72 HANDBOOK OF MECHANICAL DESIGN, 



Stress Calculations for Thin Aluminum Sheet Sections 



A condensation of the article by the same title by S. A. Kilpatrick and 0. J. Schaefer, of The Glenn L. Martin 

 Company, in Product Engineering, February, March, April, and May, 1936. 



COMPRESSION MEMBERS 



By the method presented here, compression members made of formed ahiminum sheet for 

 shapes as shown in the table below can be calculated for any length of member and any thickness 

 pf sheet. 



L = length of the column, in in. . / = ultimate compressive stress of material, 



radius of gyration generally taken as yield point 



thickness of the sheet, in in. ^ = modulus of elasticity 



= 10,500,000 for 24 ST aluminum 

 C = coefficient for end restraint, as in the 



P 

 t 

 K = shape factor at given L/p 



K„ = shape factor for short columns at about Rankine formula 



L/p = 20 P/A = failing stress = load at failure divided 



allowable stress, in lb. per sq. in. by the section area 



/ 



l+B 

 In the preceding equation, ' 



- - r^ ' (1) 



(2) 



. For compact sections, tubing, corrugated sheet, and the simplest sections, use 



^ /(I + B) 

 I + B + B^ 



First, calculate a from the equation. Apply the shape factor Ko, given in the 

 table, to the following equation : 



K = 7C ("A"' (3) 



Then, 



J = (7 tanh {Kt) (4) 



tanh = hyperbohc tangent 



Note: In general, for sections having a high shape factor, A"„, the shape factor, will be inversely proportional to the 

 external dimensions. If the shape factor thus calculated is less than 10, as would obtain if the external dimensions of 

 shape 1 were doubled, the value calculated should be squared and the value of I- should be used in place of I in Eq. (4). 



If section such as shape 3 does not have ample fixity along one edge as represented by the wood block or as obtain- 

 able by closely spaced stiffeners, the section should be calculated as a simple angle. 



As an example of the use of the table, a column of section similar to shape 2, shown 

 in the table, is to be designed to be made of 24 ST aluminum sheet 0.051 in. thick and 

 the length of the column is such that L/p is 50. The straight edges of the column are 

 restrained. 



From the table, for a short column of this section, for L/p less than 25, we get 

 Ko = 12. The yield point of the material by test, or from figures given by material 

 manufacturer, is / = 50,000, and E = 10,500,000 for 24 ST. The coefficient of end 

 restraint C is 1. 



