00 KNm [NZS3404 8.4.4.1] Member Out-of-plane Capacity (Compression) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMoz,c= 0.0000E+00 KNm [NZS3404 8.4.4.2] Member Biaxial Capacity (Tension) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. Member Biaxial Capacity (Compression) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ******************************************************************************** AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE FOR Y UP :- STAAD.Pro NZS3404 Spec. Description --------- ------------- --------------- X/x Z/z Longitudinal axis of section Y/y Y/y Minor principal axis of section Z/z X/x Major Principal axis of section STAAD PLANE -- PAGE NO. 8 * MEMBER DESIGN OUTPUT FOR PMEMBER 2 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 [NZS3404 Table 3.4] 3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per NZS3404 1.4. DESIGN SUMMARY -------------- Designation: ST UC250X89.5 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.5.1 Governing Ratio: 1.000 (PASS) Governing Location: 4.000 m from Start. SECTION PROPERTIES ------------------ d: 260.0000 mm bf: 256.0000 mm tf: 17.3000 mm tw: 10.5000 mm Ag: 11400.0000 mm2 J: 1.0400E+06 mm4 Iw: 712.3514E+09 mm6 Iz: 143.0000E+06 mm4 Sz: 1.2300E+06 mm3 (plastic) Zz: 1.1000E+06 mm3 (elastic) rz: 111.9994E+00 mm Iy: 48.4000E+06 mm4 Sy: 575.0001E+03 mm3 (plastic) Zy: 378.1251E+03 mm3 (elastic) ry: 65.1584E+00 mm MATERIAL PROPERTIES ------------------- Material Standard : AS/NZS 3679.1 Nominal Grade : 300 Residual Stress Category : HR (Hot-rolled) E (#) : 204999.984 MPa [NZS3404 1.4] G : 80000.000 MPa [NZS3404 1.4] fy, flange : 280.000 MPa [NZS3404 Table 2.1] fy, web : 320.000 MPa [NZS3404 Table 2.1] fu : 440.000 MPa [NZS3404 Table 2.1] SLENDERNESS: ACTUAL SLENDERNESS RATIO: 122.778 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 400.000 BENDING ------- Section Bending Capacity (about Z-axis) STAAD PLANE -- PAGE NO. 9 * Critical Load Case : 1* Critical Ratio : 0.869 Critical Location : 4.000 m from Start. Mz* = -269.4000E+00 KNm Section Slenderness: Compact Zez = 1.2300E+06 mm3 ϕMsz = 309.9600E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. My* = 0.0000E+00 KNm Section Slenderness: Compact Zey = 567.1876E+03 mm3 ϕMsy = 142.9313E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 1.000 Critical Location : 4.000 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 8.00 m(F ) Mz* = -269.4000E+00 KNm kt = 1.00 [NZS3404 Table 5.6.3(1)] kl = 1.40 [NZS3404 Table 5.6.3(2)] kr = 1.00 [NZS3404 Table 5.6.3(3)] le = 11.20 m [NZS3404 5.6.3] αm = 1.655 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 270.1554E+00 KNm [NZS3404 5.6.1.1.1(d)] αsz = 0.525 [NZS3404 5.6.1.1.1(c)] ϕMbz = 269.5068E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.294 Critical Location : 4.000 m from Start. Vy* = 112.2500E+00 KN ϕVvmy = 381.8150E+00 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. Vz* = 0.0000E+00 KN ϕVvmz = 1.3393E+03 KN [NZS3404 5.12.2] STAAD PLANE -- PAGE NO. 10 * 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 = 11.4000E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 11.4000E+03 mm2 ϕNs = 2.8728E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. N* = 0.0000E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 8.00 m(U ) Lez = 8.00 m αb = 0.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 75.593 [NZS3404 6.3.3] λ,z = 75.593 [NZS3404 6.3.3] ε,z = 1.352 [NZS3404 6.3.3] αc,z = 0.711 [NZS3404 6.3.3] ϕNcz = 0.2043E+4 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. N* = 0.0000E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 8.00 m(U ) Ley = 8.00 m λn,y = 129.936 [NZS3404 6.3.3] λ,y = 129.936 [NZS3404 6.3.3] ε,y = 0.831 [NZS3404 6.3.3] αc,y = 0.372 [NZS3404 6.3.3] ϕNcy = 0.1068E+4 KN [NZS3404 6.3.3] 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 = 11.4000E+03 mm2 ϕNt = 2.8728E+03 KN [NZS3404 7.2] STAAD PLANE -- PAGE NO. 11 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.869 Critical Location : 4.000 m from Start. ϕMrz = 309.9600E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMry = 142.9313E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.822 Critical Location : 4.000 m from Start. γ = 1.400 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.869 Critical Location : 4.000 m from Start. ϕMiz = 309.9600E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMiy = 142.9313E+00 KNm [NZS3404 8.4.2] Member Out-of-plane Capacity (Tension) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. αbc = 0.00 ϕNoz = 0.0000E+00 KN [NZS3404 8.4.4.1.2] ϕMoz,t= 0.0000E+00 KNm [NZS3404 8.4.4.1] Member Out-of-plane Capacity (Compression) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMoz,c= 0.0000E+00 KNm [NZS3404 8.4.4.2] Member Biaxial Capacity (Tension) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. Member Biaxial Capacity (Compression) Critical Load Case : 1* Critical Ratio : 0.000