What is the Stress in a Bolt and Spacer System?

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Discussion Overview

The discussion revolves around calculating the stress in a steel bolt and aluminum tube system used as a spacer between two plates. Participants explore the implications of various parameters, including material properties, dimensions, and assumptions related to the setup. The context includes both theoretical and practical considerations relevant to mechanics and material science.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant states the nominal diameter of the steel bolt is 20 mm with a pitch of 2.5 mm, and provides initial stress calculations based on assumed values for material properties.
  • Another participant questions the lack of provided values for the modulus of elasticity (E) for aluminum and steel, and the thickness of the plates, suggesting that these are critical for accurate calculations.
  • A participant mentions that the bolt appears to be partially threaded, which may affect the stress distribution.
  • There is a discussion about the correctness of the stated distances between the bolt head, nut, and plates, with one participant suggesting a typographical error in the stated distance of 0.35 m.
  • One participant provides a detailed breakdown of equations and parameters, including assumptions about the initial and final lengths of the bolt and tube, and stresses that only axial stress should be considered.
  • Another participant expresses confusion about circular references in their calculations, indicating difficulty in determining the axial force without first knowing other variables.
  • Hints are provided by participants to help resolve circular references and clarify relationships between forces and elongations.

Areas of Agreement / Disagreement

Participants generally agree that the problem involves complexities related to assumptions about material properties and dimensions, but there is no consensus on the correct values or methods to resolve the calculations. Disagreements persist regarding the interpretation of dimensions and the approach to solving the problem.

Contextual Notes

Participants note missing assumptions regarding material properties and the dimensions of the plates, which are critical for accurate calculations. There is also mention of potential circular references in the equations used for stress calculations.

  • #31
Yes.
 
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  • #32
((lf2-1)/l2)(l1/(lf1+1)) = (a1*e1)/(a2*e2)
 
  • #33
hatchelhoff: No, that algebra in post 32 is no good. Go back to post 26, and expand the equation, which means multiply all terms. Afterwards, get Lf1 and Lf2 on the same side of the equation. (Also, use uppercase L, not lowercase L, so we do not get confused.) Try again.
 
  • #34
(Lf2-l2)(a2*e2)/L2 = - (Lf1 - l1)(a1*e1)/L1)
(LF2 * a2 * e2 -L2* a2 * e2)/L2 = -(Lf1*a1*e1 + L1 * a1 * e1)/L1
((LF2*a2*e2)/L2) - L2/L2 * a2*e2 = ((-Lf1*a1*e1)/L1) + L1/L1 * a1*e1
((LF2*a2*e2)/L2) = ((-Lf1*a1*e1)/L1) + a1e1 + a2e2

((LF2*a2*e2)/L2)+((Lf1*a1*e1)/L1) = a1e1 + a2e2
 
  • #35
hatchelhoff: Nice work. Hint 5: Now look for an expression for Lf2 in post 15.
 
  • #36
Lf1 = ((a1*e1 + a2*e2 + 2*Tf3*a2*e2)L1)/(L1 + a1*e1*L2)
 
  • #37
hatchelhoff: Close, but currently incorrect. Show the steps you used to obtain your post 36 answer, so I can find where your algebra mistake occurred.
 
  • #38
Lf1 = (L1(a1*e1*l2 + a2*e2*L2 + 2t3 *a2*e2))/L1 + a1 * e1* L2

Substituting
L1 = 349.166667 mm
a1 = 314.1593
a2 = 876.50435

I get
Lf1 =705.626 mm which seems very high.
 
  • #39
hatchelhoff: Close, but currently incorrect. Show the steps you used to obtain your post 38 formula, so I can find where your algebra mistake occurred.
 
  • #40
Let
X = Lf1
T = t3
A = a1*e1
B = a2*e2

(X/L2) - (2TB/L2) + (AX/L1) = A+B
(X/L2) + (AX/L1) = A+B + (2TB/L2)

(1/L2 + A/L1)X = A+B + (2TB/L2)

((L1 +A*L2)/(L1*L2))*X = A+B + (2TB/L2)

X = A+B + (2TB/L2)) * ((L1*L2)/(L1 +A*L2))

X = (L1(A*L2 + B*L2 +2*T*B))/L1 + A*L2

Back Substituting


Lf1 = (L1(a1*e1*l2 + a2*e2*L2 + 2t3 *a2*e2))/L1 + a1 * e1* L2
 
  • #41
hatchelhoff: Your first equation in post 40 is currently incorrect. Show the steps you used to obtain your first equation in post 40, so I can find where your algebra mistake occurred.
 
Last edited:
  • #42
((LF2*a2*e2)/L2)+((Lf1*a1*e1)/L1) = a1e1 + a2e2 (From Post 34)
sub LF2 = Lf1-2*tf3
((Lf1-2*tf3)*a2*e2)/L2)+((Lf1*a1*e1)/L1) = a1e1 + a2e2
Let
X = Lf1
T = tf3
A = a1*e1
B = a2*e2

(X/L2) - (2*T*B/L2) + (AX/L1) = A+B
 
  • #43
hatchelhoff: The second equation (line 3) in post 42 is correct. The last equation in post 42 is currently incorrect. Check your work to go from the second equation to the last equation, and try again.
 
  • #44
((Lf1*a2*e2 - 2*tf3 * a2e2)/L2) + ((Lf1 * a1*e1)/L1) = a1*e1 + a2*e2
 
  • #45
hatchelhoff: Nice work. That is correct. Continue.
 
  • #46
Lf1 =L1((a1*e1*L2) + (a2*e2*L2) + (2*t3 * a2*e2))/(a2*e2*L1 + a1*e1*l2)
 
  • #47
hatchelhoff: Excellent work. That is correct. Use six decimal places for all numerical values. Continue.
 
  • #48
nvn thanks very much for your help over the past few weeks
I now have the correct answers
Lf1 = 349.587
Lf2 = 329.587
Stress1 = 240.85 MPa
Stress2 = -86.325 MPa.
 
  • #49
hatchelhoff: Excellent work. Your answers in post 48 are correct.
 

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