Answer to Question #91695 in Mechanics | Relativity for Louie

Question

Question 5
A “T” section consists of a vertical rectangle (Element 1) of width 8 mm and height 110 mm, and a horizontal rectangle (Element 2) of width 60 mm and height 10 mm.
Find the distance y from the horizontal bottom edge of the vertical
rectangle to the centroid of the “T” section, and the second moment of area, Ixx, of the “T” section about the centroidal horizontal axis.

Answer 1

$Y1 = 110+10/2=115 mm$

$Y2 = 110/2=55mm$

$A1= 60*10=600 mm^2$

$A2=8*110=880 mm^2$

$Y= (A1*Y1+A2*Y2)/(A1+A2)= (115*600+55*880)/(600+880)=79.32mm$

Moment of enertia rectangle 1:

$I1=1/12*b*d^3+a1*h1^2$

b = 60 mm

d = 10 mm

$h1=10/2+(110-79.32)=5+30.68=35.68 mm$

$I1=1/12*60*10^3+600*35.683=7.69*10^5 mm^4$

moment of inertia rectangle 2:

$I2=1/12bd^3+a2h2^2$

b = 8 mm

d = 110 mm

$h2=79.32-55=24.32 mm$

$I2=1/12*8*110^3+880*24.322=14.07*10^5 mm^4$

second moment of area x-axis:

$Ixx=I1+I2=7.69*10^5+14.07*10^5=21.76*10^5mm^4$