I am working the following problem:
The simply supported beam shown in Fig. 12-12a is subjected to the concentrated force P. Determine the maximum deflection of the beam. EI is constant.
The text later says:
By inspection of the elastic curve, Fig. 12-12b, the maximum deflection occurs at D, somewhere within region AB. Here the slope must be zero.
Why does the author say that, by inspection, the maximum deflection occurs at D? How do we know that? He didn't show any work or explain why it should be at D and not somewhere else.
If I consider the maximum slope to occur at a point 2 m from A, then I will take EI(dv2/dx2) = 0, then my answer is, -2((x2)^2) + 12x2 -44/3 = 0, then x = 4.29 m ....
here's the full question . in hree , we can notice that there are 2 sets of slope equation that we can use . Which is equation 5 & 7 . In equation 5 , we will get 1.633 as in the working . ( the author use by 'inspection' the max deflection occur at region AB)
However , when as @Jmac stated , we dont know where is the position where the max deflection is located , how can we use equation 5 to solve ?
solving equation 7 = 0 , i have x = 5.23 , 3 and 0.763 , which is correct ?