Cantilevered Beam Equation for Max Moment 3

[JP20]

Hello everyone, I got a question.. may be a simple one for most of you.. what's the formula for the max applied moment on this Beam shown on the FBD below...? (it's cantilevered out over two pinned connections.. symmetrically)

 

[r13]

Maximum moment occurs at where V = 0. In this case, you have to check 2 locations (at support and at mid-span between supports)

 

[strucbells]

Calculate your reactions in terms of W and draw your shear and moment diagrams.

 

[BridgeSmith]

It should take about 2 seconds to solve for anyone who has completed Engineering Statics. If the center span was longer than the end spans, it might be necessary to draw the shear and moment diagrams, but with that span ratio, it's easier than that. I don't mean to be rude, but this site is for practicing engineers, not first year engineering students or those of other educational backgrounds.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[blihpandgeorge]

@retired13 your post is misleadsing as this isnt the case for negative moments, ie a cantilever where max V & M occur simultaneously

 

[BAretired]

M_cantilever = -wA²/2 = -32w

M at midspan of B = -32w + wB²/8 = -29.8w

The negative sign indicates tension on top and compression on the bottom. Without the cantilevers, the central span would have a small positive moment but as it is, the moment is negative across all three beams.

BA

 

[r13]

blihpandgeorge,

Draw the shear diagram, see where V gets to zero along the axis (V raise above or drop below the axis).
In the cantilever, the shear is pushed up, and crosses, the axis by support reaction. But the shear will be again pushed down in the mid-span, so there are two location to check the moment for this symmetrical layout.

In a sense you are correct, my over simplified statement is misleading, as to suggest shear is zero at the cantilever, while it is a maximum. I shall have said "at where along the axis, the moment is a maxima/minima, when shear crosses the zero axis (change sign)."

 

[BAretired]

Sketch below illustrates retired13's point.

BA

 

[r13]

BA,

Thanks for understanding

 

[BAretired]

retired13,

I needed the practice in drawing.

BA

 

[r13]

Impressive, what is the program you are using? Let me know only, if it is cheap or free

Yeah, a graph better than thousand word - precious learning tool.

 

[JP20]

Thanks... I knew I could draw the shear and moment but I was wondering if anyone had/knew the formula for this condition to spare me the time.. my member is actually going to be point loaded as such so I went ahead and drew it out and figured it.. let me know If anyone sees an error I made..

 

[rb1957]

man, your calcs show much more understanding then we gleaned from your post !

M = 4307*(49.5+45.5)/12+ 1307*45.5/12 = 39 kip.ft
with your round up, M = 4.4*(49.5+45.5)/12+1.4*45.5/12 = 40.14 kip.ft … confirming your calc

hey wait … is the outer bay 49.5 or 45.5 ?
oh, I see, you conservatively moved the load to the end of the beam

another day in paradise, or is paradise one day closer ?

 

[BAretired]

retired13,

I used LibreOffice6.4 which is free. I could have used OpenOffice which is also free, but I am experimenting with LibreOffice as it offers a few more features than OpenOffice.

There seems to be a bug in both programs which I find frustrating. This sketch would have been much easier if I could have used the "FilledPolygon" procedure but it doesn't seem to be working properly. Strange, because as recently as March 5 of this year I used that feature in OpenOffice and it worked fine, but not now. Someone must have monkeyed around with the code and screwed it up. I may have to study Java programming in order to modify the program and get it right. At the moment, that alternative doesn't appeal.

The other program I sometimes use is PDF Annotator. It isn't free, but I can't remember what I paid for it...not very much as I recall. Unfortunately, PDF Annotator does not have a polygon drawing routine. I sent them an email and go a response a couple of days ago that "draw polygon" is on their to-do list but they won't guarantee it will be on the next version. Oh the pain of it all!

I have Autocad 2006 but I haven't used it in years and I always found it very confusing. It certainly can draw polygons of any description, but a person has to be using it daily in order to keep familiar with it.

Years ago, I wrote a CAD program of my own in Turbo Pascal which could draw polygons but unfortunately, my old computer crashed and I haven't tried to resurrect it. Furthermore, Borland went out of business, so Turbo Pascal is not supported any more.

I used to have BlueBeam, but lost it after my computer crashed and never have bothered to replace it. I may look into that, but I'm reluctant to spend a lot of money on a graphics program at this late date.

BA

 

[JP20]

Thanks rb1957.. appreciate you. paradise is one day closer..

 

[r13]

Interesting experiences. I will stay with the "paint" came with window for now I know little about Open Office, but not Libre Office. Maybe I shall try. Thanks.

 

[BridgeSmith]

I (and others, apparently) took your loading arrows to be representing a uniform load. I apologize if I offended with my earlier post.

For point loads, you could use superposition, also - 4.4k * (3.8'+4.125') + 1.4k * 3.8' = 40.2k-ft.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[r13]

Not much difference, 2s vs 20s, once you realize change in shear force.

 

[oengineer]

 

[oengineer]