# Analysis of Curved Plates

This page provides the chapters on the analysis of curved plates from the "Stress Analysis Manual," Air Force Flight Dynamics Laboratory, October 1986.

Other related chapters from the Air Force "Stress Analysis Manual" can be seen to the right.

Analysis of Plates

## Nomenclature

 a = plate length b = plate width C = compressive buckling coefficient for curved plates E = modulus of elasticity Es = secant modulus Et = tangent modulus F0.7, F0.85 = secant yield stress at 0.7E and 0.85E Fcr = critical normal stress Fcrs = critical shear stress
 kc = compressive buckling coefficient r = radius of curvature t = thickness Zb = length range parameter b2(1 - νe2)1/2/ rt η = plasticity reduction factor ν = inelastic Poisson's ratio νe = elastic Poisson's ratio

## 6.6 Axial Compression of Curved Plates

The radius of curvature of curved plates determines the method to be used to analyze their buckling stress. For large curvature (b2/ rt < 1), they may be analyzed as flat plates by using the relations in Section 6.3. For elastic stresses in the transition length and width ranges, Figure 6-31 may be used to find the buckling coefficient for use in Equation (6-31).

$$F_{cr} = { k_c ~\pi^2 E \over 12 (1 - \nu_2^2) } \left({ t \over b }\right)^2$$
(6-31)

For sharply curved plates, (b2/ rt > 100), Equations (6-32) and (6-33) can be used.

$$F_{cr} = \eta ~C ~E \left({ t \over r }\right)$$
(6-32)
$$\eta = {E_s \over E} {E_t \over E_s} { (1 - \nu_e^2) \over (1 - \nu^2) }$$
(6-33)

Figure 6-32 gives values of C in terms of r/t. Figure 6-33 gives η in a nondimensional form. Here the quantity ϵcr = Ct/r.

We have a number of structural calculators to choose from. Here are just a few:

$$F_{crs} = { k_s ~\pi^2 E \over 12 (1 - \nu_e^2) } \left({t \over b}\right)^2$$
$$F_{crs} = 0.37 ~(Z_b)^{1/2} (F_{crs})_{\text{flat plate}}$$