See my questions noted in red. Are you looking for the derivation of the beam deflection formula [tex] d^2y/dx^2 = M/EI [/tex] ? You might want to google it.***ALLI*** said:Homework Statement
hi i am currently trying to mathcamatically derive the beam deflection formula for a double cantilever simple beam What's that? Do you mean a beam on two simple supports? i have the beam deflection formula y= (FL^3)/(48—Iε)what's this? It looks something like the deflection at centerline of a simply supported beam with a concentrated load F at its center, but your denominator makes no sense. as well as? = M ymax / I as well as 1/p = M/EI but am not sure how to link them together. any help will be apprecieated
Thanx :)
Beam deflection derivation is the process of calculating the amount of deflection or bending that occurs in a beam when a load is applied. It involves using mathematical equations and principles of mechanics to determine the deflection at different points along the beam.
Beam deflection is important because it affects the structural integrity and stability of a beam. Too much deflection can lead to failure or collapse of the beam, while too little deflection can cause it to be too stiff and unable to withstand loads.
The amount of beam deflection is influenced by several factors, including the load applied, the length and shape of the beam, the material properties of the beam, and the support conditions at the ends of the beam.
The two most common methods for beam deflection derivation are the double integration method and the moment-area method. The double integration method involves solving differential equations, while the moment-area method uses the area under the bending moment diagram to determine deflection.
Beam deflection can be minimized by using stiffer materials, increasing the beam's cross-sectional area, reducing the length of the beam, or adding additional support points. Properly designing and reinforcing the beam can also help prevent excessive deflection.