Jawaharlal Nehru Technological University Hyderabad B.Tech III AEROSPACE VEHICLE STRUCTURES- II Previous Question Paper (March - 2021 - R13/R15)

The buckling coefficient, denoted by k, is a dimensionless parameter used to define the critical buckling stress of a plate. It accounts for the plate geometry, boundary conditions, and the mode of loading. The critical buckling stress is given by the formula:

where E is Young's modulus, ν is Poisson's ratio, t is plate thickness, and b is the width. For a simply supported rectangular plate of length a and width b, the coefficient k varies with the aspect ratio a/b. The curve follows a series of parabolas where k = (m(b/a) + (a/mb))², with m representing the number of half-waves in the longitudinal direction. The minimum value of k is 4.0 when a/b = 1, and it remains near 4.0 for higher aspect ratios as the plate buckles into multiple square cells.

To determine the buckling strength of a stiffened panel, the total load capacity is calculated by summing the critical buckling load of the skin and the load-carrying capacity of the stringers. Given E = 70 GPa and σ = 300 MPa, the effective width of the skin w_e is determined using Von Karman's formula:

Substituting the values, w_e = 1.9 * t * sqrt(70000 / 300) ≈ 29.03 * t. The total buckling strength P_cr is the sum of the load carried by the stringers and the effective skin area:

Here, A_{effective_skin} is calculated as the sum of the effective widths associated with each stringer attachment point. The total strength is obtained by multiplying the compressive stress by the total effective cross-sectional area of the stiffened panel, ensuring that the local buckling stress of the skin does not exceed the applied compressive stress.