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# continuous beam on two spans

## continuous beam on two spans

(OP)
I have to calculate stresses and deflections in a continuous beam on two span of different lenght, in 2 situations:

1) 3 hinges with 2 concentrated loads in two diffferent points of one span
2) 2 hinges and one fixed joint with 2 concentrated loads in two diffferent points in one span

I have found the equations for the two cases, but I'd prefer to check that my results are correct: so I'd like to have the formulas for bending moment and deflection.
Could You help me indicating web pages or other?
Replies continue below

### RE: continuous beam on two spans

Try www.engineerstoolbox.com which has a general beam analysis section in it and other formulae too.

### RE: continuous beam on two spans

(OP)
Thank You, Corus, but it isn't enough...: I need a closed formulation for the cases of interest.
I am studying in fact the beam under which moves a little travelling crane, and I want to check if the formulas I have obtained (integrating the equation of the elastic line known the external loads) is correct; therefore, if anybody knows a web site in which this specific case in described and resolved (two different length, concentrated loads at two points of the same span, etc) I’d like to have an indication.
Thanks a lot, Engy74

engy74,

### RE: continuous beam on two spans

You may want to design the beams using plastic design (avoids many of the problems re influence lines, etc.).

Assuming the beam is steel and the spans are somewhat similar, sketch out simple span moment diagram for both spans for maximum and minimum loading.

As a first 'guess', graphically determine the moment for the interior support that gives the closest match to the longer span moment.  The maximum positive moment should be equal to the minimum negative moment.

Repeat the process for the shorter span.

If the beam is continuous across both spans, the maximum of the two moments obtained will be the design moment for the beam; You can approximate the deflection by using 1/3 of the maximum simple span elastic deflection as a first 'guess'.  I use 0.00624ML^2/I, where M is moment in 'K, L span in feet, I is the moment of inertia in in^4.

If the combined span is greater than the normal length of rolled material, the procedure is the same, it's only a matter of determining the splice location.

Starting with the long span, the negative moment is the moment for the beam cantilevering into the the shorter span. Draw a line from the interior moment to the exterior support of the short span (This should or may intersect with both the  maximum and minimum moments drawn for the simple support condition). The value between this line and the positive moment in the span is the design moment for the spliced span.  The splice should be located approximately mid way between the intersections.  The moment value above and below the location of the splice is the minimum moment that the splice should be designed for (the Canadian steel code requires that this be a minimum of 25% of the section).

The above can be done for the opposite side and the least weight sections can be determined.

Splice can consist of bolted end plates with bolting designed for the moment and shear (including 'prying action').

The steel section should be a compact section to preclude local buckling (Canadian code: Class 1 Section).  Matter of looking at bracing of the first hinge (ie. the support) and usually use a stiffener plate (even if not required by code).

Actual elastic deflection can be determined using a computer program based on the sections and splice determined above.

### RE: continuous beam on two spans

I just stumbled onto a program call beam boy, that lets you place supports and loads anywhere you want on the beam, and then calculates the deflection, moment, and bending stress.  It displays these graphically, so you can see where on the beam the maximums occur.

http://www.geocities.com/richgetze/

What I need to know is where do I go from here?  It told me what the stresses are on my beam, but how do I know if my chosen beam can handle that stress?  Note that my backgound is in computers, so this steel stuff is new to me

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