## Joint Shear Stress

Consider the below joint is made up of two titanium brackets that are pinned together in single shear with a 30 mm pin. The brackets are 50 N in tension, which causes the pin to experience a 10 kN tension. What is the average shear stress at the overlapping bracketsâ€™ interface? Unless otherwise specified, all units are in mm.

##
__
__**Hint**

**Hint**

Shear stress:

$$$\tau=\frac{T}{A}$$$

where
$$T$$
is the shearing force, and
$$A$$
is the area.

##
__
__**Hint 2**

**Hint 2**

$$$A=\pi (r_{outer}-r_{inner})^2$$$

where
$$A$$
is the area and
$$r$$
is the radius.

Shear stress:

$$$\tau=\frac{T}{A}$$$

where
$$T$$
is the shearing force, and
$$A$$
is the area. To find
$$A$$
:

$$$A=\pi (r_{outer}-r_{inner})^2$$$

where
$$A$$
is the area and
$$r$$
is the radius. Thus,

$$$A=\pi[(25mm)^2-(\frac{30mm}{2})^2]=\pi[625mm^2-225mm^2]=1,256\:mm^2$$$

Finally,

$$$\tau=\frac{50\:N}{1,256\:mm^2}=0.04\:MPa$$$

0.04 MPa