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 brackets’ interface? Unless otherwise specified, all units are in mm.
Expand Hint
Shear stress:
$$$\tau=\frac{T}{A}$$$
where
$$T$$
is the shearing force, and
$$A$$
is the area.
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
Time Analysis
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