Stiffness, a measure of a body's compliance to deformation under a given type of load: the greater the stiffness, the smaller the deformation. In strength of materials and the theory of elasticity, stiffness is characterised by a coefficient (or by the total internal force) and the characteristic strain of an elastic solid. In the tension and compression of a rod, the stiffness is the coefficient ES in the relation ε=P/(ES) between the tensile (compressive) force P and the relative elongation ε of the rod (S is the cross-sectional area and E is Young's modulus, (see Elastic moduli). In the torsional deformation of a round rod the stiffness is the quantity GIp in the relation v=M/GIp, where G is the shear modulus, Ip is the polar moment of inertia of the section, M is the torque and v is the relative angle of twist of the rod. In the bending of a beam the stiffness EI appears in the relation μ=M/EI between the bending moment M (the moment of the normal stresses over the cross-section) and the curvature c of the bent axis of the beam (/ is the axial moment of inertia of the cross-section). In the theory of plates and shells the concept of cylindrical stiffness is used: D = Eh3 12(1-v2), where h is the thickness of the plate (shell) and v is Poisson's ratio. Stiffness is also defined for certain complex structures.