Question

A steel girder of length $l$ rests freely on two supports (figure shown above). The moment of inertia of its cross-section is equal to $I$. Neglecting the mass of the girder and assuming the sagging to be slight, if the deflection $\lambda$ due to the force $F$ applied to the middle of the girder is $\lambda =\frac{1}{(40+x)}\frac{F{l}^3}{EI}$, find the value of $x$.

Answer 1

One can think of it as analogous to the previous case but with a beam of length $\frac{l}{2}$ loaded upward by a force $\frac{F}{2}$.
Thus $\lambda =\frac{F{l}^3}{48EI}$