Question

Calculate for the following properties for the cross sections shown below (in inches): area moment of inertia about horizontal and vertical axes through the centroid, and torsional constant (10 points) I-beam Box 6 6 10 10 Thickness of all plates 0.4 Both flanges are the same Thickness of top and bottom plates 0.4 Thickness of side plates-0.2

Answer 1

since the I-beam is symmetric horizontally and vertically, the centroidal axes will be passing through lines of symmetry

moment of inertia about horizontal axis of symmetry:

depth of web = 10-0.4-0.4=9.2 in

distnace of centroid of flanges from centroid of section = (10/2)-0.4/2=4.8 in

moment of inertia of section = 2*[6*0.4³/12+6*0.4*4.8²]+0.4*9.2³/12 = 136.6 in⁴

moment of inertia of section about vertical line of symmetry = 2*0.4*6³/12 + 9.2*0.4³/12 = 14.4 in⁴

since the box-beam is symmetric horizontally and vertically, the centroidal axes will be passing through lines of symmetry

moment of inertia about horizontal axis of symmetry:

depth of each web = 10-0.4-0.4=9.2 in

moment of inertia of section about horizontal axis of symmetry = 2*[6*0.4³/12+6*0.4*4.8²]+2*[0.2*9.2³ /12]=136.6 in⁴

moment of inertia of section about vertical axis of symmetry = 2*(0.4*6³/12+9.2*0.2³/12+9.2*0.2*2.9²)=45.4 in⁴