Question

А)

In figure below, assume that a 20-mm-diameter rivet joins the plates that are each 110 mm
wide. The allowable stresses are 120 MPa for bearing in the plate material and 60 MPa for
shearing of rivet. Find the followings. Express your final answer in N/mm².
110 mm
20-mm
P
(1) Determine the minimum thickness of each plate and largest average tensile stress in the
plates.
(6 marks)

Answer 1

Image of the plate is missing, so i have attached it.

Answer:

A) t = 7.854 mm

B) σ = 26.67 MPa

Step-by-step explanation:

A) From shearing of rivet, formula for pressure is;

P = τ•A_rivets

Where;

τ is allowable stress

A_rivets is Area of rivet

We are given:

τ = 60 MPa

Diameter; d = 20 mm

A_rivets = πd²/4 = π × 20²/4 = 100π

Thus;

P = 60 × 100π

P = 6000π N

From bearing of plate material, we can calculate pressure as;

P = σ_b•A_b

We are given;

σ_b = 120 MPa

A_b is area of plate = 20t

Where t is the thickness

Thus;

6000π = 120 × 20t

t = 6000π/(120 × 20)

t = 7.854 mm

B) Largest average tensile stress is given by the formula;

σ = P/A

Where A = 110t - 20t

A = 90t

A = 90 × 7.854

Thus;

σ = 6000π/(90 × 7.854)

σ = 26.67 MPa