Statics—Conditions of Equilibrium

1.A subsystem is in equilibrium if the combined effect of all external forces produces zero translational and rotational acceleration.
        If there is to be no translational acceleration, the forces must sum to zero: ΣF=0
        If there is to be no rotational acceleration, the moments must sum to zero: ΣM_|o  =0
                                                          where O is any point on or off the body.
Force and moment summation should include all external forces acting directly on the subsystem,namely, the forces drawn in the FBD.

Statics—Representing Force Interactions

1.Represent forces of interaction as simply as possible.

• In general, two bodies contact at multiple points. Their interaction can be described by a combination of forces.

• For the purpose of Statics, any complex combination of forces can be represented by relatively simple loads,provided the simpler loads,when acting alone, would resist or cause the same motion as the actual, more complex forces.

• We seek to determine the unknown forces that two bodies exert on each other by representing the unknowns as simply as possible.

Statics—Forces, Subsystems,and Free Body Diagrams

The forces that we study in Mechanics of Materials generally keep the body in equilibrium, even if they also cause the body to deform .
         For this reason, Statics, which addresses the forces on bodies in equilibrium, is a critical prerequisite to Mechanics of Materials.

The central ideas of Statics are-

1.Force - A force describes the equal and opposite mechanical interaction between two bodies, one upon the other, which often are in contact. . Since a force has a magnitude, direction, and sense, we represent it mathematically by a vector. Two forces applied to a body at the same point have the same effect as their vector sum.

Prediction of Deformation and Failure

↠A few very general scientific principles are needed to predict deformation and failure.
↠With very general principles, we can consider bodies with a wide range of geometries and materials, which are
    subjected to many types of loads.
↠Mechanics of Materials introduces these principles and applies them to bodies and loadings that can be
    analyzed with relatively simple mathematics.

1.Separate out the effects of material and geometry by viewing a body as composed of many tiny   
   elements.
↠Any body can be viewed as an assemblage of tiny, in fact infinitesimal, cubic elements. This insight allows us
    to separate out the effect of the body’s material from its shape.
↠Since a tiny cube is a standard shape,the relations between the cube’s deformation and the forces on it depend only
    on the material, for example, the particular type of ceramic, metal, plastic, or wood
          These relations can be measured and described for a given material, and they are relevant to a body of any shape
    and size composed of that material.

Issues addressed by Mechanics of Materials

1.Account for deformation and the potential for failure when designing systems subjected to forces.
           Forces acting on designed artifacts can be significant. All bodies deform under applied forces,
and they can fail if the forces are sufficiently large.

Mechanics of Materials addresses two prime questions:
●How much does a body deform when subjected to forces?
●When will forces applied to a body be large enough to cause the body to fail?

Deformation and failure depend on the forces and on the body’s material, size, and shape.

Visual Content

• Design of products, systems, and structures demands the engineer to consider a broad range of issues. 

• The issues addressed by Mechanics of Materials are excessive deformation and material failure. A few general principles enable us to design against excessive deformation and failure for a wide range of part geometries, materials, and loadings.  

• We consider the body to be composed of elements, we study common deformation modes, and we combine contributions of each deformation mode, as needed,to assess deformation and failure.