V. EC5 - Timber Column
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 50.0 kN. Design the member for the ultimate limit state.
Details
Material properties:
- Timber class: C24
- Service classes: Class 2, moisture content ≤ 20%
- Load duration classes: 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 = 14,454 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:
Compression parallel to the grain:
The ratio of actual compressive stress to allowable compressive strength:
Check for Slenderness:
Slenderness ratios:
As timber grade is C24 (i.e., Soft Wood)
[Annex A,EN 338:2003]
Since, λrel,y is greater than 0.3, following conditions should be satisfied:
Where:
For Rectangular cross section Km = 0.70. The member is subjected to Compression only, so actual bending stress is zero.
Hence the critical ratio is 0.326 < 1.0 and the section is safe.
Results
Criteria | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Critical Ratio (Cl. 6.3.2) | 0.326 | 0.327 | negligible |
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.std .
STAAD SPACE
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 1.0 0 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 FX -50
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 0.327 1
50.00 C 0.00 0.00 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 = 0.000 fbz = 0.000 |
| fc = 3.459 |
|--------------------------------------------------------------------------|