V. EC5 - Timber Column with Bending
A timber column of length 1.0 meter, having c/s dimension of 73 mm × 198 mm, is subjected to an axial compressive force of 5.0 kN and moments of 2.0 kN·m and 1.0 kN·m about its major and minor axes respectively. Design the member for the ultimate limit state.
Details
Material properties:
- Timber Strength Class: C24
- Service classes: Class 2, moisture content <=20%
- Load duration: Medium-term
Cross section properties:
- Length of the member is 1 m.
- Rectangular cross section, b = 73 mm, h = 198 mm,
- Effective cross sectional area A = 14454 mm2,
- Radius of gyration of cross section about y-axis ry = 21 mm,
- Radius of gyration of cross section about z-axis rz = 57 mm,
- Section modulus of cross section about z-axis: Wz = 4.770x105 mm3
- Section modulus of cross section about y-axis: Wy = 1.759x105 mm3
Validation
Characteristic material properties for timber:
Modification factor Kmod = 0.80 …from table 3.1
Material factors γm = 1.30 … from table 2.3
Cross section loads:
Check for Slenderness:
Slenderness ratios:
Since, λrel,y is greater than 0.3, following conditions should be satisfied [Cl 6.3.2.3]:
Where:
For Rectangular cross section Km = 0.70.
Combined stress ratio:
Hence the critical ratio is 0.616 < 1.0 and the section is safe.
Results
Criteria | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Critical Ratio (Cl. 6.3.2) | 0.616 | 0.616 | none |
STAAD.Pro Input
The following file is included as C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\11 Timber Design\Europe\EC5 - Timber Column with Bending.std.
STAAD SPACE
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 1 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC WOOD
E 1.10316e+007
POISSON 0.15
DENSITY 0.00231749
ALPHA 5.5e-006
END DEFINE MATERIAL
CONSTANTS
MATERIAL WOOD MEMB 1
MEMBER PROPERTY
1 PRIS YD 0.198 ZD 0.073
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE NONE TITLE LOAD CASE 1
JOINT LOAD
2 FY -5.0 MX 1.0 MZ 2.0
PERFORM ANALYSIS
PARAMETER
CODE TIMBER EC5
ALPHA 0 ALL
LDC 3 ALL
SCL 2 ALL
TSC 6 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - (EC5) v1.0
***********************
ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted)
MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/
FX MY MZ LOCATION
=======================================================================
1 PRIS ZD = 0.073 YD = 0.198
PASS CL.6.3.2 0.616 1
5.00 C 1.00 -2.00 0.0000
|--------------------------------------------------------------------------|
| AX = 0.01 IY = 0.00 IZ = 0.00 |
| LEZ = 1.00 LEY = 1.00 |
| |
| ALLOWABLE STRESSES: (NEW MMS) |
| FBY = 14.769 FBZ = 14.769 |
| FC = 12.859 |
| ACTUAL STRESSES : (NEW MMS) |
| fby = 5.686 fbz = 4.193 |
| fc = 0.346 |
|--------------------------------------------------------------------------|