고체역학 (Gere) — Axially Loaded Members: Problem 2.5-25

2.5-25 A capped cast-iron pipe is compressed by a brass rod, as shown. The nut is turned until it is just snug, then add an additional quarter turn to pre-compress the cast-iron pipe. The pitch of the threads of the bolt is \( p = 1.3 \text{ mm} \). Use the numerical properties provided. (a) What stresses \( \sigma_p \) and \( \sigma_r \) will be produced in the cast-iron pipe and brass rod, respectively, by the additional quarter turn of the nut? (b) Find the bearing stress \( \sigma_b \) beneath the washer and the shear stress \( \tau_c \) in the steel cap. Numerical properties from provided data: - Cast-iron pipe: \( L_{ci} = 1.6 \text{ m} \), \( d_o = 150 \text{ mm} \), \( d_i = 143 \text{ mm} \), \( E_{ci} = 83 \text{ GPa} \) - Brass rod: \( d_r = 12 \text{ mm} \), \( E_{brass} = 96 \text{ GPa} \) - Steel cap: \( t_c = 25 \text{ mm} \), \( E_{steel} = 210 \text{ GPa} \) - Washer: \( d_w = 19 \text{ mm} \) - Thread pitch: \( p = 1.3 \text{ mm} \), rotation \( n = 1/4 \) turn.