Composite box beams including transverse shear effects. Composite I-beams. Including transverse shear effects.

Plates:

Circular - Sandwich and isotropic plates with central loading, self-weight, and uniform pressure. Includes transverse shear effects.

Rectangular:

• Isotropic with uniform pressure or hydrostatic loads.
• Sandwich with uniform pressure or hydrostatic loads including transverse shear effects.
• Buckling for axial loads for isotropic and sandwich plates including transverse shear effects.
• Stiffener requirements for uniform pressure or hydrostatic loads.

Cylinders:

• Knuckle discontinuity analysis.
• Buckling of isotropic and sandwich shells due to external pressure, lateral pressure, axial load, bending or combined loads. Materials can be isotropic or orthotropic. Laminated plate theory and classical shell theory are used. Results are per ASME RTP-1, ASME Section X, and NASA SP8007.
• Half round and trapezoidal stiffener sizing for vacuum loading.
• Composite cylinder analysis using classical laminated plate theory.

Other Design and Analysis Programs:

• Laminated Plate Theory for stress, strain, and strength calculations. Includes thermal and moisture effects and calculates coefficient of thermal expansions and effective mechanical properties.
• Horizontal tank design including saddle rings.
• Hold down lugs per ASME RTP-1.
• Guy wire analysis for stacks including preload and thermal expansion.
• ABD matrix calculation for orthotropic materials.
• Pressure losses in pipe, duct, and fittings due to friction.
• Ellipse analysis for internal pressure.
• Torisphere analysis for internal pressure.
• Stack wind load analysis per BOCA and ASCE codes. Includes vortex shedding effects.
• Pipe and Duct support spacing per SPI guidelines including the effects of wind, weight, and pressure.
• Flange analysis per ASME RTP-1 and ASME Section X.
• Seismic analysis per most building codes.
• Gusset and bracket analysis.
• Micromechanics of composites to predict overall material properties based on constituent properties.
• Finite Element analysis using ANSYS, COSMOSM, and StarDyne (limited versions).

Manufacturing Computer Programs:

• Filament winding pattern machine sheet generation.
• Chop / Hoop lay up machine sheet generation.

The programs below demonstrate some of Composites USA's engineering capabilities as related to composite materials. A brief description and partial sample printout of each program follows:

1) COMPOSITE CYLINDER ANALYSIS, RTP-1 CALCULATIONS.

This is Classical Laminated Plate theory adapted to cylinder analysis. Loads can include pressure, axial load, torque, moment, shear, and static head. Material inputs can be any isotropic or orthotropic material. Strain, stress, and strength calculations are performed per ASME RTP-1 guidelines.

2) SIMPLY SUPPORTED RECTANGULAR CORED PLATE WITH UNIFORM PRESSURE.

This program calculates stresses and deformations in rectangular sandwich plates based on Classical Plate Theory. Calculations including core shear deformation are performed using derivations from three separate authors, Dobyns, Plantema, and Allen. A Levy solution, which does not include shear deformation, is also included so that the shear contribution to the deformation can be determined.

3) SIMPLY SUPPORTED CIRCULAR CORED PLATE WITH CENTRAL LOAD, UNIFORM PRESSURE, AND UNIFORM WEIGHT.

This program calculates stresses and deformations in circular sandwich plates. Deflection due to shear deformation in the core is included. The core and face materials are assumed to be isotropic. The three loads (central load, uniform pressure, and uniform weight) produce three individual solutions, which are then superimposed to give total stresses and deformations.

4) BUCKLING OF AN ISOTROPIC CYLINDER WITH LATERAL AND LONGITUDINAL PRESSURE.

This is a comparison of four commonly used buckling calculations for isotropic cylinders. The Roark and Young formulation is exact based on Classical Shell Theory and is a special case of the anisotropic buckling calculations shown in the following program.

5) BUCKLING OF A CYLINDER WITH LATERAL AND LONGITUDINAL PRESSURE OR AXIAL COMPRESSION, NASA SP8007.

This program is exact based on Classical Shell Theory and the lay up can include any sequence of isotropic or orthotropic materials. The lay up is input into a spread sheet program and the ABD matrix (which is the constitutive relationship between the strains and curvatures to the inplane forces and moments) is then pasted into the MathCad program as material property input. If the lay up is isotropic, the solution converges to the solution calculated in Program 4 described above. For the particular case where the laminate is balanced and symmetric but not necessarily isotropic, test data has been obtained on actual buckling loads. This data has been curve fitted to calculate knockdown factors based on actual material properties and geometry. Although the NASA SP8007 test work was performed in the 1960's, it has been verified through additional testing on advanced composite materials in the 1980's.

