Calculating Rod Strength: Help with Oak Rod Homework Problem

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SUMMARY

The discussion centers on calculating the strength of an oak rod with a diameter of 12 mm and a length of 9 m, specifically addressing the maximum mass it can support and the minimum mass that will cause it to break when dropped. Key parameters include the stiffness (E) of 14000 MPa, yield tensile strength of 75 MPa, and ultimate tensile strength of 90 MPa. The conversation highlights the need for a formula to determine the resulting force from a 9-meter drop, suggesting a model where the rod behaves like a spring to calculate the stretch distance necessary for failure.

PREREQUISITES
  • Understanding of material properties such as stiffness, yield strength, and ultimate tensile strength.
  • Familiarity with basic physics concepts, including kinetic energy and force calculations.
  • Knowledge of mechanics of materials, particularly beam theory and stress-strain relationships.
  • Ability to apply equations of motion and energy conservation in impact scenarios.
NEXT STEPS
  • Research the formula for calculating impact force from a free fall, specifically using the equation F = m * g + (Δx * k), where Δx is the stretch and k is the spring constant.
  • Learn about the mechanics of materials, focusing on how to model beams under load and the concept of elastic deformation.
  • Study the principles of energy transfer during impact, particularly how kinetic energy converts to potential energy in elastic materials.
  • Explore advanced topics in material science, such as fatigue failure and the effects of repeated loading on structural integrity.
USEFUL FOR

Students in engineering or physics, particularly those studying mechanics of materials, as well as professionals involved in structural analysis and material testing.

johnlogie

Homework Statement



An example in my problem set (homework help) An oak rod is hung from a rigid support.
The rod has a diameter = 12 mm, length = 9 m, and a catch plate at its base.
a) The maximum mass of a weight that each rod can support.
b) The minimum mass of a weight that will break the rod when dropped from the top of the rod.
Numbers I think can be used: E (stiffness) = 14000 MPa
Yield Tensile strength = 75 MPa
Ultimate tensile strength = 90 MPa

Homework Equations


I can not find a formula to calculate the following question, any help would be appreciated,
Thank you for your help!

The Attempt at a Solution


I solved A but struggling in b) these are all the information provided to us in the question.
 
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Drop a mass, it falls 9 meters. What is going to happen when it strikes the catch plate? How will the oak rod stretch (and eventually fail). That is the way I think to approach it. You will need to make some assumptions (and state them) about how the collision between the mass and catch plate occurs.
 
Thank you for your reply,

The thing is, I don't have a formula in mind in which I can plug the 9m and get the resulting force, I think it's pretty obvious but I can't recall it !
 
So it has been awhile since I've done one of these. Is it possible that you could model the beam as sort of a spring? I'm not positive but I think it can be done. Then you could say that the mass has a certain amount of kinetic energy, this could be transferred into the spring (and figure out how far the "spring" stretches).
If you can figure the stretch distance necessary to break, then work backwards to see what mass will cause that amount.
 
johnlogie said:
The maximum mass of a weight that each rod can support.

The mention of "each rod" is confusing. Is there more than one wooden rod involved?

In many respects, this is a classic problem, and the OP has identified the nature of the problem when he said
johnlogie said:
I don't have a formula in mind in which I can plug the 9m and get the resulting force.

The problem is, nobody has such a formula that works in all cases. It depends upon what happens during the impact, and the time is too short for it to be well observed. What SCOTTDAVE has proposed is as good as anything for a homework problem with no further information given.
 
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johnlogie said:
a) The maximum mass of a weight that each rod can support.

Dr.D said:
The mention of "each rod" is confusing. Is there more than one wooden rod involved?
My take is that there is only one rod, and "each rod" means "each rod of this type."
 

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