Compression in a Multi-Material Component With Uniform Cross Section

When an object is constructed with two different materials, and both have uniform cross-section, and both are subjected to the same tension or compression within the elastic limit of the material, the forces, stresses, and deformation can be predicted with the following equations:

F1 = F * (A1 * E1) / ((A1 * E1) + (A2 * E2))

F2 = F * (A2 * E2) / ((A1 * E1) + (A2 * E2))

¶ = (F1 * L) / (A1 * E1) = (F2 * L) / (A2 / E2)

Stress1 = F1 / A1

Stress2 = F2 / A2

Where

¶ = = the deformation

F = the total load or force acting on the objects

F1 = the load or force carried by object 1

F2 = the load or force carried by object 2

L = the length of the objects in the direction that the force is acting

E1 = the Modulus of Elasticity of the material for object 1

E2 = the Modulus of Elasticity of the material for object 2

A1 = The cross-sectional area of object 1, perpendicular to the force

A2 = The cross-sectional area of object 2, perpendicular to the force

It is assumed that the object is constructed in such a way that there is no slippage between objects 1 & 2.

When entering the required information into the DZynSource Mold Engineering Software, it is imperative that the units used are consistent. For instance, if pounds per square inch are used for the modulus of elasticity, quantities must be entered in units of pounds and inches.  See the previous article to see you access this calculation from within DZinSource.

First choose whether you want to use p.s.i. or N/mm², then choose how many places beyond the decimal point you like the answer carried.

Enter the Force, the length, the outer objects area, the inner objects area, and the Modulus of Elasticity for each object in the text boxes next to the questions asked. When entering modulus of elasticity values, 30,000,000, as would usually be used for steel, may be entered as 30e6 as a shortcut. The area of 10 basic shapes can be calculated by choosing Strength of Materials, Moment of Inertia from the main menu, choosing the desired shape, and entering the required information.

Press Calculate. A separate answer page appears with the values for Force 1, Force 2, the deflection, and stress induced in each component are shown. Answers are valid if the stress from a static load is within the elastic limit of the material in question.

Use the Clear button to clear all entry fields, however this is not necessary in order to do another calculation. You may simply type over the previous entries.

Press OK on the answer page to close that page.

You may send the either page to your default printer by pressing Print.

Press Menu to return to the main menu selection area.