COMPOSITE CYLINDER ANALYSIS RTP-1 CALCULATIONS

LOADS: OUTPUT: PRESSURE (PSI) 10.000 N-Z (LB./IN.) 105.00 AXIAL GTH (in) 0.3728 AXIAL LOAD (LB.) 0.000 N-T (LB./IN.) 210.00 RADIAL GTH (in) 0.0405 MOMENT (IN. LB.) 0.000 N-ZT (LB./IN.) 0.00 PV/W (in.) 2.984E+04 SHEAR (LB.) 0.000 TOT. THICK. (IN.) 0.0500 E-Z (PSI) 1.8705E+06 TORQUE (IN.LB.) 0.000 OUT. RADIUS (IN.) 21.0500 E-THETA (PSI) 2.4669E+06 HEAD(PSI) 0.000 MEAN RAD. (IN.) 21.0250 G-Z,THETA (PSI) 7.6730E+05 MAT1 WT. (LB.) 0.0000 NU-TZ -0.2607 GEOMETRY: MAT2 WT. (LB.) 110.5142 NU-ZT -0.1977 MAT3 WT. (LB.) 0.0000 CTE-T (E-06) deg. F 7.6702 IN. RADIUS (IN.) 21.0000 MAT4 WT. (LB.) 0.0000 CTE-Z (E-06) deg. F 11.5498 L. OF CYL. (IN.) 238.0000 MAT5 WT. (LB.) 0.0000 CTE-TZ(E-06) deg. F 0.0000 TOT. WT. (LB.) 110.5142 END AREA (IN^2) 6.6052 VOL. (IN.^3) 329735.28 I (IN^4) 1459.9181 EI (LB.-IN.^2) 2.7308E+09 EA (LB.) 1.2355E+07 GJ (LB.-IN^2) 2.2404E+09 KAG (LB.) 2.5341E+06

MATERIAL PROPERTY INPUT:

MAT 1 MAT 2 MAT 3 MAT 4 MAT 5 24 oz. Woven Roving 5/4 weave NAME C veil/382 Roving/382 Chop/382 Uni/382 Uni/382 E11 (PSI.) 5.5000E+05 2.4400E+06 1.0300E+06 3.4200E+06 3.4200E+06 E22 (PSI) 5.5000E+05 6.0000E+05 1.0300E+06 8.0000E+05 8.0000E+05 G12 (PSI.) 2.0000E+05 1.4900E+06 3.9000E+05 2.7000E+05 2.7000E+05 NU12 0.3400 0.3378 0.3400 0.3000 0.3000 PLY THICK. (IN.) 0.0130 0.0250 0.0430 0.0147 0.0252 NUMBER OF PLIES 0 2 0 0 0 THICKNESS (IN.) 0.0000 0.0500 0.0000 0.0000 0.0000 ALPHA (DEG.) 0.0000 54.7000 0.0000 0.0000 0.0000 ALPHA (RAD.) 0.0000 0.9547 0.0000 0.0000 0.0000 VOL. FRACT. 0.039 0.400 0.161 0.315 0.315 DENS. (LB./IN.^3) 0.0486 0.0703 0.0544 0.0617 0.0617 NU21 0.3400 0.0831 0.3400 0.0702 0.0702 CTE-1 (E-06) 19.44 3.77 13.20 4.58 4.58 CTE-2 (E-06) 19.44 15.45 13.20 19.72 19.72

COEFFICIENT OF THERMAL EXPANSION CALCULATIONS:

MAT 1 MAT 2 MAT 3 MAT 4 MAT 5 CTE-Z x THICK. 0.0000 0.5775 0.0000 0.0000 0.0000 CTE-T x THICK. 0.0000 0.3835 0.0000 0.0000 0.0000 CTE-TZ x THICK. 0.0000 0.0915 0.0000 0.0000 0.0000

CLT CALC.

