Complete COSMOS: Online Solutions Manual Organization System
Chapter 9, Solution 112.
From Problem 9.111 have, I x I y - I xy = constant Now consider the following two cases Case 1: Case 2: Then or From Figure 9.13B: Now With then Finally
I x = I x , I x = I max ,
I y = I y , I y = I min ,
I xy = I xy I xy = 0
2 I x I y - I xy = I max I min
I xy = I x I y - I max I min
I x = 453 103 mm 4
I ave =
I y = 166 103 mm 4
1 1 Ix + I y = I max + I min 2 2
(
)
(
)
I max = 524 103 4
I mm min = ( 453 + 166 - 524 ) 103 mm 4 = 95.0 103 mm 4
I xy =
( 453)(166 ) - ( 524 )( 95.0 ) 103 mm 4
= 159.43 103 mm 4
The two roots corresponding to the following orientations of the cross section:
(a)
(a) I xy = -159.4 103 mm 4 (b) I xy = 159.4 103 mm 4
(b)
Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell 2007 The McGraw-Hill Companies.