## Equivalent Uniformly Distributed Loads

## Equivalent Uniformly Distributed Loads

(OP)

Does anyone know if there is a reference that exists on how to approximate the equivalent uniform distributed loading on beams when there are concentrated loads on them. The uniform distributed load would provide the same or a bit more stress and deflection in the beams. I know there are many variables involved and there is no "one method fits all" ,but, I am looking for a approximate or empirical method to calculate the equivalent uniform load for any concentrated load combination a beam.

Any help would be appreciated.

Any help would be appreciated.

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

Seems pointless.

## RE: Equivalent Uniformly Distributed Loads

I wold also back check the max shear and moment to make sure there were no problems. With all the simple to use beam programs, this should be a very easy process.

Cheers...

Mike McCann

McCann Engineering

## RE: Equivalent Uniformly Distributed Loads

First it is his contention that the final locations of concentrated loads will not be known until so late in the design development process that it will be impossible to do a precise analysis within the constraints of the project schedule.

Second he claims that a large uniform load provides an additional factor of safety to account for forces generated from operational loading.

The projects that we work on are typically cogeneration projects.

I am currently reviewing his design of a one storey turbine building for which his roof design he has used a live load of 100 psf and a piping load of 25 psf in addition to a roof snow load. He has no basis for these values other than "engineering judgement".

While I agree that these loads are more than adequate for the roof I disagree with this approach for numerous reasons. My biggest concern is that we will never know the actual state of stress in any member. This will be problematic in dealing with future structural issues.

There is also the issue of economy of design. My opinion is that engineering should produce a safe design at a reasonable cost. The results of the above has produced a very uneconomical roof.

I have reviewed this engineers work in the past and have had the same concerns. The last time I completely redid his RISA model to reflect the actual loading conditions (at quite the expense to our company) and of course his design was well within the allowables. The PM's opinion is that the design drawings are complete, the design is safe, so what's the problem?

I guess I have reached the same point as the original post. What I need is a justificaion and a basis for deterimining a design criteria that that correctly accounts for converting concentrated mechanical loads to equilivant uniform loads.

## RE: Equivalent Uniformly Distributed Loads

Wow! those are huge loads for mechanical equipment. At least if what we're talking about are typical HVAC units.

I have to agree with you on this one. It almost seems like cheating. Does this engineer have a concept of how much 100 PSF is?!

It's tremendously more economical to obtain a reasonable estimate of the actual mechanical loads. For your "engineering judgment" you could even bump those up by 50% or so. For worst case moment, place it at midspan and for worst case shear place it at the support.

If the building use changes at some point in the future, then it would fall to the new tenants or owner to assess the capacity of the roof and take appropriate measures. It seems unfair to make the current owner pay for what someone may do in the future. (Unless the owner specifically requests that the roof have adequate capacity for such a scenario.)

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

You stated that your project is a turbine building in a cogeneration project. So it is an industrial structure, not a commercial or residential one. Things are different with industrial structures. 100 psf live load for a roof does sound excessive, but perhaps the other engineer has his reasons which have not been adequately explained to him. Who makes the ultimate decisions on this type of thing in your organisation? As the reviewer, and if you can not agree with the designer, you need to talk to the managing engineer.

## RE: Equivalent Uniformly Distributed Loads

The purpose of my post was to provide an example of what some of the problems are that can arise when uniform loads are used in lieu of actual concentrated loads.

For my particular case I am well aware, as department manager, of the types of facilities that we engineer. I have been EOR on numerous power projects with price tags in the tens of millions of $.

The firm that currently employs me has expanded in the past few years from 15 to 40 employees. Unfortunately because our roots are in the mechanical and electrical disciplines the civil/structural department has no representative in the senior management staff. The person who is Director of Engineering is also the PM for the project that I mentioned above. Yes I will have a discussion with him concerning the applicable design criteria.

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

I was unaware of your experience and position when I posted. As the structural department manager, you are the person who must make the ultimate decisions about these issues. Sounds as if you have a training session ahead of you. Good luck. Old hands can be hard to change.

## RE: Equivalent Uniformly Distributed Loads

We often replace complex systems of loading with simpler loads. Sometimes udl's sometimes point loads or combinations. We do this empirically by looking at the actual loading and selecting a modified loading condition which has similar fundamental behaviour.

I have no problem with the strategy of the engineer working for Steve1. To me, the question is can 100psf be justified? There is a sub question - Can the actual loads be reasonably modelled as a udl? If they can then the only arguement is that of load intensity.

We are now really talking about safety factors versus economy of design (including design fees).

In my area of work (process structures) it is not common to have accurate loads at the start. We speak to the rest of the team to determine a level of confidence in the data available and we try to be more conservative where we feel it to be necessary.

It is not uncommon to have client organisations challenge us over utilisation ratios but I can onlt think of one case where we were callenged over our conservative assessment of loads.

## RE: Equivalent Uniformly Distributed Loads

i agree with the earlier post that said in the early days of a project you're not sure where the load will be applied. 1st short-cut, put it in the middle of the span. 2nd short-cut, if this is excessive put a "no-go" zone on the middle 1/3 of the span and apply it at the edge of this.

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

Confused.

Equation for deflection of a simply supported beam under a point load is:

(WL^3)/(48EI)= y1

Equation for deflection of a simply supported beam under a UDL load is:

(5Wa^4)/(384EI) = y2

Now, equating the above so that y1 = y2

W = Wa times L (or WaL simply put)

So if you have equivalent loads applied to the beam:

Y1 = Y2 can be seen as being :

(WaL^4)/48EI) = (5WaL^4)/(384EI)

Assuming identical material, 2nd moment etc etc, gives the ratios of load to equate equal deflection:

y1 = y2 shows:

(1/48) = (5/384) or simplified as (1/48) = (8/48)

Ergo, you can see that for equivalent centre point deflection, you require 8 times the total load when applied as a UDL against a point load.

Utter nonsence

## RE: Equivalent Uniformly Distributed Loads

(1/48)=(5/384) simplified is (1/48)=5/(8*48)

Therefore equivalent UDL is 8/5=1.6 times the total load.

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

Try it out. Computers didn't always exist.

## RE: Equivalent Uniformly Distributed Loads

there seem to be some posts tlaking about matching the deflection of the point load case to the deflection of a UDL. again, if there's a series of point loads the difference would small, but i think it'd be significant to replace a single point load with a UDL ... matching deflection would require a larger load (and i think needless math).

i was talking more in terms of how i read some of the posts(referring to what i took to be a single point load), particularly the post that seemed to propose using a UDL in lieu of a point load ('cause the location was uncertain).

## RE: Equivalent Uniformly Distributed Loads

Problem is that the loads may induce local buckling.

## RE: Equivalent Uniformly Distributed Loads

## RE: Equivalent Uniformly Distributed Loads

There is no need to throw so much load up there and there is no way to take a load of known value and turn it into a uniform load - just put the point load at the worst place for design and let them put it where ever they want.

## RE: Equivalent Uniformly Distributed Loads

There really needs to be some guidance on setting up the design critria for industrial facilities. I have noticed that over the years building codes have greatly expanded the seismic criteria for mechanical and electrical equipment, but that the uniform design load for industrial facilities has remained light and heavy loading with no specific values based on type or use of facility.