Question

5. A fluctuating external load of Ppeak = 4500 lb is applied at the bolted joint given in Problem 4.
(1) Find the factor n_f of safety against the fatigue failure using the modified Goodman criterion.
(2) Find the factor n_p of safety using the proof strength line.
(3) Find the factor n₀ of safety against joint separation.
(4) Find the factor n of safety against yielding.

(question 4 for reference)

4. For the assembly similar to the one in Problem 3, the bolt of ½ in-13-UNC-2A grade 8 with rolled
threads is proloaded to 80% of its proof strength. There is a static 1500-lb load applied to the
assembly to separate the joint. It is known that k_b = 1.2x10⁶ lbf/in and km = 8.4x10⁶ lbf/in
(1) Find the load factor nl.
(2) Find the factor of safety against static failure n.
(3) Find the factor of safety against joint separation n0.

Answer 1

5.

1) The stiffness constant of the joint is given by

Minimum proof strength of grade 8 SAE bolts is

Tensile stress area of 1/2 in bolts is

Hence bolt preload is

Static external load is

Dynamic expernal load is. We assume load is fluctuating from 0 to peak.

Max external load is

Min external load is

Max bolt load is

Min bolt load is

Alternating stress experience by the bolt is

The mid range stress is

For SAE 8 rolled threads grade 8, the enduranc stress is

The tensile strength of grade 8 bolts is

Referring to Fig 8-20 of Shigley

Using formula 8-45 of Shigley, the fatigue factor of safety is

2) Using equation 8.51 of Shigley

3) The factor of safety against joint separation is

4) The factor of safety against yielding is

For Grade 8 bolts the yield strength is

Hence

From Goodman criterion