Question

You have designed a bridge beam with an I of 1000 in4 and estimate a maximum deflection of 4 inches. In order to reduce the maximum deflection to 3.1 inches, you must increase I to ________ in4

Answer 1

1290.32 In⁴

Step-by-step explanation:

∆ = wL⁴/384EI

∆ is directly proportional to 1/I

∆1/∆2 = i2/i1

We have

∆1 = 4 inches

∆2 = 3.1 inches

i1 = 1000

i2 is unknown

So when we insert these values into the formula we have:

4/3.1 = i2/1000

From here we cross multiply

4x1000 = 3.1(i2)

4000 = 3.1(i2)

Divide through by 3.1

= 4000/3.1 = i2

= 1290.32 in⁴

i2 = 1290.32 in⁴

So, In order to reduce the maximum deflection to 3.1 inches, you must increase I to 1290.32 in⁴