The L 80 × 60 × 10 -mm structural angle has the following cross-sectional properties: I x = 0.808 × 10 6 mm 4 , I y = 0.388 × 10 6 mm 4 , and I 2 = 0.213 × 10 6 mm 4 , where I 2 is a principal centroidal moment of inertia. Assuming I x y is negative, compute (a) I 1 (the other principal centroidal moment of inertia); and (b) the principal directions.
The L 80 × 60 × 10 -mm structural angle has the following cross-sectional properties: I x = 0.808 × 10 6 mm 4 , I y = 0.388 × 10 6 mm 4 , and I 2 = 0.213 × 10 6 mm 4 , where I 2 is a principal centroidal moment of inertia. Assuming I x y is negative, compute (a) I 1 (the other principal centroidal moment of inertia); and (b) the principal directions.
Solution Summary: The author calculates the other principal centroidal moment of inertia using the relation I_1.
The
L
80
×
60
×
10
-mm
structural angle has the following cross-sectional properties:
I
x
=
0.808
×
10
6
mm
4
,
I
y
=
0.388
×
10
6
mm
4
,
and
I
2
=
0.213
×
10
6
mm
4
,
where
I
2
is a principal centroidal moment of inertia. Assuming
I
x
y
is negative, compute (a)
I
1
(the other principal centroidal moment of inertia); and (b) the principal directions.
For the beam I-section below, calculate the second moment of area about its centroidal x-axis (Ixxcentroid), where b1 = 10.50 mm, b2 = 2.50 mm, b3 = 38.50 mm, d1 = 1.50 mm, d2 = 36.50 mm and d3 = 12.50 mm.
Give your answer in mm4 to two decimal places.
Find the centroid (x̄, ȳ) of the composite area, given:
L1 = 11 in, L2 = 10 in, L3 = 6 in, L4 = 4.4 in, R = 2 in
Find the moment of inertia of the given lamina about X-X axis passing through its centroid,
where b1=110 mm, d1=35 mm, b2= 62 mm & d2=108mm.
(i) The X with bar on top value is (unit is in mm) = ______________
(i) The Y with bar on top value is (unit is in mm) = ______________
(iii) the Ixx1 value is (unit is in mm4)= ______________
(iv) the Ixx2 value is (unit is in mm4)= ______________
(v) The Ixx value is (unit is in mm4)=
Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
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