Question

Two rectangular boards of 200-mm width and 25-mm thickness are glued together and subjected to the axial load P = 1,200-N, Fig.(a). For overlapping length of 100-mm: a-What is the average normal stress in each board? b-What is the average shear stress on the glued surface? c-If instead of the glue, a single 20-mm diameter bolt is used Fig. (b), what would be the maximum average normal stress in the boards and average shear stress in the bolt?

Answer 1

a) σ1 = .24 [MPa]

b) τ1 = .06 [MPa]

c) σ2 = .24 [MPa]

d) τ2 = 3.82 [MPa]

Step-by-step explanation:

(See attachment for pictorial explanation)

Definition of normal stress:

The normal stress is the stress that occurs on a member when an axial force is applied to it. It can either be tension or compression and its equation is:

• σ = P/A

• Note that force is perpendicular to the area where it is acting on.

Definition of shear stress:

The shear stress results from a force that is acting parallel to the cross section of a loaded member. Its equation is:

• τ = P/A

Now that we know that Normal Stress and Shear Stress area, we can easily calculate them with the values given of:

• P = 1200 [N]
• Width = 200 [mm] and thickness = 25 [mm] (Used to calculate cross sectional area of boards)
• Overlapping length or glue length = 100 [mm] (Used to calculate glue shear area)
• Bolt´s diameter = 20 [mm] (Used to calculate bolt´s shear area)

Follow the steps in the attachment to complete the calculations.