DEFINITIONS. :L'7 



DEFINITIONS. The following definitions will be of service in a study of structural me- 

 chanics. 



Forces. Forces are concurrent when tin ir lines of action meet in a point; non-concurrent 

 when tin it lines of action do not meet in a point. Forces are coplanar when they lie in the same 

 plain-; or non-coplanar when they lie in different planes. Coplanar forces only will be here con- 

 sidered. A force is fully defined when its amount, its direction, and position are known. 



Moment of Forces. The moment of a force about a point is its tendency to produce rotation 

 al>out that point, and is the product of the force and the perpendicular distance of the point from 

 the line of action of the force. 



Couple. A couple is a pair of equal and opposite forces having different lines of action. 

 The moment of a couple is equal to the product of one of the forces by the distance between the 

 lines of action of the forces, or the arm of the couple. 



Stress. If a body be conceived to be divided into two parts by a plane traversing it in 

 any direction, the force exerted between these two parts at the plane of division is an internal 

 stress. Stress is force distributed over an area in such a way as to be in equilibrium. Stresses 

 are measured in pounds, tons, etc. 



Unit Stress is the measure of intensity of stress. The unit stress at any point is the number 

 of units of stress acting on a unit of area at that point. Unit stresses are expressed in pounds 

 per square inch, tons per square foot, etc. 



Ultimate Stress. Ultimate stress is the greatest stress which can be produced in a body 

 before rupture occurs. 



Tension is the name for the stress which tends to prevent the two adjoining parts of a body 

 from being pulled apart when the body is acted upon by two forces acting away from each other. 



Compression is the name of the stress which tends to keep two adjoining parts of a body from 

 being pushed together under the influence of two forces acting toward each other. 



Shear is the name of the stress which tends to keep two adjoining planes of a body from 

 sliding on each other under the influence of two equal and parallel forces acting in opposite direc- 

 tions. 



Axial Stresses. When the external forces producing tension or compression act through 

 the center of a gravity of the body the stresses are uniformly distributed over the area, and the 

 stresses are axial stresses. 



Simple Stress. If P = the force producing tension, compression, or shear and A = the 

 area over which the stress is distributed, then 



f< = P/A; f e = P/A; f, = P/A, 



where / is tensile stress, f e is compressive stress, and / is shearing stress. 



Working Stress. The working stress for any material is the unit stress that has been found 

 by experiment to be safe to allow for that particular material to give a properly designed struc- 

 ture. The working stress for any particular structure depends upon the material of which the 

 structure is built, the loads that the structure is to carry, the accuracy with which the loads and 

 stresses have been calculated, the possible defects in the material, etc. 



Factor of Safety. The factor of safety is the number by which the ultimate stress must be 

 divided to give the working stress. 



Deformation or Strain is the change in the shape of a body caused by the action of an ex- 

 ternal force. Deformation or strain is measured in linear units. Deformation may be due to 

 tension, elongation; due to compression, shortening; or due to shear, detrusion or slipping of one 

 plane past another. 



Elasticity. Up to a certain stress in an elastic body it has been found by experiment that 

 stress is proportional to strain. This principle is known as " Hooke's Law." The ability of a 

 body to return to its original form after deformation is termed elasticity. If the stress in a body 

 is carried beyond a certain limit the body does not return to its original form, but a permanent 

 set occurs. 



