JNTU B.Tech III AEROSPACE VEHICLE STRUCTURES II Previous Question Paper (February - 2022 - R13)

The failure stress in plates and stiffened panels is primarily governed by the onset of buckling or the attainment of the material yield strength. For a thin rectangular plate of width b, thickness t, and length a, simply supported on all edges and subjected to uniform compressive stress σ, the elastic buckling stress σ_cr is given by:

where E is Young's modulus, ν is Poisson's ratio, and k is the buckling coefficient depending on the aspect ratio (a/b) and edge conditions. For long plates, k approaches 4.0.

For stiffened panels, the failure mode is more complex, involving either local plate buckling between stiffeners or overall panel instability (Euler buckling). The effective width concept is used to account for the post-buckling strength of the skin. The effective width w_e of the plate that remains effective after buckling is determined by:

The failure stress of the stiffened panel is then calculated by considering the combined cross-sectional area of the stiffener and the effective width of the attached skin:

where P_ult is the ultimate load-carrying capacity, and A_st is the cross-sectional area of the stiffener. If the panel is short and stocky, failure is governed by the yield stress σ_y. If the panel is slender, the failure stress is limited by the global buckling load of the stiffener-plate combination, calculated using the effective flexural rigidity EI_eff of the section. In practice, the Johnson-Euler formula is often applied to interpolate between the elastic buckling stress and the material yield stress to predict the actual failure stress in the inelastic range.

The angle of diagonal tension, denoted as α, in a thin-webbed beam (Wagner beam) is determined by the equilibrium conditions of the web and the stiffness properties of the surrounding structure. The primary factors influencing this angle are the relative stiffness of the flanges, the stiffness of the vertical stiffeners, and the magnitude of the applied shear load.

Specifically, the angle is governed by the condition that the total strain energy of the system is minimized. The relationship is expressed by the following formula, where α is the angle of the diagonal tension field relative to the longitudinal axis:

In this expression, A_f represents the cross-sectional area of the flanges, t is the thickness of the web, and d is the depth of the web. As the flanges become more rigid, the resistance to bending increases, which forces the diagonal tension field to orient itself more steeply to maintain equilibrium.

For the case of rigid flanges, the flange area A_f approaches infinity. Substituting this into the equilibrium equation:

This implies that 2α approaches 90 degrees, resulting in an angle of diagonal tension of 45 degrees. In this theoretical limit, the web acts as a pure tension field oriented at 45 degrees to the longitudinal axis, effectively transferring the shear load through pure diagonal tension while the rigid flanges prevent any bowing or bending deformation.