The boards measuring 2in by 6in are glued loosely together t

The boards measuring 2in by 6in are glued loosely together to form a 6 times 6in beam section. The two ways considered are: If shear will only act in the plusminus y direction, and the glue has minimal shear capacity, which option (A or B) is more likely to fail the glue in shear when loaded?

Solution

solution:

1)here one board of 6*6 is formed from 3 board of dimension 2*6

2)when boards are aligned along y direction as shown in figure A,then this three board has two interfacing area between them ,hence total shear area is twice the single board area A.

as glue has shear capacity or shear stress of \'t\',hence shear load Fa on beam is given by

t=Fa/2*A

Fa=t*2*A

3)whenever boards are aligned in z direction as shown in figure B at that time ,as cross section along y direction has single area A,with same shear capacity or shear stress t,shear load Fb is given as follows

t=Fb/A

Fb=t*A

4)from above equation it is observed that figure A takes more shear load than figure B,

Fa>Fb

5)hence option with figure B is more likely fail in shear when loade along y direction as shear area is less in figure B than figure A