Question

For a bolted assembly with six bolts, the stiffness of each bolt is kb=3 Mlbf/in and the stiffness of the members is km=12 Mlbf/in per bolt. An external load of 85 kips is applies to the entire joint. Assume the load is equally distributed to all the bolts. It has been determined to use 1/2 in-13 UNC grade 8 bolts with rolled threads. Assume the bolts are preloaded to 75 percent of the proof load.

a) determine the yielding factor of safety.

np=

b) determine the overload factor of safety.

nL=

Answer 1

External Load applied (P) = 80 kips

Bolt stiffness (k_b) = 3(10⁶) lbf / in

Member stiffness (k_m) = 12(10⁶) lbf / in

Diameter of bolts (d) = 1/2 in - 13 UNC grade 8

Number of bolts = 6

For Unified Screw Threads UNC and UNF

Tensile stress area (A_t) = 0.1419 in²

SAE specifications for steel bolts for grade 8,

we have

Minimum proff strength (S_p) = 120 kpsi

Minimum tensile strength (S_ut) = 150 kpsi

Load bolt (P) = kips = 13.33 kips

given by,

Preload Stress

Stiffness Constant

a) Yielding Factor of Safety is given by,

b) Overload Factor of Safety is given by,