Formula of modulus of elasticity?

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SUMMARY

The modulus of elasticity for a pine wood rectangular cantilever beam can be calculated using the formula PL^3/(3 * ΔY * I), where P is the load, L is the length of the unsupported beam, ΔY is the deflection, and I is the area moment of inertia. In the given scenario, the user provided measurements of an area inertia of 0.413 cm4, an unsupported length of 40 cm, a deflection of 0.36 cm, and a load of 1.25 pounds. The calculated modulus of elasticity was reported as 797,775 N/cm2, which is inconsistent with typical values for pine wood, indicating a potential error in unit conversion or formula application.

PREREQUISITES
  • Understanding of the modulus of elasticity concept
  • Familiarity with cantilever beam mechanics
  • Knowledge of unit conversions between pounds and Newtons
  • Ability to apply algebraic formulas in structural engineering
NEXT STEPS
  • Review the calculation of modulus of elasticity using the formula PL^3/(3 * ΔY * I)
  • Learn about unit conversions from pounds to Newtons for accurate calculations
  • Investigate the properties of pine wood and typical modulus of elasticity values
  • Explore the effects of measurement accuracy on structural calculations
USEFUL FOR

Students in engineering disciplines, structural engineers, and anyone involved in material science or mechanics of materials will benefit from this discussion.

Matriculator
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Homework Statement


How to calculate the modulus of elasticity algebraically? Especially that of a pine wood rectangular cantilever beam? I have a few measurements here. The area inertia is .413 cm^4, the length of the unsupported part of the beam is at 40 centimeters(the whole beam is around 66 centimeters), the deflection is 0.36 centimeters with a load of 1.25 pounds. I'm trying to find the modulus of elasticity is Newtons per centimeters squares. I got 797,775 but it seems way off in comparison to the original module of elasticity. I'm thinking that it's because I'm using the wrong formula. Can someone please help me. I have been sitting here for hours but nothing.

Homework Equations


PL^3/(3 * change in Y * Inertia).
 
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You used the correct formula, but did you properly substitute into it? Did you use correct units throughout? Was the load at the very end of the beam? Did you measure the deflection directly at the load?
 
Matriculator said:

Homework Statement


How to calculate the modulus of elasticity algebraically? Especially that of a pine wood rectangular cantilever beam? I have a few measurements here. The area inertia is .413 cm^4, the length of the unsupported part of the beam is at 40 centimeters(the whole beam is around 66 centimeters), the deflection is 0.36 centimeters with a load of 1.25 pounds. I'm trying to find the modulus of elasticity is Newtons per centimeters squares. I got 797,775 but it seems way off in comparison to the original module of elasticity. I'm thinking that it's because I'm using the wrong formula. Can someone please help me. I have been sitting here for hours but nothing.

Homework Equations


PL^3/(3 * change in Y * Inertia).

Thread locked. Turns out the OP was not supposed to be asking for online help on this problem.
 

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