What is the Stress in a Bolt and Spacer System?

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SUMMARY

The discussion centers on calculating the stress in a steel bolt and an aluminum tube acting as a spacer in a mechanical assembly. The steel bolt has a nominal diameter of 20 mm and a pitch of 2.5 mm, while the aluminum tube has an outer diameter of 40 mm and an inner diameter of 22 mm. The resulting stresses calculated are 241 MPa for the bolt and -86.3 MPa for the tube, based on the given dimensions and material properties, including the modulus of elasticity for steel (200 GPa) and aluminum (69 GPa).

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Mechanical engineers, materials scientists, and students involved in structural analysis or mechanical design will benefit from this discussion, particularly those focusing on bolt and spacer systems in engineering applications.

  • #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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