Solution to Problem 131 Bearing Stress

Based on shearing of rivets:
$P = \tau \, A$

$96\,000 = 70 [ \, \frac{1}{4} \pi (22^2) n \, ]$

$n = 3.6$   say 4 rivets
 

Based on bearing of member:
$P = \sigma_b \, A_b$

$96\,000 = 140 [ \, 22(6)n \, ]$

$n = 5.2$   say 6 rivets
 

Use 6 rivets for member BC.       answer
 

Tensile stress:
$\sigma = \dfrac{P}{A} = \dfrac{96(1000)}{864 - 22(6)}$

$\sigma = 131.15 \, \text{MPa}$           answer

Based on shearing of rivets:
$P = \tau \, A$

$80\,000 = 70 [ \, \frac{1}{4} \pi (22^2)n \, ]$

$n = 3.01$   say 4 rivets
 

Based on bearing of member:
$P = \sigma_b \, A_b$

$80\,000 = 140 [ \, 22(13)n \, ]$

$n = 1.998$ say 2 rivets
 

Use 4 rivets for member BE       answer
 

Compressive stress:
$\sigma = \dfrac{P}{A} = \dfrac{80(1000)}{1780}$

$\sigma = 44.94 \, \text{MPa}$           answer