Bending Moment Indeterminate Beam

[umdupas2]

Homework Statement

I have a 20' (240 inch) beam with supports at 0in., 80 in., 160 in., 240 in. I need to give the beam a rating (maximum load; capacity) since it is a monorail for a 3 ton hoist. I've asked the question to my prof (his work is attached).

Homework Equations

I understand what the graphs represent (Bending moment due to dead load, and bending moment due to concentrated force) but I can't figure out he he got the max values (coefficients): ie. 0.08*Wdl*l^2, 0.1*Wdl*l^2, 0.025*Wdl*l^2 and second graph.. 0.07Pl, 0.175Pl, 0.075Pl

Also how does he know these act at the same position? Ie: M1, M2, M3 so that he can add them?

The Attempt at a Solution

Attached.

 

[PhanthomJay]

Since the beam is statically indeterminate to the 2nd degree, it is a tedious task to calculate the bending moments using deflection-compatability analyses or some other method, so I am sure that the prof looked up these values (coefficients) in a handbook table somewhere, for both the uniform distributed load and the concentrated load at mid-point. By the superposition principle, the moments at any point under each load case can simply be added up. He examined 3 different possible points for max moment to determine the value of the maximum load P .

 

[umdupas2]

Thanks that explains everything.