Jesii Doyle 2/28/2008 Internal Structures, Inter-Stage Skirts, Shear Stress Calculation, CAD Final Skirt Design AAE 450 Spring 2008

Inter-Stage Skirt Configuration Variable parameters: Thickness of stringer Number of stringers Number of ring supports Constant parameters: Aluminum skin/stringers Slope angle = 10° Outer skin thickness = 4mm Stringer depth = 2cm Shear Stress Analysis Incorporated Co-authored by Vince Teixeira Figure 1 by Jesii Doyle AAE 450 Spring 2008 Structures

Sample Skirt Configurations SB-HA-DA-DA Stringer thickness (mm) [ 3.0 3.0 ] No. of stringers: [ 76 75 ] No. of ring supports: [ 2 2 ] MB-HA-DA-DA Stringer thickness (mm): [ 3.0 3.0 ] No. of stringers: [ 77 68 ] LB-HA-DA-DA Stringer thickness (mm): [ 3.0 3.0 ] No. of stringers: [ 89 72 ] No. of ring supports: [ 3 2 ] Future Work Implementation of final design AAE 450 Spring 2008 Structures

Backup Slides MAT Code Version 4.0 Analysis Rocket Design Inputs Model Name: SB-HA-DA-DA Delta V = 7000 Delta V Percentages = [ 0.350 0.150 ] Inert Fractions = [ 0.270 0.300 0.240 ] Max Gs = 6 Model Name: MB-HA-DA-DA Delta V = 8100 Delta V Percentages = [ 0.450 0.150 ] Inert Fractions = [ 0.210 0.300 0.240 ] AAE 450 Spring 2008 Structures

Backup Slides MAT Code Version 4.0 Analysis (Cont.) Rocket Design Inputs Model Name: LB-HA-DA-DA Delta V = 9800 Delta V Percentages = [ 0.550 0.150 ] Inert Fractions = [ 0.120 0.270 0.240 ] Max Gs = 6 AAE 450 Spring 2008

Backup Slides Shear Stress Calculation Variables t_skin θ y Sy Shear Stress Calculation Variables t_skin = 0.004m (Const.) θ = angle between stringers (rad) yr = vertical dist. from shear center to stringer r (m) Ar = area of stringer r (m^2) r = stringer number Ixx = area moment of inertia (m^4) qr = shear flow through stringer r (N/m) σr = shear stress through stringer r (Pa) Sy = shear force at shear center (N) AAE 450 Spring 2008

Backup Slides Shear Stress Calculation (Cont.) Maximum Shear Stress – radius = radiusmin Br = Ar + (t_skin*radius*θ/6)*(2 + yr+1/yr) + (t_skin*radius*θ/6)*(2 + yr-1/yr) Ixx = Σ(Br*yr^2) qr = -(Sy/Ixx)*Br*yr σr = qr/t_skin σcrit = maxi(σr) < σsu AAE 450 Spring 2008

Backup Slides Stringer Axial Stress Equations AAE 450 Spring 2008 P h

Backup Slides Skin Critical Load Analysis E = Young’s Modulus γ = 0.33 = const. valid for 10° ≤ α ≤ 75° v = Poisson’s Ratio AAE 450 Spring 2008

References Bedford, A., Fowler, W., and Liechti, K.M., Statics and Mechanics of Materials, Pearson Education Inc., Upper Saddle River, New Jersey, 2003. “Conical Shells,” Astronautics Structures Manual, NASA, 1976. Megson, T.H.G., Aircraft Structures for Engineering Students, Vol. 3, Elsevier Butterworth-Heinemann, Burlington, MA, 1999, Ch. 10.2. AAE 450 Spring 2008