Elastic Modulus E = strain stress = ( )( )Lδ

AF = Aδ FL

This equation can be re-arranged to give:

F = δ L


hence when δ =1.0 (i.e. unit displacement) then the axial stiffness k (= F) = L


7.2.1 Beam Elements with Two Degrees−of−Freedom Consider a ‘beam element’ of length L, Young’s Modulus E and cross-sectional area A which is subject to axial forces F1 and F2 at the end nodes A and B as shown in Figure 7.2.