- #36

hatchelhoff

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Lf1 = ((a1*e1 + a2*e2 + 2*Tf3*a2*e2)L1)/(L1 + a1*e1*L2)

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In summary, a steel bolt with a nominal diameter of 20 mm and a pitch of 2.5 mm is used as a spacer in conjunction with an aluminum tube with dimensions of 40 mm OD by 22 mm ID. The distance between the two plates is 0.35 m, and the nut is pulled snug and then given a one-third additional turn. Neglecting the deformation of the plates, the resulting stress in the bolt is 241 MPa and -86.3 MPa in the tube. This is determined by calculating the elongation of the bolt and tube and using their respective moduli of elasticity, with the assumption that the bolt is a solid shank for its full length.

- #36

hatchelhoff

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Lf1 = ((a1*e1 + a2*e2 + 2*Tf3*a2*e2)L1)/(L1 + a1*e1*L2)

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- #37

nvn

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- #38

hatchelhoff

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Substituting

L1 = 349.166667 mm

a1 = 314.1593

a2 = 876.50435

I get

Lf1 =705.626 mm which seems very high.

- #39

nvn

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- #40

hatchelhoff

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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

nvn

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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

hatchelhoff

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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

nvn

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- #44

hatchelhoff

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((Lf1*a2*e2 - 2*tf3 * a2e2)/L2) + ((Lf1 * a1*e1)/L1) = a1*e1 + a2*e2

- #45

nvn

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hatchelhoff: Nice work. That is correct. Continue.

- #46

hatchelhoff

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Lf1 =L1((a1*e1*L2) + (a2*e2*L2) + (2*t3 * a2*e2))/(a2*e2*L1 + a1*e1*l2)

- #47

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- #48

hatchelhoff

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I now have the correct answers

Lf1 = 349.587

Lf2 = 329.587

Stress1 = 240.85 MPa

Stress2 = -86.325 MPa.

- #49

nvn

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hatchelhoff: Excellent work. Your answers in post 48 are correct.

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