To determine the Young’s Modulus E of wood and the Modulus of Rupture by conducting bending test.
UTM, device for Appling load and scale
THEORY AND PRINCIPLE
For a simply supported beam with central loading, deflection under the load is given by
W =Applied load.
L = effective span of the beam.
E = young’s Modulus of wood.
I = Moment of inertia.
= Deflection under the load.
Insert the bending device in the UTM. Measure the width and depth of wooden beam. Adjust the support for the required distance and clamp to the lower table. Fix the transverse test pan at the lower side of the lower cross head. Fix it on the rollers of the transverse test brackets such that the load comes at the centre and measure the length of the span of the beam between the supports for central loading. Adjust the load pointer to zero by lifting the lower table. While applying the load, the deflection corresponding to each load is found out from the vernier scale on the UTM. Note the maximum deflection and the maximum load.
OBSERVATIONS AND CALCULATIONS
Extreme working stress in bending for wood = 15.2 N/mm2
Factor of safety (F.S) = 5
i.e., Ultimate bending stress, f-max= 15.2 x 5= 76N/mm2
From bending equation
Z= I / y
M= f x Z
For simply supported beam with concentrated load at centre,
The only unknown W can be calculated and hence the range can be determined.
Young’s Modulus, E,
Take from the graph.
Modulus of Rupture. fmax
From bending equation.
For a simply supported beam with a concentrated load at centre,
Maximum Bending moment= WL/4
Where Fmax is the breaking load
1. Young’s Modulus of the material of the wooden beam =_______ N/mm2
2. Modulus of Rapture = __________N/mm2
QUESTIONS – DO YOU KNOW?
1. What is meant by Modulus of Rupture?
2. How will you calculate the fiber stress due to bending in a beam?
3. How do you apply a non-central load on UTM in bending test?
4. State the equation governing simple bending.
5. What is the central deflection of a simply supported beam under concentrated load?
6. How simple bending is incorporated in the loading arrangement.
7. Sketch the variation of bending stress in a beam cross-section.
8. Sketch the variation of shear stress in a beam cross-section.
9. Why beam are provided with depth lager than width?