6-184 DESIGN OF LAMINATES 



The results of the analysis used in Design Example 6-27 indicate that the simplified 

 analysis, No. 5, which includes the flexural deflection, with or without the core, and the 

 shear deflection of the core only, assuming uniform shear distribution, gives a conservative 

 deflection when compared with the more accurate analysis, No. 1. The difference is ap- 

 proximately 10 per cent for the simplified analysis and is considered acceptable. 



Although the comparative analysis has been made for a simple cantilever beam loaded 

 at the end, it is believed that similar comparative deflections will occur for other beam 

 loading and support conditions. Therefore it is recommended that the simplified analysis, 

 No. 5 be used in obtaining an approximate deflection for simple one-way panels. This 

 proposed method is presently used in tests to determine the shear moduli of core materials 

 (22). In this test the core material is combined with very thin faces to minimize their ef- 

 fect on the shear deflection. 



The analysis of the flexural stresses in a one-way sandwich panel or beam is similar to 

 the analysis for a composite laminate previously discussed. Design Example 6-28 indicates 

 the procedure used computing the stresses in the various components of a sandwich section. 



DESIGN EXAMPLE 6-28. STRESSES IN A CANTILEVER SANDWICH BEAM 



For the sandwich beam given in Design Example 6-27, calculate the flexural and shear 

 stresses in the facings and core. 



Bending Moment, M = PL = 100 in. -lbs. 



Shear V = P = 10 lbs. 



Bending stress at any point, y in the cross-section 



fbl , | , «M (6. 36) 



where EI = /~Ej_Ti = Stiffness factor of the entire section (6. 16) 



Tensile or compressive stress in the facings: 

 100 x 1.60 x 10 6 x .625 



ftf = fcf = 0.1397 x 106 = 716 PS1 



Tensile or compressive stress in the core: 



f tc = f cc = 100 * 0.52 x 106 x .50 „ 186 

 C 0.1397 x 10 6 



The maximum shear stress is: f s = ^yr- (6. 37) 



where V, EI, b and Q' are as previously defined. 

 Shear stress at the interface between the laminate and the balsa core: 



= 10 * 1.60 x 10 6 x 1 x 125 x .5625 

 S 1 x 0.1397 x 10 6 



= 8.1 psi 



