Additionally, how would you reduce deflection? Where and what is the equation for max. deflection?
This is a question asked in Apple’s very first technical phone screen. It’s important to know the basics which is why they ask you almost immediately!
The location of maximum deflection is at the free end of the beam, and the max bending moment is at the fixed interface between the wall and cantilever beam.
Note: In above diagram, the BMD should be in the negative direction, the diagram has it labeled incorrectly!
For a beam mounted at the wall and a point load at the free end, the equation for max deflection follows this form:
Max Deflection = (P*L^3) / 3*EI
P = Load
L = Length
E = Modulus of Elasticity (Material Property)
I = Area Moment of Inertia (Depends on the cross-section)
These are the variables you can tweak and adjust for reducing deflection of the beam.
How would you manipulate the above equation to minimize deflection?
The question shows a diagram where the weight of the beam itself is taken into consideration. The solution however does not consider that distributed load of mg/L. The shear and moment diagrams will be slightly different. Typically, in textbook problems like these the self-weight of the beam is not considered but I’d say watch out if the interviewer specifically asks you to consider it.