# V.AIJ 2005 UPT Double Angle

Verify the bending capacity and compression capacity of a double angle section beam.

## Details

The member is a 5 m long simply-supported beam. The section used is a 2x L100x100x13, with no spacing. The steel has a yield strength of 235 MPa, a modulus of elasticity of 205×(10)3 MPa, and a shear modulus of 79×(10)3 MPa.

The member is subject to the following loads:
• a -5 kN concentrated force at mid-span in the global Y direction
• a 3 kN concentrated force at mid-span in the global Z direction
• a -40 kN axial force
• a -0.2 kN·m concentrated moment at the left end

## Validation

Section Properties

Dimensions:

• Leg, D = 100 mm
• Width, B = 200 mm
• Thickness, t = 13 mm
Outstanding leg length, d = D - t = 87 mm

Area, Ax = B×t + 2d×t = 4,862 mm2

Distance from heel to centroid,

Moment of inertia about major axis,

Moment of inertia about minor axis,

Major axis section modulus,

Minor axis section modulus,

Torsional constant,

Warping constant,

Section Classification

For webs of beams (Cl. 8.1):

$d t w = 7.69 < 0.44 E F = 0.44 205,000 235 = 13.0$

Depth to thickness ratio is "OK".

Allowable Compressive Stress

The slenderness ratio of compression members (Cl. 11.1):

$λ z = K z × L z r z = 1 × 5,000 30.38 = 164.6$
$λ y = K y × L y r y = 1 × 5,000 42.53 = 117.6$

Therefore, λ = 164.6.

Slenderness ratio dividing elastic and inelastic buckling (Cl no 5.5):

λ > Λ, so the allowable compressive stress is given by Cl. 5.4:

Allowable Flexural Stress

Distance between braced points of the compression flange, lb = 5,000 mm.

The yield moment,

The modification factor for allowable flexural stress (Cl. 5.13):

$C = 1$

The elastic lateral-torsional buckling moment (Cl 5.12):

$M e = C × π 4 × E × I zz × E × I w l b 4 + π 2 × E × I zz × G × J l b 2$
$π 4 × E × I y × E × I w l b 4 = π 4 × 205,000 × 4.847 × 10 6 × 205,000 × 199.5 × 10 6 5,000 4 = 6.333 × 10 12$
$π 2 × E × I y × G × J l b 2 = π 2 × 205,000 × 4.847 × 10 6 × 79,000 × 273.9 × 10 3 5,000 2 = 8.488 × 10 15$

The maximum slenderness ratio to achieve the plastic strength (Cl. 5.12):

$p λ b = 0.3$

The elastic slenderness limit:

$e λ b = 1 0.6 = 1.291$
Slenderness ratio of the flexural member, $λ b = M y M e = 0.483$

Here, b < λb ≤ eλb, so:

$ν = 3 2 + 2 3 × λ b e λ b 2 = 3 2 + 2 3 × 0.483 1.291 2 = 1.593$

## Results

Table 1.
Allowable compressive stress (MPa) 34.49 34.48 negligible
Allowable flexural stress (MPa) 136.6 136.62 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Japan\AIJ 2005 UPT Double Angle.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 22-Oct-18
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
29 12 0 8; 30 17 0 8;
MEMBER INCIDENCES
15 29 30;
START USER TABLE
TABLE 1
UNIT METER KN
GENERAL
GE_H300X150X6.5X9
0.004678 0.3 0 0.15 0 7.21e-05 5.08e-06 9.95e-08 0.000480667 6.77333e-05 -
0.00195 0.0018 0 0 1.07545e-07 0.256
TABLE 2
UNIT METER KN
WIDE FLANGE
WF_H300X150X6.5X9
0.004678 0.3 0.0065 0.15 0.009 7.21e-05 5.08e-06 9.95e-08 0.00195 0.0018
WF2_H300X150X6.5X9
0.004678 0.3 0.0065 0.15 0.009 7.21e-05 5.08e-06 9.95e-08 0.00195 -
0.0018 0.15 0.009
TABLE 3
UNIT METER KN
ISECTION
IS_I300X150X8
0.3 0.008 0.3 0.15 0.013 0.15 0.013 0.0024 0.0026 2.69e-07
TABLE 4
UNIT METER KN
CHANNEL
CH_C380X100X10.5
0.006939 0.38 0.0105 0.1 0.016 0.000145 5.35e-06 3.99e-07 0.0241 0.00399 -
0.00213333
TABLE 5
UNIT METER KN
ANGLE
AG_L175X175X15
0.175 0.175 0.015 0.0342 0.00175 0.00175
TABLE 6
UNIT METER KN
TUBE
TB_TUB1501506
0.003363 0.15 0.15 0.006 1.15e-05 1.15e-05 1.79e-05 0.0018 0.0018
TB_RHS200X100X9
0.004867 0.2 0.1 0.009 2.35e-05 7.82e-06 1.93e-05 0.0036 0.0018
TABLE 7
UNIT METER KN
PIPE
PP_PIP165.2X7.1
0.1652 0.151 0.001763 0.001763
TABLE 8
UNIT METER KN
DOUBLE ANGLE
L100X100X13_LD
0.1 0.1 0.013 0 4.48744e-06 8.79409e-06 2.73893e-07 0.029762 0.00173333 -
0.00173333 0
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
15 UPTABLE 8 L100X100X13_LD
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
29 PINNED
30 FIXED BUT FX MY MZ
15 CON GY -5
15 CON GZ 3
30 FX -40
29 MX 0.2
PERFORM ANALYSIS
PARAMETER 1
CODE JAPANESE 2005
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH


