Beam deflection examples

 

Find v(x) and vmax for each of the following cases:

 

 

 

 

 

 

 

 

 


            Answer: EIv(x) = 2.083<x - 0>3 – 2.083<x - 40>3 – 3333x

                                                vmax  =  -0.02565” (up) at x = 23.09” 

and  0.1167” (down) at the free end

FEA solution

 

 

 

 

 

 

 

 


            Answer:  standard solution from text (e.g. Gere and Timoshenko)

 

                        v = wx(9L3 – 24Lx2 + 16x3)/384EI                0 < x < L/2

                        v = wL(8x3 -24lx2 +16 L2x –L3)/384EI          L/2 < x < L

                        Assume max. defl. is in range 0 < x < L/2 and differentiate to get v’(x)

                        Hence get vmax = 7wL4/768EI  at x = 0.416L

FEA solution

 

 

 

 

 

 

 

 

 

 

 


            Answer: EIv(x) = 3PL<x - 0>2/32  - 11P<x - 0>3/96 + P<x – L/2>3/6

 

                           EIv’(x) = 3PL<x – 0>  -  11P<x – 0>2/32  + P<x – L/2>2/2

            Guess x in range L/2 < x < L, and solve v’(x) = 0 giving x = 0.553L

            And hence vmax  =  0.00932L

                                                                        FEA solution