178 CAMBRIA STEEL. 



PROPERTIES OF ANGLES. 



The values in the Tables of Properties of Standard and Special 

 Angles, with Equal Legs, pages 198 to 203, are those stated in the 

 headings, and those in the Tables of Properties of Standard and 

 Special Angles, with Unequal Legs, on pages 204 to 209, are 

 similar, but with the addition of values for I", S" and r" about 

 the inclined axis 3-3, the position of which, in order to give the 

 minimum values, was determined by the formula on page 166 

 or the value of the tangent of 2a. After determining the position 

 of the inclined axis, the properties corresponding thereto were 

 obtained by the formula on page 166. 



MOMENTS OF INERTIA OF RECTANGLES. 



Tables of Moments of Inertia of Rectangles, about a trans- 

 verse axis through the center of gravity, are added on pages 210 

 to 213 for convenience in calculating the Moments of Inertia, 

 Section Moduli, and Radii of Gyration for compound shapes in 

 which plates are used. 



Table I is more convenient when depth of rectangle is expressed 

 without fraction, and is directly applicable to rectangles of various 

 widths, J4 to 1 inch, varying by fgths. Table II gives values 

 for 1 inch widths of rectangle only, but for all depths from -& to 

 50 if inches, varying by ^gths. Value for any other width may 

 be obtained from Table II by direct multiplication of tabular 

 value by that other width. 



GENERAL FORMULAE FOR PROPERTIES AND 

 FLEXURE. 



Formulae for obtaining the Properties of Standard Sections are 

 given on pages 166 and 167, and for various usual sections on 

 pages 168 to 175 inclusive. 



General formulas for Flexure of Beams, Bending Moments, 

 and Deflections for various cases of loading are given on pages 

 160 to 165 inclusive. 



