<p>A.5.2.2.5 Math Models 1</p><p>In the final inter-stage skirt analysis code, we incorporate stringer and ring internal supports. The skin of the skirt does not transfer any load, and simply acts as the aerodynamic fairing between stages. All static and dynamic loads are transferred through the inter-stage skirt stringers and ring supports. The inter-stage skirt stringers and ring supports are designed to support the maximum applied axial force and the maximum shear force that occurs during launch. </p><p>The number of stringers and number of ring supports are designed so that the maximum applied stress on one stringer multiplied by the reserve factor is less than the yield strength of the stringer material. The maximum applied stress equation is described by Eq. (A.5.2.2.5.1).</p><p>6P  L h     sin  cos  max 2   (A.5.2.2.5.1) bh  nring 2  where σmax is the maximum applied stress, P is the force on one stringer, b is the width of the stringer cross-section, h is the height of the stringer cross-section, L is the length of the stringer, nring is the number of ring supports, and α is the taper angle from the vertical axis.1</p><p>Then, we check that the number of stringers is sufficient to overcome the maximum applied shear force. The maximum calculated shear stress multiplied by the reserve factor must be less than the shear allowable of the stringer material. The shear stress in each stringer is determined by the following equation. t r  y  t r  y  skin  r1  skin  r1  Br  Ar  2    2   6  yr  6  yr  2 I xx   Br yr (A.5.2.2.5.2) S y qr   Br yr I xx</p><p> qr  r  tskin where Ar is the cross-sectional area of each stringer, tskin is the thickness of the inter-stage skirt skin, r is the minimum skirt radius, θ is the angle between stringers, yr is the y-</p><p>2 distance from the center of the skirt to each stringer, and Sy is the applied shear force.</p><p>Authors: Jesii Doyle A.5.2.2.5 Math Models 2</p><p>References 1 Bedford, A., Fowler, W., and Liechti, K.M., Statics and Mechanics of Materials, Pearson Education Inc., Upper Saddle River, New Jersey, 2003.</p><p>2 Megson, T.H.G., Aircraft Structures for Engineering Students, Vol. 3, Elsevier Butterworth-Heinemann, Burlington, MA, 1999, Ch. 10.2.</p><p>Authors: Jesii Doyle</p>