62 



PRACTICAL STRUCTURAL DESIGN 



The experienced structural designer uses tables of squares to 

 lighten the labor of making the computations involved in obtaining 

 the hypothenuse of a triangle. Barlow's Tables contain the 

 squares, cubes, square roots and cube roots of all numbers from 

 1 to 10,000. Smoley's Tables for the Use of Structural Designers 

 contain the squares of all lengths up to 100 ft., varying by six- 

 teenths of an inch. 



Moment of Resistance 



In Fig. 53 is illustrated a beam loaded so there is a tendency 

 to bend, which tendency is resisted by compression in the upper 



fibers and tension in 



Fig. 53 Compressive and Tensile Force Triangles 

 in a Beam 



the lower fibers. 

 The beam rests on 

 two supports. If it 

 were a cantilever 

 beam the compres- 

 sion would be in 

 the lower fibers and the tension in the upper fibers. The two 

 triangles show graphically the forces, the horizontal shading repre- 

 senting the compressive force and the vertical shading represent- 

 ing the tensile force. The overlapping portions of the triangles 

 neutralize each other, and the force triangles in Fig. 54 are the 

 result. In the case considered the beam is uniform in cross sec- 

 tion and the stresses in tension and compression are equal; there- 

 fore the triangles are equal in size and the neutral plane where 

 the triangles meet is in the center of area of the cross section. 



The neutral plane 

 is a plane in the 

 center of gravity of 

 the section, parallel 

 with the upper and 

 lower surfaces, 

 where there is no 

 tension or compres- 





Fig. 54- 



-The Usual Method of Representing Action 

 of Resisting Forces in a Beam 



sion. The stresses above and below are opposite in nature; 

 therefore the only stress along the neutral plane is horizontal 

 shear. The word " neutral" implies that in this plane opposite 

 forces are neutralized. 



This definition of the neutral plane is important. In all text 

 books the illustrations refer to beam sections of homogeneous 



