Mechanics Question - Eccentric Loading

[JTM]

I have HND level mechanics question to do on eccentric loading. It involves a metal sheet with 9 strain gauges along its centre, a load is applied at opposite ends putting the piece under tension, the question gives readings for the 9 gauges and wants you to work out what the "theoretical stress distribution" is across the metal using "simple bending theory".

Ive been searching the net for a while, and im having no luck. Can anyone shed some light?

Thanks

[hI-OOPS-CAPS]

in simple tension the load applied will produce a stress which is uniform through out the metal, if its cross section is uniform anyway (the force will be in the centre of the dotted crosses). by eccentric loading i assume you mean the force is applied away from the centre.

in that case youll get a bending moment which will pull the beam over to one side. where if you take the simple equation moment = Fd the distance is the from the centre to the applied force.

to work with stresses though its sigma = My/I = Fdy/I if you know about bending with reference to a certain axis (its in y-y plane) then itll become sigma = M y^2 / I.

[Shaun H]

A visual representation of the problem would definitely help. As outlined above there will only be a bending moment if the cross section is not continuous or if the force is not applied central to the cross section.