Finding the allowable uniform load

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To determine the allowable uniform load (w) given an allowable bending stress of 24 ksi and the relationship P=15w, the maximum moment (Mmax) must be calculated. The maximum moment is expressed as Mmax = σmax * c / I, where I is the moment of inertia and c is the distance from the neutral axis. The discussion highlights that the moment capacity is partially consumed by the moment from the point loads, requiring a careful analysis of the moment diagram. The correct approach involves combining the uniform load moment with the moment from the point loads to find w, ensuring consistent units are used throughout the calculations. Understanding these relationships is crucial for accurately solving for the allowable uniform load.
mustang1988
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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=\sigmamax/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 somone could help me with this part I would greatly appreciate it. Thanks
 

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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.
 
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.
 
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
 
O ok, so M would be equal to wL2/8+540w?
 
Yes, but be careful to use consistent units throughout. Like kip inches, or whatever.
 
ok thanks for the help
 

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