Metal stiffness calculation

[MHWood]

I am in the automotive metal stamping field and a customer has asked us to calculate the increase in stiffness of a stamped part if we increase the thickness by "x" amount or if we increase the strength by "y" amount. It has been a long time since engineering mechanics for me ('73) and I would appreciate some help in calculating this. Thanks.

 

[metman]

Stiffness or resistance to elastic deflection, is a function of Modulus of Elasticity and Moment of Inertia, related to geometry.

Since you are working with a stamping it is safe to assume it is a rectangular cross section and the primary loading is in bending. It really depends on the overall geometry and load pattern but for a simply supported beam in bending with a rectangular cross section, the moment of inertia is bh^3/12 where h = thickness or dimension parallel to the bending load. Therefore if you increase thickness by x the moi becomes b(xh)^3/12 = bx^3h^3/12. In other words the stiffness increases by x^3 (x cubed). For example if you double the thickness, x=2, and x^3=8 so stiffness is increased 8 times. Or x=1.25, 25% increase, x^3=1.25^3=1.95 or almost double the stiffness.

Increasing strength will not affect stiffness. Modulus of Elasticity is the ratio of stress over strain. increasing strength does not change this ratio.

Jesus is THE life,
Leonard

 

[MHWood]

Thank you for the quick reply. Your answer was very helpful and appreciated.