- Compute the properties of the area with respect to the
x' and y'axes
Using the usual moment-of-inertia relations, we find Ix, = Ix + Ay^2 m = 162 + 36(6)2 = 1458
in^4 (6.06 dm^4 ); /,/ = /., + Ax^2 m = 96 + 36(7)^2 = 1660 in^4 (7.74 dm^4 ); Px,y, = P^ + Axmym = O
- 36(7)(6) = 1512 in^4 (6.29 dm^4 ).
- Compute the properties of the area with respect to the
x" and y" axes
For the x" axis, /^ = Ix, COS^2 O + Iy, sin^20 - Px,y, sin 20 = 1458(0.75) + 1860(0.25) -
1512(0.866) = 249 in^4 (1.03 dm^4 ).
For the /'axis, Iy.= Ix, sin^20 + Iy, cos^28 + Px,y, sin 20 = 1458(0.25) + 1860(0.75) +
1512(0.866) = 3069 in^4 (12.77 dm^4 ).
The product of inertia is Pxy=Px,y, cos 20+ [(Ix>-Iy)l2} sin20= 1512(0.5)+ 1(1458
- 1860)/2]0.866 = 582 in^4 (2.42 dm^4 ).
Analysis of Stress and StrainThe notational system for axial stress and strain used in this section is as follows: A =
cross-sectional area of a member; L = original length of the member; A/ = increase in
length; P = axial force; s = axial stress; e = axial strain = A//L; E = modulus of elasticity
of material = sle. The units used for each of these factors are given in the calculation pro-
cedure. In all instances, it is assumed that the induced stress is below the proportional lim-
it. The basic stress and elongation equations used are s = PIA; A/ = sLIE = PLI(AE). For
steel, E = 30 x 106 lb/in^2 (206 GPa).
FIGURE 15