7laha design and anlysis of beams for bending

  7laha is a smart package of problems for never stop thinking                        

1-Two beams welded together and have the same length the first is a flange of W shape (W 410*114)                                  

The second is acore has circuit shape of radius 210 mm (as shown)                                  

a-find the stress applied to each beam                                            

b-Does the stress applied to each beam change if we use  one type of beam has the total length and under same forces?

   

Solution: 

I for w 410*114=462*10^-3 m^4

I for circuit =π*R^4/4

I circuit=1.25 *10^-3 m^4

σ=M*Y/I

shear and bending moment diagrams

Note that the moment is constant for the two beams.

σ (for core)=285.6*210*10^3/1.25=47.98 Mpa

σ (for flange) =285.6*210*10^3/462=0.129 MPa

b for you