Normal Stress

When a structural member is under load, predicting its ability to withstand that load is not possible merely from the reaction force in the member. It depends upon the internal force, cross sectional area of the element and its material properties. Thus, a quantity that gives the ratio of the internal force to the cross sectional area will define the ability of the material in with standing the loads in a better way. That quantity, i.e., the intensity of force distributed over the given area or simply the force per unit area is called the stress. σ=  P/A         ..........................................1.1 In SI units, force is expressed in newtons (N) and area in square meters. Consequently, the stress has units of newtons per square meter (N/m2) or Pascals (Pa). In above figure , the stresses are acting normal to the section XX that is perpendicular to the axis of the bar. These stresses are called normal stresses. The stress defined in equation 1.1 is obtained by dividing the force by the cross sectional area and hence it represents the average value of the stress over the entire cross section. Consider a small area ∆A on the cross section with the force acting on it ∆F as shown in above figure . Let the area contain a point C. Now, the stress at the point C can be defined as, σ =    lim    ∆F/∆A         .............................1.2         A-->0 The average stress values obtained using equation 1.1 and the stress value at a point from equation 1.2 may not be the same for all cross sections and for all loading conditions.