V.AIJ 2005 Check for MBG parameter
Verify the effect of the MBG parameter of the AIJ 2005 code on a doubly symmetric I shaped beam of span 6m, that is subjected to UDL of -20 KN/m on its span.
Details
Japanese H Shape Doubly Symmetric I Section H400X200X12X22 used in the following frame, E = 205,000 MPa, Fy = 235 MPa
where w = -20 kN/m and L = 4 m
Equation SSB-1.10 of JSME is used to evaluate Young's modulus, E, for equation 5.8 (YNG 1).
d = 400 mm, bf = 200 mm, tw = 12 mm, tf = 22 mm
Verification
Maximum Moment, MZ1 = 43.714 kN·m
Minimum Moment, MZ2 = 43.714 kN·m
Span Moment = 46.286 kN·m
Unbraced length of compression flange, lb = 6,000 mm
Area of compression flange = Af = bf × tf = 4,400 mm2
Elastic Section Modulus about Z axis on compression side Zzc = Izz/cg = 1.573×106 mm3
Iyc = tf×bf3/12 = 1.467×107 mm4
AC = tf×bf = 4,400 mm2
ri = √(Iyc/AC) = 57.735 mm
Bending Moment Factor C = 1.75 – 1.05×(-MZ2/MZ1) + 0.3×(-MZ2/MZ1)2 = 3.198, but not more than 2.3
As Span moment > MZ1, C will be 1. (Eq. 5.15)
Elastic critical slenderness ratio eλb = 1/√0.6 = 1.291 (Eq. 5.11)
Plastic slenderness ratio = pλb = 0.3 (Eq. 5.14)
My = fy × ZZ = 427.7 k·m
Me = 558.21 kN·m
(Eq. 5.16)So, λb = √(My/Me) = 0.8753 (Eq. 5.10)
So, here pλb < λb < eλb
So, we calculate Allowable bending stress as per Eq. 5.8
ν = 3/2 + 2/3×(λb/eλb)2 = 1.8065
Allowable tensile bending stress, fbzt = ft = 156.667 N/mm2
Actual tensile bending stress about Z axis = 46.286/ZZC = 29.425 N/mm2
Utilization ratio = Actual bending stress/Allowable bending stress = 29.425/156.667 = 0.1878
Allowable compressive bending stress fbzc = min(fb, ft) = 99.88 N/mm2
Actual compressive bending stress about Z axis = 46.286/ZZC = 29.425 N/mm2
Utilization ratio = Actual bending stress/Allowable bending stress = 29.425/99.88 = 0.295
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Actual bending tensile stress (N/mm2) | 29.425 | 29.42 | Negligible | |
| Allowable bending tensile stress (N/mm2) | 156.667 | 156.67 | Negligible | |
| Ratio | 0.1878 | 0.188 | Negligible | |
| My (kN·m) | 427.7 | 427.7 | None | |
| Me (kN·m) | 558.21 | 558.21 | None | |
| pλb | 0.3 | 0.3 | None | |
| C | 1 | 1 | None | |
| Actual bending compressive stress (N/mm2) | 29.425 | 29.42 | Negligible | |
| Allowable bending compressive stress (N/mm2) | 99.88 | 99.88 | None | |
| Ratio | 0.295 | 0.295 | None |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Japan\AIJ 2005 Check for MBG parameter.std is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 28-Apr-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 4 0; 3 6 4 0; 4 6 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
START USER TABLE
TABLE 1
UNIT METER KN
ANGLE
ANGLE
0.2 0.2 0.018 0.0394179 0.0024 0.0024
END
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 RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY JAPANESE
1 TO 3 TABLE ST H400X200X12X22
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
MEMBER LOAD
2 UNI GY -20
PERFORM ANALYSIS
DEFINE ENVELOPE
1 ENVELOPE 1 TYPE STRENGTH
END DEFINE ENVELOPE
LOAD LIST ENV 1
PARAMETER 1
CODE JAPANESE 2005
TRACK 2 MEMB 2
MAIN 1 MEMB 2
MISES 1 MEMB 2
