Modulus of Elasticity with shear Corrected

In summary, the problem involves calculating the Modulus of Elasticity (MOE) with shear correction in a Three point Bending Test on Wood samples. The given parameters include a force of 2400 N, deflection of 4.3 mm, span of 343 mm, length of 392 mm, b of 24.01 mm, and d of 24.25 mm. The equation used is MOE = (Force * Span^3) / (4 * Deflection * b * d^3). To calculate E/G, the equation E = MOE * (1 + (6/5) * (d/Span)^2 * (E/G)) is used. The resulting answer should be
  • #1
Pahoo
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I appreciate your help with this problem from a Three point Bending Test in Wood samples

Homework Statement



Force: 2400 N
Deflection: 4.3 mm
Span: 343 mm
Length: 392 mm
b: 24.01 mm
d: 24.25
MOE: 16445.15 MPa

How can I calculate the Modulus of Elasticity with shear corrected?


Homework Equations



I have this equation
First I got the MOE=(Force*Span^3)/4*Deflection*b*d^3)
then I should be able to calculate E but I don´t know how to get E/G
E=MOE*(1+(6/5)*(d/Span)^2*E/G)


The Attempt at a Solution


The result must be 18417.95 KPa
 
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  • #2
I assume you must estimate the E/G ratio for the particular species of wood. If your math is correct and the solution is correct (why so many significant figures??), looks like G = .05E, but I can't help much more . Might suggest search on G and E values for different species .
 
  • #3
I agree Jay's point. If deflection is 4.3 mm, then how many significant figures are reasonable for the solution? When you have worked out the answer to your question, try putting in 4.2 mm and 4.4 mm (which the deflection is NOT) and then conclude the so called accuracy of your answer...
 

What is the Modulus of Elasticity with shear Corrected?

The Modulus of Elasticity with shear Corrected, also known as the Shear Modulus or Modulus of Rigidity, is a material property that measures the stiffness of a material when it is subjected to shear stress. It is denoted by the symbol G and is measured in units of force per unit area (N/m2 or Pa).

How is the Modulus of Elasticity with shear Corrected calculated?

The Modulus of Elasticity with shear Corrected is calculated by dividing the shear stress by the shear strain. This relationship is expressed in the formula G = τ/γ, where G is the shear modulus, τ is the shear stress, and γ is the shear strain.

What is the difference between Modulus of Elasticity and Modulus of Elasticity with shear Corrected?

The Modulus of Elasticity (also known as Young's Modulus) measures the stiffness of a material when it is subjected to tensile or compressive stress. Meanwhile, the Modulus of Elasticity with shear Corrected measures the stiffness of a material when it is subjected to shear stress. Both properties are important in determining the overall mechanical behavior of a material.

Why is it important to consider the shear correction when calculating the Modulus of Elasticity?

The shear correction takes into account the effect of shear stress on the stiffness of a material. Neglecting this correction can lead to inaccurate results, especially for materials that are highly anisotropic (having different properties in different directions) or have a low Poisson's ratio (ratio of transverse strain to axial strain).

How does the Modulus of Elasticity with shear Corrected affect the strength of a material?

The Modulus of Elasticity with shear Corrected is one of the factors that affects a material's strength. A higher Modulus of Elasticity with shear Corrected means that the material is stiffer and less likely to deform under shear stress. This can result in a higher ultimate strength and a higher resistance to failure under shear loading.

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