Consider the beam shown in Figure 1 Suppose that a 180 mm

Consider the beam shown in (Figure 1) . Suppose that a = 180 mm , b = 230 mm , c = 20 mm . Determine the moment of inertia about the x axis.

Solution

>> Let there are three parts: one middle long and two (top & bottom) wide

>> Now, Total Moment of Inertia about X-Axis, Ix = I1 + I2 + I3

>> As, I1 = c*(2b - 2c)³/12 = (2/3)c*(b - c)³

and, I2 = I3 = 2a*c³/12 + (2*a*c)*(b - c/2)² = a*c³/6 + (1/2)*ac*(2b - c)²

So, Total Moment of Inertia about X-Axis, Ix = I1 + I2 + I3 =

(2/3)c*(b - c)³ +  a*c³/6 + (1/2)*ac*(2b - c)² +  a*c³/6 + (1/2)*ac*(2b - c)²

= (2/3)c*(b - c)³ +  a*c³/3 + ac*(2b - c)² mm⁴

As, a = 180 mm, b = 230 mm , c = 20 mm

So, Ix = 8.2092*10^-4 m⁴