Finding the allowable uniform load

[mustang1988]

1. Determine the allowable uniform load w if the allowable bending stress is 24ksi and
P=15w
Given: I=12,800in^4; c=16.965in



2. I know that Mmax=$$\sigma$$max/c(I); And Mmax=wL$$^{2}$$/8



3. I solved for Mmax=18,107.869 k in; but I don't understand how to solve for w with the two P forces also. If someone could help me with this part I would greatly appreciate it. Thanks

 

[pongo38]

some of the moment capacity is used up by the moment of 3P in the central portion of the beam, thus leaving less available for the uniform load. I suggest you first draw the M diagram for the whole beam.

 

[mustang1988]

Thats supposed to be a 3ft from P to the edge, sorry my drawing skills are not great. I already did the M diagram that is where i came up the max of 575. I just don't know how to solve for the w.

 

[pongo38]

Maybe you are missing the point that p=15w. Therefore M isn't just wL2/8 but also 36x15w=540w k.in at the centre

 

[mustang1988]

O ok, so M would be equal to wL2/8+540w?

 

[pongo38]

Yes, but be careful to use consistent units throughout. Like kip inches, or whatever.

 

[mustang1988]

ok thanks for the help