MAT 1 MAT 2 MAT 3 MAT 4 MAT 5 COS (ALPHA) 1.0000 0.5779 1.0000 1.0000 1.0000 SIN (ALPHA) 0.0000 0.8161 0.0000 0.0000 0.0000 TAN^2 (ALPHA) 0.0000 Q11 6.219E+05 2.510E+06 1.165E+06 3.494E+06 3.494E+06 Q12 2.114E+05 2.085E+05 3.960E+05 2.452E+05 2.452E+05 Q22 6.219E+05 6.173E+05 1.165E+06 8.172E+05 8.172E+05 Q66 4.000E+05 2.980E+06 7.800E+05 5.400E+05 5.400E+05 QBAR11 6.219E+05 1.972E+06 1.165E+06 3.494E+06 3.494E+06 QBAR12 2.114E+05 -5.142E+05 3.960E+05 2.452E+05 2.452E+05 QBAR16 (+/-) 0.000E+00 7.009E+05 0.000E+00 0.000E+00 0.000E+00 QBAR22 6.219E+05 2.601E+06 1.165E+06 8.172E+05 8.172E+05 QBAR26 (+/-) 0.000E+00 -2.749E+05 0.000E+00 0.000E+00 0.000E+00 QBAR66 2.000E+05 7.673E+05 3.900E+05 2.700E+05 2.700E+05 A MATRIX 9.861E+04 -2.571E+04 0 -2.571E+04 1.300E+05 0 0 0 3.836E+04 DET [A] 4.666E+14 A INVERSE 1.069E-05 2.114E-06 0 2.114E-06 8.107E-06 0 0 0 2.607E-05

STRAINS:

MAT1 MAT2 MAT 3 MAT 4 MAT 5 STRUCT. AXES EPS -Z 0.0000 0.0016 0.0000 0.0000 0.0000 EPS -T 0.0000 0.0019 0.0000 0.0000 0.0000 EPS -ZT 0.0000 0.0000 0.0000 0.0000 0.0000 MAT. AXES EPS-1 0.0000 0.0018 0.0000 0.0000 0.0000 EPS-2 0.0000 0.0017 0.0000 0.0000 0.0000 EPS-12 0.0000 0.0002 0.0000 0.0000 0.0000

STRESSES:

MAT1 MAT2 MAT3 MAT4 MAT5 STRUCT. AXES SIGMA-Z 0.00 2100.00 0.00 0.00 0.00 SIGMA-T 0.00 4200.00 0.00 0.00 0.00 SIGMA-ZT 0.00 568.95 0.00 0.00 0.00 MAT. AXES SIGMA-1 0.00 4035.42 0.00 0.00 0.00 SIGMA-2 0.00 2264.58 0.00 0.00 0.00 SIGMA-12 0.00 801.40 0.00 0.00 0.00

STRENGTH CALCULATIONS:

MAT1 MAT2 MAT3 MAT4 MAT5 XT (psi) 8250 36600 15450 51300 51300 XC (psi) 6600 29280 12360 41040 41040 YT (psi) 8250 900 15450 1200 1200 YC (psi) 6600 4800 12360 6400 6400 S (psi) 8320 62580 20904 11340 11340 Fxx 1.8365E-08 9.3314E-10 5.2366E-09 4.7498E-10 4.7498E-10 Fxy -9.1827E-09 -7.3486E-09 -2.6183E-09 -3.9321E-09 -3.9321E-09 Fyy 1.8365E-08 2.3148E-07 5.2366E-09 1.3021E-07 1.3021E-07 Fss 1.4446E-08 2.5535E-10 2.2884E-09 7.7763E-09 7.7763E-09 Fx -3.0303E-05 -6.8306E-06 -1.6181E-05 -4.8733E-06 -4.8733E-06 Fy -3.0303E-05 9.0278E-04 -1.6181E-05 6.7708E-04 6.7708E-04 G 0.0000E+00 1.0682E+00 0.0000E+00 0.0000E+00 0.0000E+00 H 0.0000E+00 2.0169E+00 0.0000E+00 0.0000E+00 0.0000E+00 R 0.00 0.41 0.00 0.00 0.00 F 0.41

This is based on the interactive strength theory adopted by RTP-1 1995 which is known as Tsai-Wu in the composites industry. The strengths are calculated based on allowable strain per the recommended equations on page 117. The Design Factor (F) shall be R>10 for the entire laminate and R>1.2 for all other layers for all loading conditions. Materials 1 and 3 are isotropic and 2, 4, and 5 are orthotropic.

Buckling of Isotropic Cylinder with Lateral and Longitudinal Pressure Calculations: Simply Supported Circular Cored Plate with Central Laod, Uniform Pressure, and Uniform Weight (icludes shear deformation) Calculations: