# Clamped-clamped beam load deflection with residual stress

1. Mar 1, 2013

### mike_oh

Hello,
I have a system that consists of a clamped-clamped beam with a residual stress and am trying to find an equation that governs its deflection due to a point force that takes stress into consideration. A formula I have come across:

d = (F*L^3)/(192*E*I)

does not accurately model the measured displacement of the beam.

d : maximum central deflection (m)
F : magnitude of applied point force (N)
L : length of the beam (m)
E : Young's modulus (Pa)
I : moment = (w*t^3)/12 (m^4)

Is there a formula that includes residual film stress as well? Or is there a good tutorial available for deriving such a formula?
As a word of warning, I do not have a strong background in mechanics, so I apologize if I overlooked something simple.
Thank you in advance for you help!

2. Mar 1, 2013

### rock.freak667

It depends on how you model the residual stress, are you modeling it like a UDL on one side of the beam or like a compressive/tensile force along its axis?

3. Mar 4, 2013

### mike_oh

Thank you for your response! I have been modeling it as an axial force, but perhaps that is the cause of some of my trouble? Do you recommend modeling it as a UDL?
In that case, can I just subtract the force due to stress from the applied force and use that net force quantity in the equation in my original post?

4. Mar 6, 2013