dynamic shear and torsional modulus of pine beams by seyyed
TRANSCRIPT
Dynamic Young’s Modulus, Shear and Torsional Moduli of Pine Beams In two different theories
Seyedeh Masoumeh Hashemi Tabalvandani
Mehran Roohnia, Ph.D
Seyed Mohammad Nabavi
Department of Wood and Paper Science and Technology, Islamic Azad University, Karaj Branch, Iran
Agriculture Research Centre, Islamic Azad University, Karaj Branch, Iran
Department of Wood and Paper Science and Technology, University of Tehran, Iran
Sopron, Hungary - 2011
Intr
od
uc
tio
n
• Determination of elastic constants of wooden beams (such as, Young and shear modulus) by free-free flexural vibration test
• Using resonant frequency in the flexural mode of vibration
Dynamic Young’s modulus
• Using resonant frequency in the torsional mode of vibration Dynamic shear modulus
• Basic theory is dependent on Timoshenko's bending theory
• In this study, just first mode of vibration used to assess torsional modulus
17th International Nondestructive Testing and Evaluation of Wood Symposium 2
Ma
teri
al &
Me
tho
d
• 30 rectangular clear beams of Pinus orientalis with 40×20×360mm (R×T×L) dimensions (wide samples)
• Conditioning at 65% relative humidity and 22°C for two weeks
• Free-free flexural vibration tests used to measure shear modulus
• Young and shear modulus from the Timoshenko method in LT direction
Impact points and transducer locations for transverse flexural mode (ASTM C1548-02)
3 17th International Nondestructive Testing and Evaluation of Wood Symposium
Ma
teri
al &
Me
tho
d
4 17th International Nondestructive Testing and Evaluation of Wood Symposium
Transverse (flexural) Vibration of a Free-Free Beam
• ASTM C1548-02 based on the 1st mode of vib. (Originally for Refractory Materials)
13
32
Th
L
b
mfE
2
1 585.6000.1L
hT
E: Dynamic Longitudinal Modulus of Elasticity, Pa b: Width, m h: Height, m L: Length, m m: Mass, Kg f: Modal Frequency, Hz
• Timoshenko’s bending equations based on the three initial modes of vib. (Originally for isotropic Materials)
Ma
teri
al &
Me
tho
d
• Torsional vibration test to gain torsional modulus of specimens due to ASTM C1548-02
Impact points and transducer locations in torsional vibration (ASTM C1548-02)
• Impact point and sensor located at the first nodes of transverse vibration (0.224L)
• Prevent confliction between first mode of torsional vibration and flexural vibration
5 17th International Nondestructive Testing and Evaluation of Wood Symposium
Ma
teri
al &
Me
tho
d
6 17th International Nondestructive Testing and Evaluation of Wood Symposium
Torsional Vibration of a Free-Free Beam
ASTM C1548-02:
A
B
bh
LmfG t
t1
4 2
6
6
2
2 21.025.24
b
h
b
h
b
h
b
h
h
b
B
2
32
892.903.12
0078.03504.08776.05062.0
h
b
h
b
h
b
h
b
h
b
A
Gt: Torsional Modulus, Pa ft: Fundamental Resonant Frequency of the Beam in Torsion, Hz
Ma
teri
al &
Me
tho
d
• Specimens split to 20×20×360mm (R×T×L) dimensions (thin
samples)
• Conditioning at 65% relative humidity and 22°C for two weeks
• Young and shear modulus by Timoshenko method in LR and LT direction
• Effective shear modulus (Geff);
• Flexural vibration and torsional vibration mode will overlap in thin samples
7 17th International Nondestructive Testing and Evaluation of Wood Symposium
Re
sults
& D
isc
uss
ion
Young's modulus (GPa) in free-free tests of flexural vibration (ASTM C1548-02 method)
• Thin samples can be used instead of wide samples in non-destructive tests
8 17th International Nondestructive Testing and Evaluation of Wood Symposium
Re
sults
& D
isc
uss
ion
9
Young’s modulus (GPa) in free-free tests of LT flexural vibration (ASTM C1548-02 method)
Young’s modulus (GPa) in free-free tests of flexural vibration in thin samples (ASTM C1548-02 method)
17th International Nondestructive Testing and Evaluation of Wood Symposium
Re
sults
& D
isc
uss
ion
Young's modulus (GPa) in free-free tests of flexural vibration (Timoshenko method)
• Correlation between modulus of elasticity of thin and wide specimens with a significant coefficient
10
17th International Nondestructive Testing and Evaluation of Wood Symposium
Re
sults
& D
isc
uss
ion
11
Young’s modulus (GPa) in free-free tests of LT flexural vibration (Timoshenko method)
Young’s modulus (GPa) in free-free tests of flexural vibration in thin samples (Timoshenko method)
17th International Nondestructive Testing and Evaluation of Wood Symposium
Re
sults
& D
isc
uss
ion
Torsional modulus (GPa) in wide samples
• Trosional modulus values of flexural vibration/ASTM method is NOT reliable
12 17th International Nondestructive Testing and Evaluation of Wood Symposium
Co
nc
lusi
on
• Dynamic effective Shear modulus and
Torsional Modulus could not be correlated well. Because the GLR and GLT in Timoshenko theory are only estimated values.
• Longitudinal Dynamic modulus of elasticity of a clear wood (Orthotropic) could be evaluated same as an isotropic material.
13 17th International Nondestructive Testing and Evaluation of Wood Symposium
Ac
kn
ow
led
ge
me
nt
• Islamic Azad University, Karaj branch, Iran for financially supporting this research
• NDTiranian scientific based group for computer programming (www.ndtiranian.ir)
