Question

If you needed to reduce deflection in a loaded aluminum rectangular box beam in your structural design, which of the following variables would you INCREASE? :

-Length

-Outer width

-Outer height

-Inner width

-Inner height

Which would be the MOST effective in reducing deflection?

What material could you substitute for aluminum in your design to decrease deflection? Why?

  

Answer 1

Deflection in the hollow rectangular beam is directly proportional to cube of its span (i.e., beam length).

   L³

Decrease in the Span of the beam reduces the deflection.

But, The element whose increase in the value reduces the deflection amount is :

As moment of Inertia is :

I = (Outer width x Outer height³) - ( Inner width x Inner height³) / 12

Increase the Outer height of Rectangular hollow beam increases the value of moment of inertia by a large sum.

Here, moment of inertia is inversly proportional to deflection.

Therefore, Increasing the Outer height of rectangular hollow Aluminium beam reduces the deflection developed by large amount. and is the most effective.

Aluminium has an Modulus of elasticity E = 69 Gpa [ 1 Gpa = 10⁹ N/m² ]

But, Wrought Iron has 190 - 210 Gpa and it suits the best alternative for aluminium, because young's modulus is inversly proportional to deflection.

In absence of Wrought iron, Copper will be the preferred alternative with 110 Gpa.