MBG 1 MEMB 2
CB 1 MEMB 2
CHECK CODE MEMB 2
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (AIJ-2005) V2.1 *********************** ALL UNITS ARE IN - METE KN (U.N.O.) |-----------------------------------------------------------------------------| | Member No: 2 Profile:ST H400X200X12X22 (JAPANESE SECTIONS) | | Ratio: 0.315 (PASS) Reference: Eq.6.1 Loadcase: 1 | |-----------------------------------------------------------------------------| | Location: 3.000 Criteria: Stress Load Case: 1 (Permanent)| | Px:(C) 15.749 Vy: 0.000 Vz: 0.000 | | Tx: 0.000 My: 0.000 Mz: -46.286 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES AT DISTANCE: 3000.000 MM (UNIT: MM) | | Ax: 1.32200E+04 Az: 5.86667E+03 Ay: 4.27200E+03 | | Iz: 3.64000E+08 Iy: 2.94000E+07 J: 1.64000E+06 | | Zz: 1.82000E+06 Zy: 2.94000E+05 Zx: 7.45455E+04 | | iZ: 1.65934E+02 iY: 4.71583E+01 Iw: 1.05020E+12 | |-----------------------------------------------------------------------------| | MATERIAL PROPERTIES (Unit: N/mm2) | | Fy: 235.000 E : 205000.000 G : 79000.000 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES | | Member Length: 6.000 Lz: 6.000 Ly: 6.000 UNL: 6.000 | | DESIGN PARAMETERS | | Kz: 1.000 Ky: 1.000 NSF: 1.000 Cb: 1.000 pλb: 0.000 | |-----------------------------------------------------------------------------| | Section Classification Results : Width to Thickness Ratios | |-----------------------------------------------------------------------------| | Compression | Bending | |-----------------------------------------------------------------------------| | LC# | Actual | Allowable | LC# | Actual | Allowable | |-----------------------------------------------------------------------------| | 1 | 27.5000 | 47.2567 | 1 | 27.5000 | 70.8850 | |-----------------------------------------------------------------------------| | CHECKS |Env| Stresses | | | | Loc. | Demand | L/C |Typ| Actual | Allow |Ratio | Ref. | | |(MET) |(KN-MET)| | |(N/mm2) |(N/mm2) | | | |--------------|------|--------|------|---|--------|--------|------|----------| | Tension | - | - | - | - | - | 156.67| - | Eq.5.1 | | Compression | 0.000| 15.75| 1| P | 1.19| 57.70| 0.021| Eq.5.4 | | Bending Z (T)| 3.000| -46.29| 1| P | 29.42| 156.67| 0.188| Eq.5.1 | | Bending Z (C)| 3.000| -46.29| 1| P | 29.42| 99.88| 0.295| Eq.5.8 | | Bending Y (T)| - | - | - | - | - | 156.67| - | Eq.5.1 | | Bending Y (C)| - | - | - | - | - | 156.67| - | Eq.5.1 | | Shear Z | - | - | - | - | - | 90.45| - | Eq.5.2 | | Shear Y | 0.000| 60.00| 1| P | 14.04| 90.45| 0.155| Eq.5.2 | | Comp+ Bend C | 3.000| - | 1| P | - | - | 0.315| Eq.6.1 | | Comp+ Bend T | 3.000| - | 1| P | - | - | 0.180| Eq.6.2 | | Ten + Bend T | 3.000| - | 1| P | - | - | 0.188| Eq.6.3 | | Ten + Bend C | 3.000| - | 1| P | - | - | 0.295| Eq.6.4 | | Von-Mises | 0.000| - | 1| P | 37.83| 156.67| 0.241| Eq.5.24 | | | | INTERMEDIATE RESULTS (Bending) | | Me: 5.5821E+02 KN-MET My: 4.2770E+02 KN-MET pλb: 0.300 C: 1.000 | | | | INTERMEDIATE RESULTS (Von-Mises) | | Sigmax: 28.972 N/mm2 Tou: 14.045 N/mm2 fm: 37.831 N/mm2 | |-----------------------------------------------------------------------------|