Statics and Strength of Materials
    Statics is the study of forces acting in equilibrium 
   on rigid bodies
    •
    “Bodies” are solid objects, like steel cables, gear teeth, timber beams, 
    and axle shafts (no liquids or gases);
    •
     “rigid” means the bodies do not stretch, bend, or twist;  
    •
    “equilibrium” means the rigid bodies are not accelerating. 
    In Strength of Materials, we keep the assumptions 
   of bodies in equilibrium, but we drop the “rigid” 
   assumption. 
    
    Real cables stretch under tension and real axle shafts 
    twist under torsional load.
   Strength of Materials
   Statics is the study of forces acting in equilibrium 
   on rigid bodies.
    •
    “Bodies” are solid objects, like steel cables, gear teeth, timber 
    beams, and axle shafts (no liquids or gases);
    •
     “rigid” means the bodies do not stretch, bend, or twist;  
    •
    “equilibrium” means the rigid bodies are not accelerating. 
   In Strength of Materials, we keep the assumptions 
   of bodies in equilibrium, but we drop the “rigid” 
   assumption. 
    ▫
    Real cables stretch under tension and real axle shafts 
    twist under torsional load. 
    ▫
    The most fundamental concepts in mechanics of materials 
    are stress and strain.
   Stress and Strain
  •The words “stress” and “strain” are used interchangeably: “I’m 
   feeling stressed” or “I’m under a lot of strain.”
  •In engineering, these words have specific, technical meanings. 
   If you tie a steel wire to a hook 
   in the ceiling and hang a weight 
   on the lower end, the wire will 
   stretch. 
   •
   Divide the change in length by 
   the original length, and you 
   have the strain in the wire. 
   •
   Divide the weight hanging from 
   the wire by the wire’s cross 
   sectional area, and you have the 
   tensile stress in the wire. 
     Stress and strain are ratios. 
       ▫The symbol for  stress is σ, the lower case 
        Greek letter sigma. Stress has units of force 
        per unit area
          When SI units are used, force is expressed in 
          newtons (N) and area in square meters (m2). 
                                      2
                              1N/m  = 1 
          Consequently, stress has units of newtons per 
                               2
                              Pa
          square meter (N/m ), that is, pascals (Pa).
           
          However, the pascal is such a small unit of 
          stress that it is necessary to work with large 
          multiples, usually the megapascal (MPa). 
                               6         6      2           2
                       1 MPa = 10  Pa = 10  N/ m  = 1 N/mm  
  The symbol for strain is ε, the lower case 
   Greek letter epsilon.
     Because normal strain is the ratio of two 
     lengths, it is a dimension- less quantity, that 
     is, it has no units. Therefore, strain is 
     expressed simply as a number, independent of 
     any system of units. 
     Numerical values of strain are usually very 
     small, because bars made of structural 
     materials undergo only small changes in 
     length when loaded.