                        STAAD.Pro CODE CHECKING - (AIJ-2005)   V2.1
***********************
ALL UNITS ARE IN - METE  KN   (U.N.O.)
|-----------------------------------------------------------------------------|
|   Member No:      15        Profile  : L100X100X13_LD(UPT)                    |
|  Ratio:    0.923  (PASS)  Reference: Eq.6.3            Loadcase:       1    |
|-----------------------------------------------------------------------------|
|  Location:    2.500  Criteria:     Stress      Load Case:     1  (Permanent)|
|  Px:(C)       40.000       Vy:         2.500          Vz:      -1.500       |
|  Tx:           0.200       My:        -3.750          Mz:      -6.250       |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES AT DISTANCE: 2500.000 MM              (UNIT: MM)         |
|  Ax:     4.86200E+03       Az: 1.73333E+03            Ay: 1.73333E+03       |
|  Iz:     4.48744E+06       Iy: 8.79409E+06             J: 2.73893E+05       |
|  Zz:     6.12519E+04       Zy: 8.79409E+04            Zx: 2.10687E+04       |
|  iZ:     3.03803E+01       iY: 4.25293E+01            Iw: 1.99536E+08       |
|-----------------------------------------------------------------------------|
| MATERIAL PROPERTIES   (Unit: N/mm2)                                         |
|  Fy:         235.000      E :   205000.000          G :     79000.000       |
|-----------------------------------------------------------------------------|
| DESIGN PROPERTIES                                                           |
|  Member Length:     5.000      Lz:     5.000 Ly:     5.000  UNL:      5.000 |
| DESIGN PARAMETERS                                                           |
|  Kz:   1.000     Ky:   1.000   NSF:  1.000   Cb:   0.000    pλb:  0.000     |
|-----------------------------------------------------------------------------|
| CRITICAL SLENDERNESS (Compression)                                          |
|  Actual :    164.580      Allowable :    200.000      Ratio :  0.823        |
|-----------------------------------------------------------------------------|
| Section Classification Results :    Width to Thickness Ratios               |
|-----------------------------------------------------------------------------|
|            Compression              |             Bending                   |
|-----------------------------------------------------------------------------|
|  LC#   |    Actual   |   Allowable  |   LC#   |    Actual   |   Allowable   |
|-----------------------------------------------------------------------------|
|      1 |     7.6923  |     12.9956  |      1  |     7.6923  |     12.9956   |
|-----------------------------------------------------------------------------|
| 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|   40.00|     1| P |    8.23|   34.48| 0.239| Eq.5.4   |
| Bending Z (T)| 2.500|   -6.25|     1| P |  102.04|  156.67| 0.651| Eq.5.1   |
| Bending Z (C)| 2.500|   -6.25|     1| P |   37.24|  156.67| 0.238| Eq.5.1   |
| Bending Y (T)| 2.500|   -3.75|     1| P |   42.64|  156.67| 0.272| Eq.5.1   |
| Bending Y (C)| 2.500|   -3.75|     1| P |   42.64|  136.62| 0.312| Eq.5.8   |
| Shear Z      | 0.000|   -1.50|     1| P |    0.87|   90.45| 0.010| Eq.5.2   |
| Shear Y      | 0.000|    2.50|     1| P |    1.44|   90.45| 0.016| Eq.5.2   |
| Comp+ Bend C | 2.500|   -    |     1| P |   -    |    -   | 0.788| Eq.6.1   |
| Comp+ Bend T | 2.500|   -    |     1| P |   -    |    -   | 0.871| Eq.6.2   |
| Ten + Bend T | 2.500|   -    |     1| P |   -    |    -   | 0.923| Eq.6.3   |
| Ten + Bend C | 2.500|   -    |     1| P |   -    |    -   | 0.550| Eq.6.4   |
| Von-Mises    | 2.500|   -    |     1| P |  137.82|  156.67| 0.880| Eq.5.24  |
|                                                                             |
| INTERMEDIATE RESULTS (Bending)                                              |
|  Me: 8.8679E+01 KN-MET  My: 2.0666E+01 KN-MET   pλb:   0.300  C:  1.000     |
|                                                                             |
| INTERMEDIATE RESULTS (Von-Mises)                                            |
|  Sigmax:   136.453 N/mm2   Tou:    11.175 N/mm2  fm:   137.819 N/mm2        |
|-----------------------------------------------------------------------------|