The bolted assembly as shown in the attached figure has four M20 bolts with a pi

Question

The bolted assembly as shown in the attached figure has four M20 bolts with a pitch of 1.5 mm. The threads are machined and the stress concentration factor is Kf =3.85. Tbe cylinder has an ID = 100 mm and is constrained with rigid end plates and the four standard size bolts. The bolts and cylinder are made from AISI 1080 HR steel The cylinder contains a fluid that varies continuously between 0 and 14 Mpa. Use the Sodenberg criteria to determine the preload in the bolts such that they have a factor of safety of 2. The modulus of the steel is 207 Gpa. The stress concentration factor should only be applied to the alternating stress.

Explanation / Answer

Sf is fatigue stress   

Sa is alternating stress

Sm is mean stress ,

St is tensile

Sf =St/2 .. Always correct

1/FS =Sa/Sf + Sm/St

1/2 =Sa/103.5 +Sm/207

stress concentraition factor is 3.85 and varies from 0 to 14

hence Sa =(14-0)*3.85 =53.9MPA =0.0539 Gpa

also 1/2 =Sa/103.5 +Sm/207

0.5 = 0.000521 +Sm/207

Sm =103.39 GPa

let Mt be the preload

Sm =(Smin +Smax)/2 = (Mt+0 + Mt+14)/2 =103.39

hence Mt =96.39 Gpa

load in neuton is 96.39*3.14*0.1^2 =3026.6 *10^6 N

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