Finding the allowable uniform load

In summary, The problem involves determining the allowable uniform load w when the allowable bending stress is 24ksi and P=15w. Using the equations Mmax=\sigmamax/c(I) and Mmax=wL^{2}/8, the maximum moment Mmax is found to be 18,107.869 k in, but the problem also includes two P forces. To solve for w, the moment diagram for the whole beam should be drawn, taking into account that some of the moment capacity is used up by the moment of 3P in the central portion of the beam. This results in M=wL^{2}/8+540w, with consistent units such as kip inches used throughout.
  • #1
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=[tex]\sigma[/tex]max/c(I); And Mmax=wL[tex]^{2}[/tex]/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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  • #2
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.
 
  • #3
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.
 
  • #4
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
 
  • #5
O ok, so M would be equal to wL2/8+540w?
 
  • #6
Yes, but be careful to use consistent units throughout. Like kip inches, or whatever.
 
  • #7
ok thanks for the help
 

FAQ: Finding the allowable uniform load

What is the definition of allowable uniform load?

The allowable uniform load is the maximum amount of weight that a structure or material can support without experiencing failure or damage. It takes into account factors such as the strength, stability, and durability of the material.

How is the allowable uniform load calculated?

The allowable uniform load is calculated by dividing the ultimate strength or maximum load of the material by a safety factor. The safety factor is a number that takes into account uncertainties and potential variables in the calculation.

What factors affect the allowable uniform load?

Several factors can influence the allowable uniform load, including the material's strength, stiffness, and ductility, as well as the structural design, environmental conditions, and potential hazards that the structure may face.

What are some common methods for determining the allowable uniform load?

Some common methods for determining the allowable uniform load include analytical calculations based on material properties and structural design, physical testing, and computer simulations using software programs such as finite element analysis.

Why is it important to find the allowable uniform load?

Finding the allowable uniform load is crucial for ensuring the safety and reliability of structures and materials. It helps engineers and designers determine the maximum weight that a structure can support, which is essential for preventing potential failure, collapse, or damage.

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