2 STRENGTH OF MATERIALS 



experimental determination of the physical properties, such as 

 strength and elasticity, of the various materials used in construction. 

 Although it is convenient to divide the subject in this way, it 

 must be understood that the two parts are, in reality, inseparable ; for 

 the mathematical discussion involves physical constants which can 

 be found only by experiment, while, on the other hand, experiment 

 alone is powerless to determine the form which should be given to 

 construction members in order to secure efficiency of design with 

 economy of material. 



3. Stress, strain, and deformation. Whenever an external force 

 acts on a body it creates a resisting force within the body. This, in 

 fact, is simply another way of stating Newton's third law of motion, 

 that to every action there exists a reaction equal in magnitude and 

 opposite in direction. This internal resistance is due to innumerable 

 small forces of attraction exerted between the molecules of the body, 

 called "molecular forces," or stresses. A body subjected t<> tin- urlimi 

 of stress is said to be strained, and the resulting change in shape is 

 called the deformation. 



For example, suppose a copper wire 40 in. long supports a weight of 10 ll>. and 

 is stretched by this weight so that its U-ngth iM-mmrs 4(. 1 in. Then tin- sum of 

 the stresses acting on any cross section of the \\iiv is in li>.. ami the effect of this 

 stress is to strain the wire until its deformation, or increase in k-ni:th. is . 1 in. 



4. Tension, compression, and shear. In order to determine tin- 

 relation between the stresses at any point in a solid body, only a 

 small portion of the body is considered at a time, say an infinitesimal 

 cube. This small cube is then assumed to act like a rigid body, and 

 the relations between the stresses which act on it are determined by 

 means of the conditions of equilibrium deduced in mechanics. 



By the principle of the resolution of forces, the stresses acting on 

 any face of such an elementary cube can be analyzed into two < <>m- 

 ponents, one perpendicular to the face of the cube and the other 

 lying in the plane of the face. That component of the stress whirh 

 is perpendicular to the face of the cube is called the normal stress. 

 If the normal stress pulls on the cube, and thus tends to increase its 

 dimensions, it is called tension; if it pushes on the cube, and thus 

 tends to decrease its dimensions, it is called compression. Tension is 

 indicated by the sign + and compression by the sign . 



