# Solution to Problem 129 Bearing Stress

**Problem 129**

A 7/8-in.-diameter bolt, having a diameter at the root of the threads of 0.731 in., is used to fasten two timbers together as shown in Fig. P-129. The nut is tightened to cause a tensile stress of 18 ksi in the bolt. Compute the shearing stress in the head of the bolt and in the threads. Also, determine the outside diameter of the washers if their inside diameter is 9/8 in. and the bearing stress is limited to 800 psi.

**Given:**

Diameter of bolt = 7/8 inch

Diameter at the root of the thread (bolt) = 0.731 inch

Inside diameter of washer = 9/8 inch

Tensile stress in the nut = 18 ksi

Bearing stress = 800 psi

**Required:**

Shearing stress in the head of the bolt

Shearing stress in threads of the bolt

Outside diameter of the washer

**Solution 129**

**Tensile force on the bolt:**

$P = \sigma A = 18 [ \, \frac{1}{4} \pi (\frac{7}{8})^2 \, ]$

$P = 10.82 \, \text{kips}$

**Shearing stress in the head of the bolt:**

$\tau = \dfrac{P}{A} = \dfrac{10.82}{\pi (\frac{7}{8})(\frac{1}{2})}$

$\tau = 7.872 \, \text{ ksi}$ *answer*

**Shearing stress in the threads:**

$\tau = \dfrac{P}{A} = \dfrac{10.82}{\pi (0.731)(\frac{5}{8})}$

$\tau = 7.538 \, \text{ ksi}$ *answer*

**Outside diameter of washer:**

$P = \sigma_b \, A_b$

$10.82(1000) = 800 \bigl\{ \, \frac{1}{4} \pi \, [ \, d^2 - (\frac{9}{8})^2 \, ] \, \bigr\}$

$d = 4.3 \, \text{inch}$ *answer*