MechE Interview First Principles/Technicals

What characteristics describe the internal forces of a beam?

Internal moment (caused by normal forces/couple) and shear force

When is a beam statically determinate vs indeterminate?

For a beam to be statically determinate, the number of unknown reactions must match the number of balancing equations (sum of forces in x, y, sum of moments). So if r = number of support reactions and n = number of segments/members, r=3n -> determinate, r>3n -> indeterminate, r<3n -> unstable

Sign convention for internal shear and moments

Positive internal shear tends to rotate a beam segment clockwise, positive internal moment makes a beam bend concave up

General strategy for drawing shear and bending moment diagrams

Separate the beam into sections based on where loads are applied and do sum of shear forces and moments on each section. Know that the slope of the moment graph at any point equals the value of the shear force graph at that point (dM/dx = V). Also, change in shear force between two points is equal to area under loading diagram between those two points, and change in moment diagram between two points is just area under shear diagram between those two points.

Draw shear and moment diagrams for this beam